1,1,80,102,0.055000," ","int(cos(d*x+c)^5*(a+a*cos(d*x+c)),x)","\frac{a \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{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}}{d}"," ",0,"1/d*(a*(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)+1/5*a*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c))","A"
2,1,70,82,0.049000," ","int(cos(d*x+c)^4*(a+a*cos(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}+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)}{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)+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))","A"
3,1,60,68,0.045000," ","int(cos(d*x+c)^3*(a+a*cos(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"
4,1,49,48,0.056000," ","int(cos(d*x+c)^2*(a+a*cos(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"
5,1,38,34,0.042000," ","int(cos(d*x+c)*(a+a*cos(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)+\sin \left(d x +c \right) a}{d}"," ",0,"1/d*(a*(1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c)+sin(d*x+c)*a)","A"
6,1,16,15,0.021000," ","int(a+a*cos(d*x+c),x)","a x +\frac{a \sin \left(d x +c \right)}{d}"," ",0,"a*x+a*sin(d*x+c)/d","A"
7,1,30,16,0.071000," ","int((a+a*cos(d*x+c))*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}+\frac{c a}{d}"," ",0,"a*x+1/d*a*ln(sec(d*x+c)+tan(d*x+c))+1/d*c*a","A"
8,1,32,24,0.104000," ","int((a+a*cos(d*x+c))*sec(d*x+c)^2,x)","\frac{a \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,"a*tan(d*x+c)/d+1/d*a*ln(sec(d*x+c)+tan(d*x+c))","A"
9,1,51,43,0.104000," ","int((a+a*cos(d*x+c))*sec(d*x+c)^3,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"
10,1,72,57,0.148000," ","int((a+a*cos(d*x+c))*sec(d*x+c)^4,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"
11,1,92,77,0.149000," ","int((a+a*cos(d*x+c))*sec(d*x+c)^5,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"
12,1,112,91,0.145000," ","int((a+a*cos(d*x+c))*sec(d*x+c)^6,x)","\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}+\frac{8 a \tan \left(d x +c \right)}{15 d}+\frac{a \tan \left(d x +c \right) \left(\sec^{4}\left(d x +c \right)\right)}{5 d}+\frac{4 a \tan \left(d x +c \right) \left(\sec^{2}\left(d x +c \right)\right)}{15 d}"," ",0,"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))+8/15*a*tan(d*x+c)/d+1/5/d*a*tan(d*x+c)*sec(d*x+c)^4+4/15/d*a*tan(d*x+c)*sec(d*x+c)^2","A"
13,1,121,117,0.061000," ","int(cos(d*x+c)^4*(a+a*cos(d*x+c))^2,x)","\frac{a^{2} \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{2 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}+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)}{d}"," ",0,"1/d*(a^2*(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)+2/5*a^2*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c)+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))","A"
14,1,96,95,0.056000," ","int(cos(d*x+c)^3*(a+a*cos(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"
15,1,90,79,0.055000," ","int(cos(d*x+c)^2*(a+a*cos(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"
16,1,64,55,0.050000," ","int(cos(d*x+c)*(a+a*cos(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"
17,1,52,41,0.047000," ","int((a+a*cos(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"
18,1,51,34,0.097000," ","int((a+a*cos(d*x+c))^2*sec(d*x+c),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"
19,1,50,34,0.110000," ","int((a+a*cos(d*x+c))^2*sec(d*x+c)^2,x)","a^{2} x +\frac{2 a^{2} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{a^{2} \tan \left(d x +c \right)}{d}+\frac{a^{2} c}{d}"," ",0,"a^2*x+2/d*a^2*ln(sec(d*x+c)+tan(d*x+c))+a^2*tan(d*x+c)/d+1/d*a^2*c","A"
20,1,58,50,0.130000," ","int((a+a*cos(d*x+c))^2*sec(d*x+c)^3,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"
21,1,78,64,0.127000," ","int((a+a*cos(d*x+c))^2*sec(d*x+c)^4,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"
22,1,102,88,0.135000," ","int((a+a*cos(d*x+c))^2*sec(d*x+c)^5,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"
23,1,143,117,0.056000," ","int(cos(d*x+c)^3*(a+a*cos(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"
24,1,121,95,0.051000," ","int(cos(d*x+c)^2*(a+a*cos(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"
25,1,100,79,0.045000," ","int(cos(d*x+c)*(a+a*cos(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)+a^{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^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)+a^3*sin(d*x+c))","A"
26,1,74,57,0.051000," ","int((a+a*cos(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 a^{3} \sin \left(d x +c \right)+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*a^3*sin(d*x+c)+a^3*(d*x+c))","A"
27,1,72,55,0.087000," ","int((a+a*cos(d*x+c))^3*sec(d*x+c),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"
28,1,65,48,0.138000," ","int((a+a*cos(d*x+c))^3*sec(d*x+c)^2,x)","3 a^{3} x +\frac{3 a^{3} \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{a^{3} \tan \left(d x +c \right)}{d}+\frac{3 a^{3} c}{d}"," ",0,"3*a^3*x+3/d*a^3*ln(sec(d*x+c)+tan(d*x+c))+a^3*sin(d*x+c)/d+a^3*tan(d*x+c)/d+3/d*a^3*c","A"
29,1,71,55,0.119000," ","int((a+a*cos(d*x+c))^3*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"
30,1,80,66,0.118000," ","int((a+a*cos(d*x+c))^3*sec(d*x+c)^4,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"
31,1,101,87,0.132000," ","int((a+a*cos(d*x+c))^3*sec(d*x+c)^5,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"
32,1,124,104,0.151000," ","int((a+a*cos(d*x+c))^3*sec(d*x+c)^6,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"
33,1,169,117,0.053000," ","int(cos(d*x+c)^2*(a+a*cos(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"
34,1,133,94,0.053000," ","int(cos(d*x+c)*(a+a*cos(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"
35,1,111,79,0.053000," ","int((a+a*cos(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"
36,1,94,71,0.114000," ","int((a+a*cos(d*x+c))^4*sec(d*x+c),x)","\frac{\sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\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*sin(d*x+c)*cos(d*x+c)^2*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"
37,1,86,69,0.121000," ","int((a+a*cos(d*x+c))^4*sec(d*x+c)^2,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"
38,1,86,69,0.154000," ","int((a+a*cos(d*x+c))^4*sec(d*x+c)^3,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"
39,1,93,71,0.140000," ","int((a+a*cos(d*x+c))^4*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"
40,1,102,88,0.164000," ","int((a+a*cos(d*x+c))^4*sec(d*x+c)^5,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"
41,1,123,103,0.135000," ","int((a+a*cos(d*x+c))^4*sec(d*x+c)^6,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"
42,1,146,126,0.210000," ","int((a+a*cos(d*x+c))^4*sec(d*x+c)^7,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"
43,1,171,110,0.074000," ","int(cos(d*x+c)^5/(a+a*cos(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 a d \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 a d \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 a d \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 a d \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 a d}"," ",0,"-1/a/d*tan(1/2*d*x+1/2*c)-25/4/a/d/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^7-115/12/a/d/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^5-109/12/a/d/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^3-7/4/a/d/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)+15/4/a/d*arctan(tan(1/2*d*x+1/2*c))","A"
44,1,136,88,0.071000," ","int(cos(d*x+c)^4/(a+a*cos(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)}{a d \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 a d \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)}{a d \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)}{a d}"," ",0,"1/a/d*tan(1/2*d*x+1/2*c)+5/a/d/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)^5+16/3/a/d/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)^3+3/a/d/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)-3/a/d*arctan(tan(1/2*d*x+1/2*c))","A"
45,1,103,72,0.078000," ","int(cos(d*x+c)^3/(a+a*cos(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)}{a d \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)}{a d \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)}{a d}"," ",0,"-1/a/d*tan(1/2*d*x+1/2*c)-3/a/d/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)^3-1/a/d/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)+3/a/d*arctan(tan(1/2*d*x+1/2*c))","A"
46,1,68,43,0.054000," ","int(cos(d*x+c)^2/(a+a*cos(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)}{a d \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)}{a d}"," ",0,"1/a/d*tan(1/2*d*x+1/2*c)+2/a/d*tan(1/2*d*x+1/2*c)/(1+tan(1/2*d*x+1/2*c)^2)-2/a/d*arctan(tan(1/2*d*x+1/2*c))","A"
47,1,37,29,0.050000," ","int(cos(d*x+c)/(a+a*cos(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)}{a d}"," ",0,"-1/a/d*tan(1/2*d*x+1/2*c)+2/a/d*arctan(tan(1/2*d*x+1/2*c))","A"
48,1,17,22,0.041000," ","int(1/(a+a*cos(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"
49,1,58,38,0.077000," ","int(sec(d*x+c)/(a+a*cos(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)}{a d}+\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{a d}"," ",0,"-1/a/d*tan(1/2*d*x+1/2*c)-1/a/d*ln(tan(1/2*d*x+1/2*c)-1)+1/a/d*ln(tan(1/2*d*x+1/2*c)+1)","A"
50,1,99,53,0.090000," ","int(sec(d*x+c)^2/(a+a*cos(d*x+c)),x)","\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{a d}-\frac{1}{a d \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 d}-\frac{1}{a d \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 d}"," ",0,"1/a/d*tan(1/2*d*x+1/2*c)-1/a/d/(tan(1/2*d*x+1/2*c)-1)+1/a/d*ln(tan(1/2*d*x+1/2*c)-1)-1/a/d/(tan(1/2*d*x+1/2*c)+1)-1/a/d*ln(tan(1/2*d*x+1/2*c)+1)","A"
51,1,143,79,0.108000," ","int(sec(d*x+c)^3/(a+a*cos(d*x+c)),x)","-\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{a d}+\frac{1}{2 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}+\frac{3}{2 a d \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 a d}-\frac{1}{2 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}+\frac{3}{2 a d \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 a d}"," ",0,"-1/a/d*tan(1/2*d*x+1/2*c)+1/2/a/d/(tan(1/2*d*x+1/2*c)-1)^2+3/2/a/d/(tan(1/2*d*x+1/2*c)-1)-3/2/a/d*ln(tan(1/2*d*x+1/2*c)-1)-1/2/a/d/(tan(1/2*d*x+1/2*c)+1)^2+3/2/a/d/(tan(1/2*d*x+1/2*c)+1)+3/2/a/d*ln(tan(1/2*d*x+1/2*c)+1)","A"
52,1,183,97,0.121000," ","int(sec(d*x+c)^4/(a+a*cos(d*x+c)),x)","\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{a d}-\frac{1}{3 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{3}}-\frac{1}{a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}-\frac{5}{2 a d \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 a d}-\frac{1}{3 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}+\frac{1}{a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}-\frac{5}{2 a d \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 a d}"," ",0,"1/a/d*tan(1/2*d*x+1/2*c)-1/3/a/d/(tan(1/2*d*x+1/2*c)-1)^3-1/a/d/(tan(1/2*d*x+1/2*c)-1)^2-5/2/a/d/(tan(1/2*d*x+1/2*c)-1)+3/2/a/d*ln(tan(1/2*d*x+1/2*c)-1)-1/3/a/d/(tan(1/2*d*x+1/2*c)+1)^3+1/a/d/(tan(1/2*d*x+1/2*c)+1)^2-5/2/a/d/(tan(1/2*d*x+1/2*c)+1)-3/2/a/d*ln(tan(1/2*d*x+1/2*c)+1)","A"
53,1,156,120,0.070000," ","int(cos(d*x+c)^5/(a+a*cos(d*x+c))^2,x)","-\frac{\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)}{6 d \,a^{2}}+\frac{9 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 d \,a^{2}}+\frac{10 \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{40 \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{6 \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{10 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{2}}"," ",0,"-1/6/d/a^2*tan(1/2*d*x+1/2*c)^3+9/2/d/a^2*tan(1/2*d*x+1/2*c)+10/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)^5+40/3/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)^3+6/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)-10/d/a^2*arctan(tan(1/2*d*x+1/2*c))","A"
54,1,122,104,0.054000," ","int(cos(d*x+c)^4/(a+a*cos(d*x+c))^2,x)","\frac{\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)}{6 d \,a^{2}}-\frac{7 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 d \,a^{2}}-\frac{5 \left(\tan^{3}\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)^{2}}-\frac{3 \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{7 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{2}}"," ",0,"1/6/d/a^2*tan(1/2*d*x+1/2*c)^3-7/2/d/a^2*tan(1/2*d*x+1/2*c)-5/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)^3-3/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)+7/d/a^2*arctan(tan(1/2*d*x+1/2*c))","A"
55,1,88,76,0.062000," ","int(cos(d*x+c)^3/(a+a*cos(d*x+c))^2,x)","-\frac{\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)}{6 d \,a^{2}}+\frac{5 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 d \,a^{2}}+\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 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{2}}"," ",0,"-1/6/d/a^2*tan(1/2*d*x+1/2*c)^3+5/2/d/a^2*tan(1/2*d*x+1/2*c)+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^2*arctan(tan(1/2*d*x+1/2*c))","A"
56,1,56,53,0.058000," ","int(cos(d*x+c)^2/(a+a*cos(d*x+c))^2,x)","\frac{\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)}{6 d \,a^{2}}-\frac{3 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 d \,a^{2}}+\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{2}}"," ",0,"1/6/d/a^2*tan(1/2*d*x+1/2*c)^3-3/2/d/a^2*tan(1/2*d*x+1/2*c)+2/d/a^2*arctan(tan(1/2*d*x+1/2*c))","A"
57,1,32,51,0.050000," ","int(cos(d*x+c)/(a+a*cos(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"
58,1,32,51,0.044000," ","int(1/(a+a*cos(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"
59,1,77,62,0.088000," ","int(sec(d*x+c)/(a+a*cos(d*x+c))^2,x)","-\frac{\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)}{6 d \,a^{2}}-\frac{3 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 d \,a^{2}}-\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}{d \,a^{2}}+\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{d \,a^{2}}"," ",0,"-1/6/d/a^2*tan(1/2*d*x+1/2*c)^3-3/2/d/a^2*tan(1/2*d*x+1/2*c)-1/d/a^2*ln(tan(1/2*d*x+1/2*c)-1)+1/d/a^2*ln(tan(1/2*d*x+1/2*c)+1)","A"
60,1,120,77,0.109000," ","int(sec(d*x+c)^2/(a+a*cos(d*x+c))^2,x)","\frac{\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)}{6 d \,a^{2}}+\frac{5 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 d \,a^{2}}-\frac{1}{d \,a^{2} \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)}{d \,a^{2}}-\frac{1}{d \,a^{2} \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)}{d \,a^{2}}"," ",0,"1/6/d/a^2*tan(1/2*d*x+1/2*c)^3+5/2/d/a^2*tan(1/2*d*x+1/2*c)-1/d/a^2/(tan(1/2*d*x+1/2*c)-1)+2/d/a^2*ln(tan(1/2*d*x+1/2*c)-1)-1/d/a^2/(tan(1/2*d*x+1/2*c)+1)-2/d/a^2*ln(tan(1/2*d*x+1/2*c)+1)","A"
61,1,162,109,0.140000," ","int(sec(d*x+c)^3/(a+a*cos(d*x+c))^2,x)","-\frac{\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)}{6 d \,a^{2}}-\frac{7 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 d \,a^{2}}+\frac{1}{2 d \,a^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}+\frac{5}{2 d \,a^{2} \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 d \,a^{2}}-\frac{1}{2 d \,a^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}+\frac{5}{2 d \,a^{2} \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 d \,a^{2}}"," ",0,"-1/6/d/a^2*tan(1/2*d*x+1/2*c)^3-7/2/d/a^2*tan(1/2*d*x+1/2*c)+1/2/d/a^2/(tan(1/2*d*x+1/2*c)-1)^2+5/2/d/a^2/(tan(1/2*d*x+1/2*c)-1)-7/2/d/a^2*ln(tan(1/2*d*x+1/2*c)-1)-1/2/d/a^2/(tan(1/2*d*x+1/2*c)+1)^2+5/2/d/a^2/(tan(1/2*d*x+1/2*c)+1)+7/2/d/a^2*ln(tan(1/2*d*x+1/2*c)+1)","A"
62,1,204,129,0.100000," ","int(sec(d*x+c)^4/(a+a*cos(d*x+c))^2,x)","\frac{\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)}{6 d \,a^{2}}+\frac{9 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 d \,a^{2}}-\frac{1}{3 d \,a^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{3}}-\frac{3}{2 d \,a^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}-\frac{5}{d \,a^{2} \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^{2}}-\frac{1}{3 d \,a^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}+\frac{3}{2 d \,a^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}-\frac{5}{d \,a^{2} \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^{2}}"," ",0,"1/6/d/a^2*tan(1/2*d*x+1/2*c)^3+9/2/d/a^2*tan(1/2*d*x+1/2*c)-1/3/d/a^2/(tan(1/2*d*x+1/2*c)-1)^3-3/2/d/a^2/(tan(1/2*d*x+1/2*c)-1)^2-5/d/a^2/(tan(1/2*d*x+1/2*c)-1)+5/d/a^2*ln(tan(1/2*d*x+1/2*c)-1)-1/3/d/a^2/(tan(1/2*d*x+1/2*c)+1)^3+3/2/d/a^2/(tan(1/2*d*x+1/2*c)+1)^2-5/d/a^2/(tan(1/2*d*x+1/2*c)+1)-5/d/a^2*ln(tan(1/2*d*x+1/2*c)+1)","A"
63,1,141,141,0.064000," ","int(cos(d*x+c)^5/(a+a*cos(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"
64,1,107,113,0.056000," ","int(cos(d*x+c)^4/(a+a*cos(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"
65,1,75,90,0.056000," ","int(cos(d*x+c)^3/(a+a*cos(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"
66,1,45,77,0.048000," ","int(cos(d*x+c)^2/(a+a*cos(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"
67,1,32,77,0.045000," ","int(cos(d*x+c)/(a+a*cos(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"
68,1,45,77,0.041000," ","int(1/(a+a*cos(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"
69,1,96,91,0.082000," ","int(sec(d*x+c)/(a+a*cos(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"
70,1,139,106,0.082000," ","int(sec(d*x+c)^2/(a+a*cos(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"
71,1,181,144,0.115000," ","int(sec(d*x+c)^3/(a+a*cos(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"
72,1,160,170,0.063000," ","int(cos(d*x+c)^6/(a+a*cos(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"
73,1,126,142,0.058000," ","int(cos(d*x+c)^5/(a+a*cos(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"
74,1,94,119,0.050000," ","int(cos(d*x+c)^4/(a+a*cos(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"
75,1,58,106,0.053000," ","int(cos(d*x+c)^3/(a+a*cos(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"
76,1,58,104,0.045000," ","int(cos(d*x+c)^2/(a+a*cos(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"
77,1,58,104,0.044000," ","int(cos(d*x+c)/(a+a*cos(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"
78,1,56,104,0.043000," ","int(1/(a+a*cos(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"
79,1,115,112,0.088000," ","int(sec(d*x+c)/(a+a*cos(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"
80,1,158,127,0.087000," ","int(sec(d*x+c)^2/(a+a*cos(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"
81,1,200,171,0.111000," ","int(sec(d*x+c)^3/(a+a*cos(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"
82,1,179,209,0.066000," ","int(cos(d*x+c)^7/(a+a*cos(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"
83,1,145,181,0.058000," ","int(cos(d*x+c)^6/(a+a*cos(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"
84,1,113,158,0.054000," ","int(cos(d*x+c)^5/(a+a*cos(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"
85,1,71,145,0.047000," ","int(cos(d*x+c)^4/(a+a*cos(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"
86,1,58,137,0.056000," ","int(cos(d*x+c)^3/(a+a*cos(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"
87,1,45,129,0.057000," ","int(cos(d*x+c)^2/(a+a*cos(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"
88,1,58,133,0.047000," ","int(cos(d*x+c)/(a+a*cos(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"
89,1,71,133,0.039000," ","int(1/(a+a*cos(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"
90,1,134,143,0.095000," ","int(sec(d*x+c)/(a+a*cos(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"
91,1,177,158,0.094000," ","int(sec(d*x+c)^2/(a+a*cos(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"
92,1,219,208,0.111000," ","int(sec(d*x+c)^3/(a+a*cos(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{1}{2 d \,a^{5} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}+\frac{11}{2 d \,a^{5} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{31 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}{2 d \,a^{5}}-\frac{1}{2 d \,a^{5} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}+\frac{11}{2 d \,a^{5} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}+\frac{31 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{2 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)+1/2/d/a^5/(tan(1/2*d*x+1/2*c)-1)^2+11/2/d/a^5/(tan(1/2*d*x+1/2*c)-1)-31/2/d/a^5*ln(tan(1/2*d*x+1/2*c)-1)-1/2/d/a^5/(tan(1/2*d*x+1/2*c)+1)^2+11/2/d/a^5/(tan(1/2*d*x+1/2*c)+1)+31/2/d/a^5*ln(tan(1/2*d*x+1/2*c)+1)","A"
93,1,84,172,0.055000," ","int(cos(d*x+c)^5/(a+a*cos(d*x+c))^6,x)","\frac{-\frac{\left(\tan^{11}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{11}+\frac{5 \left(\tan^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{9}-\frac{10 \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{7}+2 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\frac{5 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3}+\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{32 d \,a^{6}}"," ",0,"1/32/d/a^6*(-1/11*tan(1/2*d*x+1/2*c)^11+5/9*tan(1/2*d*x+1/2*c)^9-10/7*tan(1/2*d*x+1/2*c)^7+2*tan(1/2*d*x+1/2*c)^5-5/3*tan(1/2*d*x+1/2*c)^3+tan(1/2*d*x+1/2*c))","A"
94,1,84,164,0.048000," ","int(cos(d*x+c)^4/(a+a*cos(d*x+c))^6,x)","\frac{\frac{\left(\tan^{11}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{11}-\frac{\left(\tan^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3}+\frac{2 \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{7}+\frac{2 \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)}{32 d \,a^{6}}"," ",0,"1/32/d/a^6*(1/11*tan(1/2*d*x+1/2*c)^11-1/3*tan(1/2*d*x+1/2*c)^9+2/7*tan(1/2*d*x+1/2*c)^7+2/5*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"
95,1,97,138,0.178000," ","int(cos(d*x+c)^4*(a+a*cos(d*x+c))^(1/2),x)","\frac{2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) a \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \left(560 \left(\cos^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-800 \left(\cos^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+552 \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-104 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+107\right) \sqrt{2}}{315 \sqrt{a \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, d}"," ",0,"2/315*cos(1/2*d*x+1/2*c)*a*sin(1/2*d*x+1/2*c)*(560*cos(1/2*d*x+1/2*c)^8-800*cos(1/2*d*x+1/2*c)^6+552*cos(1/2*d*x+1/2*c)^4-104*cos(1/2*d*x+1/2*c)^2+107)*2^(1/2)/(a*cos(1/2*d*x+1/2*c)^2)^(1/2)/d","A"
96,1,84,106,0.170000," ","int(cos(d*x+c)^3*(a+a*cos(d*x+c))^(1/2),x)","\frac{2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) a \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \left(40 \left(\cos^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-36 \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+22 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+9\right) \sqrt{2}}{35 \sqrt{a \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, d}"," ",0,"2/35*cos(1/2*d*x+1/2*c)*a*sin(1/2*d*x+1/2*c)*(40*cos(1/2*d*x+1/2*c)^6-36*cos(1/2*d*x+1/2*c)^4+22*cos(1/2*d*x+1/2*c)^2+9)*2^(1/2)/(a*cos(1/2*d*x+1/2*c)^2)^(1/2)/d","A"
97,1,71,74,0.166000," ","int(cos(d*x+c)^2*(a+a*cos(d*x+c))^(1/2),x)","\frac{2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) a \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \left(12 \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-4 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+7\right) \sqrt{2}}{15 \sqrt{a \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, d}"," ",0,"2/15*cos(1/2*d*x+1/2*c)*a*sin(1/2*d*x+1/2*c)*(12*cos(1/2*d*x+1/2*c)^4-4*cos(1/2*d*x+1/2*c)^2+7)*2^(1/2)/(a*cos(1/2*d*x+1/2*c)^2)^(1/2)/d","A"
98,1,58,48,0.165000," ","int(cos(d*x+c)*(a+a*cos(d*x+c))^(1/2),x)","\frac{2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) a \sin \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) \sqrt{2}}{3 \sqrt{a \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, d}"," ",0,"2/3*cos(1/2*d*x+1/2*c)*a*sin(1/2*d*x+1/2*c)*(2*cos(1/2*d*x+1/2*c)^2+1)*2^(1/2)/(a*cos(1/2*d*x+1/2*c)^2)^(1/2)/d","A"
99,1,43,24,0.000000," ","int((a+a*cos(d*x+c))^(1/2),x)","\frac{2 a \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2}}{\sqrt{a \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, d}"," ",0,"2*a*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)*2^(1/2)/(a*cos(1/2*d*x+1/2*c)^2)^(1/2)/d","A"
100,1,180,31,0.505000," ","int((a+a*cos(d*x+c))^(1/2)*sec(d*x+c),x)","\frac{\sqrt{a}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(\ln \left(\frac{4 \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}+4 a \sqrt{2}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+8 a}{2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\sqrt{2}}\right)+\ln \left(-\frac{4 \left(\sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}-a \sqrt{2}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+2 a \right)}{-2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\sqrt{2}}\right)\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{a \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, d}"," ",0,"a^(1/2)*cos(1/2*d*x+1/2*c)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*(ln(4/(2*cos(1/2*d*x+1/2*c)+2^(1/2))*(2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)+a*2^(1/2)*cos(1/2*d*x+1/2*c)+2*a))+ln(-4/(-2*cos(1/2*d*x+1/2*c)+2^(1/2))*(2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)-a*2^(1/2)*cos(1/2*d*x+1/2*c)+2*a)))/sin(1/2*d*x+1/2*c)/(a*cos(1/2*d*x+1/2*c)^2)^(1/2)/d","B"
101,1,379,54,0.476000," ","int((a+a*cos(d*x+c))^(1/2)*sec(d*x+c)^2,x)","\frac{\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(-2 a \left(\ln \left(\frac{4 \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}+4 a \sqrt{2}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+8 a}{2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\sqrt{2}}\right)+\ln \left(-\frac{4 \left(\sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}-a \sqrt{2}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+2 a \right)}{-2 \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)+\ln \left(-\frac{4 \left(\sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}-a \sqrt{2}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+2 a \right)}{-2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\sqrt{2}}\right) a +\ln \left(\frac{4 \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}+4 a \sqrt{2}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+8 a}{2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\sqrt{2}}\right) a +2 \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}\right)}{\sqrt{a}\, \left(2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-\sqrt{2}\right) \left(2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\sqrt{2}\right) \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{a \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, d}"," ",0,"cos(1/2*d*x+1/2*c)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*a*(ln(4/(2*cos(1/2*d*x+1/2*c)+2^(1/2))*(2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)+a*2^(1/2)*cos(1/2*d*x+1/2*c)+2*a))+ln(-4/(-2*cos(1/2*d*x+1/2*c)+2^(1/2))*(2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)-a*2^(1/2)*cos(1/2*d*x+1/2*c)+2*a)))*sin(1/2*d*x+1/2*c)^2+ln(-4/(-2*cos(1/2*d*x+1/2*c)+2^(1/2))*(2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)-a*2^(1/2)*cos(1/2*d*x+1/2*c)+2*a))*a+ln(4/(2*cos(1/2*d*x+1/2*c)+2^(1/2))*(2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)+a*2^(1/2)*cos(1/2*d*x+1/2*c)+2*a))*a+2*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2))/a^(1/2)/(2*cos(1/2*d*x+1/2*c)-2^(1/2))/(2*cos(1/2*d*x+1/2*c)+2^(1/2))/sin(1/2*d*x+1/2*c)/(a*cos(1/2*d*x+1/2*c)^2)^(1/2)/d","B"
102,1,545,86,0.527000," ","int((a+a*cos(d*x+c))^(1/2)*sec(d*x+c)^3,x)","\frac{\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(12 a \left(\ln \left(\frac{4 \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}+4 a \sqrt{2}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+8 a}{2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\sqrt{2}}\right)+\ln \left(-\frac{4 \left(\sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}-a \sqrt{2}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+2 a \right)}{-2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\sqrt{2}}\right)\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(-12 \ln \left(\frac{4 \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}+4 a \sqrt{2}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+8 a}{2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\sqrt{2}}\right) a -12 \ln \left(-\frac{4 \left(\sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}-a \sqrt{2}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+2 a \right)}{-2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\sqrt{2}}\right) a -12 \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+3 \ln \left(\frac{4 \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}+4 a \sqrt{2}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+8 a}{2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\sqrt{2}}\right) a +3 \ln \left(-\frac{4 \left(\sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}-a \sqrt{2}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+2 a \right)}{-2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\sqrt{2}}\right) a +10 \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}\right)}{2 \sqrt{a}\, \left(2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\sqrt{2}\right)^{2} \left(2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-\sqrt{2}\right)^{2} \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{a \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, d}"," ",0,"1/2*cos(1/2*d*x+1/2*c)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*(12*a*(ln(4/(2*cos(1/2*d*x+1/2*c)+2^(1/2))*(2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)+a*2^(1/2)*cos(1/2*d*x+1/2*c)+2*a))+ln(-4/(-2*cos(1/2*d*x+1/2*c)+2^(1/2))*(2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)-a*2^(1/2)*cos(1/2*d*x+1/2*c)+2*a)))*sin(1/2*d*x+1/2*c)^4+(-12*ln(4/(2*cos(1/2*d*x+1/2*c)+2^(1/2))*(2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)+a*2^(1/2)*cos(1/2*d*x+1/2*c)+2*a))*a-12*ln(-4/(-2*cos(1/2*d*x+1/2*c)+2^(1/2))*(2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)-a*2^(1/2)*cos(1/2*d*x+1/2*c)+2*a))*a-12*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2))*sin(1/2*d*x+1/2*c)^2+3*ln(4/(2*cos(1/2*d*x+1/2*c)+2^(1/2))*(2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)+a*2^(1/2)*cos(1/2*d*x+1/2*c)+2*a))*a+3*ln(-4/(-2*cos(1/2*d*x+1/2*c)+2^(1/2))*(2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)-a*2^(1/2)*cos(1/2*d*x+1/2*c)+2*a))*a+10*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2))/a^(1/2)/(2*cos(1/2*d*x+1/2*c)+2^(1/2))^2/(2*cos(1/2*d*x+1/2*c)-2^(1/2))^2/sin(1/2*d*x+1/2*c)/(a*cos(1/2*d*x+1/2*c)^2)^(1/2)/d","B"
103,1,709,118,0.575000," ","int((a+a*cos(d*x+c))^(1/2)*sec(d*x+c)^4,x)","\frac{\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(-120 a \left(\ln \left(\frac{4 \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}+4 a \sqrt{2}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+8 a}{2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\sqrt{2}}\right)+\ln \left(-\frac{4 \left(\sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}-a \sqrt{2}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+2 a \right)}{-2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\sqrt{2}}\right)\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+60 \left(2 \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}+3 \ln \left(\frac{4 \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}+4 a \sqrt{2}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+8 a}{2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\sqrt{2}}\right) a +3 \ln \left(-\frac{4 \left(\sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}-a \sqrt{2}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+2 a \right)}{-2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\sqrt{2}}\right) a \right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(-90 \ln \left(-\frac{4 \left(\sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}-a \sqrt{2}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+2 a \right)}{-2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\sqrt{2}}\right) a -90 \ln \left(\frac{4 \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}+4 a \sqrt{2}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+8 a}{2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\sqrt{2}}\right) a -160 \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+15 \ln \left(-\frac{4 \left(\sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}-a \sqrt{2}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+2 a \right)}{-2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\sqrt{2}}\right) a +15 \ln \left(\frac{4 \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}+4 a \sqrt{2}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+8 a}{2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\sqrt{2}}\right) a +66 \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}\right)}{6 \sqrt{a}\, \left(2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-\sqrt{2}\right)^{3} \left(2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\sqrt{2}\right)^{3} \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{a \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, d}"," ",0,"1/6*cos(1/2*d*x+1/2*c)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*(-120*a*(ln(4/(2*cos(1/2*d*x+1/2*c)+2^(1/2))*(2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)+a*2^(1/2)*cos(1/2*d*x+1/2*c)+2*a))+ln(-4/(-2*cos(1/2*d*x+1/2*c)+2^(1/2))*(2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)-a*2^(1/2)*cos(1/2*d*x+1/2*c)+2*a)))*sin(1/2*d*x+1/2*c)^6+60*(2*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)+3*ln(4/(2*cos(1/2*d*x+1/2*c)+2^(1/2))*(2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)+a*2^(1/2)*cos(1/2*d*x+1/2*c)+2*a))*a+3*ln(-4/(-2*cos(1/2*d*x+1/2*c)+2^(1/2))*(2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)-a*2^(1/2)*cos(1/2*d*x+1/2*c)+2*a))*a)*sin(1/2*d*x+1/2*c)^4+(-90*ln(-4/(-2*cos(1/2*d*x+1/2*c)+2^(1/2))*(2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)-a*2^(1/2)*cos(1/2*d*x+1/2*c)+2*a))*a-90*ln(4/(2*cos(1/2*d*x+1/2*c)+2^(1/2))*(2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)+a*2^(1/2)*cos(1/2*d*x+1/2*c)+2*a))*a-160*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2))*sin(1/2*d*x+1/2*c)^2+15*ln(-4/(-2*cos(1/2*d*x+1/2*c)+2^(1/2))*(2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)-a*2^(1/2)*cos(1/2*d*x+1/2*c)+2*a))*a+15*ln(4/(2*cos(1/2*d*x+1/2*c)+2^(1/2))*(2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)+a*2^(1/2)*cos(1/2*d*x+1/2*c)+2*a))*a+66*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2))/a^(1/2)/(2*cos(1/2*d*x+1/2*c)-2^(1/2))^3/(2*cos(1/2*d*x+1/2*c)+2^(1/2))^3/sin(1/2*d*x+1/2*c)/(a*cos(1/2*d*x+1/2*c)^2)^(1/2)/d","B"
104,1,99,142,0.147000," ","int(cos(d*x+c)^3*(a+a*cos(d*x+c))^(3/2),x)","\frac{4 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) a^{2} \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \left(280 \left(\cos^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-220 \left(\cos^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+114 \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)+94\right) \sqrt{2}}{315 \sqrt{a \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, d}"," ",0,"4/315*cos(1/2*d*x+1/2*c)*a^2*sin(1/2*d*x+1/2*c)*(280*cos(1/2*d*x+1/2*c)^8-220*cos(1/2*d*x+1/2*c)^6+114*cos(1/2*d*x+1/2*c)^4+47*cos(1/2*d*x+1/2*c)^2+94)*2^(1/2)/(a*cos(1/2*d*x+1/2*c)^2)^(1/2)/d","A"
105,1,86,100,0.155000," ","int(cos(d*x+c)^2*(a+a*cos(d*x+c))^(3/2),x)","\frac{4 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) a^{2} \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \left(60 \left(\cos^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-12 \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)+38\right) \sqrt{2}}{105 \sqrt{a \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, d}"," ",0,"4/105*cos(1/2*d*x+1/2*c)*a^2*sin(1/2*d*x+1/2*c)*(60*cos(1/2*d*x+1/2*c)^6-12*cos(1/2*d*x+1/2*c)^4+19*cos(1/2*d*x+1/2*c)^2+38)*2^(1/2)/(a*cos(1/2*d*x+1/2*c)^2)^(1/2)/d","A"
106,1,71,74,0.162000," ","int(cos(d*x+c)*(a+a*cos(d*x+c))^(3/2),x)","\frac{4 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) a^{2} \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \left(2 \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)+2\right) \sqrt{2}}{5 \sqrt{a \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, d}"," ",0,"4/5*cos(1/2*d*x+1/2*c)*a^2*sin(1/2*d*x+1/2*c)*(2*cos(1/2*d*x+1/2*c)^4+cos(1/2*d*x+1/2*c)^2+2)*2^(1/2)/(a*cos(1/2*d*x+1/2*c)^2)^(1/2)/d","A"
107,1,58,51,0.144000," ","int((a+a*cos(d*x+c))^(3/2),x)","\frac{4 a^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \left(2+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \sqrt{2}}{3 \sqrt{a \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, d}"," ",0,"4/3*a^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)*2^(1/2)/(a*cos(1/2*d*x+1/2*c)^2)^(1/2)/d","A"
108,1,207,58,0.454000," ","int((a+a*cos(d*x+c))^(3/2)*sec(d*x+c),x)","\frac{\sqrt{a}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(2 \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}+\ln \left(\frac{4 \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}+4 a \sqrt{2}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+8 a}{2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\sqrt{2}}\right) a +\ln \left(-\frac{4 \left(\sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}-a \sqrt{2}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+2 a \right)}{-2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\sqrt{2}}\right) a \right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{a \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, d}"," ",0,"a^(1/2)*cos(1/2*d*x+1/2*c)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)+ln(4/(2*cos(1/2*d*x+1/2*c)+2^(1/2))*(2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)+a*2^(1/2)*cos(1/2*d*x+1/2*c)+2*a))*a+ln(-4/(-2*cos(1/2*d*x+1/2*c)+2^(1/2))*(2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)-a*2^(1/2)*cos(1/2*d*x+1/2*c)+2*a))*a)/sin(1/2*d*x+1/2*c)/(a*cos(1/2*d*x+1/2*c)^2)^(1/2)/d","B"
109,1,381,57,0.440000," ","int((a+a*cos(d*x+c))^(3/2)*sec(d*x+c)^2,x)","\frac{\sqrt{a}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(-6 a \left(\ln \left(\frac{4 \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}+4 a \sqrt{2}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+8 a}{2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\sqrt{2}}\right)+\ln \left(-\frac{4 \left(\sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}-a \sqrt{2}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+2 a \right)}{-2 \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)+3 \ln \left(-\frac{4 \left(\sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}-a \sqrt{2}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+2 a \right)}{-2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\sqrt{2}}\right) a +3 \ln \left(\frac{4 \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}+4 a \sqrt{2}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+8 a}{2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\sqrt{2}}\right) a +2 \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}\right)}{\left(2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-\sqrt{2}\right) \left(2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\sqrt{2}\right) \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{a \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, d}"," ",0,"a^(1/2)*cos(1/2*d*x+1/2*c)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*(-6*a*(ln(4/(2*cos(1/2*d*x+1/2*c)+2^(1/2))*(2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)+a*2^(1/2)*cos(1/2*d*x+1/2*c)+2*a))+ln(-4/(-2*cos(1/2*d*x+1/2*c)+2^(1/2))*(2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)-a*2^(1/2)*cos(1/2*d*x+1/2*c)+2*a)))*sin(1/2*d*x+1/2*c)^2+3*ln(-4/(-2*cos(1/2*d*x+1/2*c)+2^(1/2))*(2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)-a*2^(1/2)*cos(1/2*d*x+1/2*c)+2*a))*a+3*ln(4/(2*cos(1/2*d*x+1/2*c)+2^(1/2))*(2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)+a*2^(1/2)*cos(1/2*d*x+1/2*c)+2*a))*a+2*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2))/(2*cos(1/2*d*x+1/2*c)-2^(1/2))/(2*cos(1/2*d*x+1/2*c)+2^(1/2))/sin(1/2*d*x+1/2*c)/(a*cos(1/2*d*x+1/2*c)^2)^(1/2)/d","B"
110,1,545,90,0.570000," ","int((a+a*cos(d*x+c))^(3/2)*sec(d*x+c)^3,x)","\frac{\sqrt{a}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(28 a \left(\ln \left(\frac{4 \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}+4 a \sqrt{2}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+8 a}{2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\sqrt{2}}\right)+\ln \left(-\frac{4 \left(\sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}-a \sqrt{2}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+2 a \right)}{-2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\sqrt{2}}\right)\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(-28 \ln \left(-\frac{4 \left(\sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}-a \sqrt{2}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+2 a \right)}{-2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\sqrt{2}}\right) a -28 \ln \left(\frac{4 \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}+4 a \sqrt{2}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+8 a}{2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\sqrt{2}}\right) a -28 \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+7 \ln \left(-\frac{4 \left(\sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}-a \sqrt{2}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+2 a \right)}{-2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\sqrt{2}}\right) a +7 \ln \left(\frac{4 \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}+4 a \sqrt{2}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+8 a}{2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\sqrt{2}}\right) a +18 \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}\right)}{2 \left(2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-\sqrt{2}\right)^{2} \left(2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\sqrt{2}\right)^{2} \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{a \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, d}"," ",0,"1/2*a^(1/2)*cos(1/2*d*x+1/2*c)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*(28*a*(ln(4/(2*cos(1/2*d*x+1/2*c)+2^(1/2))*(2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)+a*2^(1/2)*cos(1/2*d*x+1/2*c)+2*a))+ln(-4/(-2*cos(1/2*d*x+1/2*c)+2^(1/2))*(2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)-a*2^(1/2)*cos(1/2*d*x+1/2*c)+2*a)))*sin(1/2*d*x+1/2*c)^4+(-28*ln(-4/(-2*cos(1/2*d*x+1/2*c)+2^(1/2))*(2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)-a*2^(1/2)*cos(1/2*d*x+1/2*c)+2*a))*a-28*ln(4/(2*cos(1/2*d*x+1/2*c)+2^(1/2))*(2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)+a*2^(1/2)*cos(1/2*d*x+1/2*c)+2*a))*a-28*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2))*sin(1/2*d*x+1/2*c)^2+7*ln(-4/(-2*cos(1/2*d*x+1/2*c)+2^(1/2))*(2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)-a*2^(1/2)*cos(1/2*d*x+1/2*c)+2*a))*a+7*ln(4/(2*cos(1/2*d*x+1/2*c)+2^(1/2))*(2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)+a*2^(1/2)*cos(1/2*d*x+1/2*c)+2*a))*a+18*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2))/(2*cos(1/2*d*x+1/2*c)-2^(1/2))^2/(2*cos(1/2*d*x+1/2*c)+2^(1/2))^2/sin(1/2*d*x+1/2*c)/(a*cos(1/2*d*x+1/2*c)^2)^(1/2)/d","B"
111,1,710,124,0.584000," ","int((a+a*cos(d*x+c))^(3/2)*sec(d*x+c)^4,x)","\frac{\sqrt{a}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(-264 a \left(\ln \left(\frac{4 \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}+4 a \sqrt{2}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+8 a}{2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\sqrt{2}}\right)+\ln \left(-\frac{4 \left(\sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}-a \sqrt{2}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+2 a \right)}{-2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\sqrt{2}}\right)\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+132 \left(2 \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}+3 \ln \left(\frac{4 \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}+4 a \sqrt{2}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+8 a}{2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\sqrt{2}}\right) a +3 \ln \left(-\frac{4 \left(\sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}-a \sqrt{2}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+2 a \right)}{-2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\sqrt{2}}\right) a \right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-22 \left(16 \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}+9 \ln \left(-\frac{4 \left(\sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}-a \sqrt{2}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+2 a \right)}{-2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\sqrt{2}}\right) a +9 \ln \left(\frac{4 \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}+4 a \sqrt{2}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+8 a}{2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\sqrt{2}}\right) a \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+33 \ln \left(-\frac{4 \left(\sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}-a \sqrt{2}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+2 a \right)}{-2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\sqrt{2}}\right) a +33 \ln \left(\frac{4 \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}+4 a \sqrt{2}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+8 a}{2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\sqrt{2}}\right) a +126 \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}\right)}{6 \left(2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-\sqrt{2}\right)^{3} \left(2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\sqrt{2}\right)^{3} \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{a \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, d}"," ",0,"1/6*a^(1/2)*cos(1/2*d*x+1/2*c)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*(-264*a*(ln(4/(2*cos(1/2*d*x+1/2*c)+2^(1/2))*(2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)+a*2^(1/2)*cos(1/2*d*x+1/2*c)+2*a))+ln(-4/(-2*cos(1/2*d*x+1/2*c)+2^(1/2))*(2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)-a*2^(1/2)*cos(1/2*d*x+1/2*c)+2*a)))*sin(1/2*d*x+1/2*c)^6+132*(2*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)+3*ln(4/(2*cos(1/2*d*x+1/2*c)+2^(1/2))*(2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)+a*2^(1/2)*cos(1/2*d*x+1/2*c)+2*a))*a+3*ln(-4/(-2*cos(1/2*d*x+1/2*c)+2^(1/2))*(2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)-a*2^(1/2)*cos(1/2*d*x+1/2*c)+2*a))*a)*sin(1/2*d*x+1/2*c)^4-22*(16*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)+9*ln(-4/(-2*cos(1/2*d*x+1/2*c)+2^(1/2))*(2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)-a*2^(1/2)*cos(1/2*d*x+1/2*c)+2*a))*a+9*ln(4/(2*cos(1/2*d*x+1/2*c)+2^(1/2))*(2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)+a*2^(1/2)*cos(1/2*d*x+1/2*c)+2*a))*a)*sin(1/2*d*x+1/2*c)^2+33*ln(-4/(-2*cos(1/2*d*x+1/2*c)+2^(1/2))*(2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)-a*2^(1/2)*cos(1/2*d*x+1/2*c)+2*a))*a+33*ln(4/(2*cos(1/2*d*x+1/2*c)+2^(1/2))*(2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)+a*2^(1/2)*cos(1/2*d*x+1/2*c)+2*a))*a+126*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2))/(2*cos(1/2*d*x+1/2*c)-2^(1/2))^3/(2*cos(1/2*d*x+1/2*c)+2^(1/2))^3/sin(1/2*d*x+1/2*c)/(a*cos(1/2*d*x+1/2*c)^2)^(1/2)/d","B"
112,1,112,179,0.183000," ","int(cos(d*x+c)^3*(a+a*cos(d*x+c))^(5/2),x)","\frac{8 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) a^{3} \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \left(504 \left(\cos^{10}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-364 \left(\cos^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+178 \left(\cos^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+75 \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+100 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+200\right) \sqrt{2}}{693 \sqrt{a \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, d}"," ",0,"8/693*cos(1/2*d*x+1/2*c)*a^3*sin(1/2*d*x+1/2*c)*(504*cos(1/2*d*x+1/2*c)^10-364*cos(1/2*d*x+1/2*c)^8+178*cos(1/2*d*x+1/2*c)^6+75*cos(1/2*d*x+1/2*c)^4+100*cos(1/2*d*x+1/2*c)^2+200)*2^(1/2)/(a*cos(1/2*d*x+1/2*c)^2)^(1/2)/d","A"
113,1,99,126,0.184000," ","int(cos(d*x+c)^2*(a+a*cos(d*x+c))^(5/2),x)","\frac{8 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) a^{3} \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \left(140 \left(\cos^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-20 \left(\cos^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+39 \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+52 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+104\right) \sqrt{2}}{315 \sqrt{a \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, d}"," ",0,"8/315*cos(1/2*d*x+1/2*c)*a^3*sin(1/2*d*x+1/2*c)*(140*cos(1/2*d*x+1/2*c)^8-20*cos(1/2*d*x+1/2*c)^6+39*cos(1/2*d*x+1/2*c)^4+52*cos(1/2*d*x+1/2*c)^2+104)*2^(1/2)/(a*cos(1/2*d*x+1/2*c)^2)^(1/2)/d","A"
114,1,86,100,0.143000," ","int(cos(d*x+c)*(a+a*cos(d*x+c))^(5/2),x)","\frac{8 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) a^{3} \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \left(6 \left(\cos^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+3 \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+4 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+8\right) \sqrt{2}}{21 \sqrt{a \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, d}"," ",0,"8/21*cos(1/2*d*x+1/2*c)*a^3*sin(1/2*d*x+1/2*c)*(6*cos(1/2*d*x+1/2*c)^6+3*cos(1/2*d*x+1/2*c)^4+4*cos(1/2*d*x+1/2*c)^2+8)*2^(1/2)/(a*cos(1/2*d*x+1/2*c)^2)^(1/2)/d","A"
115,1,73,77,0.000000," ","int((a+a*cos(d*x+c))^(5/2),x)","\frac{8 a^{3} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \left(3 \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+4 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+8\right) \sqrt{2}}{15 \sqrt{a \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, d}"," ",0,"8/15*a^3*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)*(3*cos(1/2*d*x+1/2*c)^4+4*cos(1/2*d*x+1/2*c)^2+8)*2^(1/2)/(a*cos(1/2*d*x+1/2*c)^2)^(1/2)/d","A"
116,1,244,84,0.564000," ","int((a+a*cos(d*x+c))^(5/2)*sec(d*x+c),x)","\frac{a^{\frac{3}{2}} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(-4 \sqrt{a}\, \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+18 \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}+3 \ln \left(\frac{4 \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}+4 a \sqrt{2}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+8 a}{2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\sqrt{2}}\right) a +3 \ln \left(-\frac{4 \left(\sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}-a \sqrt{2}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+2 a \right)}{-2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\sqrt{2}}\right) a \right)}{3 \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{a \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, d}"," ",0,"1/3*a^(3/2)*cos(1/2*d*x+1/2*c)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*(-4*a^(1/2)*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^2+18*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)+3*ln(4/(2*cos(1/2*d*x+1/2*c)+2^(1/2))*(2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)+a*2^(1/2)*cos(1/2*d*x+1/2*c)+2*a))*a+3*ln(-4/(-2*cos(1/2*d*x+1/2*c)+2^(1/2))*(2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)-a*2^(1/2)*cos(1/2*d*x+1/2*c)+2*a))*a)/sin(1/2*d*x+1/2*c)/(a*cos(1/2*d*x+1/2*c)^2)^(1/2)/d","B"
117,1,408,82,0.479000," ","int((a+a*cos(d*x+c))^(5/2)*sec(d*x+c)^2,x)","\frac{a^{\frac{3}{2}} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(\left(-8 \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}-10 \ln \left(-\frac{4 \left(\sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}-a \sqrt{2}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+2 a \right)}{-2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\sqrt{2}}\right) a -10 \ln \left(\frac{4 \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}+4 a \sqrt{2}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+8 a}{2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\sqrt{2}}\right) a \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+6 \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}+5 \ln \left(-\frac{4 \left(\sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}-a \sqrt{2}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+2 a \right)}{-2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\sqrt{2}}\right) a +5 \ln \left(\frac{4 \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}+4 a \sqrt{2}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+8 a}{2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\sqrt{2}}\right) a \right)}{\left(2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-\sqrt{2}\right) \left(2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\sqrt{2}\right) \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{a \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, d}"," ",0,"a^(3/2)*cos(1/2*d*x+1/2*c)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*((-8*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)-10*ln(-4/(-2*cos(1/2*d*x+1/2*c)+2^(1/2))*(2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)-a*2^(1/2)*cos(1/2*d*x+1/2*c)+2*a))*a-10*ln(4/(2*cos(1/2*d*x+1/2*c)+2^(1/2))*(2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)+a*2^(1/2)*cos(1/2*d*x+1/2*c)+2*a))*a)*sin(1/2*d*x+1/2*c)^2+6*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)+5*ln(-4/(-2*cos(1/2*d*x+1/2*c)+2^(1/2))*(2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)-a*2^(1/2)*cos(1/2*d*x+1/2*c)+2*a))*a+5*ln(4/(2*cos(1/2*d*x+1/2*c)+2^(1/2))*(2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)+a*2^(1/2)*cos(1/2*d*x+1/2*c)+2*a))*a)/(2*cos(1/2*d*x+1/2*c)-2^(1/2))/(2*cos(1/2*d*x+1/2*c)+2^(1/2))/sin(1/2*d*x+1/2*c)/(a*cos(1/2*d*x+1/2*c)^2)^(1/2)/d","B"
118,1,545,90,0.527000," ","int((a+a*cos(d*x+c))^(5/2)*sec(d*x+c)^3,x)","\frac{a^{\frac{3}{2}} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(76 a \left(\ln \left(\frac{4 \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}+4 a \sqrt{2}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+8 a}{2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\sqrt{2}}\right)+\ln \left(-\frac{4 \left(\sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}-a \sqrt{2}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+2 a \right)}{-2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\sqrt{2}}\right)\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(-76 \ln \left(-\frac{4 \left(\sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}-a \sqrt{2}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+2 a \right)}{-2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\sqrt{2}}\right) a -76 \ln \left(\frac{4 \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}+4 a \sqrt{2}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+8 a}{2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\sqrt{2}}\right) a -44 \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+19 \ln \left(-\frac{4 \left(\sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}-a \sqrt{2}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+2 a \right)}{-2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\sqrt{2}}\right) a +19 \ln \left(\frac{4 \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}+4 a \sqrt{2}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+8 a}{2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\sqrt{2}}\right) a +26 \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}\right)}{2 \left(2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-\sqrt{2}\right)^{2} \left(2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\sqrt{2}\right)^{2} \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{a \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, d}"," ",0,"1/2*a^(3/2)*cos(1/2*d*x+1/2*c)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*(76*a*(ln(4/(2*cos(1/2*d*x+1/2*c)+2^(1/2))*(2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)+a*2^(1/2)*cos(1/2*d*x+1/2*c)+2*a))+ln(-4/(-2*cos(1/2*d*x+1/2*c)+2^(1/2))*(2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)-a*2^(1/2)*cos(1/2*d*x+1/2*c)+2*a)))*sin(1/2*d*x+1/2*c)^4+(-76*ln(-4/(-2*cos(1/2*d*x+1/2*c)+2^(1/2))*(2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)-a*2^(1/2)*cos(1/2*d*x+1/2*c)+2*a))*a-76*ln(4/(2*cos(1/2*d*x+1/2*c)+2^(1/2))*(2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)+a*2^(1/2)*cos(1/2*d*x+1/2*c)+2*a))*a-44*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2))*sin(1/2*d*x+1/2*c)^2+19*ln(-4/(-2*cos(1/2*d*x+1/2*c)+2^(1/2))*(2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)-a*2^(1/2)*cos(1/2*d*x+1/2*c)+2*a))*a+19*ln(4/(2*cos(1/2*d*x+1/2*c)+2^(1/2))*(2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)+a*2^(1/2)*cos(1/2*d*x+1/2*c)+2*a))*a+26*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2))/(2*cos(1/2*d*x+1/2*c)-2^(1/2))^2/(2*cos(1/2*d*x+1/2*c)+2^(1/2))^2/sin(1/2*d*x+1/2*c)/(a*cos(1/2*d*x+1/2*c)^2)^(1/2)/d","B"
119,1,709,124,0.563000," ","int((a+a*cos(d*x+c))^(5/2)*sec(d*x+c)^4,x)","\frac{a^{\frac{3}{2}} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(-600 a \left(\ln \left(\frac{4 \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}+4 a \sqrt{2}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+8 a}{2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\sqrt{2}}\right)+\ln \left(-\frac{4 \left(\sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}-a \sqrt{2}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+2 a \right)}{-2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\sqrt{2}}\right)\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+300 \left(2 \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}+3 \ln \left(\frac{4 \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}+4 a \sqrt{2}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+8 a}{2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\sqrt{2}}\right) a +3 \ln \left(-\frac{4 \left(\sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}-a \sqrt{2}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+2 a \right)}{-2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\sqrt{2}}\right) a \right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(-450 \ln \left(-\frac{4 \left(\sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}-a \sqrt{2}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+2 a \right)}{-2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\sqrt{2}}\right) a -450 \ln \left(\frac{4 \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}+4 a \sqrt{2}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+8 a}{2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\sqrt{2}}\right) a -736 \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+75 \ln \left(-\frac{4 \left(\sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}-a \sqrt{2}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+2 a \right)}{-2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\sqrt{2}}\right) a +75 \ln \left(\frac{4 \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}+4 a \sqrt{2}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+8 a}{2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\sqrt{2}}\right) a +234 \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}\right)}{6 \left(2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-\sqrt{2}\right)^{3} \left(2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\sqrt{2}\right)^{3} \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{a \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, d}"," ",0,"1/6*a^(3/2)*cos(1/2*d*x+1/2*c)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*(-600*a*(ln(4/(2*cos(1/2*d*x+1/2*c)+2^(1/2))*(2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)+a*2^(1/2)*cos(1/2*d*x+1/2*c)+2*a))+ln(-4/(-2*cos(1/2*d*x+1/2*c)+2^(1/2))*(2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)-a*2^(1/2)*cos(1/2*d*x+1/2*c)+2*a)))*sin(1/2*d*x+1/2*c)^6+300*(2*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)+3*ln(4/(2*cos(1/2*d*x+1/2*c)+2^(1/2))*(2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)+a*2^(1/2)*cos(1/2*d*x+1/2*c)+2*a))*a+3*ln(-4/(-2*cos(1/2*d*x+1/2*c)+2^(1/2))*(2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)-a*2^(1/2)*cos(1/2*d*x+1/2*c)+2*a))*a)*sin(1/2*d*x+1/2*c)^4+(-450*ln(-4/(-2*cos(1/2*d*x+1/2*c)+2^(1/2))*(2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)-a*2^(1/2)*cos(1/2*d*x+1/2*c)+2*a))*a-450*ln(4/(2*cos(1/2*d*x+1/2*c)+2^(1/2))*(2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)+a*2^(1/2)*cos(1/2*d*x+1/2*c)+2*a))*a-736*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2))*sin(1/2*d*x+1/2*c)^2+75*ln(-4/(-2*cos(1/2*d*x+1/2*c)+2^(1/2))*(2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)-a*2^(1/2)*cos(1/2*d*x+1/2*c)+2*a))*a+75*ln(4/(2*cos(1/2*d*x+1/2*c)+2^(1/2))*(2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)+a*2^(1/2)*cos(1/2*d*x+1/2*c)+2*a))*a+234*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2))/(2*cos(1/2*d*x+1/2*c)-2^(1/2))^3/(2*cos(1/2*d*x+1/2*c)+2^(1/2))^3/sin(1/2*d*x+1/2*c)/(a*cos(1/2*d*x+1/2*c)^2)^(1/2)/d","B"
120,1,872,158,0.598000," ","int((a+a*cos(d*x+c))^(5/2)*sec(d*x+c)^5,x)","\frac{a^{\frac{3}{2}} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(7824 a \left(\ln \left(\frac{4 \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}+4 a \sqrt{2}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+8 a}{2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\sqrt{2}}\right)+\ln \left(-\frac{4 \left(\sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}-a \sqrt{2}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+2 a \right)}{-2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\sqrt{2}}\right)\right) \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-7824 \left(\sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}+2 \ln \left(-\frac{4 \left(\sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}-a \sqrt{2}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+2 a \right)}{-2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\sqrt{2}}\right) a +2 \ln \left(\frac{4 \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}+4 a \sqrt{2}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+8 a}{2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\sqrt{2}}\right) a \right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1304 \left(11 \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}+9 \ln \left(-\frac{4 \left(\sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}-a \sqrt{2}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+2 a \right)}{-2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\sqrt{2}}\right) a +9 \ln \left(\frac{4 \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}+4 a \sqrt{2}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+8 a}{2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\sqrt{2}}\right) a \right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(-3912 \ln \left(-\frac{4 \left(\sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}-a \sqrt{2}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+2 a \right)}{-2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\sqrt{2}}\right) a -3912 \ln \left(\frac{4 \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}+4 a \sqrt{2}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+8 a}{2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\sqrt{2}}\right) a -9212 \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+489 \ln \left(-\frac{4 \left(\sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}-a \sqrt{2}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+2 a \right)}{-2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\sqrt{2}}\right) a +489 \ln \left(\frac{4 \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}+4 a \sqrt{2}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+8 a}{2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\sqrt{2}}\right) a +2094 \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}\right)}{24 \left(2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-\sqrt{2}\right)^{4} \left(2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\sqrt{2}\right)^{4} \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{a \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, d}"," ",0,"1/24*a^(3/2)*cos(1/2*d*x+1/2*c)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*(7824*a*(ln(4/(2*cos(1/2*d*x+1/2*c)+2^(1/2))*(2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)+a*2^(1/2)*cos(1/2*d*x+1/2*c)+2*a))+ln(-4/(-2*cos(1/2*d*x+1/2*c)+2^(1/2))*(2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)-a*2^(1/2)*cos(1/2*d*x+1/2*c)+2*a)))*sin(1/2*d*x+1/2*c)^8-7824*(2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)+2*ln(-4/(-2*cos(1/2*d*x+1/2*c)+2^(1/2))*(2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)-a*2^(1/2)*cos(1/2*d*x+1/2*c)+2*a))*a+2*ln(4/(2*cos(1/2*d*x+1/2*c)+2^(1/2))*(2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)+a*2^(1/2)*cos(1/2*d*x+1/2*c)+2*a))*a)*sin(1/2*d*x+1/2*c)^6+1304*(11*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)+9*ln(-4/(-2*cos(1/2*d*x+1/2*c)+2^(1/2))*(2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)-a*2^(1/2)*cos(1/2*d*x+1/2*c)+2*a))*a+9*ln(4/(2*cos(1/2*d*x+1/2*c)+2^(1/2))*(2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)+a*2^(1/2)*cos(1/2*d*x+1/2*c)+2*a))*a)*sin(1/2*d*x+1/2*c)^4+(-3912*ln(-4/(-2*cos(1/2*d*x+1/2*c)+2^(1/2))*(2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)-a*2^(1/2)*cos(1/2*d*x+1/2*c)+2*a))*a-3912*ln(4/(2*cos(1/2*d*x+1/2*c)+2^(1/2))*(2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)+a*2^(1/2)*cos(1/2*d*x+1/2*c)+2*a))*a-9212*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2))*sin(1/2*d*x+1/2*c)^2+489*ln(-4/(-2*cos(1/2*d*x+1/2*c)+2^(1/2))*(2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)-a*2^(1/2)*cos(1/2*d*x+1/2*c)+2*a))*a+489*ln(4/(2*cos(1/2*d*x+1/2*c)+2^(1/2))*(2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)+a*2^(1/2)*cos(1/2*d*x+1/2*c)+2*a))*a+2094*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2))/(2*cos(1/2*d*x+1/2*c)-2^(1/2))^4/(2*cos(1/2*d*x+1/2*c)+2^(1/2))^4/sin(1/2*d*x+1/2*c)/(a*cos(1/2*d*x+1/2*c)^2)^(1/2)/d","B"
121,1,86,103,0.159000," ","int((a+a*cos(d*x+c))^(7/2),x)","\frac{16 a^{4} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \left(5 \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)+8 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+16\right) \sqrt{2}}{35 \sqrt{a \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, d}"," ",0,"16/35*a^4*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)*(5*cos(1/2*d*x+1/2*c)^6+6*cos(1/2*d*x+1/2*c)^4+8*cos(1/2*d*x+1/2*c)^2+16)*2^(1/2)/(a*cos(1/2*d*x+1/2*c)^2)^(1/2)/d","A"
122,1,194,149,0.460000," ","int(cos(d*x+c)^4/(a+a*cos(d*x+c))^(1/2),x)","\frac{\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(-240 \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}\, \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+336 \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}\, \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-280 \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}\, \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+105 \ln \left(\frac{4 \sqrt{a}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}+4 a}{\cos \left(\frac{d x}{2}+\frac{c}{2}\right)}\right) a \right)}{105 a^{\frac{3}{2}} \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{a \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, d}"," ",0,"1/105*cos(1/2*d*x+1/2*c)*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*(-240*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)*sin(1/2*d*x+1/2*c)^6+336*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)*sin(1/2*d*x+1/2*c)^4-280*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)*sin(1/2*d*x+1/2*c)^2+105*ln(4/cos(1/2*d*x+1/2*c)*(a^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)+a))*a)/a^(3/2)/sin(1/2*d*x+1/2*c)/(a*cos(1/2*d*x+1/2*c)^2)^(1/2)/d","A"
123,1,183,119,0.388000," ","int(cos(d*x+c)^3/(a+a*cos(d*x+c))^(1/2),x)","-\frac{\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(-24 \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}\, \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+20 \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}\, \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+15 \ln \left(\frac{4 \sqrt{a}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}+4 a}{\cos \left(\frac{d x}{2}+\frac{c}{2}\right)}\right) a -30 \sqrt{a}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\right)}{15 a^{\frac{3}{2}} \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{a \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, d}"," ",0,"-1/15*cos(1/2*d*x+1/2*c)*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*(-24*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)*sin(1/2*d*x+1/2*c)^4+20*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)*sin(1/2*d*x+1/2*c)^2+15*ln(4/cos(1/2*d*x+1/2*c)*(a^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)+a))*a-30*a^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2))/a^(3/2)/sin(1/2*d*x+1/2*c)/(a*cos(1/2*d*x+1/2*c)^2)^(1/2)/d","A"
124,1,135,87,0.288000," ","int(cos(d*x+c)^2/(a+a*cos(d*x+c))^(1/2),x)","\frac{\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(-4 \sqrt{a}\, \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+3 \sqrt{2}\, \ln \left(\frac{4 \sqrt{a}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}+4 a}{\cos \left(\frac{d x}{2}+\frac{c}{2}\right)}\right) a \right)}{3 a^{\frac{3}{2}} \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{a \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, d}"," ",0,"1/3*cos(1/2*d*x+1/2*c)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*(-4*a^(1/2)*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^2+3*2^(1/2)*ln(4/cos(1/2*d*x+1/2*c)*(a^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)+a))*a)/a^(3/2)/sin(1/2*d*x+1/2*c)/(a*cos(1/2*d*x+1/2*c)^2)^(1/2)/d","A"
125,1,120,62,0.312000," ","int(cos(d*x+c)/(a+a*cos(d*x+c))^(1/2),x)","-\frac{\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(\ln \left(\frac{4 \sqrt{a}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}+4 a}{\cos \left(\frac{d x}{2}+\frac{c}{2}\right)}\right) a -2 \sqrt{a}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\right)}{a^{\frac{3}{2}} \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{a \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, d}"," ",0,"-cos(1/2*d*x+1/2*c)*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*(ln(4/cos(1/2*d*x+1/2*c)*(a^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)+a))*a-2*a^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2))/a^(3/2)/sin(1/2*d*x+1/2*c)/(a*cos(1/2*d*x+1/2*c)^2)^(1/2)/d","A"
126,1,54,37,0.064000," ","int(1/(a+a*cos(d*x+c))^(1/2),x)","\frac{\sqrt{2}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \mathrm{am}^{-1}\left(\frac{d x}{2}+\frac{c}{2}| 1\right)}{d \sqrt{a \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \mathrm{csgn}\left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}"," ",0,"1/d*2^(1/2)/(a*cos(1/2*d*x+1/2*c)^2)^(1/2)/csgn(cos(1/2*d*x+1/2*c))*cos(1/2*d*x+1/2*c)*InverseJacobiAM(1/2*d*x+1/2*c,1)","C"
127,1,224,70,0.608000," ","int(sec(d*x+c)/(a+a*cos(d*x+c))^(1/2),x)","-\frac{\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(\sqrt{2}\, \ln \left(\frac{4 \sqrt{a}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}+4 a}{\cos \left(\frac{d x}{2}+\frac{c}{2}\right)}\right)-\ln \left(\frac{4 \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}+4 a \sqrt{2}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+8 a}{2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\sqrt{2}}\right)-\ln \left(-\frac{4 \left(\sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}-a \sqrt{2}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+2 a \right)}{-2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\sqrt{2}}\right)\right)}{\sqrt{a}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{a \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, d}"," ",0,"-cos(1/2*d*x+1/2*c)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*(2^(1/2)*ln(4/cos(1/2*d*x+1/2*c)*(a^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)+a))-ln(4/(2*cos(1/2*d*x+1/2*c)+2^(1/2))*(2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)+a*2^(1/2)*cos(1/2*d*x+1/2*c)+2*a))-ln(-4/(-2*cos(1/2*d*x+1/2*c)+2^(1/2))*(2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)-a*2^(1/2)*cos(1/2*d*x+1/2*c)+2*a)))/a^(1/2)/sin(1/2*d*x+1/2*c)/(a*cos(1/2*d*x+1/2*c)^2)^(1/2)/d","B"
128,1,466,91,0.673000," ","int(sec(d*x+c)^2/(a+a*cos(d*x+c))^(1/2),x)","\frac{\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(-2 a \left(2 \sqrt{2}\, \ln \left(\frac{4 \sqrt{a}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}+4 a}{\cos \left(\frac{d x}{2}+\frac{c}{2}\right)}\right)-\ln \left(-\frac{4 \left(\sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}-a \sqrt{2}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+2 a \right)}{-2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\sqrt{2}}\right)-\ln \left(\frac{4 \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}+4 a \sqrt{2}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+8 a}{2 \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)+2 \sqrt{2}\, \ln \left(\frac{4 \sqrt{a}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}+4 a}{\cos \left(\frac{d x}{2}+\frac{c}{2}\right)}\right) a +2 \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}-\ln \left(-\frac{4 \left(\sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}-a \sqrt{2}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+2 a \right)}{-2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\sqrt{2}}\right) a -\ln \left(\frac{4 \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}+4 a \sqrt{2}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+8 a}{2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\sqrt{2}}\right) a \right)}{a^{\frac{3}{2}} \left(2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-\sqrt{2}\right) \left(2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\sqrt{2}\right) \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{a \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, d}"," ",0,"cos(1/2*d*x+1/2*c)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*a*(2*2^(1/2)*ln(4/cos(1/2*d*x+1/2*c)*(a^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)+a))-ln(-4/(-2*cos(1/2*d*x+1/2*c)+2^(1/2))*(2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)-a*2^(1/2)*cos(1/2*d*x+1/2*c)+2*a))-ln(4/(2*cos(1/2*d*x+1/2*c)+2^(1/2))*(2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)+a*2^(1/2)*cos(1/2*d*x+1/2*c)+2*a)))*sin(1/2*d*x+1/2*c)^2+2*2^(1/2)*ln(4/cos(1/2*d*x+1/2*c)*(a^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)+a))*a+2*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)-ln(-4/(-2*cos(1/2*d*x+1/2*c)+2^(1/2))*(2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)-a*2^(1/2)*cos(1/2*d*x+1/2*c)+2*a))*a-ln(4/(2*cos(1/2*d*x+1/2*c)+2^(1/2))*(2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)+a*2^(1/2)*cos(1/2*d*x+1/2*c)+2*a))*a)/a^(3/2)/(2*cos(1/2*d*x+1/2*c)-2^(1/2))/(2*cos(1/2*d*x+1/2*c)+2^(1/2))/sin(1/2*d*x+1/2*c)/(a*cos(1/2*d*x+1/2*c)^2)^(1/2)/d","B"
129,1,671,122,0.676000," ","int(sec(d*x+c)^3/(a+a*cos(d*x+c))^(1/2),x)","-\frac{\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(-4 a \left(-8 \sqrt{2}\, \ln \left(\frac{4 \sqrt{a}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}+4 a}{\cos \left(\frac{d x}{2}+\frac{c}{2}\right)}\right)+7 \ln \left(\frac{4 \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}+4 a \sqrt{2}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+8 a}{2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\sqrt{2}}\right)+7 \ln \left(-\frac{4 \left(\sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}-a \sqrt{2}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+2 a \right)}{-2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\sqrt{2}}\right)\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(-32 \sqrt{2}\, \ln \left(\frac{4 \sqrt{a}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}+4 a}{\cos \left(\frac{d x}{2}+\frac{c}{2}\right)}\right) a +28 \ln \left(-\frac{4 \left(\sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}-a \sqrt{2}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+2 a \right)}{-2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\sqrt{2}}\right) a +28 \ln \left(\frac{4 \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}+4 a \sqrt{2}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+8 a}{2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\sqrt{2}}\right) a -4 \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+8 \sqrt{2}\, \ln \left(\frac{4 \sqrt{a}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}+4 a}{\cos \left(\frac{d x}{2}+\frac{c}{2}\right)}\right) a -7 \ln \left(-\frac{4 \left(\sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}-a \sqrt{2}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+2 a \right)}{-2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\sqrt{2}}\right) a -7 \ln \left(\frac{4 \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}+4 a \sqrt{2}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+8 a}{2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\sqrt{2}}\right) a -2 \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}\right)}{2 a^{\frac{3}{2}} \left(2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-\sqrt{2}\right)^{2} \left(2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\sqrt{2}\right)^{2} \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{a \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, d}"," ",0,"-1/2*cos(1/2*d*x+1/2*c)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*(-4*a*(-8*2^(1/2)*ln(4/cos(1/2*d*x+1/2*c)*(a^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)+a))+7*ln(4/(2*cos(1/2*d*x+1/2*c)+2^(1/2))*(2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)+a*2^(1/2)*cos(1/2*d*x+1/2*c)+2*a))+7*ln(-4/(-2*cos(1/2*d*x+1/2*c)+2^(1/2))*(2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)-a*2^(1/2)*cos(1/2*d*x+1/2*c)+2*a)))*sin(1/2*d*x+1/2*c)^4+(-32*2^(1/2)*ln(4/cos(1/2*d*x+1/2*c)*(a^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)+a))*a+28*ln(-4/(-2*cos(1/2*d*x+1/2*c)+2^(1/2))*(2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)-a*2^(1/2)*cos(1/2*d*x+1/2*c)+2*a))*a+28*ln(4/(2*cos(1/2*d*x+1/2*c)+2^(1/2))*(2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)+a*2^(1/2)*cos(1/2*d*x+1/2*c)+2*a))*a-4*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2))*sin(1/2*d*x+1/2*c)^2+8*2^(1/2)*ln(4/cos(1/2*d*x+1/2*c)*(a^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)+a))*a-7*ln(-4/(-2*cos(1/2*d*x+1/2*c)+2^(1/2))*(2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)-a*2^(1/2)*cos(1/2*d*x+1/2*c)+2*a))*a-7*ln(4/(2*cos(1/2*d*x+1/2*c)+2^(1/2))*(2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)+a*2^(1/2)*cos(1/2*d*x+1/2*c)+2*a))*a-2*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2))/a^(3/2)/(2*cos(1/2*d*x+1/2*c)-2^(1/2))^2/(2*cos(1/2*d*x+1/2*c)+2^(1/2))^2/sin(1/2*d*x+1/2*c)/(a*cos(1/2*d*x+1/2*c)^2)^(1/2)/d","B"
130,1,875,152,0.624000," ","int(sec(d*x+c)^4/(a+a*cos(d*x+c))^(1/2),x)","\frac{\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(24 a \left(-16 \sqrt{2}\, \ln \left(\frac{4 \sqrt{a}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}+4 a}{\cos \left(\frac{d x}{2}+\frac{c}{2}\right)}\right)+9 \ln \left(\frac{4 \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}+4 a \sqrt{2}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+8 a}{2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\sqrt{2}}\right)+9 \ln \left(-\frac{4 \left(\sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}-a \sqrt{2}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+2 a \right)}{-2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\sqrt{2}}\right)\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(576 \sqrt{2}\, \ln \left(\frac{4 \sqrt{a}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}+4 a}{\cos \left(\frac{d x}{2}+\frac{c}{2}\right)}\right) a -324 \ln \left(-\frac{4 \left(\sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}-a \sqrt{2}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+2 a \right)}{-2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\sqrt{2}}\right) a -324 \ln \left(\frac{4 \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}+4 a \sqrt{2}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+8 a}{2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\sqrt{2}}\right) a +168 \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(-288 \sqrt{2}\, \ln \left(\frac{4 \sqrt{a}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}+4 a}{\cos \left(\frac{d x}{2}+\frac{c}{2}\right)}\right) a +162 \ln \left(-\frac{4 \left(\sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}-a \sqrt{2}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+2 a \right)}{-2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\sqrt{2}}\right) a +162 \ln \left(\frac{4 \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}+4 a \sqrt{2}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+8 a}{2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\sqrt{2}}\right) a -160 \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+48 \sqrt{2}\, \ln \left(\frac{4 \sqrt{a}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}+4 a}{\cos \left(\frac{d x}{2}+\frac{c}{2}\right)}\right) a -27 \ln \left(-\frac{4 \left(\sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}-a \sqrt{2}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+2 a \right)}{-2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\sqrt{2}}\right) a -27 \ln \left(\frac{4 \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}+4 a \sqrt{2}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+8 a}{2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\sqrt{2}}\right) a +54 \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}\right)}{6 a^{\frac{3}{2}} \left(2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-\sqrt{2}\right)^{3} \left(2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\sqrt{2}\right)^{3} \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{a \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, d}"," ",0,"1/6*cos(1/2*d*x+1/2*c)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*(24*a*(-16*2^(1/2)*ln(4/cos(1/2*d*x+1/2*c)*(a^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)+a))+9*ln(4/(2*cos(1/2*d*x+1/2*c)+2^(1/2))*(2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)+a*2^(1/2)*cos(1/2*d*x+1/2*c)+2*a))+9*ln(-4/(-2*cos(1/2*d*x+1/2*c)+2^(1/2))*(2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)-a*2^(1/2)*cos(1/2*d*x+1/2*c)+2*a)))*sin(1/2*d*x+1/2*c)^6+(576*2^(1/2)*ln(4/cos(1/2*d*x+1/2*c)*(a^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)+a))*a-324*ln(-4/(-2*cos(1/2*d*x+1/2*c)+2^(1/2))*(2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)-a*2^(1/2)*cos(1/2*d*x+1/2*c)+2*a))*a-324*ln(4/(2*cos(1/2*d*x+1/2*c)+2^(1/2))*(2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)+a*2^(1/2)*cos(1/2*d*x+1/2*c)+2*a))*a+168*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2))*sin(1/2*d*x+1/2*c)^4+(-288*2^(1/2)*ln(4/cos(1/2*d*x+1/2*c)*(a^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)+a))*a+162*ln(-4/(-2*cos(1/2*d*x+1/2*c)+2^(1/2))*(2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)-a*2^(1/2)*cos(1/2*d*x+1/2*c)+2*a))*a+162*ln(4/(2*cos(1/2*d*x+1/2*c)+2^(1/2))*(2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)+a*2^(1/2)*cos(1/2*d*x+1/2*c)+2*a))*a-160*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2))*sin(1/2*d*x+1/2*c)^2+48*2^(1/2)*ln(4/cos(1/2*d*x+1/2*c)*(a^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)+a))*a-27*ln(-4/(-2*cos(1/2*d*x+1/2*c)+2^(1/2))*(2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)-a*2^(1/2)*cos(1/2*d*x+1/2*c)+2*a))*a-27*ln(4/(2*cos(1/2*d*x+1/2*c)+2^(1/2))*(2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)+a*2^(1/2)*cos(1/2*d*x+1/2*c)+2*a))*a+54*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2))/a^(3/2)/(2*cos(1/2*d*x+1/2*c)-2^(1/2))^3/(2*cos(1/2*d*x+1/2*c)+2^(1/2))^3/sin(1/2*d*x+1/2*c)/(a*cos(1/2*d*x+1/2*c)^2)^(1/2)/d","B"
131,1,265,156,0.317000," ","int(cos(d*x+c)^4/(a+a*cos(d*x+c))^(3/2),x)","-\frac{\sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(32 \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}\, \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-32 \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}\, \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+80 \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}\, \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-75 \ln \left(\frac{4 \sqrt{a}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}+4 a}{\cos \left(\frac{d x}{2}+\frac{c}{2}\right)}\right) a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-85 \sqrt{a}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}+75 \ln \left(\frac{4 \sqrt{a}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}+4 a}{\cos \left(\frac{d x}{2}+\frac{c}{2}\right)}\right) a \right)}{20 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) a^{\frac{5}{2}} \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{a \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, d}"," ",0,"-1/20/cos(1/2*d*x+1/2*c)*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*(32*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)*sin(1/2*d*x+1/2*c)^6-32*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)*sin(1/2*d*x+1/2*c)^4+80*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)*sin(1/2*d*x+1/2*c)^2-75*ln(4/cos(1/2*d*x+1/2*c)*(a^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)+a))*a*sin(1/2*d*x+1/2*c)^2-85*a^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)+75*ln(4/cos(1/2*d*x+1/2*c)*(a^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)+a))*a)/a^(5/2)/sin(1/2*d*x+1/2*c)/(a*cos(1/2*d*x+1/2*c)^2)^(1/2)/d","A"
132,1,234,122,0.319000," ","int(cos(d*x+c)^3/(a+a*cos(d*x+c))^(3/2),x)","\frac{\sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(16 \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}\, \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+8 \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}\, \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-33 \ln \left(\frac{4 \sqrt{a}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}+4 a}{\cos \left(\frac{d x}{2}+\frac{c}{2}\right)}\right) a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-27 \sqrt{a}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}+33 \ln \left(\frac{4 \sqrt{a}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}+4 a}{\cos \left(\frac{d x}{2}+\frac{c}{2}\right)}\right) a \right)}{12 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) a^{\frac{5}{2}} \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{a \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, d}"," ",0,"1/12/cos(1/2*d*x+1/2*c)*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*(16*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)*sin(1/2*d*x+1/2*c)^4+8*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)*sin(1/2*d*x+1/2*c)^2-33*ln(4/cos(1/2*d*x+1/2*c)*(a^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)+a))*a*sin(1/2*d*x+1/2*c)^2-27*a^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)+33*ln(4/cos(1/2*d*x+1/2*c)*(a^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)+a))*a)/a^(5/2)/sin(1/2*d*x+1/2*c)/(a*cos(1/2*d*x+1/2*c)^2)^(1/2)/d","A"
133,1,173,88,0.310000," ","int(cos(d*x+c)^2/(a+a*cos(d*x+c))^(3/2),x)","\frac{\sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(-7 \sqrt{2}\, \ln \left(\frac{4 \sqrt{a}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}+4 a}{\cos \left(\frac{d x}{2}+\frac{c}{2}\right)}\right) a \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+8 \sqrt{a}\, \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}\right)}{4 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) a^{\frac{5}{2}} \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{a \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, d}"," ",0,"1/4/cos(1/2*d*x+1/2*c)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*(-7*2^(1/2)*ln(2*(2*a^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)+2*a)/cos(1/2*d*x+1/2*c))*a*cos(1/2*d*x+1/2*c)^2+8*a^(1/2)*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*cos(1/2*d*x+1/2*c)^2+2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2))/a^(5/2)/sin(1/2*d*x+1/2*c)/(a*cos(1/2*d*x+1/2*c)^2)^(1/2)/d","A"
134,1,140,62,0.302000," ","int(cos(d*x+c)/(a+a*cos(d*x+c))^(3/2),x)","\frac{\sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(3 \sqrt{2}\, \ln \left(\frac{4 \sqrt{a}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}+4 a}{\cos \left(\frac{d x}{2}+\frac{c}{2}\right)}\right) a \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}\right)}{4 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) a^{\frac{5}{2}} \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{a \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, d}"," ",0,"1/4*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*(3*2^(1/2)*ln(2*(2*a^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)+2*a)/cos(1/2*d*x+1/2*c))*a*cos(1/2*d*x+1/2*c)^2-2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2))/cos(1/2*d*x+1/2*c)/a^(5/2)/sin(1/2*d*x+1/2*c)/(a*cos(1/2*d*x+1/2*c)^2)^(1/2)/d","B"
135,1,138,62,0.000000," ","int(1/(a+a*cos(d*x+c))^(3/2),x)","\frac{\sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(\sqrt{2}\, \ln \left(\frac{4 \sqrt{a}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}+4 a}{\cos \left(\frac{d x}{2}+\frac{c}{2}\right)}\right) a \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}\right)}{4 a^{\frac{5}{2}} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{a \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, d}"," ",0,"1/4/a^(5/2)/cos(1/2*d*x+1/2*c)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*(2^(1/2)*ln(2*(2*a^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)+2*a)/cos(1/2*d*x+1/2*c))*a*cos(1/2*d*x+1/2*c)^2+2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2))/sin(1/2*d*x+1/2*c)/(a*cos(1/2*d*x+1/2*c)^2)^(1/2)/d","B"
136,1,290,93,0.667000," ","int(sec(d*x+c)/(a+a*cos(d*x+c))^(3/2),x)","-\frac{\sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(5 \sqrt{2}\, \ln \left(\frac{4 \sqrt{a}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}+4 a}{\cos \left(\frac{d x}{2}+\frac{c}{2}\right)}\right) a \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-4 \ln \left(-\frac{4 \left(a \sqrt{2}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-\sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}-2 a \right)}{2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-\sqrt{2}}\right) \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a -4 \ln \left(\frac{4 \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}+4 a \sqrt{2}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+8 a}{2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\sqrt{2}}\right) \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +\sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}\right)}{4 a^{\frac{5}{2}} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{a \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, d}"," ",0,"-1/4*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*(5*2^(1/2)*ln(2*(2*a^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)+2*a)/cos(1/2*d*x+1/2*c))*a*cos(1/2*d*x+1/2*c)^2-4*ln(-4*(a*2^(1/2)*cos(1/2*d*x+1/2*c)-2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)-2*a)/(2*cos(1/2*d*x+1/2*c)-2^(1/2)))*cos(1/2*d*x+1/2*c)^2*a-4*ln(4/(2*cos(1/2*d*x+1/2*c)+2^(1/2))*(2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)+a*2^(1/2)*cos(1/2*d*x+1/2*c)+2*a))*cos(1/2*d*x+1/2*c)^2*a+2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2))/a^(5/2)/cos(1/2*d*x+1/2*c)/sin(1/2*d*x+1/2*c)/(a*cos(1/2*d*x+1/2*c)^2)^(1/2)/d","B"
137,1,567,119,0.628000," ","int(sec(d*x+c)^2/(a+a*cos(d*x+c))^(3/2),x)","\frac{\sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(18 \sqrt{2}\, \ln \left(\frac{4 \sqrt{a}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}+4 a}{\cos \left(\frac{d x}{2}+\frac{c}{2}\right)}\right) a \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-12 \ln \left(-\frac{4 \left(a \sqrt{2}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-\sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}-2 a \right)}{2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-\sqrt{2}}\right) \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a -12 \ln \left(\frac{4 \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}+4 a \sqrt{2}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+8 a}{2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\sqrt{2}}\right) \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a -9 \sqrt{2}\, \ln \left(\frac{4 \sqrt{a}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}+4 a}{\cos \left(\frac{d x}{2}+\frac{c}{2}\right)}\right) a \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+6 \sqrt{a}\, \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+6 \ln \left(-\frac{4 \left(a \sqrt{2}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-\sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}-2 a \right)}{2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-\sqrt{2}}\right) \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +6 \ln \left(\frac{4 \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}+4 a \sqrt{2}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+8 a}{2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\sqrt{2}}\right) \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a -\sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}\right)}{2 a^{\frac{5}{2}} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-\sqrt{2}\right) \left(2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\sqrt{2}\right) \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{a \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, d}"," ",0,"1/2*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*(18*2^(1/2)*ln(2*(2*a^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)+2*a)/cos(1/2*d*x+1/2*c))*a*cos(1/2*d*x+1/2*c)^4-12*ln(-4*(a*2^(1/2)*cos(1/2*d*x+1/2*c)-2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)-2*a)/(2*cos(1/2*d*x+1/2*c)-2^(1/2)))*cos(1/2*d*x+1/2*c)^4*a-12*ln(4/(2*cos(1/2*d*x+1/2*c)+2^(1/2))*(2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)+a*2^(1/2)*cos(1/2*d*x+1/2*c)+2*a))*cos(1/2*d*x+1/2*c)^4*a-9*2^(1/2)*ln(2*(2*a^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)+2*a)/cos(1/2*d*x+1/2*c))*a*cos(1/2*d*x+1/2*c)^2+6*a^(1/2)*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*cos(1/2*d*x+1/2*c)^2+6*ln(-4*(a*2^(1/2)*cos(1/2*d*x+1/2*c)-2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)-2*a)/(2*cos(1/2*d*x+1/2*c)-2^(1/2)))*cos(1/2*d*x+1/2*c)^2*a+6*ln(4/(2*cos(1/2*d*x+1/2*c)+2^(1/2))*(2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)+a*2^(1/2)*cos(1/2*d*x+1/2*c)+2*a))*cos(1/2*d*x+1/2*c)^2*a-2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2))/a^(5/2)/cos(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)-2^(1/2))/(2*cos(1/2*d*x+1/2*c)+2^(1/2))/sin(1/2*d*x+1/2*c)/(a*cos(1/2*d*x+1/2*c)^2)^(1/2)/d","B"
138,1,807,156,1.052000," ","int(sec(d*x+c)^3/(a+a*cos(d*x+c))^(3/2),x)","-\frac{\sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(104 \sqrt{2}\, \ln \left(\frac{4 \sqrt{a}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}+4 a}{\cos \left(\frac{d x}{2}+\frac{c}{2}\right)}\right) \left(\cos^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a -76 \ln \left(-\frac{4 \left(a \sqrt{2}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-\sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}-2 a \right)}{2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-\sqrt{2}}\right) \left(\cos^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a -76 \ln \left(\frac{4 \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}+4 a \sqrt{2}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+8 a}{2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\sqrt{2}}\right) \left(\cos^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a -104 \sqrt{2}\, \ln \left(\frac{4 \sqrt{a}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}+4 a}{\cos \left(\frac{d x}{2}+\frac{c}{2}\right)}\right) a \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+28 \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}\, \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+76 \ln \left(-\frac{4 \left(a \sqrt{2}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-\sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}-2 a \right)}{2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-\sqrt{2}}\right) \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +76 \ln \left(\frac{4 \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}+4 a \sqrt{2}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+8 a}{2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\sqrt{2}}\right) \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +26 \sqrt{2}\, \ln \left(\frac{4 \sqrt{a}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}+4 a}{\cos \left(\frac{d x}{2}+\frac{c}{2}\right)}\right) a \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-22 \sqrt{a}\, \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-19 \ln \left(-\frac{4 \left(a \sqrt{2}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-\sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}-2 a \right)}{2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-\sqrt{2}}\right) \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a -19 \ln \left(\frac{4 \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}+4 a \sqrt{2}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+8 a}{2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\sqrt{2}}\right) \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}\right)}{2 a^{\frac{5}{2}} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-\sqrt{2}\right)^{2} \left(2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\sqrt{2}\right)^{2} \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{a \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, d}"," ",0,"-1/2*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*(104*2^(1/2)*ln(2*(2*a^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)+2*a)/cos(1/2*d*x+1/2*c))*cos(1/2*d*x+1/2*c)^6*a-76*ln(-4*(a*2^(1/2)*cos(1/2*d*x+1/2*c)-2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)-2*a)/(2*cos(1/2*d*x+1/2*c)-2^(1/2)))*cos(1/2*d*x+1/2*c)^6*a-76*ln(4/(2*cos(1/2*d*x+1/2*c)+2^(1/2))*(2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)+a*2^(1/2)*cos(1/2*d*x+1/2*c)+2*a))*cos(1/2*d*x+1/2*c)^6*a-104*2^(1/2)*ln(2*(2*a^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)+2*a)/cos(1/2*d*x+1/2*c))*a*cos(1/2*d*x+1/2*c)^4+28*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)*cos(1/2*d*x+1/2*c)^4+76*ln(-4*(a*2^(1/2)*cos(1/2*d*x+1/2*c)-2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)-2*a)/(2*cos(1/2*d*x+1/2*c)-2^(1/2)))*cos(1/2*d*x+1/2*c)^4*a+76*ln(4/(2*cos(1/2*d*x+1/2*c)+2^(1/2))*(2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)+a*2^(1/2)*cos(1/2*d*x+1/2*c)+2*a))*cos(1/2*d*x+1/2*c)^4*a+26*2^(1/2)*ln(2*(2*a^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)+2*a)/cos(1/2*d*x+1/2*c))*a*cos(1/2*d*x+1/2*c)^2-22*a^(1/2)*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*cos(1/2*d*x+1/2*c)^2-19*ln(-4*(a*2^(1/2)*cos(1/2*d*x+1/2*c)-2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)-2*a)/(2*cos(1/2*d*x+1/2*c)-2^(1/2)))*cos(1/2*d*x+1/2*c)^2*a-19*ln(4/(2*cos(1/2*d*x+1/2*c)+2^(1/2))*(2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)+a*2^(1/2)*cos(1/2*d*x+1/2*c)+2*a))*cos(1/2*d*x+1/2*c)^2*a+2*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2))/a^(5/2)/cos(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)-2^(1/2))^2/(2*cos(1/2*d*x+1/2*c)+2^(1/2))^2/sin(1/2*d*x+1/2*c)/(a*cos(1/2*d*x+1/2*c)^2)^(1/2)/d","B"
139,1,242,156,0.321000," ","int(cos(d*x+c)^4/(a+a*cos(d*x+c))^(5/2),x)","\frac{\sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(128 \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}\, \left(\cos^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+489 \sqrt{2}\, \ln \left(\frac{4 \sqrt{a}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}+4 a}{\cos \left(\frac{d x}{2}+\frac{c}{2}\right)}\right) a \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-512 \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}\, \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-87 \sqrt{a}\, \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+6 \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}\right)}{96 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)^{3} a^{\frac{7}{2}} \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{a \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, d}"," ",0,"1/96*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*(128*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)*cos(1/2*d*x+1/2*c)^6+489*2^(1/2)*ln(2*(2*a^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)+2*a)/cos(1/2*d*x+1/2*c))*a*cos(1/2*d*x+1/2*c)^4-512*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)*cos(1/2*d*x+1/2*c)^4-87*a^(1/2)*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*cos(1/2*d*x+1/2*c)^2+6*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2))/cos(1/2*d*x+1/2*c)^3/a^(7/2)/sin(1/2*d*x+1/2*c)/(a*cos(1/2*d*x+1/2*c)^2)^(1/2)/d","A"
140,1,208,122,0.419000," ","int(cos(d*x+c)^3/(a+a*cos(d*x+c))^(5/2),x)","\frac{\sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(-75 \sqrt{2}\, \ln \left(\frac{4 \sqrt{a}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}+4 a}{\cos \left(\frac{d x}{2}+\frac{c}{2}\right)}\right) a \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+64 \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}\, \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+21 \sqrt{a}\, \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-2 \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}\right)}{32 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)^{3} a^{\frac{7}{2}} \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{a \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, d}"," ",0,"1/32/cos(1/2*d*x+1/2*c)^3*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*(-75*2^(1/2)*ln(2*(2*a^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)+2*a)/cos(1/2*d*x+1/2*c))*a*cos(1/2*d*x+1/2*c)^4+64*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)*cos(1/2*d*x+1/2*c)^4+21*a^(1/2)*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*cos(1/2*d*x+1/2*c)^2-2*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2))/a^(7/2)/sin(1/2*d*x+1/2*c)/(a*cos(1/2*d*x+1/2*c)^2)^(1/2)/d","A"
141,1,174,88,0.356000," ","int(cos(d*x+c)^2/(a+a*cos(d*x+c))^(5/2),x)","\frac{\sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(19 \sqrt{2}\, \ln \left(\frac{4 \sqrt{a}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}+4 a}{\cos \left(\frac{d x}{2}+\frac{c}{2}\right)}\right) a \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-13 \sqrt{a}\, \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+2 \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}\right)}{32 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)^{3} a^{\frac{7}{2}} \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{a \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, d}"," ",0,"1/32*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*(19*2^(1/2)*ln(2*(2*a^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)+2*a)/cos(1/2*d*x+1/2*c))*a*cos(1/2*d*x+1/2*c)^4-13*a^(1/2)*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*cos(1/2*d*x+1/2*c)^2+2*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2))/cos(1/2*d*x+1/2*c)^3/a^(7/2)/sin(1/2*d*x+1/2*c)/(a*cos(1/2*d*x+1/2*c)^2)^(1/2)/d","A"
142,1,174,88,0.311000," ","int(cos(d*x+c)/(a+a*cos(d*x+c))^(5/2),x)","\frac{\sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(5 \sqrt{2}\, \ln \left(\frac{4 \sqrt{a}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}+4 a}{\cos \left(\frac{d x}{2}+\frac{c}{2}\right)}\right) a \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+5 \sqrt{a}\, \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-2 \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}\right)}{32 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)^{3} a^{\frac{7}{2}} \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{a \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, d}"," ",0,"1/32/cos(1/2*d*x+1/2*c)^3*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*(5*2^(1/2)*ln(2*(2*a^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)+2*a)/cos(1/2*d*x+1/2*c))*a*cos(1/2*d*x+1/2*c)^4+5*a^(1/2)*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*cos(1/2*d*x+1/2*c)^2-2*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2))/a^(7/2)/sin(1/2*d*x+1/2*c)/(a*cos(1/2*d*x+1/2*c)^2)^(1/2)/d","A"
143,1,174,88,0.302000," ","int(1/(a+a*cos(d*x+c))^(5/2),x)","\frac{\sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(3 \sqrt{2}\, \ln \left(\frac{4 \sqrt{a}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}+4 a}{\cos \left(\frac{d x}{2}+\frac{c}{2}\right)}\right) a \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+3 \sqrt{a}\, \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+2 \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}\right)}{32 a^{\frac{7}{2}} \cos \left(\frac{d x}{2}+\frac{c}{2}\right)^{3} \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{a \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, d}"," ",0,"1/32/a^(7/2)/cos(1/2*d*x+1/2*c)^3*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*(3*2^(1/2)*ln(2*(2*a^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)+2*a)/cos(1/2*d*x+1/2*c))*a*cos(1/2*d*x+1/2*c)^4+3*a^(1/2)*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*cos(1/2*d*x+1/2*c)^2+2*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2))/sin(1/2*d*x+1/2*c)/(a*cos(1/2*d*x+1/2*c)^2)^(1/2)/d","A"
144,1,325,119,0.609000," ","int(sec(d*x+c)/(a+a*cos(d*x+c))^(5/2),x)","-\frac{\sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(43 \sqrt{2}\, \ln \left(\frac{4 \sqrt{a}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}+4 a}{\cos \left(\frac{d x}{2}+\frac{c}{2}\right)}\right) a \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-32 \ln \left(\frac{4 \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}+4 a \sqrt{2}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+8 a}{2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\sqrt{2}}\right) \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a -32 \ln \left(-\frac{4 \left(a \sqrt{2}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-\sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}-2 a \right)}{2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-\sqrt{2}}\right) \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +11 \sqrt{a}\, \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+2 \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}\right)}{32 a^{\frac{7}{2}} \cos \left(\frac{d x}{2}+\frac{c}{2}\right)^{3} \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{a \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, d}"," ",0,"-1/32/a^(7/2)/cos(1/2*d*x+1/2*c)^3*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*(43*2^(1/2)*ln(2*(2*a^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)+2*a)/cos(1/2*d*x+1/2*c))*a*cos(1/2*d*x+1/2*c)^4-32*ln(4/(2*cos(1/2*d*x+1/2*c)+2^(1/2))*(2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)+a*2^(1/2)*cos(1/2*d*x+1/2*c)+2*a))*cos(1/2*d*x+1/2*c)^4*a-32*ln(-4*(a*2^(1/2)*cos(1/2*d*x+1/2*c)-2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)-2*a)/(2*cos(1/2*d*x+1/2*c)-2^(1/2)))*cos(1/2*d*x+1/2*c)^4*a+11*a^(1/2)*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*cos(1/2*d*x+1/2*c)^2+2*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2))/sin(1/2*d*x+1/2*c)/(a*cos(1/2*d*x+1/2*c)^2)^(1/2)/d","B"
145,1,601,145,0.603000," ","int(sec(d*x+c)^2/(a+a*cos(d*x+c))^(5/2),x)","\frac{\sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(230 \sqrt{2}\, \ln \left(\frac{4 \sqrt{a}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}+4 a}{\cos \left(\frac{d x}{2}+\frac{c}{2}\right)}\right) \left(\cos^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a -160 \ln \left(\frac{4 \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}+4 a \sqrt{2}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+8 a}{2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\sqrt{2}}\right) \left(\cos^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a -160 \ln \left(-\frac{4 \left(a \sqrt{2}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-\sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}-2 a \right)}{2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-\sqrt{2}}\right) \left(\cos^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a -115 \sqrt{2}\, \ln \left(\frac{4 \sqrt{a}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}+4 a}{\cos \left(\frac{d x}{2}+\frac{c}{2}\right)}\right) a \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+70 \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}\, \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+80 \ln \left(\frac{4 \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}+4 a \sqrt{2}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+8 a}{2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\sqrt{2}}\right) \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +80 \ln \left(-\frac{4 \left(a \sqrt{2}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-\sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}-2 a \right)}{2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-\sqrt{2}}\right) \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a -15 \sqrt{a}\, \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-2 \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}\right)}{16 a^{\frac{7}{2}} \cos \left(\frac{d x}{2}+\frac{c}{2}\right)^{3} \left(2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-\sqrt{2}\right) \left(2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\sqrt{2}\right) \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{a \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, d}"," ",0,"1/16*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*(230*2^(1/2)*ln(2*(2*a^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)+2*a)/cos(1/2*d*x+1/2*c))*cos(1/2*d*x+1/2*c)^6*a-160*ln(4/(2*cos(1/2*d*x+1/2*c)+2^(1/2))*(2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)+a*2^(1/2)*cos(1/2*d*x+1/2*c)+2*a))*cos(1/2*d*x+1/2*c)^6*a-160*ln(-4*(a*2^(1/2)*cos(1/2*d*x+1/2*c)-2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)-2*a)/(2*cos(1/2*d*x+1/2*c)-2^(1/2)))*cos(1/2*d*x+1/2*c)^6*a-115*2^(1/2)*ln(2*(2*a^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)+2*a)/cos(1/2*d*x+1/2*c))*a*cos(1/2*d*x+1/2*c)^4+70*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)*cos(1/2*d*x+1/2*c)^4+80*ln(4/(2*cos(1/2*d*x+1/2*c)+2^(1/2))*(2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)+a*2^(1/2)*cos(1/2*d*x+1/2*c)+2*a))*cos(1/2*d*x+1/2*c)^4*a+80*ln(-4*(a*2^(1/2)*cos(1/2*d*x+1/2*c)-2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)-2*a)/(2*cos(1/2*d*x+1/2*c)-2^(1/2)))*cos(1/2*d*x+1/2*c)^4*a-15*a^(1/2)*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*cos(1/2*d*x+1/2*c)^2-2*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2))/a^(7/2)/cos(1/2*d*x+1/2*c)^3/(2*cos(1/2*d*x+1/2*c)-2^(1/2))/(2*cos(1/2*d*x+1/2*c)+2^(1/2))/sin(1/2*d*x+1/2*c)/(a*cos(1/2*d*x+1/2*c)^2)^(1/2)/d","B"
146,1,270,147,0.421000," ","int(cos(d*x+c)^(5/2)*(a+a*cos(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"
147,1,219,127,0.547000," ","int(cos(d*x+c)^(3/2)*(a+a*cos(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"
148,1,225,107,0.561000," ","int(cos(d*x+c)^(1/2)*(a+a*cos(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"
149,1,150,87,0.404000," ","int((a+a*cos(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)}\, 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"
150,1,146,107,0.451000," ","int((a+a*cos(d*x+c))/cos(d*x+c)^(3/2),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"
151,1,369,127,0.945000," ","int((a+a*cos(d*x+c))/cos(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(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)+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*(-(-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)^4-4*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)*(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+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"
152,1,384,147,0.834000," ","int((a+a*cos(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)}}{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"
153,1,260,179,0.513000," ","int(cos(d*x+c)^(5/2)*(a+a*cos(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"
154,1,272,157,0.457000," ","int(cos(d*x+c)^(3/2)*(a+a*cos(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"
155,1,250,135,0.451000," ","int(cos(d*x+c)^(1/2)*(a+a*cos(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"
156,1,228,113,0.484000," ","int((a+a*cos(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(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"
157,1,104,68,0.500000," ","int((a+a*cos(d*x+c))^2/cos(d*x+c)^(3/2),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"
158,1,371,135,0.816000," ","int((a+a*cos(d*x+c))^2/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^{2} \left(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) \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*(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+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"
159,1,386,157,0.818000," ","int((a+a*cos(d*x+c))^2/cos(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^{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"
160,1,260,179,0.730000," ","int(cos(d*x+c)^(3/2)*(a+a*cos(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"
161,1,272,157,0.515000," ","int(cos(d*x+c)^(1/2)*(a+a*cos(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"
162,1,250,135,0.915000," ","int((a+a*cos(d*x+c))^3/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^{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"
163,1,172,135,0.556000," ","int((a+a*cos(d*x+c))^3/cos(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"
164,1,371,135,0.934000," ","int((a+a*cos(d*x+c))^3/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^{3} \left(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) \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*(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+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"
165,1,386,157,0.908000," ","int((a+a*cos(d*x+c))^3/cos(d*x+c)^(7/2),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"
166,1,439,179,0.948000," ","int((a+a*cos(d*x+c))^3/cos(d*x+c)^(9/2),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"
167,1,273,201,0.494000," ","int(cos(d*x+c)^(3/2)*(a+a*cos(d*x+c))^4,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"
168,1,260,179,0.543000," ","int(cos(d*x+c)^(1/2)*(a+a*cos(d*x+c))^4,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"
169,1,272,157,0.493000," ","int((a+a*cos(d*x+c))^4/cos(d*x+c)^(1/2),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"
170,1,194,157,0.523000," ","int((a+a*cos(d*x+c))^4/cos(d*x+c)^(3/2),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"
171,1,292,112,0.861000," ","int((a+a*cos(d*x+c))^4/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^{4} \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 \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)-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*(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^4/(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*(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)^2-14*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"
172,1,386,157,0.903000," ","int((a+a*cos(d*x+c))^4/cos(d*x+c)^(7/2),x)","-\frac{32 \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(-\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{41 \sqrt{\frac{1}{2}-\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)}{60 \sqrt{-2 \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)}}{320 \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}-\frac{33 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)}{40 \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)}}{24 \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,"-32*(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^4*(-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)))+41/60*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+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))-1/320*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)^3-33/40*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)-1/24*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"
173,1,439,179,1.201000," ","int((a+a*cos(d*x+c))^4/cos(d*x+c)^(9/2),x)","-\frac{32 \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(\frac{253 \sqrt{\frac{1}{2}-\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)}{420 \sqrt{-2 \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{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{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)}}{896 \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)}}{672 \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,"-32*(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^4*(253/420*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+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))-1/80*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)^3-4/5*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)-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)))-1/896*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)^4-47/672*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"
174,1,229,166,0.534000," ","int(cos(d*x+c)^(7/2)/(a+a*cos(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(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)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(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"
175,1,215,144,0.627000," ","int(cos(d*x+c)^(5/2)/(a+a*cos(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(9 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+5 \EllipticF \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)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(9*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+5*EllipticF(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"
176,1,199,122,0.614000," ","int(cos(d*x+c)^(3/2)/(a+a*cos(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,"((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)/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"
177,1,198,120,0.480000," ","int(cos(d*x+c)^(1/2)/(a+a*cos(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"
178,1,200,120,0.484000," ","int(1/cos(d*x+c)^(1/2)/(a+a*cos(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)-\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)*(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))-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"
179,1,253,144,0.534000," ","int(1/cos(d*x+c)^(3/2)/(a+a*cos(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"
180,1,413,166,0.889000," ","int(1/cos(d*x+c)^(5/2)/(a+a*cos(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}}\, \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) \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}}\, \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) \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}}\, \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) \cos \left(\frac{d x}{2}+\frac{c}{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) \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 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sin \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) \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/cos(1/2*d*x+1/2*c)/sin(1/2*d*x+1/2*c)^3/(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)*(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))*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)*(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))*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)*(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))*cos(1/2*d*x+1/2*c)+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))*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"
181,1,283,198,0.536000," ","int(cos(d*x+c)^(9/2)/(a+a*cos(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"
182,1,270,176,0.539000," ","int(cos(d*x+c)^(7/2)/(a+a*cos(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*((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)/a^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)^3/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
183,1,257,154,0.559000," ","int(cos(d*x+c)^(5/2)/(a+a*cos(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*((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)/a^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)^3/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
184,1,257,153,0.584000," ","int(cos(d*x+c)^(3/2)/(a+a*cos(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*((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)/a^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)^3/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
185,1,188,77,0.477000," ","int(cos(d*x+c)^(1/2)/(a+a*cos(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"
186,1,257,153,0.515000," ","int(1/cos(d*x+c)^(1/2)/(a+a*cos(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"
187,1,405,176,0.604000," ","int(1/cos(d*x+c)^(3/2)/(a+a*cos(d*x+c))^2,x)","-\frac{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)}\, \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^{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)}\, \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)^2-1)^(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)*(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)^2-1)^(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)*(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"
188,1,413,198,1.028000," ","int(1/cos(d*x+c)^(5/2)/(a+a*cos(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"
189,1,296,235,0.640000," ","int(cos(d*x+c)^(11/2)/(a+a*cos(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"
190,1,283,213,0.469000," ","int(cos(d*x+c)^(9/2)/(a+a*cos(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"
191,1,270,191,0.746000," ","int(cos(d*x+c)^(7/2)/(a+a*cos(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"
192,1,270,191,0.483000," ","int(cos(d*x+c)^(5/2)/(a+a*cos(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"
193,1,270,191,0.521000," ","int(cos(d*x+c)^(3/2)/(a+a*cos(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"
194,1,270,191,0.500000," ","int(cos(d*x+c)^(1/2)/(a+a*cos(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"
195,1,268,191,0.604000," ","int(1/cos(d*x+c)^(1/2)/(a+a*cos(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"
196,1,555,213,0.731000," ","int(1/cos(d*x+c)^(3/2)/(a+a*cos(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"
197,1,453,235,1.121000," ","int(1/cos(d*x+c)^(5/2)/(a+a*cos(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"
198,1,196,128,0.282000," ","int(cos(d*x+c)^(5/2)*(a+a*cos(d*x+c))^(1/2),x)","-\frac{\left(\cos^{\frac{5}{2}}\left(d x +c \right)\right) \sqrt{a \left(1+\cos \left(d x +c \right)\right)}\, \left(-1+\cos \left(d x +c \right)\right)^{3} \left(8 \sqrt{\frac{\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 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right) \sin \left(d x +c \right)+15 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+15 \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}{\cos \left(d x +c \right)}\right)\right)}{24 d \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \sin \left(d x +c \right)^{6}}"," ",0,"-1/24/d*cos(d*x+c)^(5/2)*(a*(1+cos(d*x+c)))^(1/2)*(-1+cos(d*x+c))^3*(8*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2*sin(d*x+c)+10*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)*sin(d*x+c)+15*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+15*arctan(sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)/cos(d*x+c)))/(cos(d*x+c)/(1+cos(d*x+c)))^(5/2)/sin(d*x+c)^6","A"
199,1,161,96,0.174000," ","int(cos(d*x+c)^(3/2)*(a+a*cos(d*x+c))^(1/2),x)","\frac{\left(\cos^{\frac{3}{2}}\left(d x +c \right)\right) \sqrt{a \left(1+\cos \left(d x +c \right)\right)}\, \left(-1+\cos \left(d x +c \right)\right)^{2} \left(2 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right) \sin \left(d x +c \right)+3 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+3 \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}{\cos \left(d x +c \right)}\right)\right)}{4 d \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sin \left(d x +c \right)^{4}}"," ",0,"1/4/d*cos(d*x+c)^(3/2)*(a*(1+cos(d*x+c)))^(1/2)*(-1+cos(d*x+c))^2*(2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)*sin(d*x+c)+3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+3*arctan(sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)/cos(d*x+c)))/(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)/sin(d*x+c)^4","A"
200,1,123,62,0.183000," ","int(cos(d*x+c)^(1/2)*(a+a*cos(d*x+c))^(1/2),x)","-\frac{\left(\sqrt{\cos}\left(d x +c \right)\right) \sqrt{a \left(1+\cos \left(d x +c \right)\right)}\, \left(\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\arctan \left(\frac{\sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}{\cos \left(d x +c \right)}\right)\right) \left(-1+\cos \left(d x +c \right)\right)}{d \sin \left(d x +c \right)^{2} \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}"," ",0,"-1/d*cos(d*x+c)^(1/2)*(a*(1+cos(d*x+c)))^(1/2)*((cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+arctan(sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)/cos(d*x+c)))*(-1+cos(d*x+c))/sin(d*x+c)^2/(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)","A"
201,1,80,31,0.137000," ","int((a+a*cos(d*x+c))^(1/2)/cos(d*x+c)^(1/2),x)","\frac{2 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{a \left(1+\cos \left(d x +c \right)\right)}\, \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}{\cos \left(d x +c \right)}\right)}{d \sqrt{\cos \left(d x +c \right)}}"," ",0,"2/d/cos(d*x+c)^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*(a*(1+cos(d*x+c)))^(1/2)*arctan(sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)/cos(d*x+c))","B"
202,1,42,32,0.152000," ","int((a+a*cos(d*x+c))^(1/2)/cos(d*x+c)^(3/2),x)","-\frac{2 \left(-1+\cos \left(d x +c \right)\right) \sqrt{a \left(1+\cos \left(d x +c \right)\right)}}{d \sin \left(d x +c \right) \sqrt{\cos \left(d x +c \right)}}"," ",0,"-2/d*(-1+cos(d*x+c))*(a*(1+cos(d*x+c)))^(1/2)/sin(d*x+c)/cos(d*x+c)^(1/2)","A"
203,1,54,65,0.176000," ","int((a+a*cos(d*x+c))^(1/2)/cos(d*x+c)^(5/2),x)","-\frac{2 \left(2 \left(\cos^{2}\left(d x +c \right)\right)-\cos \left(d x +c \right)-1\right) \sqrt{a \left(1+\cos \left(d x +c \right)\right)}}{3 d \sin \left(d x +c \right) \cos \left(d x +c \right)^{\frac{3}{2}}}"," ",0,"-2/3/d*(2*cos(d*x+c)^2-cos(d*x+c)-1)*(a*(1+cos(d*x+c)))^(1/2)/sin(d*x+c)/cos(d*x+c)^(3/2)","A"
204,1,64,97,0.155000," ","int((a+a*cos(d*x+c))^(1/2)/cos(d*x+c)^(7/2),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{a \left(1+\cos \left(d x +c \right)\right)}}{15 d \sin \left(d x +c \right) \cos \left(d x +c \right)^{\frac{5}{2}}}"," ",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)))^(1/2)/sin(d*x+c)/cos(d*x+c)^(5/2)","A"
205,1,74,129,0.163000," ","int((a+a*cos(d*x+c))^(1/2)/cos(d*x+c)^(9/2),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{a \left(1+\cos \left(d x +c \right)\right)}}{35 d \sin \left(d x +c \right) \cos \left(d x +c \right)^{\frac{7}{2}}}"," ",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)))^(1/2)/sin(d*x+c)/cos(d*x+c)^(7/2)","A"
206,1,197,134,0.209000," ","int(cos(d*x+c)^(3/2)*(a+a*cos(d*x+c))^(3/2),x)","\frac{\left(-1+\cos \left(d x +c \right)\right)^{2} \left(8 \sqrt{\frac{\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)+22 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right) \sin \left(d x +c \right)+33 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+33 \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}{\cos \left(d x +c \right)}\right)\right) \sqrt{a \left(1+\cos \left(d x +c \right)\right)}\, \left(\cos^{\frac{3}{2}}\left(d x +c \right)\right) a}{24 d \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sin \left(d x +c \right)^{4}}"," ",0,"1/24/d*(-1+cos(d*x+c))^2*(8*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2*sin(d*x+c)+22*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)*sin(d*x+c)+33*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+33*arctan(sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)/cos(d*x+c)))*(a*(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^(3/2)/(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)/sin(d*x+c)^4*a","A"
207,1,160,100,0.173000," ","int(cos(d*x+c)^(1/2)*(a+a*cos(d*x+c))^(3/2),x)","-\frac{\left(-1+\cos \left(d x +c \right)\right) \left(2 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right) \sin \left(d x +c \right)+7 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+7 \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}{\cos \left(d x +c \right)}\right)\right) \sqrt{a \left(1+\cos \left(d x +c \right)\right)}\, \left(\sqrt{\cos}\left(d x +c \right)\right) a}{4 d \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)^{2}}"," ",0,"-1/4/d*(-1+cos(d*x+c))*(2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)*sin(d*x+c)+7*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+7*arctan(sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)/cos(d*x+c)))*(a*(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^(1/2)/(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)/sin(d*x+c)^2*a","A"
208,1,168,65,0.164000," ","int((a+a*cos(d*x+c))^(3/2)/cos(d*x+c)^(1/2),x)","\frac{\left(3 \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}{\cos \left(d x +c \right)}\right)+\cos \left(d x +c \right) \sin \left(d x +c \right)+3 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}{\cos \left(d x +c \right)}\right)\right) \sqrt{a \left(1+\cos \left(d x +c \right)\right)}\, a}{d \sqrt{\cos \left(d x +c \right)}\, \left(1+\cos \left(d x +c \right)\right)}"," ",0,"1/d*(3*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)/cos(d*x+c))+cos(d*x+c)*sin(d*x+c)+3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)/cos(d*x+c)))*(a*(1+cos(d*x+c)))^(1/2)/cos(d*x+c)^(1/2)/(1+cos(d*x+c))*a","B"
209,1,249,66,0.174000," ","int((a+a*cos(d*x+c))^(3/2)/cos(d*x+c)^(3/2),x)","-\frac{2 \left(\left(\cos^{2}\left(d x +c \right)\right) \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}{\cos \left(d x +c \right)}\right)+2 \cos \left(d x +c \right) \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}{\cos \left(d x +c \right)}\right)+\left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}{\cos \left(d x +c \right)}\right)+\cos \left(d x +c \right) \sin \left(d x +c \right)\right) \sqrt{a \left(1+\cos \left(d x +c \right)\right)}\, \left(\sin^{2}\left(d x +c \right)\right) a}{d \left(-1+\cos \left(d x +c \right)\right) \left(1+\cos \left(d x +c \right)\right)^{2} \cos \left(d x +c \right)^{\frac{3}{2}}}"," ",0,"-2/d*(cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*arctan(sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)/cos(d*x+c))+2*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*arctan(sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)/cos(d*x+c))+(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*arctan(sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)/cos(d*x+c))+cos(d*x+c)*sin(d*x+c))*(a*(1+cos(d*x+c)))^(1/2)*sin(d*x+c)^2/(-1+cos(d*x+c))/(1+cos(d*x+c))^2/cos(d*x+c)^(3/2)*a","B"
210,1,55,69,0.143000," ","int((a+a*cos(d*x+c))^(3/2)/cos(d*x+c)^(5/2),x)","-\frac{2 \left(5 \left(\cos^{2}\left(d x +c \right)\right)-4 \cos \left(d x +c \right)-1\right) \sqrt{a \left(1+\cos \left(d x +c \right)\right)}\, a}{3 d \sin \left(d x +c \right) \cos \left(d x +c \right)^{\frac{3}{2}}}"," ",0,"-2/3/d*(5*cos(d*x+c)^2-4*cos(d*x+c)-1)*(a*(1+cos(d*x+c)))^(1/2)/sin(d*x+c)/cos(d*x+c)^(3/2)*a","A"
211,1,65,103,0.137000," ","int((a+a*cos(d*x+c))^(3/2)/cos(d*x+c)^(7/2),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{a \left(1+\cos \left(d x +c \right)\right)}\, a}{5 d \sin \left(d x +c \right) \cos \left(d x +c \right)^{\frac{5}{2}}}"," ",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)))^(1/2)/sin(d*x+c)/cos(d*x+c)^(5/2)*a","A"
212,1,75,137,0.145000," ","int((a+a*cos(d*x+c))^(3/2)/cos(d*x+c)^(9/2),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{a \left(1+\cos \left(d x +c \right)\right)}\, a}{105 d \sin \left(d x +c \right) \cos \left(d x +c \right)^{\frac{7}{2}}}"," ",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)))^(1/2)/sin(d*x+c)/cos(d*x+c)^(7/2)*a","A"
213,1,234,168,0.237000," ","int(cos(d*x+c)^(3/2)*(a+a*cos(d*x+c))^(5/2),x)","\frac{\left(-1+\cos \left(d x +c \right)\right)^{2} \left(48 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+184 \sqrt{\frac{\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)+326 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right) \sin \left(d x +c \right)+489 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+489 \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}{\cos \left(d x +c \right)}\right)\right) \sqrt{a \left(1+\cos \left(d x +c \right)\right)}\, \left(\cos^{\frac{3}{2}}\left(d x +c \right)\right) a^{2}}{192 d \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sin \left(d x +c \right)^{4}}"," ",0,"1/192/d*(-1+cos(d*x+c))^2*(48*cos(d*x+c)^3*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+184*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2*sin(d*x+c)+326*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)*sin(d*x+c)+489*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+489*arctan(sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)/cos(d*x+c)))*(a*(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^(3/2)/(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)/sin(d*x+c)^4*a^2","A"
214,1,197,134,0.196000," ","int(cos(d*x+c)^(1/2)*(a+a*cos(d*x+c))^(5/2),x)","-\frac{\left(-1+\cos \left(d x +c \right)\right) \left(8 \sqrt{\frac{\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)+34 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right) \sin \left(d x +c \right)+75 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+75 \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}{\cos \left(d x +c \right)}\right)\right) \sqrt{a \left(1+\cos \left(d x +c \right)\right)}\, \left(\sqrt{\cos}\left(d x +c \right)\right) a^{2}}{24 d \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)^{2}}"," ",0,"-1/24/d*(-1+cos(d*x+c))*(8*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2*sin(d*x+c)+34*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)*sin(d*x+c)+75*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+75*arctan(sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)/cos(d*x+c)))*(a*(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^(1/2)/(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)/sin(d*x+c)^2*a^2","A"
215,1,188,100,0.196000," ","int((a+a*cos(d*x+c))^(5/2)/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)+19 \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}{\cos \left(d x +c \right)}\right)+11 \cos \left(d x +c \right) \sin \left(d x +c \right)+19 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}{\cos \left(d x +c \right)}\right)\right) \sqrt{a \left(1+\cos \left(d x +c \right)\right)}\, a^{2}}{4 d \sqrt{\cos \left(d x +c \right)}\, \left(1+\cos \left(d x +c \right)\right)}"," ",0,"1/4/d*(2*cos(d*x+c)^2*sin(d*x+c)+19*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)/cos(d*x+c))+11*cos(d*x+c)*sin(d*x+c)+19*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)/cos(d*x+c)))*(a*(1+cos(d*x+c)))^(1/2)/cos(d*x+c)^(1/2)/(1+cos(d*x+c))*a^2","A"
216,1,269,100,0.178000," ","int((a+a*cos(d*x+c))^(5/2)/cos(d*x+c)^(3/2),x)","-\frac{\left(5 \left(\cos^{2}\left(d x +c \right)\right) \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}{\cos \left(d x +c \right)}\right)+10 \cos \left(d x +c \right) \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}{\cos \left(d x +c \right)}\right)+5 \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}{\cos \left(d x +c \right)}\right)+\left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+2 \cos \left(d x +c \right) \sin \left(d x +c \right)\right) \sqrt{a \left(1+\cos \left(d x +c \right)\right)}\, \left(\sin^{2}\left(d x +c \right)\right) a^{2}}{d \left(-1+\cos \left(d x +c \right)\right) \left(1+\cos \left(d x +c \right)\right)^{2} \cos \left(d x +c \right)^{\frac{3}{2}}}"," ",0,"-1/d*(5*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*arctan(sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)/cos(d*x+c))+10*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*arctan(sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)/cos(d*x+c))+5*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*arctan(sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)/cos(d*x+c))+cos(d*x+c)^2*sin(d*x+c)+2*cos(d*x+c)*sin(d*x+c))*(a*(1+cos(d*x+c)))^(1/2)*sin(d*x+c)^2/(-1+cos(d*x+c))/(1+cos(d*x+c))^2/cos(d*x+c)^(3/2)*a^2","B"
217,1,333,100,0.187000," ","int((a+a*cos(d*x+c))^(5/2)/cos(d*x+c)^(5/2),x)","\frac{2 \left(3 \left(\cos^{3}\left(d x +c \right)\right) \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}{\cos \left(d x +c \right)}\right)+9 \left(\cos^{2}\left(d x +c \right)\right) \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}{\cos \left(d x +c \right)}\right)+9 \cos \left(d x +c \right) \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}{\cos \left(d x +c \right)}\right)+3 \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}{\cos \left(d x +c \right)}\right)+8 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+\cos \left(d x +c \right) \sin \left(d x +c \right)\right) \sqrt{a \left(1+\cos \left(d x +c \right)\right)}\, \left(\sin^{4}\left(d x +c \right)\right) a^{2}}{3 d \left(-1+\cos \left(d x +c \right)\right)^{2} \left(1+\cos \left(d x +c \right)\right)^{3} \cos \left(d x +c \right)^{\frac{5}{2}}}"," ",0,"2/3/d*(3*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*arctan(sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)/cos(d*x+c))+9*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*arctan(sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)/cos(d*x+c))+9*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*arctan(sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)/cos(d*x+c))+3*(cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*arctan(sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)/cos(d*x+c))+8*cos(d*x+c)^2*sin(d*x+c)+cos(d*x+c)*sin(d*x+c))*(a*(1+cos(d*x+c)))^(1/2)*sin(d*x+c)^4/(-1+cos(d*x+c))^2/(1+cos(d*x+c))^3/cos(d*x+c)^(5/2)*a^2","B"
218,1,67,103,0.167000," ","int((a+a*cos(d*x+c))^(5/2)/cos(d*x+c)^(7/2),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{a \left(1+\cos \left(d x +c \right)\right)}\, a^{2}}{15 d \sin \left(d x +c \right) \cos \left(d x +c \right)^{\frac{5}{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)))^(1/2)/sin(d*x+c)/cos(d*x+c)^(5/2)*a^2","A"
219,1,77,137,0.140000," ","int((a+a*cos(d*x+c))^(5/2)/cos(d*x+c)^(9/2),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{a \left(1+\cos \left(d x +c \right)\right)}\, a^{2}}{21 d \sin \left(d x +c \right) \cos \left(d x +c \right)^{\frac{7}{2}}}"," ",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)))^(1/2)/sin(d*x+c)/cos(d*x+c)^(7/2)*a^2","A"
220,1,87,171,0.158000," ","int((a+a*cos(d*x+c))^(5/2)/cos(d*x+c)^(11/2),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{a \left(1+\cos \left(d x +c \right)\right)}\, a^{2}}{315 d \sin \left(d x +c \right) \cos \left(d x +c \right)^{\frac{9}{2}}}"," ",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)))^(1/2)/sin(d*x+c)/cos(d*x+c)^(9/2)*a^2","A"
221,0,0,34,0.155000," ","int((a+a*cos(d*x+c))^(3/2)/cos(d*x+c)^(5/4),x)","\int \frac{\left(a +a \cos \left(d x +c \right)\right)^{\frac{3}{2}}}{\cos \left(d x +c \right)^{\frac{5}{4}}}\, dx"," ",0,"int((a+a*cos(d*x+c))^(3/2)/cos(d*x+c)^(5/4),x)","F"
222,1,80,31,0.105000," ","int((a+a*cos(f*x+e))^(1/2)/cos(f*x+e)^(1/2),x)","\frac{2 \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sqrt{a \left(1+\cos \left(f x +e \right)\right)}\, \arctan \left(\frac{\sin \left(f x +e \right) \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}}{\cos \left(f x +e \right)}\right)}{f \sqrt{\cos \left(f x +e \right)}}"," ",0,"2/f/cos(f*x+e)^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*(a*(1+cos(f*x+e)))^(1/2)*arctan(sin(f*x+e)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)/cos(f*x+e))","B"
223,1,91,32,0.168000," ","int((a-a*cos(f*x+e))^(1/2)/(-cos(f*x+e))^(1/2),x)","-\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sqrt{-2 a \left(-1+\cos \left(f x +e \right)\right)}\, \sin \left(f x +e \right) \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sqrt{2}}{2}\right)}{f \sqrt{-\cos \left(f x +e \right)}\, \left(-1+\cos \left(f x +e \right)\right)}"," ",0,"-1/f*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*(-2*a*(-1+cos(f*x+e)))^(1/2)*sin(f*x+e)*arctan(1/2*(-2*cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*2^(1/2))/(-cos(f*x+e))^(1/2)/(-1+cos(f*x+e))","B"
224,1,196,140,0.214000," ","int(cos(d*x+c)^(5/2)/(a+a*cos(d*x+c))^(1/2),x)","-\frac{\left(\cos^{\frac{5}{2}}\left(d x +c \right)\right) \sqrt{a \left(1+\cos \left(d x +c \right)\right)}\, \left(-1+\cos \left(d x +c \right)\right)^{3} \left(2 \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}-\sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+7 \sqrt{2}\, \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}{\cos \left(d x +c \right)}\right)+8 \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)\right) \sqrt{2}}{8 d \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \sin \left(d x +c \right)^{6} a}"," ",0,"-1/8/d*cos(d*x+c)^(5/2)*(a*(1+cos(d*x+c)))^(1/2)*(-1+cos(d*x+c))^3*(2*sin(d*x+c)*cos(d*x+c)*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)-2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+7*2^(1/2)*arctan(sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)/cos(d*x+c))+8*arcsin((-1+cos(d*x+c))/sin(d*x+c)))/(cos(d*x+c)/(1+cos(d*x+c)))^(5/2)/sin(d*x+c)^6*2^(1/2)/a","A"
225,1,159,107,0.182000," ","int(cos(d*x+c)^(3/2)/(a+a*cos(d*x+c))^(1/2),x)","-\frac{\left(\cos^{\frac{3}{2}}\left(d x +c \right)\right) \sqrt{a \left(1+\cos \left(d x +c \right)\right)}\, \left(-1+\cos \left(d x +c \right)\right)^{2} \left(-\sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\sqrt{2}\, \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}{\cos \left(d x +c \right)}\right)+2 \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)\right) \sqrt{2}}{2 d \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sin \left(d x +c \right)^{4} a}"," ",0,"-1/2/d*cos(d*x+c)^(3/2)*(a*(1+cos(d*x+c)))^(1/2)*(-1+cos(d*x+c))^2*(-2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+2^(1/2)*arctan(sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)/cos(d*x+c))+2*arcsin((-1+cos(d*x+c))/sin(d*x+c)))/(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)/sin(d*x+c)^4*2^(1/2)/a","A"
226,1,125,78,0.175000," ","int(cos(d*x+c)^(1/2)/(a+a*cos(d*x+c))^(1/2),x)","-\frac{\left(\sqrt{\cos}\left(d x +c \right)\right) \sqrt{a \left(1+\cos \left(d x +c \right)\right)}\, \left(-1+\cos \left(d x +c \right)\right) \left(\sqrt{2}\, \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}{\cos \left(d x +c \right)}\right)+\arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)\right) \sqrt{2}}{d \sin \left(d x +c \right)^{2} \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, a}"," ",0,"-1/d*cos(d*x+c)^(1/2)*(a*(1+cos(d*x+c)))^(1/2)*(-1+cos(d*x+c))*(2^(1/2)*arctan(sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)/cos(d*x+c))+arcsin((-1+cos(d*x+c))/sin(d*x+c)))/sin(d*x+c)^2/(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2)/a","A"
227,1,69,45,0.127000," ","int(1/cos(d*x+c)^(1/2)/(a+a*cos(d*x+c))^(1/2),x)","-\frac{\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{a \left(1+\cos \left(d x +c \right)\right)}\, \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \sqrt{2}}{d \sqrt{\cos \left(d x +c \right)}\, a}"," ",0,"-1/d/cos(d*x+c)^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*(a*(1+cos(d*x+c)))^(1/2)*arcsin((-1+cos(d*x+c))/sin(d*x+c))*2^(1/2)/a","A"
228,1,206,78,0.171000," ","int(1/cos(d*x+c)^(3/2)/(a+a*cos(d*x+c))^(1/2),x)","-\frac{\left(\arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \left(\cos^{2}\left(d x +c \right)\right) \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}}+2 \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \cos \left(d x +c \right) \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}}+\arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}}+\sqrt{2}\, \cos \left(d x +c \right) \sin \left(d x +c \right)\right) \left(\sin^{2}\left(d x +c \right)\right) \sqrt{a \left(1+\cos \left(d x +c \right)\right)}\, \sqrt{2}}{d \left(-1+\cos \left(d x +c \right)\right) \left(1+\cos \left(d x +c \right)\right)^{2} \cos \left(d x +c \right)^{\frac{3}{2}} a}"," ",0,"-1/d*(arcsin((-1+cos(d*x+c))/sin(d*x+c))*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)+2*arcsin((-1+cos(d*x+c))/sin(d*x+c))*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)+arcsin((-1+cos(d*x+c))/sin(d*x+c))*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)+2^(1/2)*cos(d*x+c)*sin(d*x+c))*sin(d*x+c)^2*(a*(1+cos(d*x+c)))^(1/2)/(-1+cos(d*x+c))/(1+cos(d*x+c))^2/cos(d*x+c)^(3/2)*2^(1/2)/a","B"
229,1,274,108,0.178000," ","int(1/cos(d*x+c)^(5/2)/(a+a*cos(d*x+c))^(1/2),x)","-\frac{\left(3 \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \left(\cos^{3}\left(d x +c \right)\right) \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}}+9 \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \left(\cos^{2}\left(d x +c \right)\right) \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}}+9 \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \cos \left(d x +c \right) \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}}+3 \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \left(\frac{\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) \sin \left(d x +c \right) \sqrt{2}-\sqrt{2}\, \cos \left(d x +c \right) \sin \left(d x +c \right)\right) \left(\sin^{4}\left(d x +c \right)\right) \sqrt{a \left(1+\cos \left(d x +c \right)\right)}\, \sqrt{2}}{3 d \left(-1+\cos \left(d x +c \right)\right)^{2} \left(1+\cos \left(d x +c \right)\right)^{3} \cos \left(d x +c \right)^{\frac{5}{2}} a}"," ",0,"-1/3/d*(3*arcsin((-1+cos(d*x+c))/sin(d*x+c))*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(5/2)+9*arcsin((-1+cos(d*x+c))/sin(d*x+c))*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(5/2)+9*arcsin((-1+cos(d*x+c))/sin(d*x+c))*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(5/2)+3*arcsin((-1+cos(d*x+c))/sin(d*x+c))*(cos(d*x+c)/(1+cos(d*x+c)))^(5/2)+cos(d*x+c)^2*sin(d*x+c)*2^(1/2)-2^(1/2)*cos(d*x+c)*sin(d*x+c))*sin(d*x+c)^4*(a*(1+cos(d*x+c)))^(1/2)/(-1+cos(d*x+c))^2/(1+cos(d*x+c))^3/cos(d*x+c)^(5/2)*2^(1/2)/a","B"
230,1,341,140,0.273000," ","int(1/cos(d*x+c)^(7/2)/(a+a*cos(d*x+c))^(1/2),x)","-\frac{\left(15 \left(\cos^{4}\left(d x +c \right)\right) \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{7}{2}}+60 \left(\cos^{3}\left(d x +c \right)\right) \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{7}{2}}+90 \left(\cos^{2}\left(d x +c \right)\right) \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{7}{2}}+60 \cos \left(d x +c \right) \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{7}{2}}+15 \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{7}{2}}+13 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{2}-\left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{2}+3 \sqrt{2}\, \cos \left(d x +c \right) \sin \left(d x +c \right)\right) \left(\sin^{6}\left(d x +c \right)\right) \sqrt{a \left(1+\cos \left(d x +c \right)\right)}\, \sqrt{2}}{15 d \left(-1+\cos \left(d x +c \right)\right)^{3} \left(1+\cos \left(d x +c \right)\right)^{4} \cos \left(d x +c \right)^{\frac{7}{2}} a}"," ",0,"-1/15/d*(15*cos(d*x+c)^4*arcsin((-1+cos(d*x+c))/sin(d*x+c))*(cos(d*x+c)/(1+cos(d*x+c)))^(7/2)+60*cos(d*x+c)^3*arcsin((-1+cos(d*x+c))/sin(d*x+c))*(cos(d*x+c)/(1+cos(d*x+c)))^(7/2)+90*cos(d*x+c)^2*arcsin((-1+cos(d*x+c))/sin(d*x+c))*(cos(d*x+c)/(1+cos(d*x+c)))^(7/2)+60*cos(d*x+c)*arcsin((-1+cos(d*x+c))/sin(d*x+c))*(cos(d*x+c)/(1+cos(d*x+c)))^(7/2)+15*arcsin((-1+cos(d*x+c))/sin(d*x+c))*(cos(d*x+c)/(1+cos(d*x+c)))^(7/2)+13*cos(d*x+c)^3*sin(d*x+c)*2^(1/2)-cos(d*x+c)^2*sin(d*x+c)*2^(1/2)+3*2^(1/2)*cos(d*x+c)*sin(d*x+c))*sin(d*x+c)^6*(a*(1+cos(d*x+c)))^(1/2)/(-1+cos(d*x+c))^3/(1+cos(d*x+c))^4/cos(d*x+c)^(7/2)*2^(1/2)/a","B"
231,1,187,108,0.165000," ","int(cos(d*x+c)^(5/2)/(1+cos(d*x+c))^(1/2),x)","-\frac{\sqrt{2+2 \cos \left(d x +c \right)}\, \left(\cos^{\frac{5}{2}}\left(d x +c \right)\right) \left(-1+\cos \left(d x +c \right)\right)^{3} \left(2 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right) \sin \left(d x +c \right)+4 \sqrt{2}\, \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)-\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+7 \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}{\cos \left(d x +c \right)}\right)\right) \sqrt{2}}{8 d \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \sin \left(d x +c \right)^{6}}"," ",0,"-1/8/d*(2+2*cos(d*x+c))^(1/2)*cos(d*x+c)^(5/2)*(-1+cos(d*x+c))^3*(2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)*sin(d*x+c)+4*2^(1/2)*arcsin((-1+cos(d*x+c))/sin(d*x+c))-(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+7*arctan(sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)/cos(d*x+c)))/(cos(d*x+c)/(1+cos(d*x+c)))^(5/2)/sin(d*x+c)^6*2^(1/2)","A"
232,1,151,77,0.137000," ","int(cos(d*x+c)^(3/2)/(1+cos(d*x+c))^(1/2),x)","-\frac{\left(\cos^{\frac{3}{2}}\left(d x +c \right)\right) \sqrt{2+2 \cos \left(d x +c \right)}\, \left(-1+\cos \left(d x +c \right)\right)^{2} \left(\sqrt{2}\, \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)-\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\arctan \left(\frac{\sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}{\cos \left(d x +c \right)}\right)\right) \sqrt{2}}{2 d \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sin \left(d x +c \right)^{4}}"," ",0,"-1/2/d*cos(d*x+c)^(3/2)*(2+2*cos(d*x+c))^(1/2)*(-1+cos(d*x+c))^2*(2^(1/2)*arcsin((-1+cos(d*x+c))/sin(d*x+c))-(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+arctan(sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)/cos(d*x+c)))/(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)/sin(d*x+c)^4*2^(1/2)","A"
233,1,124,50,0.144000," ","int(cos(d*x+c)^(1/2)/(1+cos(d*x+c))^(1/2),x)","-\frac{\sqrt{2+2 \cos \left(d x +c \right)}\, \left(\sqrt{\cos}\left(d x +c \right)\right) \left(-1+\cos \left(d x +c \right)\right) \left(\sqrt{2}\, \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)+2 \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}{\cos \left(d x +c \right)}\right)\right) \sqrt{2}}{2 d \sin \left(d x +c \right)^{2} \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}"," ",0,"-1/2/d*(2+2*cos(d*x+c))^(1/2)*cos(d*x+c)^(1/2)*(-1+cos(d*x+c))*(2^(1/2)*arcsin((-1+cos(d*x+c))/sin(d*x+c))+2*arctan(sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)/cos(d*x+c)))/sin(d*x+c)^2/(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2)","B"
234,1,63,25,0.094000," ","int(1/cos(d*x+c)^(1/2)/(1+cos(d*x+c))^(1/2),x)","-\frac{\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2+2 \cos \left(d x +c \right)}\, \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)}{d \sqrt{\cos \left(d x +c \right)}}"," ",0,"-1/d/cos(d*x+c)^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*(2+2*cos(d*x+c))^(1/2)*arcsin((-1+cos(d*x+c))/sin(d*x+c))","B"
235,1,210,56,0.146000," ","int(1/cos(d*x+c)^(3/2)/(1+cos(d*x+c))^(1/2),x)","-\frac{\left(\sqrt{2}\, \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \left(\cos^{2}\left(d x +c \right)\right) \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}}+2 \sqrt{2}\, \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \cos \left(d x +c \right) \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}}+\sqrt{2}\, \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}}+2 \cos \left(d x +c \right) \sin \left(d x +c \right)\right) \left(\sin^{2}\left(d x +c \right)\right) \sqrt{2+2 \cos \left(d x +c \right)}\, \sqrt{2}}{2 d \left(-1+\cos \left(d x +c \right)\right) \left(1+\cos \left(d x +c \right)\right)^{2} \cos \left(d x +c \right)^{\frac{3}{2}}}"," ",0,"-1/2/d*(2^(1/2)*arcsin((-1+cos(d*x+c))/sin(d*x+c))*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)+2*2^(1/2)*arcsin((-1+cos(d*x+c))/sin(d*x+c))*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)+2^(1/2)*arcsin((-1+cos(d*x+c))/sin(d*x+c))*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)+2*cos(d*x+c)*sin(d*x+c))*sin(d*x+c)^2*(2+2*cos(d*x+c))^(1/2)/(-1+cos(d*x+c))/(1+cos(d*x+c))^2/cos(d*x+c)^(3/2)*2^(1/2)","B"
236,1,278,84,0.145000," ","int(1/cos(d*x+c)^(5/2)/(1+cos(d*x+c))^(1/2),x)","-\frac{\left(3 \sqrt{2}\, \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \left(\cos^{3}\left(d x +c \right)\right) \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}}+9 \sqrt{2}\, \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \left(\cos^{2}\left(d x +c \right)\right) \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}}+9 \sqrt{2}\, \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \cos \left(d x +c \right) \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}}+3 \sqrt{2}\, \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}}+2 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)-2 \cos \left(d x +c \right) \sin \left(d x +c \right)\right) \left(\sin^{4}\left(d x +c \right)\right) \sqrt{2+2 \cos \left(d x +c \right)}\, \sqrt{2}}{6 d \left(-1+\cos \left(d x +c \right)\right)^{2} \left(1+\cos \left(d x +c \right)\right)^{3} \cos \left(d x +c \right)^{\frac{5}{2}}}"," ",0,"-1/6/d*(3*2^(1/2)*arcsin((-1+cos(d*x+c))/sin(d*x+c))*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(5/2)+9*2^(1/2)*arcsin((-1+cos(d*x+c))/sin(d*x+c))*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(5/2)+9*2^(1/2)*arcsin((-1+cos(d*x+c))/sin(d*x+c))*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(5/2)+3*2^(1/2)*arcsin((-1+cos(d*x+c))/sin(d*x+c))*(cos(d*x+c)/(1+cos(d*x+c)))^(5/2)+2*cos(d*x+c)^2*sin(d*x+c)-2*cos(d*x+c)*sin(d*x+c))*sin(d*x+c)^4*(2+2*cos(d*x+c))^(1/2)/(-1+cos(d*x+c))^2/(1+cos(d*x+c))^3/cos(d*x+c)^(5/2)*2^(1/2)","B"
237,1,344,114,0.169000," ","int(1/cos(d*x+c)^(7/2)/(1+cos(d*x+c))^(1/2),x)","-\frac{\left(15 \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \sqrt{2}\, \left(\cos^{4}\left(d x +c \right)\right) \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{7}{2}}+60 \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \sqrt{2}\, \left(\cos^{3}\left(d x +c \right)\right) \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{7}{2}}+90 \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \sqrt{2}\, \left(\cos^{2}\left(d x +c \right)\right) \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{7}{2}}+60 \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \sqrt{2}\, \cos \left(d x +c \right) \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{7}{2}}+15 \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \sqrt{2}\, \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{7}{2}}+26 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)-2 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+6 \cos \left(d x +c \right) \sin \left(d x +c \right)\right) \left(\sin^{6}\left(d x +c \right)\right) \sqrt{2+2 \cos \left(d x +c \right)}\, \sqrt{2}}{30 d \left(-1+\cos \left(d x +c \right)\right)^{3} \left(1+\cos \left(d x +c \right)\right)^{4} \cos \left(d x +c \right)^{\frac{7}{2}}}"," ",0,"-1/30/d*(15*arcsin((-1+cos(d*x+c))/sin(d*x+c))*2^(1/2)*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(7/2)+60*arcsin((-1+cos(d*x+c))/sin(d*x+c))*2^(1/2)*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(7/2)+90*arcsin((-1+cos(d*x+c))/sin(d*x+c))*2^(1/2)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(7/2)+60*arcsin((-1+cos(d*x+c))/sin(d*x+c))*2^(1/2)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(7/2)+15*arcsin((-1+cos(d*x+c))/sin(d*x+c))*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(7/2)+26*cos(d*x+c)^3*sin(d*x+c)-2*cos(d*x+c)^2*sin(d*x+c)+6*cos(d*x+c)*sin(d*x+c))*sin(d*x+c)^6*(2+2*cos(d*x+c))^(1/2)/(-1+cos(d*x+c))^3/(1+cos(d*x+c))^4/cos(d*x+c)^(7/2)*2^(1/2)","B"
238,1,227,143,0.184000," ","int(cos(d*x+c)^(5/2)/(a+a*cos(d*x+c))^(3/2),x)","\frac{\left(\cos^{\frac{5}{2}}\left(d x +c \right)\right) \left(-1+\cos \left(d x +c \right)\right)^{3} \sqrt{a \left(1+\cos \left(d x +c \right)\right)}\, \left(2 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+\cos \left(d x +c \right) \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+6 \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}{\cos \left(d x +c \right)}\right) \sqrt{2}\, \sin \left(d x +c \right)+9 \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \sin \left(d x +c \right)-3 \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\right) \sqrt{2}}{4 d \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \sin \left(d x +c \right)^{7} a^{2}}"," ",0,"1/4/d*cos(d*x+c)^(5/2)*(-1+cos(d*x+c))^3*(a*(1+cos(d*x+c)))^(1/2)*(2*cos(d*x+c)^2*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+cos(d*x+c)*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+6*arctan(sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)/cos(d*x+c))*2^(1/2)*sin(d*x+c)+9*arcsin((-1+cos(d*x+c))/sin(d*x+c))*sin(d*x+c)-3*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2))/(cos(d*x+c)/(1+cos(d*x+c)))^(5/2)/sin(d*x+c)^7*2^(1/2)/a^2","A"
239,1,195,109,0.167000," ","int(cos(d*x+c)^(3/2)/(a+a*cos(d*x+c))^(3/2),x)","\frac{\left(\cos^{\frac{3}{2}}\left(d x +c \right)\right) \left(-1+\cos \left(d x +c \right)\right)^{2} \sqrt{a \left(1+\cos \left(d x +c \right)\right)}\, \left(4 \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}{\cos \left(d x +c \right)}\right) \sqrt{2}\, \sin \left(d x +c \right)+\cos \left(d x +c \right) \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+5 \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \sin \left(d x +c \right)-\sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\right) \sqrt{2}}{4 d \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sin \left(d x +c \right)^{5} a^{2}}"," ",0,"1/4/d*cos(d*x+c)^(3/2)*(-1+cos(d*x+c))^2*(a*(1+cos(d*x+c)))^(1/2)*(4*arctan(sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)/cos(d*x+c))*2^(1/2)*sin(d*x+c)+cos(d*x+c)*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+5*arcsin((-1+cos(d*x+c))/sin(d*x+c))*sin(d*x+c)-2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2))/(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)/sin(d*x+c)^5*2^(1/2)/a^2","A"
240,1,146,78,0.146000," ","int(cos(d*x+c)^(1/2)/(a+a*cos(d*x+c))^(3/2),x)","\frac{\left(\sqrt{\cos}\left(d x +c \right)\right) \sqrt{a \left(1+\cos \left(d x +c \right)\right)}\, \left(-1+\cos \left(d x +c \right)\right) \left(\cos \left(d x +c \right) \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}-\sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+\arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \sin \left(d x +c \right)\right) \sqrt{2}}{4 d \sin \left(d x +c \right)^{3} \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, a^{2}}"," ",0,"1/4/d*cos(d*x+c)^(1/2)*(a*(1+cos(d*x+c)))^(1/2)*(-1+cos(d*x+c))*(cos(d*x+c)*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)-2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+arcsin((-1+cos(d*x+c))/sin(d*x+c))*sin(d*x+c))/sin(d*x+c)^3/(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2)/a^2","A"
241,1,170,78,0.142000," ","int(1/cos(d*x+c)^(1/2)/(a+a*cos(d*x+c))^(3/2),x)","-\frac{\sqrt{a \left(1+\cos \left(d x +c \right)\right)}\, \left(3 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \sin \left(d x +c \right) \cos \left(d x +c \right)+3 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \sin \left(d x +c \right)-\left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}+\cos \left(d x +c \right) \sqrt{2}\right) \sqrt{2}}{4 d \left(1+\cos \left(d x +c \right)\right) \sqrt{\cos \left(d x +c \right)}\, \sin \left(d x +c \right) a^{2}}"," ",0,"-1/4/d*(a*(1+cos(d*x+c)))^(1/2)*(3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arcsin((-1+cos(d*x+c))/sin(d*x+c))*sin(d*x+c)*cos(d*x+c)+3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arcsin((-1+cos(d*x+c))/sin(d*x+c))*sin(d*x+c)-cos(d*x+c)^2*2^(1/2)+cos(d*x+c)*2^(1/2))/(1+cos(d*x+c))/cos(d*x+c)^(1/2)/sin(d*x+c)*2^(1/2)/a^2","B"
242,1,245,112,0.180000," ","int(1/cos(d*x+c)^(3/2)/(a+a*cos(d*x+c))^(3/2),x)","\frac{\left(-7 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}}-14 \cos \left(d x +c \right) \sin \left(d x +c \right) \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}}-7 \sin \left(d x +c \right) \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}}+5 \left(\cos^{3}\left(d x +c \right)\right) \sqrt{2}-\left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}-4 \cos \left(d x +c \right) \sqrt{2}\right) \sin \left(d x +c \right) \sqrt{a \left(1+\cos \left(d x +c \right)\right)}\, \sqrt{2}}{4 d \left(-1+\cos \left(d x +c \right)\right) \left(1+\cos \left(d x +c \right)\right)^{2} \cos \left(d x +c \right)^{\frac{3}{2}} a^{2}}"," ",0,"1/4/d*(-7*cos(d*x+c)^2*sin(d*x+c)*arcsin((-1+cos(d*x+c))/sin(d*x+c))*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)-14*cos(d*x+c)*sin(d*x+c)*arcsin((-1+cos(d*x+c))/sin(d*x+c))*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)-7*sin(d*x+c)*arcsin((-1+cos(d*x+c))/sin(d*x+c))*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)+5*cos(d*x+c)^3*2^(1/2)-cos(d*x+c)^2*2^(1/2)-4*cos(d*x+c)*2^(1/2))*sin(d*x+c)*(a*(1+cos(d*x+c)))^(1/2)/(-1+cos(d*x+c))/(1+cos(d*x+c))^2/cos(d*x+c)^(3/2)*2^(1/2)/a^2","B"
243,1,313,146,0.192000," ","int(1/cos(d*x+c)^(5/2)/(a+a*cos(d*x+c))^(3/2),x)","-\frac{\left(33 \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)+99 \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+99 \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \cos \left(d x +c \right) \sin \left(d x +c \right)+33 \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \sin \left(d x +c \right)-19 \left(\cos^{4}\left(d x +c \right)\right) \sqrt{2}+7 \left(\cos^{3}\left(d x +c \right)\right) \sqrt{2}+16 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}-4 \cos \left(d x +c \right) \sqrt{2}\right) \left(\sin^{3}\left(d x +c \right)\right) \sqrt{a \left(1+\cos \left(d x +c \right)\right)}\, \sqrt{2}}{12 d \left(-1+\cos \left(d x +c \right)\right)^{2} \left(1+\cos \left(d x +c \right)\right)^{3} \cos \left(d x +c \right)^{\frac{5}{2}} a^{2}}"," ",0,"-1/12/d*(33*(cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*arcsin((-1+cos(d*x+c))/sin(d*x+c))*cos(d*x+c)^3*sin(d*x+c)+99*(cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*arcsin((-1+cos(d*x+c))/sin(d*x+c))*cos(d*x+c)^2*sin(d*x+c)+99*(cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*arcsin((-1+cos(d*x+c))/sin(d*x+c))*cos(d*x+c)*sin(d*x+c)+33*(cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*arcsin((-1+cos(d*x+c))/sin(d*x+c))*sin(d*x+c)-19*cos(d*x+c)^4*2^(1/2)+7*cos(d*x+c)^3*2^(1/2)+16*cos(d*x+c)^2*2^(1/2)-4*cos(d*x+c)*2^(1/2))*sin(d*x+c)^3*(a*(1+cos(d*x+c)))^(1/2)/(-1+cos(d*x+c))^2/(1+cos(d*x+c))^3/cos(d*x+c)^(5/2)*2^(1/2)/a^2","B"
244,1,344,177,0.189000," ","int(cos(d*x+c)^(7/2)/(a+a*cos(d*x+c))^(5/2),x)","\frac{\left(\cos^{\frac{7}{2}}\left(d x +c \right)\right) \sqrt{a \left(1+\cos \left(d x +c \right)\right)}\, \left(-1+\cos \left(d x +c \right)\right)^{5} \left(16 \left(\cos^{3}\left(d x +c \right)\right) \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+39 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+80 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{2}\, \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}{\cos \left(d x +c \right)}\right)+115 \cos \left(d x +c \right) \sin \left(d x +c \right) \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)-20 \cos \left(d x +c \right) \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+80 \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}{\cos \left(d x +c \right)}\right) \sqrt{2}\, \sin \left(d x +c \right)+115 \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \sin \left(d x +c \right)-35 \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\right) \sqrt{2}}{32 d \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{7}{2}} \sin \left(d x +c \right)^{11} a^{3}}"," ",0,"1/32/d*cos(d*x+c)^(7/2)*(a*(1+cos(d*x+c)))^(1/2)*(-1+cos(d*x+c))^5*(16*cos(d*x+c)^3*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+39*cos(d*x+c)^2*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+80*cos(d*x+c)*sin(d*x+c)*2^(1/2)*arctan(sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)/cos(d*x+c))+115*cos(d*x+c)*sin(d*x+c)*arcsin((-1+cos(d*x+c))/sin(d*x+c))-20*cos(d*x+c)*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+80*arctan(sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)/cos(d*x+c))*2^(1/2)*sin(d*x+c)+115*arcsin((-1+cos(d*x+c))/sin(d*x+c))*sin(d*x+c)-35*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2))/(cos(d*x+c)/(1+cos(d*x+c)))^(7/2)/sin(d*x+c)^11*2^(1/2)/a^3","A"
245,1,312,143,0.174000," ","int(cos(d*x+c)^(5/2)/(a+a*cos(d*x+c))^(5/2),x)","\frac{\left(\cos^{\frac{5}{2}}\left(d x +c \right)\right) \left(-1+\cos \left(d x +c \right)\right)^{4} \sqrt{a \left(1+\cos \left(d x +c \right)\right)}\, \left(15 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+32 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{2}\, \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}{\cos \left(d x +c \right)}\right)+43 \cos \left(d x +c \right) \sin \left(d x +c \right) \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)-4 \cos \left(d x +c \right) \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+32 \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}{\cos \left(d x +c \right)}\right) \sqrt{2}\, \sin \left(d x +c \right)+43 \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \sin \left(d x +c \right)-11 \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\right) \sqrt{2}}{32 d \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \sin \left(d x +c \right)^{9} a^{3}}"," ",0,"1/32/d*cos(d*x+c)^(5/2)*(-1+cos(d*x+c))^4*(a*(1+cos(d*x+c)))^(1/2)*(15*cos(d*x+c)^2*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+32*cos(d*x+c)*sin(d*x+c)*2^(1/2)*arctan(sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)/cos(d*x+c))+43*cos(d*x+c)*sin(d*x+c)*arcsin((-1+cos(d*x+c))/sin(d*x+c))-4*cos(d*x+c)*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+32*arctan(sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)/cos(d*x+c))*2^(1/2)*sin(d*x+c)+43*arcsin((-1+cos(d*x+c))/sin(d*x+c))*sin(d*x+c)-11*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2))/(cos(d*x+c)/(1+cos(d*x+c)))^(5/2)/sin(d*x+c)^9*2^(1/2)/a^3","B"
246,1,214,112,0.158000," ","int(cos(d*x+c)^(3/2)/(a+a*cos(d*x+c))^(5/2),x)","\frac{\sqrt{a \left(1+\cos \left(d x +c \right)\right)}\, \left(-1+\cos \left(d x +c \right)\right)^{3} \left(\cos^{\frac{3}{2}}\left(d x +c \right)\right) \left(7 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}-4 \cos \left(d x +c \right) \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+3 \cos \left(d x +c \right) \sin \left(d x +c \right) \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)-3 \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+3 \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \sin \left(d x +c \right)\right) \sqrt{2}}{32 d \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sin \left(d x +c \right)^{7} a^{3}}"," ",0,"1/32/d*(a*(1+cos(d*x+c)))^(1/2)*(-1+cos(d*x+c))^3*cos(d*x+c)^(3/2)*(7*cos(d*x+c)^2*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)-4*cos(d*x+c)*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+3*cos(d*x+c)*sin(d*x+c)*arcsin((-1+cos(d*x+c))/sin(d*x+c))-3*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+3*arcsin((-1+cos(d*x+c))/sin(d*x+c))*sin(d*x+c))/(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)/sin(d*x+c)^7*2^(1/2)/a^3","A"
247,1,213,112,0.156000," ","int(cos(d*x+c)^(1/2)/(a+a*cos(d*x+c))^(5/2),x)","-\frac{\left(\sqrt{\cos}\left(d x +c \right)\right) \sqrt{a \left(1+\cos \left(d x +c \right)\right)}\, \left(-1+\cos \left(d x +c \right)\right)^{2} \left(\left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+4 \cos \left(d x +c \right) \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+5 \cos \left(d x +c \right) \sin \left(d x +c \right) \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)-5 \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+5 \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \sin \left(d x +c \right)\right) \sqrt{2}}{32 d \sin \left(d x +c \right)^{5} \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, a^{3}}"," ",0,"-1/32/d*cos(d*x+c)^(1/2)*(a*(1+cos(d*x+c)))^(1/2)*(-1+cos(d*x+c))^2*(cos(d*x+c)^2*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+4*cos(d*x+c)*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+5*cos(d*x+c)*sin(d*x+c)*arcsin((-1+cos(d*x+c))/sin(d*x+c))-5*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+5*arcsin((-1+cos(d*x+c))/sin(d*x+c))*sin(d*x+c))/sin(d*x+c)^5/(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2)/a^3","A"
248,1,245,112,0.174000," ","int(1/cos(d*x+c)^(1/2)/(a+a*cos(d*x+c))^(5/2),x)","\frac{\sqrt{a \left(1+\cos \left(d x +c \right)\right)}\, \left(-1+\cos \left(d x +c \right)\right) \left(19 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+38 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \sin \left(d x +c \right) \cos \left(d x +c \right)-9 \left(\cos^{3}\left(d x +c \right)\right) \sqrt{2}+19 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \sin \left(d x +c \right)-4 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}+13 \cos \left(d x +c \right) \sqrt{2}\right) \sqrt{2}}{32 d \left(1+\cos \left(d x +c \right)\right) \sqrt{\cos \left(d x +c \right)}\, \sin \left(d x +c \right)^{3} a^{3}}"," ",0,"1/32/d*(a*(1+cos(d*x+c)))^(1/2)*(-1+cos(d*x+c))*(19*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arcsin((-1+cos(d*x+c))/sin(d*x+c))*cos(d*x+c)^2*sin(d*x+c)+38*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arcsin((-1+cos(d*x+c))/sin(d*x+c))*sin(d*x+c)*cos(d*x+c)-9*cos(d*x+c)^3*2^(1/2)+19*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arcsin((-1+cos(d*x+c))/sin(d*x+c))*sin(d*x+c)-4*cos(d*x+c)^2*2^(1/2)+13*cos(d*x+c)*2^(1/2))/(1+cos(d*x+c))/cos(d*x+c)^(1/2)/sin(d*x+c)^3*2^(1/2)/a^3","B"
249,1,303,146,0.187000," ","int(1/cos(d*x+c)^(3/2)/(a+a*cos(d*x+c))^(5/2),x)","\frac{\left(75 \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)+225 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}}+225 \cos \left(d x +c \right) \sin \left(d x +c \right) \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}}+75 \sin \left(d x +c \right) \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}}-49 \left(\cos^{4}\left(d x +c \right)\right) \sqrt{2}-36 \left(\cos^{3}\left(d x +c \right)\right) \sqrt{2}+53 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}+32 \cos \left(d x +c \right) \sqrt{2}\right) \sqrt{a \left(1+\cos \left(d x +c \right)\right)}\, \sqrt{2}}{32 d \sin \left(d x +c \right) \left(1+\cos \left(d x +c \right)\right)^{2} \cos \left(d x +c \right)^{\frac{3}{2}} a^{3}}"," ",0,"1/32/d*(75*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*arcsin((-1+cos(d*x+c))/sin(d*x+c))*cos(d*x+c)^3*sin(d*x+c)+225*cos(d*x+c)^2*sin(d*x+c)*arcsin((-1+cos(d*x+c))/sin(d*x+c))*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)+225*cos(d*x+c)*sin(d*x+c)*arcsin((-1+cos(d*x+c))/sin(d*x+c))*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)+75*sin(d*x+c)*arcsin((-1+cos(d*x+c))/sin(d*x+c))*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)-49*cos(d*x+c)^4*2^(1/2)-36*cos(d*x+c)^3*2^(1/2)+53*cos(d*x+c)^2*2^(1/2)+32*cos(d*x+c)*2^(1/2))*(a*(1+cos(d*x+c)))^(1/2)/sin(d*x+c)/(1+cos(d*x+c))^2/cos(d*x+c)^(3/2)*2^(1/2)/a^3","B"
250,1,377,180,0.192000," ","int(1/cos(d*x+c)^(5/2)/(a+a*cos(d*x+c))^(5/2),x)","\frac{\left(489 \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \left(\cos^{4}\left(d x +c \right)\right) \sin \left(d x +c \right) \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}}+1956 \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)+2934 \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+1956 \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \cos \left(d x +c \right) \sin \left(d x +c \right)+489 \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \sin \left(d x +c \right)-299 \sqrt{2}\, \left(\cos^{5}\left(d x +c \right)\right)-204 \left(\cos^{4}\left(d x +c \right)\right) \sqrt{2}+343 \left(\cos^{3}\left(d x +c \right)\right) \sqrt{2}+192 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}-32 \cos \left(d x +c \right) \sqrt{2}\right) \sin \left(d x +c \right) \sqrt{a \left(1+\cos \left(d x +c \right)\right)}\, \sqrt{2}}{96 d \left(-1+\cos \left(d x +c \right)\right) \left(1+\cos \left(d x +c \right)\right)^{3} \cos \left(d x +c \right)^{\frac{5}{2}} a^{3}}"," ",0,"1/96/d*(489*arcsin((-1+cos(d*x+c))/sin(d*x+c))*cos(d*x+c)^4*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(5/2)+1956*(cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*arcsin((-1+cos(d*x+c))/sin(d*x+c))*cos(d*x+c)^3*sin(d*x+c)+2934*(cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*arcsin((-1+cos(d*x+c))/sin(d*x+c))*cos(d*x+c)^2*sin(d*x+c)+1956*(cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*arcsin((-1+cos(d*x+c))/sin(d*x+c))*cos(d*x+c)*sin(d*x+c)+489*(cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*arcsin((-1+cos(d*x+c))/sin(d*x+c))*sin(d*x+c)-299*2^(1/2)*cos(d*x+c)^5-204*cos(d*x+c)^4*2^(1/2)+343*cos(d*x+c)^3*2^(1/2)+192*cos(d*x+c)^2*2^(1/2)-32*cos(d*x+c)*2^(1/2))*sin(d*x+c)*(a*(1+cos(d*x+c)))^(1/2)/(-1+cos(d*x+c))/(1+cos(d*x+c))^3/cos(d*x+c)^(5/2)*2^(1/2)/a^3","B"
251,1,464,211,0.194000," ","int(cos(d*x+c)^(9/2)/(a+a*cos(d*x+c))^(7/2),x)","\frac{\left(\cos^{\frac{9}{2}}\left(d x +c \right)\right) \left(-1+\cos \left(d x +c \right)\right)^{7} \sqrt{a \left(1+\cos \left(d x +c \right)\right)}\, \left(192 \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \left(\cos^{4}\left(d x +c \right)\right)+907 \left(\cos^{3}\left(d x +c \right)\right) \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+1344 \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}{\cos \left(d x +c \right)}\right) \sqrt{2}\, \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+1911 \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+343 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+2688 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{2}\, \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}{\cos \left(d x +c \right)}\right)+3822 \cos \left(d x +c \right) \sin \left(d x +c \right) \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)-875 \cos \left(d x +c \right) \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+1344 \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}{\cos \left(d x +c \right)}\right) \sqrt{2}\, \sin \left(d x +c \right)+1911 \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \sin \left(d x +c \right)-567 \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\right) \sqrt{2}}{384 d \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{9}{2}} \sin \left(d x +c \right)^{15} a^{4}}"," ",0,"1/384/d*cos(d*x+c)^(9/2)*(-1+cos(d*x+c))^7*(a*(1+cos(d*x+c)))^(1/2)*(192*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^4+907*cos(d*x+c)^3*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+1344*arctan(sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)/cos(d*x+c))*2^(1/2)*cos(d*x+c)^2*sin(d*x+c)+1911*arcsin((-1+cos(d*x+c))/sin(d*x+c))*cos(d*x+c)^2*sin(d*x+c)+343*cos(d*x+c)^2*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+2688*cos(d*x+c)*sin(d*x+c)*2^(1/2)*arctan(sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)/cos(d*x+c))+3822*cos(d*x+c)*sin(d*x+c)*arcsin((-1+cos(d*x+c))/sin(d*x+c))-875*cos(d*x+c)*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+1344*arctan(sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)/cos(d*x+c))*2^(1/2)*sin(d*x+c)+1911*arcsin((-1+cos(d*x+c))/sin(d*x+c))*sin(d*x+c)-567*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2))/(cos(d*x+c)/(1+cos(d*x+c)))^(9/2)/sin(d*x+c)^15*2^(1/2)/a^4","B"
252,1,432,177,0.177000," ","int(cos(d*x+c)^(7/2)/(a+a*cos(d*x+c))^(7/2),x)","\frac{\left(\cos^{\frac{7}{2}}\left(d x +c \right)\right) \left(-1+\cos \left(d x +c \right)\right)^{6} \sqrt{a \left(1+\cos \left(d x +c \right)\right)}\, \left(384 \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}{\cos \left(d x +c \right)}\right) \sqrt{2}\, \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+247 \left(\cos^{3}\left(d x +c \right)\right) \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+768 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{2}\, \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}{\cos \left(d x +c \right)}\right)+115 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+531 \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+384 \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}{\cos \left(d x +c \right)}\right) \sqrt{2}\, \sin \left(d x +c \right)-215 \cos \left(d x +c \right) \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+1062 \cos \left(d x +c \right) \sin \left(d x +c \right) \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)-147 \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+531 \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \sin \left(d x +c \right)\right) \sqrt{2}}{384 d \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{7}{2}} \sin \left(d x +c \right)^{13} a^{4}}"," ",0,"1/384/d*cos(d*x+c)^(7/2)*(-1+cos(d*x+c))^6*(a*(1+cos(d*x+c)))^(1/2)*(384*arctan(sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)/cos(d*x+c))*2^(1/2)*cos(d*x+c)^2*sin(d*x+c)+247*cos(d*x+c)^3*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+768*cos(d*x+c)*sin(d*x+c)*2^(1/2)*arctan(sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)/cos(d*x+c))+115*cos(d*x+c)^2*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+531*arcsin((-1+cos(d*x+c))/sin(d*x+c))*cos(d*x+c)^2*sin(d*x+c)+384*arctan(sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)/cos(d*x+c))*2^(1/2)*sin(d*x+c)-215*cos(d*x+c)*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+1062*cos(d*x+c)*sin(d*x+c)*arcsin((-1+cos(d*x+c))/sin(d*x+c))-147*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+531*arcsin((-1+cos(d*x+c))/sin(d*x+c))*sin(d*x+c))/(cos(d*x+c)/(1+cos(d*x+c)))^(7/2)/sin(d*x+c)^13*2^(1/2)/a^4","B"
253,1,280,146,0.184000," ","int(cos(d*x+c)^(5/2)/(a+a*cos(d*x+c))^(7/2),x)","\frac{\left(\cos^{\frac{5}{2}}\left(d x +c \right)\right) \left(-1+\cos \left(d x +c \right)\right)^{5} \sqrt{a \left(1+\cos \left(d x +c \right)\right)}\, \left(67 \left(\cos^{3}\left(d x +c \right)\right) \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+15 \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)-17 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+30 \cos \left(d x +c \right) \sin \left(d x +c \right) \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)-35 \cos \left(d x +c \right) \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+15 \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \sin \left(d x +c \right)-15 \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\right) \sqrt{2}}{384 d \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \sin \left(d x +c \right)^{11} a^{4}}"," ",0,"1/384/d*cos(d*x+c)^(5/2)*(-1+cos(d*x+c))^5*(a*(1+cos(d*x+c)))^(1/2)*(67*cos(d*x+c)^3*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+15*arcsin((-1+cos(d*x+c))/sin(d*x+c))*cos(d*x+c)^2*sin(d*x+c)-17*cos(d*x+c)^2*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+30*cos(d*x+c)*sin(d*x+c)*arcsin((-1+cos(d*x+c))/sin(d*x+c))-35*cos(d*x+c)*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+15*arcsin((-1+cos(d*x+c))/sin(d*x+c))*sin(d*x+c)-15*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2))/(cos(d*x+c)/(1+cos(d*x+c)))^(5/2)/sin(d*x+c)^11*2^(1/2)/a^4","A"
254,1,280,146,0.180000," ","int(cos(d*x+c)^(3/2)/(a+a*cos(d*x+c))^(7/2),x)","-\frac{\left(\cos^{\frac{3}{2}}\left(d x +c \right)\right) \sqrt{a \left(1+\cos \left(d x +c \right)\right)}\, \left(-1+\cos \left(d x +c \right)\right)^{4} \left(17 \left(\cos^{3}\left(d x +c \right)\right) \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+53 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+21 \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)-49 \cos \left(d x +c \right) \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+42 \cos \left(d x +c \right) \sin \left(d x +c \right) \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)-21 \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+21 \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \sin \left(d x +c \right)\right) \sqrt{2}}{384 d \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sin \left(d x +c \right)^{9} a^{4}}"," ",0,"-1/384/d*cos(d*x+c)^(3/2)*(a*(1+cos(d*x+c)))^(1/2)*(-1+cos(d*x+c))^4*(17*cos(d*x+c)^3*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+53*cos(d*x+c)^2*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+21*arcsin((-1+cos(d*x+c))/sin(d*x+c))*cos(d*x+c)^2*sin(d*x+c)-49*cos(d*x+c)*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+42*cos(d*x+c)*sin(d*x+c)*arcsin((-1+cos(d*x+c))/sin(d*x+c))-21*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+21*arcsin((-1+cos(d*x+c))/sin(d*x+c))*sin(d*x+c))/(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)/sin(d*x+c)^9*2^(1/2)/a^4","A"
255,1,280,146,0.169000," ","int(cos(d*x+c)^(1/2)/(a+a*cos(d*x+c))^(7/2),x)","\frac{\left(\sqrt{\cos}\left(d x +c \right)\right) \sqrt{a \left(1+\cos \left(d x +c \right)\right)}\, \left(-1+\cos \left(d x +c \right)\right)^{3} \left(-5 \left(\cos^{3}\left(d x +c \right)\right) \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+39 \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+7 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+78 \cos \left(d x +c \right) \sin \left(d x +c \right) \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)+37 \cos \left(d x +c \right) \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+39 \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \sin \left(d x +c \right)-39 \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\right) \sqrt{2}}{384 d \sin \left(d x +c \right)^{7} \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, a^{4}}"," ",0,"1/384/d*cos(d*x+c)^(1/2)*(a*(1+cos(d*x+c)))^(1/2)*(-1+cos(d*x+c))^3*(-5*cos(d*x+c)^3*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+39*arcsin((-1+cos(d*x+c))/sin(d*x+c))*cos(d*x+c)^2*sin(d*x+c)+7*cos(d*x+c)^2*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+78*cos(d*x+c)*sin(d*x+c)*arcsin((-1+cos(d*x+c))/sin(d*x+c))+37*cos(d*x+c)*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+39*arcsin((-1+cos(d*x+c))/sin(d*x+c))*sin(d*x+c)-39*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2))/sin(d*x+c)^7/(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2)/a^4","A"
256,1,313,146,0.168000," ","int(1/cos(d*x+c)^(1/2)/(a+a*cos(d*x+c))^(7/2),x)","\frac{\sqrt{a \left(1+\cos \left(d x +c \right)\right)}\, \left(-1+\cos \left(d x +c \right)\right)^{2} \left(-189 \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+103 \left(\cos^{4}\left(d x +c \right)\right) \sqrt{2}-567 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+163 \left(\cos^{3}\left(d x +c \right)\right) \sqrt{2}-567 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \sin \left(d x +c \right) \cos \left(d x +c \right)-71 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}-189 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \sin \left(d x +c \right)-195 \cos \left(d x +c \right) \sqrt{2}\right) \sqrt{2}}{384 d \left(1+\cos \left(d x +c \right)\right) \sqrt{\cos \left(d x +c \right)}\, \sin \left(d x +c \right)^{5} a^{4}}"," ",0,"1/384/d*(a*(1+cos(d*x+c)))^(1/2)*(-1+cos(d*x+c))^2*(-189*arcsin((-1+cos(d*x+c))/sin(d*x+c))*cos(d*x+c)^3*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+103*cos(d*x+c)^4*2^(1/2)-567*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arcsin((-1+cos(d*x+c))/sin(d*x+c))*cos(d*x+c)^2*sin(d*x+c)+163*cos(d*x+c)^3*2^(1/2)-567*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arcsin((-1+cos(d*x+c))/sin(d*x+c))*sin(d*x+c)*cos(d*x+c)-71*cos(d*x+c)^2*2^(1/2)-189*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arcsin((-1+cos(d*x+c))/sin(d*x+c))*sin(d*x+c)-195*cos(d*x+c)*2^(1/2))/(1+cos(d*x+c))/cos(d*x+c)^(1/2)/sin(d*x+c)^5*2^(1/2)/a^4","B"
257,1,377,180,0.207000," ","int(1/cos(d*x+c)^(3/2)/(a+a*cos(d*x+c))^(7/2),x)","\frac{\left(-1+\cos \left(d x +c \right)\right) \left(-1089 \left(\cos^{4}\left(d x +c \right)\right) \sin \left(d x +c \right) \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}}-4356 \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)-6534 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}}+691 \sqrt{2}\, \left(\cos^{5}\left(d x +c \right)\right)-4356 \cos \left(d x +c \right) \sin \left(d x +c \right) \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}}+1183 \left(\cos^{4}\left(d x +c \right)\right) \sqrt{2}-1089 \sin \left(d x +c \right) \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}}-275 \left(\cos^{3}\left(d x +c \right)\right) \sqrt{2}-1215 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}-384 \cos \left(d x +c \right) \sqrt{2}\right) \sqrt{a \left(1+\cos \left(d x +c \right)\right)}\, \sqrt{2}}{384 d \sin \left(d x +c \right)^{3} \left(1+\cos \left(d x +c \right)\right)^{2} \cos \left(d x +c \right)^{\frac{3}{2}} a^{4}}"," ",0,"1/384/d*(-1+cos(d*x+c))*(-1089*cos(d*x+c)^4*sin(d*x+c)*arcsin((-1+cos(d*x+c))/sin(d*x+c))*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)-4356*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*arcsin((-1+cos(d*x+c))/sin(d*x+c))*cos(d*x+c)^3*sin(d*x+c)-6534*cos(d*x+c)^2*sin(d*x+c)*arcsin((-1+cos(d*x+c))/sin(d*x+c))*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)+691*2^(1/2)*cos(d*x+c)^5-4356*cos(d*x+c)*sin(d*x+c)*arcsin((-1+cos(d*x+c))/sin(d*x+c))*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)+1183*cos(d*x+c)^4*2^(1/2)-1089*sin(d*x+c)*arcsin((-1+cos(d*x+c))/sin(d*x+c))*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)-275*cos(d*x+c)^3*2^(1/2)-1215*cos(d*x+c)^2*2^(1/2)-384*cos(d*x+c)*2^(1/2))*(a*(1+cos(d*x+c)))^(1/2)/sin(d*x+c)^3/(1+cos(d*x+c))^2/cos(d*x+c)^(3/2)*2^(1/2)/a^4","B"
258,1,435,214,0.207000," ","int(1/cos(d*x+c)^(5/2)/(a+a*cos(d*x+c))^(7/2),x)","\frac{\left(-3045 \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \left(\cos^{5}\left(d x +c \right)\right) \sin \left(d x +c \right) \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}}-15225 \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \left(\cos^{4}\left(d x +c \right)\right) \sin \left(d x +c \right) \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}}-30450 \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)-30450 \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)-15225 \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \cos \left(d x +c \right) \sin \left(d x +c \right)+1887 \sqrt{2}\, \left(\cos^{6}\left(d x +c \right)\right)-3045 \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \sin \left(d x +c \right)+3195 \sqrt{2}\, \left(\cos^{5}\left(d x +c \right)\right)-831 \left(\cos^{4}\left(d x +c \right)\right) \sqrt{2}-3355 \left(\cos^{3}\left(d x +c \right)\right) \sqrt{2}-1024 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}+128 \cos \left(d x +c \right) \sqrt{2}\right) \sqrt{a \left(1+\cos \left(d x +c \right)\right)}\, \sqrt{2}}{384 d \sin \left(d x +c \right) \left(1+\cos \left(d x +c \right)\right)^{3} \cos \left(d x +c \right)^{\frac{5}{2}} a^{4}}"," ",0,"1/384/d*(-3045*arcsin((-1+cos(d*x+c))/sin(d*x+c))*cos(d*x+c)^5*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(5/2)-15225*arcsin((-1+cos(d*x+c))/sin(d*x+c))*cos(d*x+c)^4*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(5/2)-30450*(cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*arcsin((-1+cos(d*x+c))/sin(d*x+c))*cos(d*x+c)^3*sin(d*x+c)-30450*(cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*arcsin((-1+cos(d*x+c))/sin(d*x+c))*cos(d*x+c)^2*sin(d*x+c)-15225*(cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*arcsin((-1+cos(d*x+c))/sin(d*x+c))*cos(d*x+c)*sin(d*x+c)+1887*2^(1/2)*cos(d*x+c)^6-3045*(cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*arcsin((-1+cos(d*x+c))/sin(d*x+c))*sin(d*x+c)+3195*2^(1/2)*cos(d*x+c)^5-831*cos(d*x+c)^4*2^(1/2)-3355*cos(d*x+c)^3*2^(1/2)-1024*cos(d*x+c)^2*2^(1/2)+128*cos(d*x+c)*2^(1/2))*(a*(1+cos(d*x+c)))^(1/2)/sin(d*x+c)/(1+cos(d*x+c))^3/cos(d*x+c)^(5/2)*2^(1/2)/a^4","B"
259,1,346,180,0.190000," ","int(cos(d*x+c)^(7/2)/(a+a*cos(d*x+c))^(9/2),x)","\frac{\left(\cos^{\frac{7}{2}}\left(d x +c \right)\right) \left(-1+\cos \left(d x +c \right)\right)^{7} \sqrt{a \left(1+\cos \left(d x +c \right)\right)}\, \left(853 \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \left(\cos^{4}\left(d x +c \right)\right)+105 \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)-34 \left(\cos^{3}\left(d x +c \right)\right) \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+315 \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)-364 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+315 \cos \left(d x +c \right) \sin \left(d x +c \right) \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)-350 \cos \left(d x +c \right) \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+105 \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \sin \left(d x +c \right)-105 \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\right) \sqrt{2}}{6144 d \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{7}{2}} \sin \left(d x +c \right)^{15} a^{5}}"," ",0,"1/6144/d*cos(d*x+c)^(7/2)*(-1+cos(d*x+c))^7*(a*(1+cos(d*x+c)))^(1/2)*(853*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^4+105*arcsin((-1+cos(d*x+c))/sin(d*x+c))*cos(d*x+c)^3*sin(d*x+c)-34*cos(d*x+c)^3*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+315*arcsin((-1+cos(d*x+c))/sin(d*x+c))*cos(d*x+c)^2*sin(d*x+c)-364*cos(d*x+c)^2*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+315*cos(d*x+c)*sin(d*x+c)*arcsin((-1+cos(d*x+c))/sin(d*x+c))-350*cos(d*x+c)*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+105*arcsin((-1+cos(d*x+c))/sin(d*x+c))*sin(d*x+c)-105*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2))/(cos(d*x+c)/(1+cos(d*x+c)))^(7/2)/sin(d*x+c)^15*2^(1/2)/a^5","A"
260,1,346,180,0.186000," ","int(cos(d*x+c)^(5/2)/(a+a*cos(d*x+c))^(9/2),x)","-\frac{\left(\cos^{\frac{5}{2}}\left(d x +c \right)\right) \left(-1+\cos \left(d x +c \right)\right)^{6} \sqrt{a \left(1+\cos \left(d x +c \right)\right)}\, \left(73 \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \left(\cos^{4}\left(d x +c \right)\right)+278 \left(\cos^{3}\left(d x +c \right)\right) \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+45 \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)-156 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+135 \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)-150 \cos \left(d x +c \right) \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+135 \cos \left(d x +c \right) \sin \left(d x +c \right) \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)-45 \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+45 \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \sin \left(d x +c \right)\right) \sqrt{2}}{2048 d \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \sin \left(d x +c \right)^{13} a^{5}}"," ",0,"-1/2048/d*cos(d*x+c)^(5/2)*(-1+cos(d*x+c))^6*(a*(1+cos(d*x+c)))^(1/2)*(73*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^4+278*cos(d*x+c)^3*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+45*arcsin((-1+cos(d*x+c))/sin(d*x+c))*cos(d*x+c)^3*sin(d*x+c)-156*cos(d*x+c)^2*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+135*arcsin((-1+cos(d*x+c))/sin(d*x+c))*cos(d*x+c)^2*sin(d*x+c)-150*cos(d*x+c)*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+135*cos(d*x+c)*sin(d*x+c)*arcsin((-1+cos(d*x+c))/sin(d*x+c))-45*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+45*arcsin((-1+cos(d*x+c))/sin(d*x+c))*sin(d*x+c))/(cos(d*x+c)/(1+cos(d*x+c)))^(5/2)/sin(d*x+c)^13*2^(1/2)/a^5","A"
261,1,36,14,0.054000," ","int(1/cos(x)^(1/2)/(cos(x)+1)^(1/2),x)","-\frac{\sqrt{\frac{\cos \left(x \right)}{\cos \left(x \right)+1}}\, \sqrt{2+2 \cos \left(x \right)}\, \arcsin \left(\frac{-1+\cos \left(x \right)}{\sin \left(x \right)}\right)}{\sqrt{\cos \left(x \right)}}"," ",0,"-1/cos(x)^(1/2)*(cos(x)/(cos(x)+1))^(1/2)*(2+2*cos(x))^(1/2)*arcsin((-1+cos(x))/sin(x))","B"
262,1,42,30,0.063000," ","int(1/cos(x)^(1/2)/(a+a*cos(x))^(1/2),x)","-\frac{\sqrt{\frac{\cos \left(x \right)}{\cos \left(x \right)+1}}\, \sqrt{a \left(\cos \left(x \right)+1\right)}\, \arcsin \left(\frac{-1+\cos \left(x \right)}{\sin \left(x \right)}\right) \sqrt{2}}{\sqrt{\cos \left(x \right)}\, a}"," ",0,"-1/cos(x)^(1/2)*(cos(x)/(cos(x)+1))^(1/2)*(a*(cos(x)+1))^(1/2)*arcsin((-1+cos(x))/sin(x))*2^(1/2)/a","A"
263,1,165,107,0.205000," ","int(cos(d*x+c)^(3/2)*(a-a*cos(d*x+c))^(1/2),x)","\frac{\left(-1+\cos \left(d x +c \right)\right) \left(2 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \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)}}\, \cos \left(d x +c \right)-3 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+3 \arctanh \left(\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\right)\right) \sqrt{-2 a \left(-1+\cos \left(d x +c \right)\right)}\, \left(\cos^{\frac{3}{2}}\left(d x +c \right)\right) \sqrt{2}}{8 d \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sin \left(d x +c \right)^{3}}"," ",0,"1/8/d*(-1+cos(d*x+c))*(2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2-(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)-3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+3*arctanh((cos(d*x+c)/(1+cos(d*x+c)))^(1/2)))*(-2*a*(-1+cos(d*x+c)))^(1/2)*cos(d*x+c)^(3/2)/(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)/sin(d*x+c)^3*2^(1/2)","A"
264,1,94,73,0.146000," ","int(cos(d*x+c)^(1/2)*(a-a*cos(d*x+c))^(1/2),x)","-\frac{\left(1+\cos \left(d x +c \right)\right) \left(-\arctanh \left(\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+\cos \left(d x +c \right)\right) \sqrt{-2 a \left(-1+\cos \left(d x +c \right)\right)}\, \sqrt{2}}{2 d \sqrt{\cos \left(d x +c \right)}\, \sin \left(d x +c \right)}"," ",0,"-1/2/d*(1+cos(d*x+c))*(-arctanh((cos(d*x+c)/(1+cos(d*x+c)))^(1/2))*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+cos(d*x+c))/cos(d*x+c)^(1/2)/sin(d*x+c)*(-2*a*(-1+cos(d*x+c)))^(1/2)*2^(1/2)","A"
265,1,84,40,0.118000," ","int((a-a*cos(d*x+c))^(1/2)/cos(d*x+c)^(1/2),x)","\frac{\sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{-2 a \left(-1+\cos \left(d x +c \right)\right)}\, \sin \left(d x +c \right) \arctanh \left(\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\right)}{d \sqrt{\cos \left(d x +c \right)}\, \left(-1+\cos \left(d x +c \right)\right)}"," ",0,"1/d*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*(-2*a*(-1+cos(d*x+c)))^(1/2)*sin(d*x+c)*arctanh((cos(d*x+c)/(1+cos(d*x+c)))^(1/2))/cos(d*x+c)^(1/2)/(-1+cos(d*x+c))","B"
266,1,46,33,0.124000," ","int((a-a*cos(d*x+c))^(1/2)/cos(d*x+c)^(3/2),x)","-\frac{\sqrt{-2 a \left(-1+\cos \left(d x +c \right)\right)}\, \sin \left(d x +c \right) \sqrt{2}}{d \left(-1+\cos \left(d x +c \right)\right) \sqrt{\cos \left(d x +c \right)}}"," ",0,"-1/d*(-2*a*(-1+cos(d*x+c)))^(1/2)*sin(d*x+c)/(-1+cos(d*x+c))/cos(d*x+c)^(1/2)*2^(1/2)","A"
267,1,56,67,0.132000," ","int((a-a*cos(d*x+c))^(1/2)/cos(d*x+c)^(5/2),x)","\frac{\left(-1+2 \cos \left(d x +c \right)\right) \sqrt{-2 a \left(-1+\cos \left(d x +c \right)\right)}\, \sin \left(d x +c \right) \sqrt{2}}{3 d \left(-1+\cos \left(d x +c \right)\right) \cos \left(d x +c \right)^{\frac{3}{2}}}"," ",0,"1/3/d*(-1+2*cos(d*x+c))*(-2*a*(-1+cos(d*x+c)))^(1/2)*sin(d*x+c)/(-1+cos(d*x+c))/cos(d*x+c)^(3/2)*2^(1/2)","A"
268,1,66,100,0.125000," ","int((a-a*cos(d*x+c))^(1/2)/cos(d*x+c)^(7/2),x)","-\frac{\left(8 \left(\cos^{2}\left(d x +c \right)\right)-4 \cos \left(d x +c \right)+3\right) \sqrt{-2 a \left(-1+\cos \left(d x +c \right)\right)}\, \sin \left(d x +c \right) \sqrt{2}}{15 d \left(-1+\cos \left(d x +c \right)\right) \cos \left(d x +c \right)^{\frac{5}{2}}}"," ",0,"-1/15/d*(8*cos(d*x+c)^2-4*cos(d*x+c)+3)*(-2*a*(-1+cos(d*x+c)))^(1/2)*sin(d*x+c)/(-1+cos(d*x+c))/cos(d*x+c)^(5/2)*2^(1/2)","A"
269,1,164,96,0.148000," ","int((1-cos(d*x+c))^(1/2)*cos(d*x+c)^(3/2),x)","\frac{\left(-1+\cos \left(d x +c \right)\right) \left(2 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \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)}}\, \cos \left(d x +c \right)-3 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+3 \arctanh \left(\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\right)\right) \sqrt{2-2 \cos \left(d x +c \right)}\, \left(\cos^{\frac{3}{2}}\left(d x +c \right)\right) \sqrt{2}}{8 d \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sin \left(d x +c \right)^{3}}"," ",0,"1/8/d*(-1+cos(d*x+c))*(2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2-(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)-3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+3*arctanh((cos(d*x+c)/(1+cos(d*x+c)))^(1/2)))*(2-2*cos(d*x+c))^(1/2)*cos(d*x+c)^(3/2)/(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)/sin(d*x+c)^3*2^(1/2)","A"
270,1,94,64,0.128000," ","int((1-cos(d*x+c))^(1/2)*cos(d*x+c)^(1/2),x)","\frac{\left(1+\cos \left(d x +c \right)\right) \left(\arctanh \left(\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}-\cos \left(d x +c \right)\right) \sqrt{2-2 \cos \left(d x +c \right)}\, \sqrt{2}}{2 d \sqrt{\cos \left(d x +c \right)}\, \sin \left(d x +c \right)}"," ",0,"1/2/d*(1+cos(d*x+c))*(arctanh((cos(d*x+c)/(1+cos(d*x+c)))^(1/2))*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)-cos(d*x+c))*(2-2*cos(d*x+c))^(1/2)/cos(d*x+c)^(1/2)/sin(d*x+c)*2^(1/2)","A"
271,1,83,33,0.087000," ","int((1-cos(d*x+c))^(1/2)/cos(d*x+c)^(1/2),x)","\frac{\sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2-2 \cos \left(d x +c \right)}\, \sin \left(d x +c \right) \arctanh \left(\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\right)}{d \sqrt{\cos \left(d x +c \right)}\, \left(-1+\cos \left(d x +c \right)\right)}"," ",0,"1/d*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*(2-2*cos(d*x+c))^(1/2)*sin(d*x+c)*arctanh((cos(d*x+c)/(1+cos(d*x+c)))^(1/2))/cos(d*x+c)^(1/2)/(-1+cos(d*x+c))","B"
272,1,45,31,0.101000," ","int((1-cos(d*x+c))^(1/2)/cos(d*x+c)^(3/2),x)","-\frac{\sin \left(d x +c \right) \sqrt{2-2 \cos \left(d x +c \right)}\, \sqrt{2}}{d \left(-1+\cos \left(d x +c \right)\right) \sqrt{\cos \left(d x +c \right)}}"," ",0,"-1/d*sin(d*x+c)*(2-2*cos(d*x+c))^(1/2)/(-1+cos(d*x+c))/cos(d*x+c)^(1/2)*2^(1/2)","A"
273,1,55,63,0.107000," ","int((1-cos(d*x+c))^(1/2)/cos(d*x+c)^(5/2),x)","\frac{\left(-1+2 \cos \left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{2-2 \cos \left(d x +c \right)}\, \sqrt{2}}{3 d \left(-1+\cos \left(d x +c \right)\right) \cos \left(d x +c \right)^{\frac{3}{2}}}"," ",0,"1/3/d*(-1+2*cos(d*x+c))*sin(d*x+c)*(2-2*cos(d*x+c))^(1/2)/(-1+cos(d*x+c))/cos(d*x+c)^(3/2)*2^(1/2)","A"
274,1,65,94,0.109000," ","int((1-cos(d*x+c))^(1/2)/cos(d*x+c)^(7/2),x)","-\frac{\left(8 \left(\cos^{2}\left(d x +c \right)\right)-4 \cos \left(d x +c \right)+3\right) \sqrt{2-2 \cos \left(d x +c \right)}\, \sin \left(d x +c \right) \sqrt{2}}{15 d \left(-1+\cos \left(d x +c \right)\right) \cos \left(d x +c \right)^{\frac{5}{2}}}"," ",0,"-1/15/d*(8*cos(d*x+c)^2-4*cos(d*x+c)+3)*(2-2*cos(d*x+c))^(1/2)*sin(d*x+c)/(-1+cos(d*x+c))/cos(d*x+c)^(5/2)*2^(1/2)","A"
275,1,197,152,0.165000," ","int(cos(d*x+c)^(5/2)/(a-a*cos(d*x+c))^(1/2),x)","\frac{\left(\cos^{\frac{5}{2}}\left(d x +c \right)\right) \left(-1+\cos \left(d x +c \right)\right)^{3} \left(-2 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right)+4 \sqrt{2}\, \arctanh \left(\frac{\sqrt{2}}{2 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)-3 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right)-7 \arctanh \left(\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\right)-\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\right) \sqrt{2}}{4 d \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \sqrt{-2 a \left(-1+\cos \left(d x +c \right)\right)}\, \sin \left(d x +c \right)^{5}}"," ",0,"1/4/d*cos(d*x+c)^(5/2)*(-1+cos(d*x+c))^3*(-2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2+4*2^(1/2)*arctanh(1/2*2^(1/2)/(cos(d*x+c)/(1+cos(d*x+c)))^(1/2))-3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)-7*arctanh((cos(d*x+c)/(1+cos(d*x+c)))^(1/2))-(cos(d*x+c)/(1+cos(d*x+c)))^(1/2))/(cos(d*x+c)/(1+cos(d*x+c)))^(5/2)/(-2*a*(-1+cos(d*x+c)))^(1/2)/sin(d*x+c)^5*2^(1/2)","A"
276,1,167,118,0.151000," ","int(cos(d*x+c)^(3/2)/(a-a*cos(d*x+c))^(1/2),x)","-\frac{\left(\cos^{\frac{3}{2}}\left(d x +c \right)\right) \left(-1+\cos \left(d x +c \right)\right)^{2} \left(\sqrt{2}\, \arctanh \left(\frac{\sqrt{2}}{2 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)-\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right)-\arctanh \left(\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\right)-\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\right) \sqrt{2}}{d \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sqrt{-2 a \left(-1+\cos \left(d x +c \right)\right)}\, \sin \left(d x +c \right)^{3}}"," ",0,"-1/d*cos(d*x+c)^(3/2)*(-1+cos(d*x+c))^2*(2^(1/2)*arctanh(1/2*2^(1/2)/(cos(d*x+c)/(1+cos(d*x+c)))^(1/2))-(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)-arctanh((cos(d*x+c)/(1+cos(d*x+c)))^(1/2))-(cos(d*x+c)/(1+cos(d*x+c)))^(1/2))/(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)/(-2*a*(-1+cos(d*x+c)))^(1/2)/sin(d*x+c)^3*2^(1/2)","A"
277,1,118,88,0.110000," ","int(cos(d*x+c)^(1/2)/(a-a*cos(d*x+c))^(1/2),x)","-\frac{\left(\sqrt{\cos}\left(d x +c \right)\right) \left(-1+\cos \left(d x +c \right)\right) \left(-\sqrt{2}\, \arctanh \left(\frac{\sqrt{2}}{2 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)+2 \arctanh \left(\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\right)\right) \sqrt{2}}{d \sqrt{-2 a \left(-1+\cos \left(d x +c \right)\right)}\, \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}"," ",0,"-1/d*cos(d*x+c)^(1/2)*(-1+cos(d*x+c))*(-2^(1/2)*arctanh(1/2*2^(1/2)/(cos(d*x+c)/(1+cos(d*x+c)))^(1/2))+2*arctanh((cos(d*x+c)/(1+cos(d*x+c)))^(1/2)))/(-2*a*(-1+cos(d*x+c)))^(1/2)/sin(d*x+c)/(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2)","A"
278,1,77,47,0.136000," ","int(1/cos(d*x+c)^(1/2)/(a-a*cos(d*x+c))^(1/2),x)","-\frac{2 \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctanh \left(\frac{\sqrt{2}}{2 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)}{d \sqrt{-2 a \left(-1+\cos \left(d x +c \right)\right)}\, \sqrt{\cos \left(d x +c \right)}}"," ",0,"-2/d*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*2^(1/2)/(cos(d*x+c)/(1+cos(d*x+c)))^(1/2))/(-2*a*(-1+cos(d*x+c)))^(1/2)/cos(d*x+c)^(1/2)","A"
279,1,160,80,0.145000," ","int(1/cos(d*x+c)^(3/2)/(a-a*cos(d*x+c))^(1/2),x)","\frac{\left(\sin^{3}\left(d x +c \right)\right) \left(\sqrt{2}\, \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \arctanh \left(\frac{\sqrt{2}}{2 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right) \cos \left(d x +c \right)+\sqrt{2}\, \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \arctanh \left(\frac{\sqrt{2}}{2 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)-2 \cos \left(d x +c \right)\right) \sqrt{2}}{d \sqrt{-2 a \left(-1+\cos \left(d x +c \right)\right)}\, \cos \left(d x +c \right)^{\frac{3}{2}} \left(\cos^{2}\left(d x +c \right)-1\right)}"," ",0,"1/d*sin(d*x+c)^3*(2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*arctanh(1/2*2^(1/2)/(cos(d*x+c)/(1+cos(d*x+c)))^(1/2))*cos(d*x+c)+2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*arctanh(1/2*2^(1/2)/(cos(d*x+c)/(1+cos(d*x+c)))^(1/2))-2*cos(d*x+c))/(-2*a*(-1+cos(d*x+c)))^(1/2)/cos(d*x+c)^(3/2)/(cos(d*x+c)^2-1)*2^(1/2)","A"
280,1,171,112,0.168000," ","int(1/cos(d*x+c)^(5/2)/(a-a*cos(d*x+c))^(1/2),x)","-\frac{\left(\sin^{5}\left(d x +c \right)\right) \left(3 \sqrt{2}\, \cos \left(d x +c \right) \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \arctanh \left(\frac{\sqrt{2}}{2 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)+3 \sqrt{2}\, \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \arctanh \left(\frac{\sqrt{2}}{2 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)-2 \cos \left(d x +c \right)\right) \sqrt{2}}{3 d \left(-1+\cos \left(d x +c \right)\right)^{2} \sqrt{-2 a \left(-1+\cos \left(d x +c \right)\right)}\, \left(1+\cos \left(d x +c \right)\right) \cos \left(d x +c \right)^{\frac{5}{2}}}"," ",0,"-1/3/d*sin(d*x+c)^5*(3*2^(1/2)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*arctanh(1/2*2^(1/2)/(cos(d*x+c)/(1+cos(d*x+c)))^(1/2))+3*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*arctanh(1/2*2^(1/2)/(cos(d*x+c)/(1+cos(d*x+c)))^(1/2))-2*cos(d*x+c))/(-1+cos(d*x+c))^2/(-2*a*(-1+cos(d*x+c)))^(1/2)/(1+cos(d*x+c))/cos(d*x+c)^(5/2)*2^(1/2)","A"
281,1,305,144,0.198000," ","int(1/cos(d*x+c)^(7/2)/(a-a*cos(d*x+c))^(1/2),x)","\frac{\left(\sin^{7}\left(d x +c \right)\right) \left(15 \sqrt{2}\, \left(\cos^{3}\left(d x +c \right)\right) \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{7}{2}} \arctanh \left(\frac{\sqrt{2}}{2 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)+45 \sqrt{2}\, \left(\cos^{2}\left(d x +c \right)\right) \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{7}{2}} \arctanh \left(\frac{\sqrt{2}}{2 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)+45 \sqrt{2}\, \cos \left(d x +c \right) \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{7}{2}} \arctanh \left(\frac{\sqrt{2}}{2 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)+15 \sqrt{2}\, \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{7}{2}} \arctanh \left(\frac{\sqrt{2}}{2 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)-26 \left(\cos^{3}\left(d x +c \right)\right)-2 \left(\cos^{2}\left(d x +c \right)\right)-6 \cos \left(d x +c \right)\right) \sqrt{2}}{15 d \left(-1+\cos \left(d x +c \right)\right)^{3} \sqrt{-2 a \left(-1+\cos \left(d x +c \right)\right)}\, \left(1+\cos \left(d x +c \right)\right)^{3} \cos \left(d x +c \right)^{\frac{7}{2}}}"," ",0,"1/15/d*sin(d*x+c)^7*(15*2^(1/2)*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(7/2)*arctanh(1/2*2^(1/2)/(cos(d*x+c)/(1+cos(d*x+c)))^(1/2))+45*2^(1/2)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(7/2)*arctanh(1/2*2^(1/2)/(cos(d*x+c)/(1+cos(d*x+c)))^(1/2))+45*2^(1/2)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(7/2)*arctanh(1/2*2^(1/2)/(cos(d*x+c)/(1+cos(d*x+c)))^(1/2))+15*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(7/2)*arctanh(1/2*2^(1/2)/(cos(d*x+c)/(1+cos(d*x+c)))^(1/2))-26*cos(d*x+c)^3-2*cos(d*x+c)^2-6*cos(d*x+c))/(-1+cos(d*x+c))^3/(-2*a*(-1+cos(d*x+c)))^(1/2)/(1+cos(d*x+c))^3/cos(d*x+c)^(7/2)*2^(1/2)","B"
282,1,194,136,0.147000," ","int(cos(d*x+c)^(5/2)/(1-cos(d*x+c))^(1/2),x)","-\frac{\left(\cos^{\frac{5}{2}}\left(d x +c \right)\right) \left(-1+\cos \left(d x +c \right)\right)^{3} \left(2 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right)+3 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right)-4 \sqrt{2}\, \arctanh \left(\frac{\sqrt{2}}{2 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)+7 \arctanh \left(\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\right)+\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\right) \sqrt{2}}{4 d \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \sin \left(d x +c \right)^{5} \sqrt{2-2 \cos \left(d x +c \right)}}"," ",0,"-1/4/d*cos(d*x+c)^(5/2)*(-1+cos(d*x+c))^3*(2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2+3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)-4*2^(1/2)*arctanh(1/2*2^(1/2)/(cos(d*x+c)/(1+cos(d*x+c)))^(1/2))+7*arctanh((cos(d*x+c)/(1+cos(d*x+c)))^(1/2))+(cos(d*x+c)/(1+cos(d*x+c)))^(1/2))/(cos(d*x+c)/(1+cos(d*x+c)))^(5/2)/sin(d*x+c)^5/(2-2*cos(d*x+c))^(1/2)*2^(1/2)","A"
283,1,166,103,0.133000," ","int(cos(d*x+c)^(3/2)/(1-cos(d*x+c))^(1/2),x)","-\frac{\left(\cos^{\frac{3}{2}}\left(d x +c \right)\right) \left(-1+\cos \left(d x +c \right)\right)^{2} \left(\sqrt{2}\, \arctanh \left(\frac{\sqrt{2}}{2 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)-\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right)-\arctanh \left(\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\right)-\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\right) \sqrt{2}}{d \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sqrt{2-2 \cos \left(d x +c \right)}\, \sin \left(d x +c \right)^{3}}"," ",0,"-1/d*cos(d*x+c)^(3/2)*(-1+cos(d*x+c))^2*(2^(1/2)*arctanh(1/2*2^(1/2)/(cos(d*x+c)/(1+cos(d*x+c)))^(1/2))-(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)-arctanh((cos(d*x+c)/(1+cos(d*x+c)))^(1/2))-(cos(d*x+c)/(1+cos(d*x+c)))^(1/2))/(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)/(2-2*cos(d*x+c))^(1/2)/sin(d*x+c)^3*2^(1/2)","A"
284,1,117,74,0.097000," ","int(cos(d*x+c)^(1/2)/(1-cos(d*x+c))^(1/2),x)","-\frac{\left(\sqrt{\cos}\left(d x +c \right)\right) \left(-1+\cos \left(d x +c \right)\right) \left(-\sqrt{2}\, \arctanh \left(\frac{\sqrt{2}}{2 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)+2 \arctanh \left(\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\right)\right) \sqrt{2}}{d \sin \left(d x +c \right) \sqrt{2-2 \cos \left(d x +c \right)}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}"," ",0,"-1/d*cos(d*x+c)^(1/2)*(-1+cos(d*x+c))*(-2^(1/2)*arctanh(1/2*2^(1/2)/(cos(d*x+c)/(1+cos(d*x+c)))^(1/2))+2*arctanh((cos(d*x+c)/(1+cos(d*x+c)))^(1/2)))/sin(d*x+c)/(2-2*cos(d*x+c))^(1/2)/(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2)","A"
285,1,84,40,0.128000," ","int(1/(1-cos(d*x+c))^(1/2)/cos(d*x+c)^(1/2),x)","\frac{4 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \left(-1+\cos \left(d x +c \right)\right) \sin \left(d x +c \right) \arctanh \left(\frac{\sqrt{2}}{2 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)}{d \sqrt{\cos \left(d x +c \right)}\, \left(2-2 \cos \left(d x +c \right)\right)^{\frac{3}{2}}}"," ",0,"4/d*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*(-1+cos(d*x+c))*sin(d*x+c)*arctanh(1/2*2^(1/2)/(cos(d*x+c)/(1+cos(d*x+c)))^(1/2))/cos(d*x+c)^(1/2)/(2-2*cos(d*x+c))^(3/2)","B"
286,1,159,72,0.133000," ","int(1/(1-cos(d*x+c))^(1/2)/cos(d*x+c)^(3/2),x)","\frac{\left(\sin^{3}\left(d x +c \right)\right) \left(\sqrt{2}\, \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \arctanh \left(\frac{\sqrt{2}}{2 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right) \cos \left(d x +c \right)+\sqrt{2}\, \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \arctanh \left(\frac{\sqrt{2}}{2 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)-2 \cos \left(d x +c \right)\right) \sqrt{2}}{d \sqrt{2-2 \cos \left(d x +c \right)}\, \cos \left(d x +c \right)^{\frac{3}{2}} \left(\cos^{2}\left(d x +c \right)-1\right)}"," ",0,"1/d*sin(d*x+c)^3*(2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*arctanh(1/2*2^(1/2)/(cos(d*x+c)/(1+cos(d*x+c)))^(1/2))*cos(d*x+c)+2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*arctanh(1/2*2^(1/2)/(cos(d*x+c)/(1+cos(d*x+c)))^(1/2))-2*cos(d*x+c))/(2-2*cos(d*x+c))^(1/2)/cos(d*x+c)^(3/2)/(cos(d*x+c)^2-1)*2^(1/2)","B"
287,1,170,103,0.148000," ","int(1/(1-cos(d*x+c))^(1/2)/cos(d*x+c)^(5/2),x)","-\frac{\left(\sin^{5}\left(d x +c \right)\right) \left(3 \sqrt{2}\, \cos \left(d x +c \right) \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \arctanh \left(\frac{\sqrt{2}}{2 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)+3 \sqrt{2}\, \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \arctanh \left(\frac{\sqrt{2}}{2 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right)-2 \cos \left(d x +c \right)\right) \sqrt{2}}{3 d \left(-1+\cos \left(d x +c \right)\right)^{2} \sqrt{2-2 \cos \left(d x +c \right)}\, \left(1+\cos \left(d x +c \right)\right) \cos \left(d x +c \right)^{\frac{5}{2}}}"," ",0,"-1/3/d*sin(d*x+c)^5*(3*2^(1/2)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*arctanh(1/2*2^(1/2)/(cos(d*x+c)/(1+cos(d*x+c)))^(1/2))+3*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*arctanh(1/2*2^(1/2)/(cos(d*x+c)/(1+cos(d*x+c)))^(1/2))-2*cos(d*x+c))/(-1+cos(d*x+c))^2/(2-2*cos(d*x+c))^(1/2)/(1+cos(d*x+c))/cos(d*x+c)^(5/2)*2^(1/2)","A"
288,0,0,60,0.130000," ","int(cos(d*x+c)^(4/3)*(a+a*cos(d*x+c))^(1/3),x)","\int \left(\cos^{\frac{4}{3}}\left(d x +c \right)\right) \left(a +a \cos \left(d x +c \right)\right)^{\frac{1}{3}}\, dx"," ",0,"int(cos(d*x+c)^(4/3)*(a+a*cos(d*x+c))^(1/3),x)","F"
289,0,0,61,0.139000," ","int(cos(d*x+c)^(4/3)*(a+a*cos(d*x+c))^(2/3),x)","\int \left(\cos^{\frac{4}{3}}\left(d x +c \right)\right) \left(a +a \cos \left(d x +c \right)\right)^{\frac{2}{3}}\, dx"," ",0,"int(cos(d*x+c)^(4/3)*(a+a*cos(d*x+c))^(2/3),x)","F"
290,0,0,61,0.129000," ","int(cos(d*x+c)^(5/3)*(a+a*cos(d*x+c))^(2/3),x)","\int \left(\cos^{\frac{5}{3}}\left(d x +c \right)\right) \left(a +a \cos \left(d x +c \right)\right)^{\frac{2}{3}}\, dx"," ",0,"int(cos(d*x+c)^(5/3)*(a+a*cos(d*x+c))^(2/3),x)","F"
291,1,384,179,0.792000," ","int((a+a*cos(d*x+c))*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 \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"
292,1,369,159,0.981000," ","int((a+a*cos(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(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)+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*(-(-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)^4-4*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)*(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+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"
293,1,146,139,0.609000," ","int((a+a*cos(d*x+c))*sec(d*x+c)^(3/2),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"
294,1,150,119,0.513000," ","int((a+a*cos(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"
295,1,225,139,0.508000," ","int((a+a*cos(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 \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"
296,1,219,159,0.494000," ","int((a+a*cos(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(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"
297,1,270,179,0.546000," ","int((a+a*cos(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(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"
298,1,386,189,1.025000," ","int((a+a*cos(d*x+c))^2*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^{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"
299,1,371,167,0.984000," ","int((a+a*cos(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(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) \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*(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+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"
300,1,104,84,0.553000," ","int((a+a*cos(d*x+c))^2*sec(d*x+c)^(3/2),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"
301,1,228,145,0.466000," ","int((a+a*cos(d*x+c))^2*sec(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(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"
302,1,250,167,0.752000," ","int((a+a*cos(d*x+c))^2/sec(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(-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"
303,1,272,189,0.597000," ","int((a+a*cos(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(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"
304,1,439,211,1.051000," ","int((a+a*cos(d*x+c))^3*sec(d*x+c)^(9/2),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"
305,1,386,189,0.951000," ","int((a+a*cos(d*x+c))^3*sec(d*x+c)^(7/2),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"
306,1,371,167,0.877000," ","int((a+a*cos(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(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) \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*(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+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"
307,1,172,167,0.755000," ","int((a+a*cos(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"
308,1,250,167,0.556000," ","int((a+a*cos(d*x+c))^3*sec(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^{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"
309,1,272,189,0.707000," ","int((a+a*cos(d*x+c))^3/sec(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^{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"
310,1,260,211,0.602000," ","int((a+a*cos(d*x+c))^3/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^{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"
311,1,439,211,1.022000," ","int((a+a*cos(d*x+c))^4*sec(d*x+c)^(9/2),x)","-\frac{32 \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(\frac{253 \sqrt{\frac{1}{2}-\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)}{420 \sqrt{-2 \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{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{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)}}{896 \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)}}{672 \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,"-32*(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^4*(253/420*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+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))-1/80*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)^3-4/5*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)-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)))-1/896*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)^4-47/672*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"
312,1,386,189,1.081000," ","int((a+a*cos(d*x+c))^4*sec(d*x+c)^(7/2),x)","-\frac{32 \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(-\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{41 \sqrt{\frac{1}{2}-\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)}{60 \sqrt{-2 \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)}}{320 \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}-\frac{33 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)}{40 \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)}}{24 \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,"-32*(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^4*(-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)))+41/60*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+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))-1/320*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)^3-33/40*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)-1/24*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"
313,1,292,128,0.825000," ","int((a+a*cos(d*x+c))^4*sec(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^{4} \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 \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)-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*(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^4/(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*(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)^2-14*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"
314,1,194,189,0.680000," ","int((a+a*cos(d*x+c))^4*sec(d*x+c)^(3/2),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"
315,1,272,189,0.539000," ","int((a+a*cos(d*x+c))^4*sec(d*x+c)^(1/2),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"
316,1,260,211,0.582000," ","int((a+a*cos(d*x+c))^4/sec(d*x+c)^(1/2),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"
317,1,413,198,0.898000," ","int(sec(d*x+c)^(5/2)/(a+a*cos(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}}\, \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) \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}}\, \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) \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}}\, \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) \cos \left(\frac{d x}{2}+\frac{c}{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) \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 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sin \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) \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/cos(1/2*d*x+1/2*c)/sin(1/2*d*x+1/2*c)^3/(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)*(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))*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)*(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))*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)*(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))*cos(1/2*d*x+1/2*c)+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))*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"
318,1,253,176,0.657000," ","int(sec(d*x+c)^(3/2)/(a+a*cos(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"
319,1,200,152,0.519000," ","int(sec(d*x+c)^(1/2)/(a+a*cos(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)-\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)*(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))-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"
320,1,198,152,0.605000," ","int(1/(a+a*cos(d*x+c))/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(\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"
321,1,199,154,0.529000," ","int(1/(a+a*cos(d*x+c))/sec(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(\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,"((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)/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"
322,1,215,176,0.831000," ","int(1/(a+a*cos(d*x+c))/sec(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(\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(9 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+5 \EllipticF \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)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(9*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+5*EllipticF(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"
323,1,229,198,0.589000," ","int(1/(a+a*cos(d*x+c))/sec(d*x+c)^(7/2),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(-\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(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)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(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"
324,1,413,230,0.992000," ","int(sec(d*x+c)^(5/2)/(a+a*cos(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"
325,1,405,208,0.746000," ","int(sec(d*x+c)^(3/2)/(a+a*cos(d*x+c))^2,x)","-\frac{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)}\, \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^{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)}\, \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)^2-1)^(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)*(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)^2-1)^(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)*(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"
326,1,257,185,0.649000," ","int(sec(d*x+c)^(1/2)/(a+a*cos(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"
327,1,188,93,0.564000," ","int(1/(a+a*cos(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(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"
328,1,257,185,0.689000," ","int(1/(a+a*cos(d*x+c))^2/sec(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(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*((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)/a^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)^3/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
329,1,257,186,0.648000," ","int(1/(a+a*cos(d*x+c))^2/sec(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(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*((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)/a^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)^3/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
330,1,270,208,0.644000," ","int(1/(a+a*cos(d*x+c))^2/sec(d*x+c)^(7/2),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*((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)/a^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)^3/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
331,1,283,230,0.669000," ","int(1/(a+a*cos(d*x+c))^2/sec(d*x+c)^(9/2),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"
332,1,555,245,0.909000," ","int(sec(d*x+c)^(3/2)/(a+a*cos(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"
333,1,268,223,0.556000," ","int(sec(d*x+c)^(1/2)/(a+a*cos(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"
334,1,270,223,0.631000," ","int(1/(a+a*cos(d*x+c))^3/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(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"
335,1,270,223,0.639000," ","int(1/(a+a*cos(d*x+c))^3/sec(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(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"
336,1,270,223,0.657000," ","int(1/(a+a*cos(d*x+c))^3/sec(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(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"
337,1,270,223,0.891000," ","int(1/(a+a*cos(d*x+c))^3/sec(d*x+c)^(7/2),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(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"
338,1,283,245,0.778000," ","int(1/(a+a*cos(d*x+c))^3/sec(d*x+c)^(9/2),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(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"
339,1,82,129,0.225000," ","int(sec(d*x+c)^(9/2)*(a+a*cos(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) \cos \left(d x +c \right) \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{9}{2}} \sqrt{a \left(1+\cos \left(d x +c \right)\right)}}{35 d \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)*cos(d*x+c)*(1/cos(d*x+c))^(9/2)*(a*(1+cos(d*x+c)))^(1/2)/sin(d*x+c)","A"
340,1,72,97,0.212000," ","int(sec(d*x+c)^(7/2)*(a+a*cos(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) \cos \left(d x +c \right) \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{7}{2}} \sqrt{a \left(1+\cos \left(d x +c \right)\right)}}{15 d \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)*cos(d*x+c)*(1/cos(d*x+c))^(7/2)*(a*(1+cos(d*x+c)))^(1/2)/sin(d*x+c)","A"
341,1,62,65,0.197000," ","int(sec(d*x+c)^(5/2)*(a+a*cos(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) \cos \left(d x +c \right) \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \sqrt{a \left(1+\cos \left(d x +c \right)\right)}}{3 d \sin \left(d x +c \right)}"," ",0,"-2/3/d*(2*cos(d*x+c)^2-cos(d*x+c)-1)*cos(d*x+c)*(1/cos(d*x+c))^(5/2)*(a*(1+cos(d*x+c)))^(1/2)/sin(d*x+c)","A"
342,1,50,32,0.198000," ","int(sec(d*x+c)^(3/2)*(a+a*cos(d*x+c))^(1/2),x)","-\frac{2 \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}} \sqrt{a \left(1+\cos \left(d x +c \right)\right)}}{d \sin \left(d x +c \right)}"," ",0,"-2/d*(-1+cos(d*x+c))*cos(d*x+c)*(1/cos(d*x+c))^(3/2)*(a*(1+cos(d*x+c)))^(1/2)/sin(d*x+c)","A"
343,1,100,47,0.233000," ","int(sec(d*x+c)^(1/2)*(a+a*cos(d*x+c))^(1/2),x)","-\frac{2 \sqrt{\frac{1}{\cos \left(d x +c \right)}}\, \sqrt{a \left(1+\cos \left(d x +c \right)\right)}\, \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}{\cos \left(d x +c \right)}\right) \sqrt{\frac{\cos \left(d x +c \right)}{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,"-2/d*(1/cos(d*x+c))^(1/2)*(a*(1+cos(d*x+c)))^(1/2)*arctan(sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)/cos(d*x+c))*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)/sin(d*x+c)^2*(cos(d*x+c)^2-1)","B"
344,1,132,78,0.219000," ","int((a+a*cos(d*x+c))^(1/2)/sec(d*x+c)^(1/2),x)","\frac{\sqrt{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(\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\arctan \left(\frac{\sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}{\cos \left(d x +c \right)}\right)\right)}{d \sqrt{\frac{1}{\cos \left(d x +c \right)}}\, \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sin \left(d x +c \right)^{4}}"," ",0,"1/d*(a*(1+cos(d*x+c)))^(1/2)*cos(d*x+c)*(-1+cos(d*x+c))^2*((cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+arctan(sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)/cos(d*x+c)))/(1/cos(d*x+c))^(1/2)/(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)/sin(d*x+c)^4","A"
345,1,169,112,0.242000," ","int((a+a*cos(d*x+c))^(1/2)/sec(d*x+c)^(3/2),x)","-\frac{\sqrt{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)^{3} \left(2 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right) \sin \left(d x +c \right)+3 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+3 \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}{\cos \left(d x +c \right)}\right)\right)}{4 d \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \sin \left(d x +c \right)^{6}}"," ",0,"-1/4/d*(a*(1+cos(d*x+c)))^(1/2)*cos(d*x+c)*(-1+cos(d*x+c))^3*(2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)*sin(d*x+c)+3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+3*arctan(sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)/cos(d*x+c)))/(1/cos(d*x+c))^(3/2)/(cos(d*x+c)/(1+cos(d*x+c)))^(5/2)/sin(d*x+c)^6","A"
346,1,83,137,0.197000," ","int((a+a*cos(d*x+c))^(3/2)*sec(d*x+c)^(9/2),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) \cos \left(d x +c \right) \sqrt{a \left(1+\cos \left(d x +c \right)\right)}\, \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{9}{2}} a}{105 d \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)*cos(d*x+c)*(a*(1+cos(d*x+c)))^(1/2)*(1/cos(d*x+c))^(9/2)/sin(d*x+c)*a","A"
347,1,73,103,0.195000," ","int((a+a*cos(d*x+c))^(3/2)*sec(d*x+c)^(7/2),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) \cos \left(d x +c \right) \sqrt{a \left(1+\cos \left(d x +c \right)\right)}\, \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{7}{2}} a}{5 d \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)*cos(d*x+c)*(a*(1+cos(d*x+c)))^(1/2)*(1/cos(d*x+c))^(7/2)/sin(d*x+c)*a","A"
348,1,63,69,0.184000," ","int((a+a*cos(d*x+c))^(3/2)*sec(d*x+c)^(5/2),x)","-\frac{2 \left(5 \left(\cos^{2}\left(d x +c \right)\right)-4 \cos \left(d x +c \right)-1\right) \cos \left(d x +c \right) \sqrt{a \left(1+\cos \left(d x +c \right)\right)}\, \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{5}{2}} a}{3 d \sin \left(d x +c \right)}"," ",0,"-2/3/d*(5*cos(d*x+c)^2-4*cos(d*x+c)-1)*cos(d*x+c)*(a*(1+cos(d*x+c)))^(1/2)*(1/cos(d*x+c))^(5/2)/sin(d*x+c)*a","A"
349,1,168,82,0.216000," ","int((a+a*cos(d*x+c))^(3/2)*sec(d*x+c)^(3/2),x)","\frac{2 \left(\cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}{\cos \left(d x +c \right)}\right)+\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}{\cos \left(d x +c \right)}\right)+\sin \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{a \left(1+\cos \left(d x +c \right)\right)}\, a}{d \left(1+\cos \left(d x +c \right)\right)}"," ",0,"2/d*(cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)/cos(d*x+c))+(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)/cos(d*x+c))+sin(d*x+c))*cos(d*x+c)*(1/cos(d*x+c))^(3/2)*(a*(1+cos(d*x+c)))^(1/2)/(1+cos(d*x+c))*a","B"
350,1,130,81,0.221000," ","int((a+a*cos(d*x+c))^(3/2)*sec(d*x+c)^(1/2),x)","-\frac{\left(\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+3 \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}{\cos \left(d x +c \right)}\right)\right) \sqrt{\frac{1}{\cos \left(d x +c \right)}}\, \sqrt{a \left(1+\cos \left(d x +c \right)\right)}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)-1\right) a}{d \sin \left(d x +c \right)^{2}}"," ",0,"-1/d*((cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+3*arctan(sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)/cos(d*x+c)))*(1/cos(d*x+c))^(1/2)*(a*(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)/sin(d*x+c)^2*(cos(d*x+c)^2-1)*a","A"
351,1,170,116,0.237000," ","int((a+a*cos(d*x+c))^(3/2)/sec(d*x+c)^(1/2),x)","\frac{\left(-1+\cos \left(d x +c \right)\right)^{2} \left(2 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right) \sin \left(d x +c \right)+7 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+7 \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}{\cos \left(d x +c \right)}\right)\right) \cos \left(d x +c \right) \sqrt{a \left(1+\cos \left(d x +c \right)\right)}\, a}{4 d \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sqrt{\frac{1}{\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)^{4}}"," ",0,"1/4/d*(-1+cos(d*x+c))^2*(2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)*sin(d*x+c)+7*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+7*arctan(sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)/cos(d*x+c)))*cos(d*x+c)*(a*(1+cos(d*x+c)))^(1/2)/(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)/(1/cos(d*x+c))^(1/2)/sin(d*x+c)^4*a","A"
352,1,205,150,0.257000," ","int((a+a*cos(d*x+c))^(3/2)/sec(d*x+c)^(3/2),x)","-\frac{\left(-1+\cos \left(d x +c \right)\right)^{3} \left(8 \sqrt{\frac{\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)+22 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right) \sin \left(d x +c \right)+33 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+33 \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}{\cos \left(d x +c \right)}\right)\right) \cos \left(d x +c \right) \sqrt{a \left(1+\cos \left(d x +c \right)\right)}\, a}{24 d \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sin \left(d x +c \right)^{6}}"," ",0,"-1/24/d*(-1+cos(d*x+c))^3*(8*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2*sin(d*x+c)+22*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)*sin(d*x+c)+33*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+33*arctan(sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)/cos(d*x+c)))*cos(d*x+c)*(a*(1+cos(d*x+c)))^(1/2)/(cos(d*x+c)/(1+cos(d*x+c)))^(5/2)/(1/cos(d*x+c))^(3/2)/sin(d*x+c)^6*a","A"
353,1,95,171,0.207000," ","int((a+a*cos(d*x+c))^(5/2)*sec(d*x+c)^(11/2),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) \cos \left(d x +c \right) \sqrt{a \left(1+\cos \left(d x +c \right)\right)}\, \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{11}{2}} a^{2}}{315 d \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)*cos(d*x+c)*(a*(1+cos(d*x+c)))^(1/2)*(1/cos(d*x+c))^(11/2)/sin(d*x+c)*a^2","A"
354,1,85,137,0.199000," ","int((a+a*cos(d*x+c))^(5/2)*sec(d*x+c)^(9/2),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) \cos \left(d x +c \right) \sqrt{a \left(1+\cos \left(d x +c \right)\right)}\, \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{9}{2}} a^{2}}{21 d \sin \left(d x +c \right)}"," ",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)*cos(d*x+c)*(a*(1+cos(d*x+c)))^(1/2)*(1/cos(d*x+c))^(9/2)/sin(d*x+c)*a^2","A"
355,1,75,103,0.187000," ","int((a+a*cos(d*x+c))^(5/2)*sec(d*x+c)^(7/2),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) \cos \left(d x +c \right) \sqrt{a \left(1+\cos \left(d x +c \right)\right)}\, \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{7}{2}} a^{2}}{15 d \sin \left(d x +c \right)}"," ",0,"-2/15/d*(43*cos(d*x+c)^3-29*cos(d*x+c)^2-11*cos(d*x+c)-3)*cos(d*x+c)*(a*(1+cos(d*x+c)))^(1/2)*(1/cos(d*x+c))^(7/2)/sin(d*x+c)*a^2","A"
356,1,268,116,0.224000," ","int((a+a*cos(d*x+c))^(5/2)*sec(d*x+c)^(5/2),x)","-\frac{2 \left(3 \left(\cos^{2}\left(d x +c \right)\right) \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}{\cos \left(d x +c \right)}\right)+6 \cos \left(d x +c \right) \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}{\cos \left(d x +c \right)}\right)+3 \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}{\cos \left(d x +c \right)}\right)+8 \cos \left(d x +c \right) \sin \left(d x +c \right)+\sin \left(d x +c \right)\right) \cos \left(d x +c \right) \left(\sin^{2}\left(d x +c \right)\right) \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \sqrt{a \left(1+\cos \left(d x +c \right)\right)}\, a^{2}}{3 d \left(-1+\cos \left(d x +c \right)\right) \left(1+\cos \left(d x +c \right)\right)^{2}}"," ",0,"-2/3/d*(3*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*arctan(sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)/cos(d*x+c))+6*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*arctan(sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)/cos(d*x+c))+3*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*arctan(sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)/cos(d*x+c))+8*cos(d*x+c)*sin(d*x+c)+sin(d*x+c))*cos(d*x+c)*sin(d*x+c)^2*(1/cos(d*x+c))^(5/2)*(a*(1+cos(d*x+c)))^(1/2)/(-1+cos(d*x+c))/(1+cos(d*x+c))^2*a^2","B"
357,1,186,116,0.224000," ","int((a+a*cos(d*x+c))^(5/2)*sec(d*x+c)^(3/2),x)","\frac{\left(5 \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}{\cos \left(d x +c \right)}\right)+\cos \left(d x +c \right) \sin \left(d x +c \right)+5 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}{\cos \left(d x +c \right)}\right)+2 \sin \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{a \left(1+\cos \left(d x +c \right)\right)}\, a^{2}}{d \left(1+\cos \left(d x +c \right)\right)}"," ",0,"1/d*(5*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)/cos(d*x+c))+cos(d*x+c)*sin(d*x+c)+5*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)/cos(d*x+c))+2*sin(d*x+c))*cos(d*x+c)*(1/cos(d*x+c))^(3/2)*(a*(1+cos(d*x+c)))^(1/2)/(1+cos(d*x+c))*a^2","A"
358,1,166,116,0.241000," ","int((a+a*cos(d*x+c))^(5/2)*sec(d*x+c)^(1/2),x)","-\frac{\left(2 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right) \sin \left(d x +c \right)+11 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+19 \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}{\cos \left(d x +c \right)}\right)\right) \sqrt{a \left(1+\cos \left(d x +c \right)\right)}\, \sqrt{\frac{1}{\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)-1\right) a^{2}}{4 d \sin \left(d x +c \right)^{2}}"," ",0,"-1/4/d*(2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)*sin(d*x+c)+11*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+19*arctan(sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)/cos(d*x+c)))*(a*(1+cos(d*x+c)))^(1/2)*(1/cos(d*x+c))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)/sin(d*x+c)^2*(cos(d*x+c)^2-1)*a^2","A"
359,1,207,150,0.253000," ","int((a+a*cos(d*x+c))^(5/2)/sec(d*x+c)^(1/2),x)","\frac{\left(-1+\cos \left(d x +c \right)\right)^{2} \left(8 \sqrt{\frac{\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)+34 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right) \sin \left(d x +c \right)+75 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+75 \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}{\cos \left(d x +c \right)}\right)\right) \cos \left(d x +c \right) \sqrt{a \left(1+\cos \left(d x +c \right)\right)}\, a^{2}}{24 d \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sqrt{\frac{1}{\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)^{4}}"," ",0,"1/24/d*(-1+cos(d*x+c))^2*(8*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2*sin(d*x+c)+34*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)*sin(d*x+c)+75*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+75*arctan(sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)/cos(d*x+c)))*cos(d*x+c)*(a*(1+cos(d*x+c)))^(1/2)/(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)/(1/cos(d*x+c))^(1/2)/sin(d*x+c)^4*a^2","A"
360,1,242,184,0.268000," ","int((a+a*cos(d*x+c))^(5/2)/sec(d*x+c)^(3/2),x)","-\frac{\left(-1+\cos \left(d x +c \right)\right)^{3} \left(48 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+184 \sqrt{\frac{\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)+326 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right) \sin \left(d x +c \right)+489 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+489 \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}{\cos \left(d x +c \right)}\right)\right) \cos \left(d x +c \right) \sqrt{a \left(1+\cos \left(d x +c \right)\right)}\, a^{2}}{192 d \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sin \left(d x +c \right)^{6}}"," ",0,"-1/192/d*(-1+cos(d*x+c))^3*(48*cos(d*x+c)^3*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+184*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2*sin(d*x+c)+326*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)*sin(d*x+c)+489*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+489*arctan(sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)/cos(d*x+c)))*cos(d*x+c)*(a*(1+cos(d*x+c)))^(1/2)/(cos(d*x+c)/(1+cos(d*x+c)))^(5/2)/(1/cos(d*x+c))^(3/2)/sin(d*x+c)^6*a^2","A"
361,1,294,130,0.224000," ","int(sec(d*x+c)^(7/2)/(1+cos(d*x+c))^(1/2),x)","\frac{\left(15 \sqrt{2}\, \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \left(\cos^{3}\left(d x +c \right)\right) \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}}+45 \sqrt{2}\, \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \left(\cos^{2}\left(d x +c \right)\right) \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}}+45 \sqrt{2}\, \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \cos \left(d x +c \right) \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}}+15 \sqrt{2}\, \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}}+26 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)-2 \cos \left(d x +c \right) \sin \left(d x +c \right)+6 \sin \left(d x +c \right)\right) \cos \left(d x +c \right) \sqrt{2+2 \cos \left(d x +c \right)}\, \left(\sin^{4}\left(d x +c \right)\right) \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{7}{2}} \sqrt{2}}{30 d \left(-1+\cos \left(d x +c \right)\right)^{2} \left(1+\cos \left(d x +c \right)\right)^{3}}"," ",0,"1/30/d*(15*2^(1/2)*arcsin((-1+cos(d*x+c))/sin(d*x+c))*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(5/2)+45*2^(1/2)*arcsin((-1+cos(d*x+c))/sin(d*x+c))*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(5/2)+45*2^(1/2)*arcsin((-1+cos(d*x+c))/sin(d*x+c))*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(5/2)+15*2^(1/2)*arcsin((-1+cos(d*x+c))/sin(d*x+c))*(cos(d*x+c)/(1+cos(d*x+c)))^(5/2)+26*cos(d*x+c)^2*sin(d*x+c)-2*cos(d*x+c)*sin(d*x+c)+6*sin(d*x+c))*cos(d*x+c)*(2+2*cos(d*x+c))^(1/2)*sin(d*x+c)^4*(1/cos(d*x+c))^(7/2)/(-1+cos(d*x+c))^2/(1+cos(d*x+c))^3*2^(1/2)","B"
362,1,228,100,0.216000," ","int(sec(d*x+c)^(5/2)/(1+cos(d*x+c))^(1/2),x)","\frac{\left(3 \sqrt{2}\, \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \left(\cos^{2}\left(d x +c \right)\right) \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}}+6 \sqrt{2}\, \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \cos \left(d x +c \right) \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}}+3 \sqrt{2}\, \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}}+2 \cos \left(d x +c \right) \sin \left(d x +c \right)-2 \sin \left(d x +c \right)\right) \cos \left(d x +c \right) \sqrt{2+2 \cos \left(d x +c \right)}\, \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \left(\sin^{2}\left(d x +c \right)\right) \sqrt{2}}{6 d \left(-1+\cos \left(d x +c \right)\right) \left(1+\cos \left(d x +c \right)\right)^{2}}"," ",0,"1/6/d*(3*2^(1/2)*arcsin((-1+cos(d*x+c))/sin(d*x+c))*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)+6*2^(1/2)*arcsin((-1+cos(d*x+c))/sin(d*x+c))*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)+3*2^(1/2)*arcsin((-1+cos(d*x+c))/sin(d*x+c))*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)+2*cos(d*x+c)*sin(d*x+c)-2*sin(d*x+c))*cos(d*x+c)*(2+2*cos(d*x+c))^(1/2)*(1/cos(d*x+c))^(5/2)*sin(d*x+c)^2/(-1+cos(d*x+c))/(1+cos(d*x+c))^2*2^(1/2)","B"
363,1,144,72,0.180000," ","int(sec(d*x+c)^(3/2)/(1+cos(d*x+c))^(1/2),x)","\frac{\left(\arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \sqrt{2}\, \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+\arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+2 \sin \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{2+2 \cos \left(d x +c \right)}\, \sqrt{2}}{2 d \left(1+\cos \left(d x +c \right)\right)}"," ",0,"1/2/d*(arcsin((-1+cos(d*x+c))/sin(d*x+c))*2^(1/2)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+arcsin((-1+cos(d*x+c))/sin(d*x+c))*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+2*sin(d*x+c))*cos(d*x+c)*(1/cos(d*x+c))^(3/2)*(2+2*cos(d*x+c))^(1/2)/(1+cos(d*x+c))*2^(1/2)","A"
364,1,82,41,0.186000," ","int(sec(d*x+c)^(1/2)/(1+cos(d*x+c))^(1/2),x)","\frac{\sqrt{\frac{1}{\cos \left(d x +c \right)}}\, \sqrt{2+2 \cos \left(d x +c \right)}\, \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \sqrt{\frac{\cos \left(d x +c \right)}{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)*(2+2*cos(d*x+c))^(1/2)*arcsin((-1+cos(d*x+c))/sin(d*x+c))*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)/sin(d*x+c)^2*(cos(d*x+c)^2-1)","A"
365,1,134,82,0.207000," ","int(1/sec(d*x+c)^(1/2)/(1+cos(d*x+c))^(1/2),x)","\frac{\sqrt{2+2 \cos \left(d x +c \right)}\, \cos \left(d x +c \right) \left(-1+\cos \left(d x +c \right)\right)^{2} \left(\sqrt{2}\, \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)+2 \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}{\cos \left(d x +c \right)}\right)\right) \sqrt{2}}{2 d \sqrt{\frac{1}{\cos \left(d x +c \right)}}\, \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sin \left(d x +c \right)^{4}}"," ",0,"1/2/d*(2+2*cos(d*x+c))^(1/2)*cos(d*x+c)*(-1+cos(d*x+c))^2*(2^(1/2)*arcsin((-1+cos(d*x+c))/sin(d*x+c))+2*arctan(sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)/cos(d*x+c)))/(1/cos(d*x+c))^(1/2)/(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)/sin(d*x+c)^4*2^(1/2)","A"
366,1,159,109,0.220000," ","int(1/sec(d*x+c)^(3/2)/(1+cos(d*x+c))^(1/2),x)","\frac{\sqrt{2+2 \cos \left(d x +c \right)}\, \cos \left(d x +c \right) \left(-1+\cos \left(d x +c \right)\right)^{3} \left(\sqrt{2}\, \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)-\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\arctan \left(\frac{\sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}{\cos \left(d x +c \right)}\right)\right) \sqrt{2}}{2 d \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \sin \left(d x +c \right)^{6}}"," ",0,"1/2/d*(2+2*cos(d*x+c))^(1/2)*cos(d*x+c)*(-1+cos(d*x+c))^3*(2^(1/2)*arcsin((-1+cos(d*x+c))/sin(d*x+c))-(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+arctan(sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)/cos(d*x+c)))/(1/cos(d*x+c))^(3/2)/(cos(d*x+c)/(1+cos(d*x+c)))^(5/2)/sin(d*x+c)^6*2^(1/2)","A"
367,1,294,156,0.250000," ","int(sec(d*x+c)^(7/2)/(a+a*cos(d*x+c))^(1/2),x)","\frac{\left(15 \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \left(\cos^{3}\left(d x +c \right)\right) \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}}+45 \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \left(\cos^{2}\left(d x +c \right)\right) \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}}+45 \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \cos \left(d x +c \right) \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}}+15 \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}}+13 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{2}-\sqrt{2}\, \cos \left(d x +c \right) \sin \left(d x +c \right)+3 \sin \left(d x +c \right) \sqrt{2}\right) \cos \left(d x +c \right) \left(\sin^{4}\left(d x +c \right)\right) \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{7}{2}} \sqrt{a \left(1+\cos \left(d x +c \right)\right)}\, \sqrt{2}}{15 d \left(-1+\cos \left(d x +c \right)\right)^{2} \left(1+\cos \left(d x +c \right)\right)^{3} a}"," ",0,"1/15/d*(15*arcsin((-1+cos(d*x+c))/sin(d*x+c))*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(5/2)+45*arcsin((-1+cos(d*x+c))/sin(d*x+c))*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(5/2)+45*arcsin((-1+cos(d*x+c))/sin(d*x+c))*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(5/2)+15*arcsin((-1+cos(d*x+c))/sin(d*x+c))*(cos(d*x+c)/(1+cos(d*x+c)))^(5/2)+13*cos(d*x+c)^2*sin(d*x+c)*2^(1/2)-2^(1/2)*cos(d*x+c)*sin(d*x+c)+3*sin(d*x+c)*2^(1/2))*cos(d*x+c)*sin(d*x+c)^4*(1/cos(d*x+c))^(7/2)*(a*(1+cos(d*x+c)))^(1/2)/(-1+cos(d*x+c))^2/(1+cos(d*x+c))^3*2^(1/2)/a","A"
368,1,227,124,0.228000," ","int(sec(d*x+c)^(5/2)/(a+a*cos(d*x+c))^(1/2),x)","\frac{\left(3 \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \left(\cos^{2}\left(d x +c \right)\right) \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}}+6 \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \cos \left(d x +c \right) \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}}+3 \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}}+\sqrt{2}\, \cos \left(d x +c \right) \sin \left(d x +c \right)-\sin \left(d x +c \right) \sqrt{2}\right) \cos \left(d x +c \right) \left(\sin^{2}\left(d x +c \right)\right) \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \sqrt{a \left(1+\cos \left(d x +c \right)\right)}\, \sqrt{2}}{3 d \left(-1+\cos \left(d x +c \right)\right) \left(1+\cos \left(d x +c \right)\right)^{2} a}"," ",0,"1/3/d*(3*arcsin((-1+cos(d*x+c))/sin(d*x+c))*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)+6*arcsin((-1+cos(d*x+c))/sin(d*x+c))*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)+3*arcsin((-1+cos(d*x+c))/sin(d*x+c))*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)+2^(1/2)*cos(d*x+c)*sin(d*x+c)-sin(d*x+c)*2^(1/2))*cos(d*x+c)*sin(d*x+c)^2*(1/cos(d*x+c))^(5/2)*(a*(1+cos(d*x+c)))^(1/2)/(-1+cos(d*x+c))/(1+cos(d*x+c))^2*2^(1/2)/a","A"
369,1,142,94,0.213000," ","int(sec(d*x+c)^(3/2)/(a+a*cos(d*x+c))^(1/2),x)","\frac{\left(\cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)+\sin \left(d x +c \right) \sqrt{2}+\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)\right) \cos \left(d x +c \right) \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sqrt{a \left(1+\cos \left(d x +c \right)\right)}\, \sqrt{2}}{d \left(1+\cos \left(d x +c \right)\right) a}"," ",0,"1/d*(cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arcsin((-1+cos(d*x+c))/sin(d*x+c))+sin(d*x+c)*2^(1/2)+(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arcsin((-1+cos(d*x+c))/sin(d*x+c)))*cos(d*x+c)*(1/cos(d*x+c))^(3/2)*(a*(1+cos(d*x+c)))^(1/2)/(1+cos(d*x+c))*2^(1/2)/a","A"
370,1,88,45,0.209000," ","int(sec(d*x+c)^(1/2)/(a+a*cos(d*x+c))^(1/2),x)","\frac{\sqrt{\frac{1}{\cos \left(d x +c \right)}}\, \sqrt{a \left(1+\cos \left(d x +c \right)\right)}\, \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)-1\right) \sqrt{2}}{d \sin \left(d x +c \right)^{2} a}"," ",0,"1/d*(1/cos(d*x+c))^(1/2)*(a*(1+cos(d*x+c)))^(1/2)*arcsin((-1+cos(d*x+c))/sin(d*x+c))*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)/sin(d*x+c)^2*(cos(d*x+c)^2-1)*2^(1/2)/a","A"
371,1,134,86,0.218000," ","int(1/sec(d*x+c)^(1/2)/(a+a*cos(d*x+c))^(1/2),x)","\frac{\sqrt{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(\sqrt{2}\, \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}{\cos \left(d x +c \right)}\right)+\arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)\right) \sqrt{2}}{d \sqrt{\frac{1}{\cos \left(d x +c \right)}}\, \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sin \left(d x +c \right)^{4} a}"," ",0,"1/d*(a*(1+cos(d*x+c)))^(1/2)*cos(d*x+c)*(-1+cos(d*x+c))^2*(2^(1/2)*arctan(sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)/cos(d*x+c))+arcsin((-1+cos(d*x+c))/sin(d*x+c)))/(1/cos(d*x+c))^(1/2)/(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)/sin(d*x+c)^4*2^(1/2)/a","A"
372,1,167,139,0.224000," ","int(1/sec(d*x+c)^(3/2)/(a+a*cos(d*x+c))^(1/2),x)","\frac{\sqrt{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)^{3} \left(-\sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\sqrt{2}\, \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}{\cos \left(d x +c \right)}\right)+2 \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)\right) \sqrt{2}}{2 d \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \sin \left(d x +c \right)^{6} a}"," ",0,"1/2/d*(a*(1+cos(d*x+c)))^(1/2)*cos(d*x+c)*(-1+cos(d*x+c))^3*(-2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+2^(1/2)*arctan(sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)/cos(d*x+c))+2*arcsin((-1+cos(d*x+c))/sin(d*x+c)))/(1/cos(d*x+c))^(3/2)/(cos(d*x+c)/(1+cos(d*x+c)))^(5/2)/sin(d*x+c)^6*2^(1/2)/a","A"
373,1,258,162,0.215000," ","int(sec(d*x+c)^(5/2)/(a+a*cos(d*x+c))^(3/2),x)","\frac{\left(33 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}}+66 \cos \left(d x +c \right) \sin \left(d x +c \right) \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}}+33 \sin \left(d x +c \right) \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}}-19 \left(\cos^{3}\left(d x +c \right)\right) \sqrt{2}+7 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}+16 \cos \left(d x +c \right) \sqrt{2}-4 \sqrt{2}\right) \cos \left(d x +c \right) \sin \left(d x +c \right) \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \sqrt{a \left(1+\cos \left(d x +c \right)\right)}\, \sqrt{2}}{12 d \left(-1+\cos \left(d x +c \right)\right) \left(1+\cos \left(d x +c \right)\right)^{2} a^{2}}"," ",0,"1/12/d*(33*cos(d*x+c)^2*sin(d*x+c)*arcsin((-1+cos(d*x+c))/sin(d*x+c))*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)+66*cos(d*x+c)*sin(d*x+c)*arcsin((-1+cos(d*x+c))/sin(d*x+c))*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)+33*sin(d*x+c)*arcsin((-1+cos(d*x+c))/sin(d*x+c))*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)-19*cos(d*x+c)^3*2^(1/2)+7*cos(d*x+c)^2*2^(1/2)+16*cos(d*x+c)*2^(1/2)-4*2^(1/2))*cos(d*x+c)*sin(d*x+c)*(1/cos(d*x+c))^(5/2)*(a*(1+cos(d*x+c)))^(1/2)/(-1+cos(d*x+c))/(1+cos(d*x+c))^2*2^(1/2)/a^2","A"
374,1,184,128,0.202000," ","int(sec(d*x+c)^(3/2)/(a+a*cos(d*x+c))^(3/2),x)","-\frac{\left(-7 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \sin \left(d x +c \right) \cos \left(d x +c \right)+5 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}-7 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \sin \left(d x +c \right)-\cos \left(d x +c \right) \sqrt{2}-4 \sqrt{2}\right) \cos \left(d x +c \right) \sqrt{a \left(1+\cos \left(d x +c \right)\right)}\, \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sqrt{2}}{4 d \sin \left(d x +c \right) \left(1+\cos \left(d x +c \right)\right) a^{2}}"," ",0,"-1/4/d*(-7*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arcsin((-1+cos(d*x+c))/sin(d*x+c))*sin(d*x+c)*cos(d*x+c)+5*cos(d*x+c)^2*2^(1/2)-7*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arcsin((-1+cos(d*x+c))/sin(d*x+c))*sin(d*x+c)-cos(d*x+c)*2^(1/2)-4*2^(1/2))*cos(d*x+c)*(a*(1+cos(d*x+c)))^(1/2)*(1/cos(d*x+c))^(3/2)/sin(d*x+c)/(1+cos(d*x+c))*2^(1/2)/a^2","A"
375,1,151,94,0.204000," ","int(sec(d*x+c)^(1/2)/(a+a*cos(d*x+c))^(3/2),x)","-\frac{\sqrt{\frac{1}{\cos \left(d x +c \right)}}\, \sqrt{a \left(1+\cos \left(d x +c \right)\right)}\, \left(\cos \left(d x +c \right) \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}-3 \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \sin \left(d x +c \right)-\sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)-1\right) \sqrt{2}}{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)))^(1/2)*(cos(d*x+c)*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)-3*arcsin((-1+cos(d*x+c))/sin(d*x+c))*sin(d*x+c)-2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2))*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)/sin(d*x+c)^3*(cos(d*x+c)^2-1)*2^(1/2)/a^2","A"
376,1,156,94,0.207000," ","int(1/(a+a*cos(d*x+c))^(3/2)/sec(d*x+c)^(1/2),x)","-\frac{\sqrt{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(\cos \left(d x +c \right) \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}-\sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+\arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \sin \left(d x +c \right)\right) \sqrt{2}}{4 d \sqrt{\frac{1}{\cos \left(d x +c \right)}}\, \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sin \left(d x +c \right)^{5} a^{2}}"," ",0,"-1/4/d*(a*(1+cos(d*x+c)))^(1/2)*cos(d*x+c)*(-1+cos(d*x+c))^2*(cos(d*x+c)*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)-2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+arcsin((-1+cos(d*x+c))/sin(d*x+c))*sin(d*x+c))/(1/cos(d*x+c))^(1/2)/(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)/sin(d*x+c)^5*2^(1/2)/a^2","A"
377,1,203,141,0.209000," ","int(1/(a+a*cos(d*x+c))^(3/2)/sec(d*x+c)^(3/2),x)","-\frac{\sqrt{a \left(1+\cos \left(d x +c \right)\right)}\, \left(-1+\cos \left(d x +c \right)\right)^{3} \cos \left(d x +c \right) \left(4 \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}{\cos \left(d x +c \right)}\right) \sqrt{2}\, \sin \left(d x +c \right)+\cos \left(d x +c \right) \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+5 \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \sin \left(d x +c \right)-\sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\right) \sqrt{2}}{4 d \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \sin \left(d x +c \right)^{7} a^{2}}"," ",0,"-1/4/d*(a*(1+cos(d*x+c)))^(1/2)*(-1+cos(d*x+c))^3*cos(d*x+c)*(4*arctan(sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)/cos(d*x+c))*2^(1/2)*sin(d*x+c)+cos(d*x+c)*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+5*arcsin((-1+cos(d*x+c))/sin(d*x+c))*sin(d*x+c)-2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2))/(1/cos(d*x+c))^(3/2)/(cos(d*x+c)/(1+cos(d*x+c)))^(5/2)/sin(d*x+c)^7*2^(1/2)/a^2","A"
378,1,235,175,0.218000," ","int(1/(a+a*cos(d*x+c))^(3/2)/sec(d*x+c)^(5/2),x)","-\frac{\sqrt{a \left(1+\cos \left(d x +c \right)\right)}\, \left(-1+\cos \left(d x +c \right)\right)^{4} \cos \left(d x +c \right) \left(2 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+\cos \left(d x +c \right) \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+6 \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}{\cos \left(d x +c \right)}\right) \sqrt{2}\, \sin \left(d x +c \right)+9 \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \sin \left(d x +c \right)-3 \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\right) \sqrt{2}}{4 d \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{7}{2}} \sin \left(d x +c \right)^{9} a^{2}}"," ",0,"-1/4/d*(a*(1+cos(d*x+c)))^(1/2)*(-1+cos(d*x+c))^4*cos(d*x+c)*(2*cos(d*x+c)^2*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+cos(d*x+c)*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+6*arctan(sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)/cos(d*x+c))*2^(1/2)*sin(d*x+c)+9*arcsin((-1+cos(d*x+c))/sin(d*x+c))*sin(d*x+c)-3*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2))/(1/cos(d*x+c))^(5/2)/(cos(d*x+c)/(1+cos(d*x+c)))^(7/2)/sin(d*x+c)^9*2^(1/2)/a^2","A"
379,1,316,196,0.236000," ","int(sec(d*x+c)^(5/2)/(a+a*cos(d*x+c))^(5/2),x)","-\frac{\left(489 \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)+1467 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}}+1467 \cos \left(d x +c \right) \sin \left(d x +c \right) \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}}+489 \sin \left(d x +c \right) \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}}-299 \left(\cos^{4}\left(d x +c \right)\right) \sqrt{2}-204 \left(\cos^{3}\left(d x +c \right)\right) \sqrt{2}+343 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}+192 \cos \left(d x +c \right) \sqrt{2}-32 \sqrt{2}\right) \cos \left(d x +c \right) \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \sqrt{a \left(1+\cos \left(d x +c \right)\right)}\, \sqrt{2}}{96 d \sin \left(d x +c \right) \left(1+\cos \left(d x +c \right)\right)^{2} a^{3}}"," ",0,"-1/96/d*(489*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*arcsin((-1+cos(d*x+c))/sin(d*x+c))*cos(d*x+c)^3*sin(d*x+c)+1467*cos(d*x+c)^2*sin(d*x+c)*arcsin((-1+cos(d*x+c))/sin(d*x+c))*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)+1467*cos(d*x+c)*sin(d*x+c)*arcsin((-1+cos(d*x+c))/sin(d*x+c))*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)+489*sin(d*x+c)*arcsin((-1+cos(d*x+c))/sin(d*x+c))*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)-299*cos(d*x+c)^4*2^(1/2)-204*cos(d*x+c)^3*2^(1/2)+343*cos(d*x+c)^2*2^(1/2)+192*cos(d*x+c)*2^(1/2)-32*2^(1/2))*cos(d*x+c)*(1/cos(d*x+c))^(5/2)*(a*(1+cos(d*x+c)))^(1/2)/sin(d*x+c)/(1+cos(d*x+c))^2*2^(1/2)/a^3","A"
380,1,258,162,0.224000," ","int(sec(d*x+c)^(3/2)/(a+a*cos(d*x+c))^(5/2),x)","-\frac{\left(-1+\cos \left(d x +c \right)\right) \left(75 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+150 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \sin \left(d x +c \right) \cos \left(d x +c \right)-49 \left(\cos^{3}\left(d x +c \right)\right) \sqrt{2}+75 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \sin \left(d x +c \right)-36 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}+53 \cos \left(d x +c \right) \sqrt{2}+32 \sqrt{2}\right) \cos \left(d x +c \right) \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sqrt{a \left(1+\cos \left(d x +c \right)\right)}\, \sqrt{2}}{32 d \sin \left(d x +c \right)^{3} \left(1+\cos \left(d x +c \right)\right) a^{3}}"," ",0,"-1/32/d*(-1+cos(d*x+c))*(75*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arcsin((-1+cos(d*x+c))/sin(d*x+c))*cos(d*x+c)^2*sin(d*x+c)+150*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arcsin((-1+cos(d*x+c))/sin(d*x+c))*sin(d*x+c)*cos(d*x+c)-49*cos(d*x+c)^3*2^(1/2)+75*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arcsin((-1+cos(d*x+c))/sin(d*x+c))*sin(d*x+c)-36*cos(d*x+c)^2*2^(1/2)+53*cos(d*x+c)*2^(1/2)+32*2^(1/2))*cos(d*x+c)*(1/cos(d*x+c))^(3/2)*(a*(1+cos(d*x+c)))^(1/2)/sin(d*x+c)^3/(1+cos(d*x+c))*2^(1/2)/a^3","A"
381,1,222,128,0.209000," ","int(sec(d*x+c)^(1/2)/(a+a*cos(d*x+c))^(5/2),x)","\frac{\sqrt{\frac{1}{\cos \left(d x +c \right)}}\, \sqrt{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(9 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}-19 \cos \left(d x +c \right) \sin \left(d x +c \right) \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)+4 \cos \left(d x +c \right) \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}-19 \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \sin \left(d x +c \right)-13 \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\right) \sqrt{2}}{32 d \sin \left(d x +c \right)^{5} \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, a^{3}}"," ",0,"1/32/d*(1/cos(d*x+c))^(1/2)*(a*(1+cos(d*x+c)))^(1/2)*cos(d*x+c)*(-1+cos(d*x+c))^2*(9*cos(d*x+c)^2*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)-19*cos(d*x+c)*sin(d*x+c)*arcsin((-1+cos(d*x+c))/sin(d*x+c))+4*cos(d*x+c)*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)-19*arcsin((-1+cos(d*x+c))/sin(d*x+c))*sin(d*x+c)-13*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2))/sin(d*x+c)^5/(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2)/a^3","A"
382,1,221,128,0.227000," ","int(1/(a+a*cos(d*x+c))^(5/2)/sec(d*x+c)^(1/2),x)","\frac{\sqrt{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)^{3} \left(\left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+4 \cos \left(d x +c \right) \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+5 \cos \left(d x +c \right) \sin \left(d x +c \right) \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)-5 \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+5 \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \sin \left(d x +c \right)\right) \sqrt{2}}{32 d \sqrt{\frac{1}{\cos \left(d x +c \right)}}\, \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sin \left(d x +c \right)^{7} a^{3}}"," ",0,"1/32/d*(a*(1+cos(d*x+c)))^(1/2)*cos(d*x+c)*(-1+cos(d*x+c))^3*(cos(d*x+c)^2*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+4*cos(d*x+c)*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+5*cos(d*x+c)*sin(d*x+c)*arcsin((-1+cos(d*x+c))/sin(d*x+c))-5*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+5*arcsin((-1+cos(d*x+c))/sin(d*x+c))*sin(d*x+c))/(1/cos(d*x+c))^(1/2)/(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)/sin(d*x+c)^7*2^(1/2)/a^3","A"
383,1,222,128,0.222000," ","int(1/(a+a*cos(d*x+c))^(5/2)/sec(d*x+c)^(3/2),x)","-\frac{\sqrt{a \left(1+\cos \left(d x +c \right)\right)}\, \left(-1+\cos \left(d x +c \right)\right)^{4} \cos \left(d x +c \right) \left(7 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}-4 \cos \left(d x +c \right) \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+3 \cos \left(d x +c \right) \sin \left(d x +c \right) \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)-3 \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+3 \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \sin \left(d x +c \right)\right) \sqrt{2}}{32 d \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \sin \left(d x +c \right)^{9} a^{3}}"," ",0,"-1/32/d*(a*(1+cos(d*x+c)))^(1/2)*(-1+cos(d*x+c))^4*cos(d*x+c)*(7*cos(d*x+c)^2*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)-4*cos(d*x+c)*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+3*cos(d*x+c)*sin(d*x+c)*arcsin((-1+cos(d*x+c))/sin(d*x+c))-3*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+3*arcsin((-1+cos(d*x+c))/sin(d*x+c))*sin(d*x+c))/(1/cos(d*x+c))^(3/2)/(cos(d*x+c)/(1+cos(d*x+c)))^(5/2)/sin(d*x+c)^9*2^(1/2)/a^3","A"
384,1,320,175,0.224000," ","int(1/(a+a*cos(d*x+c))^(5/2)/sec(d*x+c)^(5/2),x)","-\frac{\sqrt{a \left(1+\cos \left(d x +c \right)\right)}\, \left(-1+\cos \left(d x +c \right)\right)^{5} \cos \left(d x +c \right) \left(15 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+32 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{2}\, \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}{\cos \left(d x +c \right)}\right)+43 \cos \left(d x +c \right) \sin \left(d x +c \right) \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)-4 \cos \left(d x +c \right) \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+32 \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}{\cos \left(d x +c \right)}\right) \sqrt{2}\, \sin \left(d x +c \right)+43 \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \sin \left(d x +c \right)-11 \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\right) \sqrt{2}}{32 d \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{7}{2}} \sin \left(d x +c \right)^{11} a^{3}}"," ",0,"-1/32/d*(a*(1+cos(d*x+c)))^(1/2)*(-1+cos(d*x+c))^5*cos(d*x+c)*(15*cos(d*x+c)^2*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+32*cos(d*x+c)*sin(d*x+c)*2^(1/2)*arctan(sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)/cos(d*x+c))+43*cos(d*x+c)*sin(d*x+c)*arcsin((-1+cos(d*x+c))/sin(d*x+c))-4*cos(d*x+c)*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+32*arctan(sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)/cos(d*x+c))*2^(1/2)*sin(d*x+c)+43*arcsin((-1+cos(d*x+c))/sin(d*x+c))*sin(d*x+c)-11*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2))/(1/cos(d*x+c))^(5/2)/(cos(d*x+c)/(1+cos(d*x+c)))^(7/2)/sin(d*x+c)^11*2^(1/2)/a^3","A"
385,1,352,209,0.236000," ","int(1/(a+a*cos(d*x+c))^(5/2)/sec(d*x+c)^(7/2),x)","-\frac{\sqrt{a \left(1+\cos \left(d x +c \right)\right)}\, \left(-1+\cos \left(d x +c \right)\right)^{6} \cos \left(d x +c \right) \left(16 \left(\cos^{3}\left(d x +c \right)\right) \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+39 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+80 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{2}\, \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}{\cos \left(d x +c \right)}\right)+115 \cos \left(d x +c \right) \sin \left(d x +c \right) \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)-20 \cos \left(d x +c \right) \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+80 \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}{\cos \left(d x +c \right)}\right) \sqrt{2}\, \sin \left(d x +c \right)+115 \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \sin \left(d x +c \right)-35 \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\right) \sqrt{2}}{32 d \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{7}{2}} \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{9}{2}} \sin \left(d x +c \right)^{13} a^{3}}"," ",0,"-1/32/d*(a*(1+cos(d*x+c)))^(1/2)*(-1+cos(d*x+c))^6*cos(d*x+c)*(16*cos(d*x+c)^3*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+39*cos(d*x+c)^2*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+80*cos(d*x+c)*sin(d*x+c)*2^(1/2)*arctan(sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)/cos(d*x+c))+115*cos(d*x+c)*sin(d*x+c)*arcsin((-1+cos(d*x+c))/sin(d*x+c))-20*cos(d*x+c)*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+80*arctan(sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)/cos(d*x+c))*2^(1/2)*sin(d*x+c)+115*arcsin((-1+cos(d*x+c))/sin(d*x+c))*sin(d*x+c)-35*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2))/(1/cos(d*x+c))^(7/2)/(cos(d*x+c)/(1+cos(d*x+c)))^(9/2)/sin(d*x+c)^13*2^(1/2)/a^3","A"
386,1,390,230,0.253000," ","int(sec(d*x+c)^(5/2)/(a+a*cos(d*x+c))^(7/2),x)","\frac{\left(-1+\cos \left(d x +c \right)\right) \left(3045 \left(\cos^{4}\left(d x +c \right)\right) \sin \left(d x +c \right) \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}}+12180 \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)+18270 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}}+12180 \cos \left(d x +c \right) \sin \left(d x +c \right) \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}}-1887 \sqrt{2}\, \left(\cos^{5}\left(d x +c \right)\right)+3045 \sin \left(d x +c \right) \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}}-3195 \left(\cos^{4}\left(d x +c \right)\right) \sqrt{2}+831 \left(\cos^{3}\left(d x +c \right)\right) \sqrt{2}+3355 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}+1024 \cos \left(d x +c \right) \sqrt{2}-128 \sqrt{2}\right) \cos \left(d x +c \right) \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \sqrt{a \left(1+\cos \left(d x +c \right)\right)}\, \sqrt{2}}{384 d \sin \left(d x +c \right)^{3} \left(1+\cos \left(d x +c \right)\right)^{2} a^{4}}"," ",0,"1/384/d*(-1+cos(d*x+c))*(3045*cos(d*x+c)^4*sin(d*x+c)*arcsin((-1+cos(d*x+c))/sin(d*x+c))*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)+12180*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*arcsin((-1+cos(d*x+c))/sin(d*x+c))*cos(d*x+c)^3*sin(d*x+c)+18270*cos(d*x+c)^2*sin(d*x+c)*arcsin((-1+cos(d*x+c))/sin(d*x+c))*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)+12180*cos(d*x+c)*sin(d*x+c)*arcsin((-1+cos(d*x+c))/sin(d*x+c))*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)-1887*2^(1/2)*cos(d*x+c)^5+3045*sin(d*x+c)*arcsin((-1+cos(d*x+c))/sin(d*x+c))*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)-3195*cos(d*x+c)^4*2^(1/2)+831*cos(d*x+c)^3*2^(1/2)+3355*cos(d*x+c)^2*2^(1/2)+1024*cos(d*x+c)*2^(1/2)-128*2^(1/2))*cos(d*x+c)*(1/cos(d*x+c))^(5/2)*(a*(1+cos(d*x+c)))^(1/2)/sin(d*x+c)^3/(1+cos(d*x+c))^2*2^(1/2)/a^4","A"
387,1,326,196,0.241000," ","int(sec(d*x+c)^(3/2)/(a+a*cos(d*x+c))^(7/2),x)","-\frac{\left(-1+\cos \left(d x +c \right)\right)^{2} \left(-1089 \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+691 \left(\cos^{4}\left(d x +c \right)\right) \sqrt{2}-3267 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+1183 \left(\cos^{3}\left(d x +c \right)\right) \sqrt{2}-3267 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \sin \left(d x +c \right) \cos \left(d x +c \right)-275 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}-1089 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \sin \left(d x +c \right)-1215 \cos \left(d x +c \right) \sqrt{2}-384 \sqrt{2}\right) \cos \left(d x +c \right) \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sqrt{a \left(1+\cos \left(d x +c \right)\right)}\, \sqrt{2}}{384 d \sin \left(d x +c \right)^{5} \left(1+\cos \left(d x +c \right)\right) a^{4}}"," ",0,"-1/384/d*(-1+cos(d*x+c))^2*(-1089*arcsin((-1+cos(d*x+c))/sin(d*x+c))*cos(d*x+c)^3*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+691*cos(d*x+c)^4*2^(1/2)-3267*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arcsin((-1+cos(d*x+c))/sin(d*x+c))*cos(d*x+c)^2*sin(d*x+c)+1183*cos(d*x+c)^3*2^(1/2)-3267*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arcsin((-1+cos(d*x+c))/sin(d*x+c))*sin(d*x+c)*cos(d*x+c)-275*cos(d*x+c)^2*2^(1/2)-1089*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arcsin((-1+cos(d*x+c))/sin(d*x+c))*sin(d*x+c)-1215*cos(d*x+c)*2^(1/2)-384*2^(1/2))*cos(d*x+c)*(1/cos(d*x+c))^(3/2)*(a*(1+cos(d*x+c)))^(1/2)/sin(d*x+c)^5/(1+cos(d*x+c))*2^(1/2)/a^4","A"
388,1,288,162,0.222000," ","int(sec(d*x+c)^(1/2)/(a+a*cos(d*x+c))^(7/2),x)","-\frac{\sqrt{\frac{1}{\cos \left(d x +c \right)}}\, \sqrt{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)^{3} \left(103 \left(\cos^{3}\left(d x +c \right)\right) \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}-189 \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+163 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}-378 \cos \left(d x +c \right) \sin \left(d x +c \right) \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)-71 \cos \left(d x +c \right) \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}-189 \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \sin \left(d x +c \right)-195 \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\right) \sqrt{2}}{384 d \sin \left(d x +c \right)^{7} \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, a^{4}}"," ",0,"-1/384/d*(1/cos(d*x+c))^(1/2)*(a*(1+cos(d*x+c)))^(1/2)*cos(d*x+c)*(-1+cos(d*x+c))^3*(103*cos(d*x+c)^3*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)-189*arcsin((-1+cos(d*x+c))/sin(d*x+c))*cos(d*x+c)^2*sin(d*x+c)+163*cos(d*x+c)^2*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)-378*cos(d*x+c)*sin(d*x+c)*arcsin((-1+cos(d*x+c))/sin(d*x+c))-71*cos(d*x+c)*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)-189*arcsin((-1+cos(d*x+c))/sin(d*x+c))*sin(d*x+c)-195*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2))/sin(d*x+c)^7/(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2)/a^4","A"
389,1,288,162,0.224000," ","int(1/(a+a*cos(d*x+c))^(7/2)/sec(d*x+c)^(1/2),x)","\frac{\sqrt{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)^{4} \left(5 \left(\cos^{3}\left(d x +c \right)\right) \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}-39 \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)-7 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}-78 \cos \left(d x +c \right) \sin \left(d x +c \right) \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)-37 \cos \left(d x +c \right) \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}-39 \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \sin \left(d x +c \right)+39 \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\right) \sqrt{2}}{384 d \sqrt{\frac{1}{\cos \left(d x +c \right)}}\, \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sin \left(d x +c \right)^{9} a^{4}}"," ",0,"1/384/d*(a*(1+cos(d*x+c)))^(1/2)*cos(d*x+c)*(-1+cos(d*x+c))^4*(5*cos(d*x+c)^3*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)-39*arcsin((-1+cos(d*x+c))/sin(d*x+c))*cos(d*x+c)^2*sin(d*x+c)-7*cos(d*x+c)^2*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)-78*cos(d*x+c)*sin(d*x+c)*arcsin((-1+cos(d*x+c))/sin(d*x+c))-37*cos(d*x+c)*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)-39*arcsin((-1+cos(d*x+c))/sin(d*x+c))*sin(d*x+c)+39*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2))/(1/cos(d*x+c))^(1/2)/(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)/sin(d*x+c)^9*2^(1/2)/a^4","A"
390,1,288,162,0.222000," ","int(1/(a+a*cos(d*x+c))^(7/2)/sec(d*x+c)^(3/2),x)","\frac{\sqrt{a \left(1+\cos \left(d x +c \right)\right)}\, \left(-1+\cos \left(d x +c \right)\right)^{5} \cos \left(d x +c \right) \left(17 \left(\cos^{3}\left(d x +c \right)\right) \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+53 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+21 \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)-49 \cos \left(d x +c \right) \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+42 \cos \left(d x +c \right) \sin \left(d x +c \right) \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)-21 \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+21 \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \sin \left(d x +c \right)\right) \sqrt{2}}{384 d \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \sin \left(d x +c \right)^{11} a^{4}}"," ",0,"1/384/d*(a*(1+cos(d*x+c)))^(1/2)*(-1+cos(d*x+c))^5*cos(d*x+c)*(17*cos(d*x+c)^3*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+53*cos(d*x+c)^2*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+21*arcsin((-1+cos(d*x+c))/sin(d*x+c))*cos(d*x+c)^2*sin(d*x+c)-49*cos(d*x+c)*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+42*cos(d*x+c)*sin(d*x+c)*arcsin((-1+cos(d*x+c))/sin(d*x+c))-21*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+21*arcsin((-1+cos(d*x+c))/sin(d*x+c))*sin(d*x+c))/(1/cos(d*x+c))^(3/2)/(cos(d*x+c)/(1+cos(d*x+c)))^(5/2)/sin(d*x+c)^11*2^(1/2)/a^4","A"
391,1,288,162,0.211000," ","int(1/(a+a*cos(d*x+c))^(7/2)/sec(d*x+c)^(5/2),x)","-\frac{\sqrt{a \left(1+\cos \left(d x +c \right)\right)}\, \left(-1+\cos \left(d x +c \right)\right)^{6} \cos \left(d x +c \right) \left(67 \left(\cos^{3}\left(d x +c \right)\right) \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+15 \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)-17 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+30 \cos \left(d x +c \right) \sin \left(d x +c \right) \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)-35 \cos \left(d x +c \right) \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+15 \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \sin \left(d x +c \right)-15 \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\right) \sqrt{2}}{384 d \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{7}{2}} \sin \left(d x +c \right)^{13} a^{4}}"," ",0,"-1/384/d*(a*(1+cos(d*x+c)))^(1/2)*(-1+cos(d*x+c))^6*cos(d*x+c)*(67*cos(d*x+c)^3*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+15*arcsin((-1+cos(d*x+c))/sin(d*x+c))*cos(d*x+c)^2*sin(d*x+c)-17*cos(d*x+c)^2*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+30*cos(d*x+c)*sin(d*x+c)*arcsin((-1+cos(d*x+c))/sin(d*x+c))-35*cos(d*x+c)*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+15*arcsin((-1+cos(d*x+c))/sin(d*x+c))*sin(d*x+c)-15*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2))/(1/cos(d*x+c))^(5/2)/(cos(d*x+c)/(1+cos(d*x+c)))^(7/2)/sin(d*x+c)^13*2^(1/2)/a^4","A"
392,1,440,209,0.257000," ","int(1/(a+a*cos(d*x+c))^(7/2)/sec(d*x+c)^(7/2),x)","-\frac{\sqrt{a \left(1+\cos \left(d x +c \right)\right)}\, \left(-1+\cos \left(d x +c \right)\right)^{7} \cos \left(d x +c \right) \left(384 \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}{\cos \left(d x +c \right)}\right) \sqrt{2}\, \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+247 \left(\cos^{3}\left(d x +c \right)\right) \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+768 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{2}\, \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}{\cos \left(d x +c \right)}\right)+115 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+531 \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+384 \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}{\cos \left(d x +c \right)}\right) \sqrt{2}\, \sin \left(d x +c \right)-215 \cos \left(d x +c \right) \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+1062 \cos \left(d x +c \right) \sin \left(d x +c \right) \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)-147 \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+531 \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \sin \left(d x +c \right)\right) \sqrt{2}}{384 d \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{7}{2}} \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{9}{2}} \sin \left(d x +c \right)^{15} a^{4}}"," ",0,"-1/384/d*(a*(1+cos(d*x+c)))^(1/2)*(-1+cos(d*x+c))^7*cos(d*x+c)*(384*arctan(sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)/cos(d*x+c))*2^(1/2)*cos(d*x+c)^2*sin(d*x+c)+247*cos(d*x+c)^3*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+768*cos(d*x+c)*sin(d*x+c)*2^(1/2)*arctan(sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)/cos(d*x+c))+115*cos(d*x+c)^2*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+531*arcsin((-1+cos(d*x+c))/sin(d*x+c))*cos(d*x+c)^2*sin(d*x+c)+384*arctan(sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)/cos(d*x+c))*2^(1/2)*sin(d*x+c)-215*cos(d*x+c)*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+1062*cos(d*x+c)*sin(d*x+c)*arcsin((-1+cos(d*x+c))/sin(d*x+c))-147*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+531*arcsin((-1+cos(d*x+c))/sin(d*x+c))*sin(d*x+c))/(1/cos(d*x+c))^(7/2)/(cos(d*x+c)/(1+cos(d*x+c)))^(9/2)/sin(d*x+c)^15*2^(1/2)/a^4","B"
393,1,472,243,0.257000," ","int(1/(a+a*cos(d*x+c))^(7/2)/sec(d*x+c)^(9/2),x)","-\frac{\sqrt{a \left(1+\cos \left(d x +c \right)\right)}\, \left(-1+\cos \left(d x +c \right)\right)^{8} \cos \left(d x +c \right) \left(192 \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \left(\cos^{4}\left(d x +c \right)\right)+907 \left(\cos^{3}\left(d x +c \right)\right) \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+1344 \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}{\cos \left(d x +c \right)}\right) \sqrt{2}\, \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+1911 \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+343 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+2688 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{2}\, \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}{\cos \left(d x +c \right)}\right)+3822 \cos \left(d x +c \right) \sin \left(d x +c \right) \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)-875 \cos \left(d x +c \right) \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+1344 \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}{\cos \left(d x +c \right)}\right) \sqrt{2}\, \sin \left(d x +c \right)+1911 \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \sin \left(d x +c \right)-567 \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\right) \sqrt{2}}{384 d \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{9}{2}} \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{11}{2}} \sin \left(d x +c \right)^{17} a^{4}}"," ",0,"-1/384/d*(a*(1+cos(d*x+c)))^(1/2)*(-1+cos(d*x+c))^8*cos(d*x+c)*(192*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^4+907*cos(d*x+c)^3*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+1344*arctan(sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)/cos(d*x+c))*2^(1/2)*cos(d*x+c)^2*sin(d*x+c)+1911*arcsin((-1+cos(d*x+c))/sin(d*x+c))*cos(d*x+c)^2*sin(d*x+c)+343*cos(d*x+c)^2*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+2688*cos(d*x+c)*sin(d*x+c)*2^(1/2)*arctan(sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)/cos(d*x+c))+3822*cos(d*x+c)*sin(d*x+c)*arcsin((-1+cos(d*x+c))/sin(d*x+c))-875*cos(d*x+c)*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+1344*arctan(sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)/cos(d*x+c))*2^(1/2)*sin(d*x+c)+1911*arcsin((-1+cos(d*x+c))/sin(d*x+c))*sin(d*x+c)-567*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2))/(1/cos(d*x+c))^(9/2)/(cos(d*x+c)/(1+cos(d*x+c)))^(11/2)/sin(d*x+c)^17*2^(1/2)/a^4","A"
394,1,354,196,0.250000," ","int(1/(a+a*cos(d*x+c))^(9/2)/sec(d*x+c)^(5/2),x)","\frac{\sqrt{a \left(1+\cos \left(d x +c \right)\right)}\, \left(-1+\cos \left(d x +c \right)\right)^{7} \cos \left(d x +c \right) \left(73 \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \left(\cos^{4}\left(d x +c \right)\right)+278 \left(\cos^{3}\left(d x +c \right)\right) \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+45 \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)-156 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+135 \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)-150 \cos \left(d x +c \right) \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+135 \cos \left(d x +c \right) \sin \left(d x +c \right) \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)-45 \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+45 \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \sin \left(d x +c \right)\right) \sqrt{2}}{2048 d \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{7}{2}} \sin \left(d x +c \right)^{15} a^{5}}"," ",0,"1/2048/d*(a*(1+cos(d*x+c)))^(1/2)*(-1+cos(d*x+c))^7*cos(d*x+c)*(73*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^4+278*cos(d*x+c)^3*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+45*arcsin((-1+cos(d*x+c))/sin(d*x+c))*cos(d*x+c)^3*sin(d*x+c)-156*cos(d*x+c)^2*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+135*arcsin((-1+cos(d*x+c))/sin(d*x+c))*cos(d*x+c)^2*sin(d*x+c)-150*cos(d*x+c)*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+135*cos(d*x+c)*sin(d*x+c)*arcsin((-1+cos(d*x+c))/sin(d*x+c))-45*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+45*arcsin((-1+cos(d*x+c))/sin(d*x+c))*sin(d*x+c))/(1/cos(d*x+c))^(5/2)/(cos(d*x+c)/(1+cos(d*x+c)))^(7/2)/sin(d*x+c)^15*2^(1/2)/a^5","A"
395,1,354,196,0.252000," ","int(1/(a+a*cos(d*x+c))^(9/2)/sec(d*x+c)^(7/2),x)","-\frac{\sqrt{a \left(1+\cos \left(d x +c \right)\right)}\, \left(-1+\cos \left(d x +c \right)\right)^{8} \cos \left(d x +c \right) \left(853 \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \left(\cos^{4}\left(d x +c \right)\right)+105 \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)-34 \left(\cos^{3}\left(d x +c \right)\right) \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+315 \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)-364 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+315 \cos \left(d x +c \right) \sin \left(d x +c \right) \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)-350 \cos \left(d x +c \right) \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+105 \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \sin \left(d x +c \right)-105 \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\right) \sqrt{2}}{6144 d \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{7}{2}} \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{9}{2}} \sin \left(d x +c \right)^{17} a^{5}}"," ",0,"-1/6144/d*(a*(1+cos(d*x+c)))^(1/2)*(-1+cos(d*x+c))^8*cos(d*x+c)*(853*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^4+105*arcsin((-1+cos(d*x+c))/sin(d*x+c))*cos(d*x+c)^3*sin(d*x+c)-34*cos(d*x+c)^3*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+315*arcsin((-1+cos(d*x+c))/sin(d*x+c))*cos(d*x+c)^2*sin(d*x+c)-364*cos(d*x+c)^2*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+315*cos(d*x+c)*sin(d*x+c)*arcsin((-1+cos(d*x+c))/sin(d*x+c))-350*cos(d*x+c)*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+105*arcsin((-1+cos(d*x+c))/sin(d*x+c))*sin(d*x+c)-105*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2))/(1/cos(d*x+c))^(7/2)/(cos(d*x+c)/(1+cos(d*x+c)))^(9/2)/sin(d*x+c)^17*2^(1/2)/a^5","A"
396,0,0,34,0.226000," ","int((a+a*cos(d*x+c))^(3/2)*sec(d*x+c)^(5/4),x)","\int \left(a +a \cos \left(d x +c \right)\right)^{\frac{3}{2}} \left(\sec^{\frac{5}{4}}\left(d x +c \right)\right)\, dx"," ",0,"int((a+a*cos(d*x+c))^(3/2)*sec(d*x+c)^(5/4),x)","F"
397,0,0,290,3.820000," ","int(cos(d*x+c)^m*(a+a*cos(d*x+c))^4,x)","\int \left(\cos^{m}\left(d x +c \right)\right) \left(a +a \cos \left(d x +c \right)\right)^{4}\, dx"," ",0,"int(cos(d*x+c)^m*(a+a*cos(d*x+c))^4,x)","F"
398,0,0,220,2.712000," ","int(cos(d*x+c)^m*(a+a*cos(d*x+c))^3,x)","\int \left(\cos^{m}\left(d x +c \right)\right) \left(a +a \cos \left(d x +c \right)\right)^{3}\, dx"," ",0,"int(cos(d*x+c)^m*(a+a*cos(d*x+c))^3,x)","F"
399,0,0,161,3.568000," ","int(cos(d*x+c)^m*(a+a*cos(d*x+c))^2,x)","\int \left(\cos^{m}\left(d x +c \right)\right) \left(a +a \cos \left(d x +c \right)\right)^{2}\, dx"," ",0,"int(cos(d*x+c)^m*(a+a*cos(d*x+c))^2,x)","F"
400,0,0,119,1.041000," ","int(cos(d*x+c)^m*(a+a*cos(d*x+c)),x)","\int \left(\cos^{m}\left(d x +c \right)\right) \left(a +a \cos \left(d x +c \right)\right)\, dx"," ",0,"int(cos(d*x+c)^m*(a+a*cos(d*x+c)),x)","F"
401,0,0,144,0.817000," ","int(cos(d*x+c)^m/(a+a*cos(d*x+c)),x)","\int \frac{\cos^{m}\left(d x +c \right)}{a +a \cos \left(d x +c \right)}\, dx"," ",0,"int(cos(d*x+c)^m/(a+a*cos(d*x+c)),x)","F"
402,0,0,209,0.399000," ","int(cos(d*x+c)^m/(a+a*cos(d*x+c))^2,x)","\int \frac{\cos^{m}\left(d x +c \right)}{\left(a +a \cos \left(d x +c \right)\right)^{2}}\, dx"," ",0,"int(cos(d*x+c)^m/(a+a*cos(d*x+c))^2,x)","F"
403,1,100,136,0.040000," ","int(cos(d*x+c)^7*(a+b*cos(d*x+c)),x)","\frac{b \left(\frac{\left(\cos^{7}\left(d x +c \right)+\frac{7 \left(\cos^{5}\left(d x +c \right)\right)}{6}+\frac{35 \left(\cos^{3}\left(d x +c \right)\right)}{24}+\frac{35 \cos \left(d x +c \right)}{16}\right) \sin \left(d x +c \right)}{8}+\frac{35 d x}{128}+\frac{35 c}{128}\right)+\frac{a \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}}{d}"," ",0,"1/d*(b*(1/8*(cos(d*x+c)^7+7/6*cos(d*x+c)^5+35/24*cos(d*x+c)^3+35/16*cos(d*x+c))*sin(d*x+c)+35/128*d*x+35/128*c)+1/7*a*(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))","A"
404,1,90,116,0.037000," ","int(cos(d*x+c)^6*(a+b*cos(d*x+c)),x)","\frac{\frac{b \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}+a \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)}{d}"," ",0,"1/d*(1/7*b*(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)+a*(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))","A"
405,1,80,102,0.045000," ","int(cos(d*x+c)^5*(a+b*cos(d*x+c)),x)","\frac{b \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{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}}{d}"," ",0,"1/d*(b*(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)+1/5*a*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c))","A"
406,1,70,82,0.040000," ","int(cos(d*x+c)^4*(a+b*cos(d*x+c)),x)","\frac{\frac{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}+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)}{d}"," ",0,"1/d*(1/5*b*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c)+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))","A"
407,1,60,68,0.043000," ","int(cos(d*x+c)^3*(a+b*cos(d*x+c)),x)","\frac{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{a \left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3}}{d}"," ",0,"1/d*(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*a*(2+cos(d*x+c)^2)*sin(d*x+c))","A"
408,1,49,48,0.039000," ","int(cos(d*x+c)^2*(a+b*cos(d*x+c)),x)","\frac{\frac{b \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*b*(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"
409,1,38,34,0.042000," ","int(cos(d*x+c)*(a+b*cos(d*x+c)),x)","\frac{b \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}{d}"," ",0,"1/d*(b*(1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c)+sin(d*x+c)*a)","A"
410,1,16,15,0.015000," ","int(a+b*cos(d*x+c),x)","a x +\frac{b \sin \left(d x +c \right)}{d}"," ",0,"a*x+b*sin(d*x+c)/d","A"
411,1,30,16,0.063000," ","int((a+b*cos(d*x+c))*sec(d*x+c),x)","b x +\frac{a \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{b c}{d}"," ",0,"b*x+1/d*a*ln(sec(d*x+c)+tan(d*x+c))+b*c/d","A"
412,1,32,24,0.073000," ","int((a+b*cos(d*x+c))*sec(d*x+c)^2,x)","\frac{b \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*b*ln(sec(d*x+c)+tan(d*x+c))+a*tan(d*x+c)/d","A"
413,1,51,43,0.078000," ","int((a+b*cos(d*x+c))*sec(d*x+c)^3,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{b \tan \left(d x +c \right)}{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))+b*tan(d*x+c)/d","A"
414,1,72,57,0.082000," ","int((a+b*cos(d*x+c))*sec(d*x+c)^4,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 \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,"2/3*a*tan(d*x+c)/d+1/3/d*a*tan(d*x+c)*sec(d*x+c)^2+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"
415,1,92,77,0.091000," ","int((a+b*cos(d*x+c))*sec(d*x+c)^5,x)","\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}+\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,"1/4*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))+2/3*b*tan(d*x+c)/d+1/3/d*b*tan(d*x+c)*sec(d*x+c)^2","A"
416,1,112,91,0.086000," ","int((a+b*cos(d*x+c))*sec(d*x+c)^6,x)","\frac{8 a \tan \left(d x +c \right)}{15 d}+\frac{a \tan \left(d x +c \right) \left(\sec^{4}\left(d x +c \right)\right)}{5 d}+\frac{4 a \tan \left(d x +c \right) \left(\sec^{2}\left(d x +c \right)\right)}{15 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,"8/15*a*tan(d*x+c)/d+1/5/d*a*tan(d*x+c)*sec(d*x+c)^4+4/15/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"
417,1,120,138,0.046000," ","int(cos(d*x+c)^4*(a+b*cos(d*x+c))^2,x)","\frac{b^{2} \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{2 a 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}+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)}{d}"," ",0,"1/d*(b^2*(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)+2/5*a*b*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c)+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))","A"
418,1,95,101,0.042000," ","int(cos(d*x+c)^3*(a+b*cos(d*x+c))^2,x)","\frac{\frac{b^{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{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*b^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*a^2*(2+cos(d*x+c)^2)*sin(d*x+c))","A"
419,1,89,93,0.048000," ","int(cos(d*x+c)^2*(a+b*cos(d*x+c))^2,x)","\frac{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{2 a b \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*(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)+2/3*a*b*(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"
420,1,63,65,0.039000," ","int(cos(d*x+c)*(a+b*cos(d*x+c))^2,x)","\frac{\frac{b^{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)+a^{2} \sin \left(d x +c \right)}{d}"," ",0,"1/d*(1/3*b^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)+a^2*sin(d*x+c))","A"
421,1,51,46,0.036000," ","int((a+b*cos(d*x+c))^2,x)","\frac{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)+2 a b \sin \left(d x +c \right)+a^{2} \left(d x +c \right)}{d}"," ",0,"1/d*(b^2*(1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c)+2*a*b*sin(d*x+c)+a^2*(d*x+c))","A"
422,1,49,33,0.079000," ","int((a+b*cos(d*x+c))^2*sec(d*x+c),x)","2 a b x +\frac{b^{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 b c}{d}"," ",0,"2*a*b*x+b^2*sin(d*x+c)/d+1/d*a^2*ln(sec(d*x+c)+tan(d*x+c))+2/d*a*b*c","A"
423,1,49,33,0.079000," ","int((a+b*cos(d*x+c))^2*sec(d*x+c)^2,x)","b^{2} x +\frac{a^{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{c \,b^{2}}{d}"," ",0,"b^2*x+a^2*tan(d*x+c)/d+2/d*a*b*ln(sec(d*x+c)+tan(d*x+c))+1/d*c*b^2","A"
424,1,78,55,0.096000," ","int((a+b*cos(d*x+c))^2*sec(d*x+c)^3,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{2 a b \tan \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}"," ",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))+2*a*b*tan(d*x+c)/d+1/d*b^2*ln(sec(d*x+c)+tan(d*x+c))","A"
425,1,89,76,0.106000," ","int((a+b*cos(d*x+c))^2*sec(d*x+c)^4,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 \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{b^{2} \tan \left(d x +c \right)}{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+a*b*sec(d*x+c)*tan(d*x+c)/d+1/d*a*b*ln(sec(d*x+c)+tan(d*x+c))+1/d*b^2*tan(d*x+c)","A"
426,1,142,102,0.099000," ","int((a+b*cos(d*x+c))^2*sec(d*x+c)^5,x)","\frac{a^{2} \left(\sec^{3}\left(d x +c \right)\right) \tan \left(d x +c \right)}{4 d}+\frac{3 a^{2} \sec \left(d x +c \right) \tan \left(d x +c \right)}{8 d}+\frac{3 a^{2} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 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} \tan \left(d x +c \right) \sec \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,"1/4*a^2*sec(d*x+c)^3*tan(d*x+c)/d+3/8*a^2*sec(d*x+c)*tan(d*x+c)/d+3/8/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+1/2/d*b^2*tan(d*x+c)*sec(d*x+c)+1/2/d*b^2*ln(sec(d*x+c)+tan(d*x+c))","A"
427,1,157,123,0.098000," ","int((a+b*cos(d*x+c))^2*sec(d*x+c)^6,x)","\frac{8 a^{2} \tan \left(d x +c \right)}{15 d}+\frac{a^{2} \left(\sec^{4}\left(d x +c \right)\right) \tan \left(d x +c \right)}{5 d}+\frac{4 a^{2} \left(\sec^{2}\left(d x +c \right)\right) \tan \left(d x +c \right)}{15 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{2 b^{2} \tan \left(d x +c \right)}{3 d}+\frac{b^{2} \tan \left(d x +c \right) \left(\sec^{2}\left(d x +c \right)\right)}{3 d}"," ",0,"8/15*a^2*tan(d*x+c)/d+1/5*a^2*sec(d*x+c)^4*tan(d*x+c)/d+4/15*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))+2/3/d*b^2*tan(d*x+c)+1/3/d*b^2*tan(d*x+c)*sec(d*x+c)^2","A"
428,1,145,156,0.044000," ","int(cos(d*x+c)^3*(a+b*cos(d*x+c))^3,x)","\frac{b^{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 b^{2} 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}+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)+\frac{a^{3} \left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3}}{d}"," ",0,"1/d*(b^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*b^2*a*(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)+1/3*a^3*(2+cos(d*x+c)^2)*sin(d*x+c))","A"
429,1,123,168,0.044000," ","int(cos(d*x+c)^2*(a+b*cos(d*x+c))^3,x)","\frac{\frac{b^{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 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)+a^{2} b \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*b^3*(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)+a^2*b*(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"
430,1,102,111,0.043000," ","int(cos(d*x+c)*(a+b*cos(d*x+c))^3,x)","\frac{b^{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)+b^{2} a \left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+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)+a^{3} \sin \left(d x +c \right)}{d}"," ",0,"1/d*(b^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)+b^2*a*(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)+a^3*sin(d*x+c))","A"
431,1,76,70,0.038000," ","int((a+b*cos(d*x+c))^3,x)","\frac{\frac{b^{3} \left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3}+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)+3 a^{2} b \sin \left(d x +c \right)+a^{3} \left(d x +c \right)}{d}"," ",0,"1/d*(1/3*b^3*(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)+3*a^2*b*sin(d*x+c)+a^3*(d*x+c))","A"
432,1,90,67,0.077000," ","int((a+b*cos(d*x+c))^3*sec(d*x+c),x)","\frac{a^{3} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+3 a^{2} b x +\frac{3 a^{2} b c}{d}+\frac{3 a \,b^{2} \sin \left(d x +c \right)}{d}+\frac{b^{3} \cos \left(d x +c \right) \sin \left(d x +c \right)}{2 d}+\frac{b^{3} x}{2}+\frac{c \,b^{3}}{2 d}"," ",0,"1/d*a^3*ln(sec(d*x+c)+tan(d*x+c))+3*a^2*b*x+3/d*a^2*b*c+3*a*b^2*sin(d*x+c)/d+1/2/d*b^3*cos(d*x+c)*sin(d*x+c)+1/2*b^3*x+1/2/d*c*b^3","A"
433,1,68,68,0.084000," ","int((a+b*cos(d*x+c))^3*sec(d*x+c)^2,x)","3 a \,b^{2} x +\frac{a^{3} \tan \left(d x +c \right)}{d}+\frac{b^{3} \sin \left(d x +c \right)}{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} c}{d}"," ",0,"3*a*b^2*x+a^3*tan(d*x+c)/d+1/d*b^3*sin(d*x+c)+3/d*a^2*b*ln(sec(d*x+c)+tan(d*x+c))+3/d*a*b^2*c","A"
434,1,95,73,0.096000," ","int((a+b*cos(d*x+c))^3*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{3 a^{2} b \tan \left(d x +c \right)}{d}+\frac{3 b^{2} a \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+b^{3} x +\frac{c \,b^{3}}{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))+3*a^2*b*tan(d*x+c)/d+3/d*b^2*a*ln(sec(d*x+c)+tan(d*x+c))+b^3*x+1/d*c*b^3","A"
435,1,118,101,0.098000," ","int((a+b*cos(d*x+c))^3*sec(d*x+c)^4,x)","\frac{2 a^{3} \tan \left(d x +c \right)}{3 d}+\frac{a^{3} \tan \left(d x +c \right) \left(\sec^{2}\left(d x +c \right)\right)}{3 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{3 b^{2} a \tan \left(d x +c \right)}{d}+\frac{b^{3} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}"," ",0,"2/3*a^3*tan(d*x+c)/d+1/3/d*a^3*tan(d*x+c)*sec(d*x+c)^2+3/2*a^2*b*sec(d*x+c)*tan(d*x+c)/d+3/2/d*a^2*b*ln(sec(d*x+c)+tan(d*x+c))+3/d*b^2*a*tan(d*x+c)+1/d*b^3*ln(sec(d*x+c)+tan(d*x+c))","A"
436,1,160,125,0.112000," ","int((a+b*cos(d*x+c))^3*sec(d*x+c)^5,x)","\frac{a^{3} \left(\sec^{3}\left(d x +c \right)\right) \tan \left(d x +c \right)}{4 d}+\frac{3 a^{3} \sec \left(d x +c \right) \tan \left(d x +c \right)}{8 d}+\frac{3 a^{3} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}+\frac{2 a^{2} b \tan \left(d x +c \right)}{d}+\frac{a^{2} b \left(\sec^{2}\left(d x +c \right)\right) \tan \left(d x +c \right)}{d}+\frac{3 b^{2} a \tan \left(d x +c \right) \sec \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{b^{3} \tan \left(d x +c \right)}{d}"," ",0,"1/4*a^3*sec(d*x+c)^3*tan(d*x+c)/d+3/8*a^3*sec(d*x+c)*tan(d*x+c)/d+3/8/d*a^3*ln(sec(d*x+c)+tan(d*x+c))+2*a^2*b*tan(d*x+c)/d+a^2*b*sec(d*x+c)^2*tan(d*x+c)/d+3/2/d*b^2*a*tan(d*x+c)*sec(d*x+c)+3/2/d*b^2*a*ln(sec(d*x+c)+tan(d*x+c))+1/d*b^3*tan(d*x+c)","A"
437,1,206,157,0.115000," ","int((a+b*cos(d*x+c))^3*sec(d*x+c)^6,x)","\frac{8 a^{3} \tan \left(d x +c \right)}{15 d}+\frac{a^{3} \tan \left(d x +c \right) \left(\sec^{4}\left(d x +c \right)\right)}{5 d}+\frac{4 a^{3} \tan \left(d x +c \right) \left(\sec^{2}\left(d x +c \right)\right)}{15 d}+\frac{3 a^{2} b \left(\sec^{3}\left(d x +c \right)\right) \tan \left(d x +c \right)}{4 d}+\frac{9 a^{2} b \sec \left(d x +c \right) \tan \left(d x +c \right)}{8 d}+\frac{9 a^{2} b \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}+\frac{2 b^{2} a \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) \sec \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,"8/15*a^3*tan(d*x+c)/d+1/5/d*a^3*tan(d*x+c)*sec(d*x+c)^4+4/15/d*a^3*tan(d*x+c)*sec(d*x+c)^2+3/4*a^2*b*sec(d*x+c)^3*tan(d*x+c)/d+9/8*a^2*b*sec(d*x+c)*tan(d*x+c)/d+9/8/d*a^2*b*ln(sec(d*x+c)+tan(d*x+c))+2/d*b^2*a*tan(d*x+c)+1/d*b^2*a*tan(d*x+c)*sec(d*x+c)^2+1/2/d*b^3*tan(d*x+c)*sec(d*x+c)+1/2/d*b^3*ln(sec(d*x+c)+tan(d*x+c))","A"
438,1,190,231,0.046000," ","int(cos(d*x+c)^3*(a+b*cos(d*x+c))^4,x)","\frac{\frac{b^{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 \,b^{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{6 a^{2} b^{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}+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)+\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*b^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*b^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)+6/5*a^2*b^2*(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)+1/3*a^4*(2+cos(d*x+c)^2)*sin(d*x+c))","A"
439,1,174,221,0.050000," ","int(cos(d*x+c)^2*(a+b*cos(d*x+c))^4,x)","\frac{b^{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 \,b^{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}+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^{3} b \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*(b^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*b^3*(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^3*b*(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"
440,1,138,158,0.040000," ","int(cos(d*x+c)*(a+b*cos(d*x+c))^4,x)","\frac{\frac{b^{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 \,b^{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)+2 a^{2} b^{2} \left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+4 a^{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)+a^{4} \sin \left(d x +c \right)}{d}"," ",0,"1/d*(1/5*b^4*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c)+4*a*b^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)+2*a^2*b^2*(2+cos(d*x+c)^2)*sin(d*x+c)+4*a^3*b*(1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c)+a^4*sin(d*x+c))","A"
441,1,116,127,0.041000," ","int((a+b*cos(d*x+c))^4,x)","\frac{b^{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 \,b^{3} \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^{3} b \sin \left(d x +c \right)+a^{4} \left(d x +c \right)}{d}"," ",0,"1/d*(b^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*b^3*(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^3*b*sin(d*x+c)+a^4*(d*x+c))","A"
442,1,131,101,0.082000," ","int((a+b*cos(d*x+c))^4*sec(d*x+c),x)","\frac{a^{4} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+4 a^{3} b x +\frac{4 a^{3} b c}{d}+\frac{6 a^{2} b^{2} \sin \left(d x +c \right)}{d}+\frac{2 a \,b^{3} \cos \left(d x +c \right) \sin \left(d x +c \right)}{d}+2 a \,b^{3} x +\frac{2 a \,b^{3} c}{d}+\frac{\sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) b^{4}}{3 d}+\frac{2 b^{4} \sin \left(d x +c \right)}{3 d}"," ",0,"1/d*a^4*ln(sec(d*x+c)+tan(d*x+c))+4*a^3*b*x+4/d*a^3*b*c+6/d*a^2*b^2*sin(d*x+c)+2*a*b^3*cos(d*x+c)*sin(d*x+c)/d+2*a*b^3*x+2/d*a*b^3*c+1/3/d*sin(d*x+c)*cos(d*x+c)^2*b^4+2/3/d*b^4*sin(d*x+c)","A"
443,1,109,110,0.089000," ","int((a+b*cos(d*x+c))^4*sec(d*x+c)^2,x)","\frac{a^{4} \tan \left(d x +c \right)}{d}+\frac{4 a^{3} b \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+6 a^{2} b^{2} x +\frac{6 a^{2} b^{2} c}{d}+\frac{4 a \,b^{3} \sin \left(d x +c \right)}{d}+\frac{b^{4} \cos \left(d x +c \right) \sin \left(d x +c \right)}{2 d}+\frac{b^{4} x}{2}+\frac{b^{4} c}{2 d}"," ",0,"a^4*tan(d*x+c)/d+4/d*a^3*b*ln(sec(d*x+c)+tan(d*x+c))+6*a^2*b^2*x+6/d*a^2*b^2*c+4/d*a*b^3*sin(d*x+c)+1/2/d*b^4*cos(d*x+c)*sin(d*x+c)+1/2*b^4*x+1/2/d*b^4*c","A"
444,1,114,102,0.101000," ","int((a+b*cos(d*x+c))^4*sec(d*x+c)^3,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{4 a^{3} b \tan \left(d x +c \right)}{d}+\frac{6 a^{2} b^{2} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+4 a \,b^{3} x +\frac{4 a \,b^{3} c}{d}+\frac{b^{4} \sin \left(d x +c \right)}{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))+4*a^3*b*tan(d*x+c)/d+6/d*a^2*b^2*ln(sec(d*x+c)+tan(d*x+c))+4*a*b^3*x+4/d*a*b^3*c+1/d*b^4*sin(d*x+c)","A"
445,1,135,109,0.099000," ","int((a+b*cos(d*x+c))^4*sec(d*x+c)^4,x)","\frac{2 a^{4} \tan \left(d x +c \right)}{3 d}+\frac{a^{4} \tan \left(d x +c \right) \left(\sec^{2}\left(d x +c \right)\right)}{3 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{6 a^{2} b^{2} \tan \left(d x +c \right)}{d}+\frac{4 a \,b^{3} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+b^{4} x +\frac{b^{4} c}{d}"," ",0,"2/3*a^4*tan(d*x+c)/d+1/3/d*a^4*tan(d*x+c)*sec(d*x+c)^2+2*a^3*b*sec(d*x+c)*tan(d*x+c)/d+2/d*a^3*b*ln(sec(d*x+c)+tan(d*x+c))+6/d*a^2*b^2*tan(d*x+c)+4/d*a*b^3*ln(sec(d*x+c)+tan(d*x+c))+b^4*x+1/d*b^4*c","A"
446,1,188,144,0.110000," ","int((a+b*cos(d*x+c))^4*sec(d*x+c)^5,x)","\frac{a^{4} \left(\sec^{3}\left(d x +c \right)\right) \tan \left(d x +c \right)}{4 d}+\frac{3 a^{4} \sec \left(d x +c \right) \tan \left(d x +c \right)}{8 d}+\frac{3 a^{4} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}+\frac{8 a^{3} b \tan \left(d x +c \right)}{3 d}+\frac{4 a^{3} b \left(\sec^{2}\left(d x +c \right)\right) \tan \left(d x +c \right)}{3 d}+\frac{3 a^{2} b^{2} \tan \left(d x +c \right) \sec \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{4 a \,b^{3} \tan \left(d x +c \right)}{d}+\frac{b^{4} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}"," ",0,"1/4*a^4*sec(d*x+c)^3*tan(d*x+c)/d+3/8*a^4*sec(d*x+c)*tan(d*x+c)/d+3/8/d*a^4*ln(sec(d*x+c)+tan(d*x+c))+8/3*a^3*b*tan(d*x+c)/d+4/3*a^3*b*sec(d*x+c)^2*tan(d*x+c)/d+3/d*a^2*b^2*tan(d*x+c)*sec(d*x+c)+3/d*a^2*b^2*ln(sec(d*x+c)+tan(d*x+c))+4/d*a*b^3*tan(d*x+c)+1/d*b^4*ln(sec(d*x+c)+tan(d*x+c))","A"
447,1,225,176,0.125000," ","int((a+b*cos(d*x+c))^4*sec(d*x+c)^6,x)","\frac{8 a^{4} \tan \left(d x +c \right)}{15 d}+\frac{a^{4} \tan \left(d x +c \right) \left(\sec^{4}\left(d x +c \right)\right)}{5 d}+\frac{4 a^{4} \tan \left(d x +c \right) \left(\sec^{2}\left(d x +c \right)\right)}{15 d}+\frac{a^{3} b \left(\sec^{3}\left(d x +c \right)\right) \tan \left(d x +c \right)}{d}+\frac{3 a^{3} b \sec \left(d x +c \right) \tan \left(d x +c \right)}{2 d}+\frac{3 a^{3} b \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 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{2 a \,b^{3} \tan \left(d x +c \right) \sec \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{b^{4} \tan \left(d x +c \right)}{d}"," ",0,"8/15*a^4*tan(d*x+c)/d+1/5/d*a^4*tan(d*x+c)*sec(d*x+c)^4+4/15/d*a^4*tan(d*x+c)*sec(d*x+c)^2+a^3*b*sec(d*x+c)^3*tan(d*x+c)/d+3/2*a^3*b*sec(d*x+c)*tan(d*x+c)/d+3/2/d*a^3*b*ln(sec(d*x+c)+tan(d*x+c))+4/d*a^2*b^2*tan(d*x+c)+2/d*a^2*b^2*tan(d*x+c)*sec(d*x+c)^2+2/d*a*b^3*tan(d*x+c)*sec(d*x+c)+2/d*a*b^3*ln(sec(d*x+c)+tan(d*x+c))+1/d*b^4*tan(d*x+c)","A"
448,1,302,208,0.115000," ","int((a+b*cos(d*x+c))^4*sec(d*x+c)^7,x)","\frac{a^{4} \left(\sec^{5}\left(d x +c \right)\right) \tan \left(d x +c \right)}{6 d}+\frac{5 a^{4} \left(\sec^{3}\left(d x +c \right)\right) \tan \left(d x +c \right)}{24 d}+\frac{5 a^{4} \sec \left(d x +c \right) \tan \left(d x +c \right)}{16 d}+\frac{5 a^{4} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{16 d}+\frac{32 a^{3} b \tan \left(d x +c \right)}{15 d}+\frac{4 a^{3} b \left(\sec^{4}\left(d x +c \right)\right) \tan \left(d x +c \right)}{5 d}+\frac{16 a^{3} b \left(\sec^{2}\left(d x +c \right)\right) \tan \left(d x +c \right)}{15 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} \tan \left(d x +c \right) \sec \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{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) \sec \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,"1/6*a^4*sec(d*x+c)^5*tan(d*x+c)/d+5/24*a^4*sec(d*x+c)^3*tan(d*x+c)/d+5/16*a^4*sec(d*x+c)*tan(d*x+c)/d+5/16/d*a^4*ln(sec(d*x+c)+tan(d*x+c))+32/15*a^3*b*tan(d*x+c)/d+4/5*a^3*b*sec(d*x+c)^4*tan(d*x+c)/d+16/15*a^3*b*sec(d*x+c)^2*tan(d*x+c)/d+3/2/d*a^2*b^2*tan(d*x+c)*sec(d*x+c)^3+9/4/d*a^2*b^2*tan(d*x+c)*sec(d*x+c)+9/4/d*a^2*b^2*ln(sec(d*x+c)+tan(d*x+c))+8/3/d*a*b^3*tan(d*x+c)+4/3/d*a*b^3*tan(d*x+c)*sec(d*x+c)^2+1/2/d*b^4*tan(d*x+c)*sec(d*x+c)+1/2/d*b^4*ln(sec(d*x+c)+tan(d*x+c))","A"
449,1,672,174,0.063000," ","int(cos(d*x+c)^5/(a+b*cos(d*x+c)),x)","-\frac{2 a^{5} \arctan \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} \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{2 \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{3}}{d \,b^{4} \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) a^{2}}{d \,b^{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) a}{d \,b^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{5 \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 d b \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) a^{3}}{d \,b^{4} \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) a}{3 d \,b^{2} \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 b \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) a^{2}}{d \,b^{3} \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) a^{2}}{d \,b^{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 b \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) a^{3}}{d \,b^{4} \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) a}{3 d \,b^{2} \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) a^{2}}{d \,b^{3} \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 b \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) a^{3}}{d \,b^{4} \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) a}{d \,b^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{4}}{d \,b^{5}}+\frac{\arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{2}}{d \,b^{3}}+\frac{3 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 d b}"," ",0,"-2/d*a^5/b^5/((a-b)*(a+b))^(1/2)*arctan(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))-2/d/b^4/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^7*a^3-1/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^7*a^2-2/d/b^2/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^7*a-5/4/d/b/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^7-6/d/b^4/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^5*a^3-10/3/d/b^2/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^5*a+3/4/d/b/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^5-1/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^5*a^2+1/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^3*a^2-3/4/d/b/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^3-6/d/b^4/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^3*a^3-10/3/d/b^2/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^3*a+1/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)*a^2+5/4/d/b/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)-2/d/b^4/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)*a^3-2/d/b^2/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)*a+2/d/b^5*arctan(tan(1/2*d*x+1/2*c))*a^4+1/d/b^3*arctan(tan(1/2*d*x+1/2*c))*a^2+3/4/d/b*arctan(tan(1/2*d*x+1/2*c))","B"
450,1,367,131,0.058000," ","int(cos(d*x+c)^4/(a+b*cos(d*x+c)),x)","\frac{2 a^{4} \arctan \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{2 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{2}}{d \,b^{3} \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) a}{d \,b^{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)}{d b \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) a^{2}}{d \,b^{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 b \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) a^{2}}{d \,b^{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 b \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) a}{d \,b^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}-\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{3}}{d \,b^{4}}-\frac{\arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) a}{d \,b^{2}}"," ",0,"2/d*a^4/b^4/((a-b)*(a+b))^(1/2)*arctan(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))+2/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)^5*a^2+1/d/b^2/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)^5*a+2/d/b/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)^5+4/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)^3*a^2+4/3/d/b/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)^3+2/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)*a^2+2/d/b/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)-1/d/b^2/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)*a-2/d/b^4*arctan(tan(1/2*d*x+1/2*c))*a^3-1/d/b^2*arctan(tan(1/2*d*x+1/2*c))*a","B"
451,1,222,97,0.063000," ","int(cos(d*x+c)^3/(a+b*cos(d*x+c)),x)","-\frac{2 a^{3} \arctan \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{2 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a}{d \,b^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}-\frac{\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)}{d b \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) a}{d \,b^{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 b \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{2}}{d \,b^{3}}+\frac{\arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d b}"," ",0,"-2/d*a^3/b^3/((a-b)*(a+b))^(1/2)*arctan(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))-2/d/b^2/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)^3*a-1/d/b/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)^3-2/d/b^2/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)*a+1/d/b/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)+2/d/b^3*arctan(tan(1/2*d*x+1/2*c))*a^2+1/d/b*arctan(tan(1/2*d*x+1/2*c))","B"
452,1,102,67,0.046000," ","int(cos(d*x+c)^2/(a+b*cos(d*x+c)),x)","\frac{2 a^{2} \arctan \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{2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d b \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) a}{d \,b^{2}}"," ",0,"2/d*a^2/b^2/((a-b)*(a+b))^(1/2)*arctan(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))+2/d/b*tan(1/2*d*x+1/2*c)/(1+tan(1/2*d*x+1/2*c)^2)-2/d/b^2*arctan(tan(1/2*d*x+1/2*c))*a","A"
453,1,67,50,0.049000," ","int(cos(d*x+c)/(a+b*cos(d*x+c)),x)","-\frac{2 a \arctan \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{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d b}"," ",0,"-2/d*a/b/((a-b)*(a+b))^(1/2)*arctan(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))+2/d/b*arctan(tan(1/2*d*x+1/2*c))","A"
454,1,44,40,0.037000," ","int(1/(a+b*cos(d*x+c)),x)","\frac{2 \arctan \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)*arctan(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))","A"
455,1,88,59,0.070000," ","int(sec(d*x+c)/(a+b*cos(d*x+c)),x)","-\frac{2 b \arctan \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{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}{a d}+\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{a d}"," ",0,"-2/d/a*b/((a-b)*(a+b))^(1/2)*arctan(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))-1/a/d*ln(tan(1/2*d*x+1/2*c)-1)+1/a/d*ln(tan(1/2*d*x+1/2*c)+1)","A"
456,1,134,76,0.084000," ","int(sec(d*x+c)^2/(a+b*cos(d*x+c)),x)","\frac{2 b^{2} \arctan \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{1}{a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{b \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}{d \,a^{2}}-\frac{1}{a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}-\frac{b \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{d \,a^{2}}"," ",0,"2/d*b^2/a^2/((a-b)*(a+b))^(1/2)*arctan(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))-1/a/d/(tan(1/2*d*x+1/2*c)-1)+1/d*b/a^2*ln(tan(1/2*d*x+1/2*c)-1)-1/a/d/(tan(1/2*d*x+1/2*c)+1)-1/d*b/a^2*ln(tan(1/2*d*x+1/2*c)+1)","A"
457,1,262,106,0.106000," ","int(sec(d*x+c)^3/(a+b*cos(d*x+c)),x)","-\frac{2 b^{3} \arctan \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{1}{2 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}+\frac{1}{2 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{b}{d \,a^{2} \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)}{2 a d}-\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right) b^{2}}{d \,a^{3}}-\frac{1}{2 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}+\frac{1}{2 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}+\frac{b}{d \,a^{2} \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)}{2 a d}+\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right) b^{2}}{d \,a^{3}}"," ",0,"-2/d*b^3/a^3/((a-b)*(a+b))^(1/2)*arctan(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))+1/2/a/d/(tan(1/2*d*x+1/2*c)-1)^2+1/2/a/d/(tan(1/2*d*x+1/2*c)-1)+1/d/a^2/(tan(1/2*d*x+1/2*c)-1)*b-1/2/a/d*ln(tan(1/2*d*x+1/2*c)-1)-1/d/a^3*ln(tan(1/2*d*x+1/2*c)-1)*b^2-1/2/a/d/(tan(1/2*d*x+1/2*c)+1)^2+1/2/a/d/(tan(1/2*d*x+1/2*c)+1)+1/d/a^2/(tan(1/2*d*x+1/2*c)+1)*b+1/2/a/d*ln(tan(1/2*d*x+1/2*c)+1)+1/d/a^3*ln(tan(1/2*d*x+1/2*c)+1)*b^2","B"
458,1,400,140,0.110000," ","int(sec(d*x+c)^4/(a+b*cos(d*x+c)),x)","\frac{2 b^{4} \arctan \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{1}{3 d a \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{3}}-\frac{1}{2 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}-\frac{b}{2 d \,a^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}-\frac{1}{a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{b}{2 d \,a^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{b^{2}}{d \,a^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{b \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}{2 d \,a^{2}}+\frac{b^{3} \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}{d \,a^{4}}-\frac{1}{3 d a \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}+\frac{1}{2 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}+\frac{b}{2 d \,a^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}-\frac{1}{a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}-\frac{b}{2 d \,a^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}-\frac{b^{2}}{d \,a^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}-\frac{b \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{2 d \,a^{2}}-\frac{b^{3} \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{d \,a^{4}}"," ",0,"2/d*b^4/a^4/((a-b)*(a+b))^(1/2)*arctan(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))-1/3/d/a/(tan(1/2*d*x+1/2*c)-1)^3-1/2/a/d/(tan(1/2*d*x+1/2*c)-1)^2-1/2/d/a^2/(tan(1/2*d*x+1/2*c)-1)^2*b-1/a/d/(tan(1/2*d*x+1/2*c)-1)-1/2/d/a^2/(tan(1/2*d*x+1/2*c)-1)*b-1/d/a^3/(tan(1/2*d*x+1/2*c)-1)*b^2+1/2/d*b/a^2*ln(tan(1/2*d*x+1/2*c)-1)+1/d*b^3/a^4*ln(tan(1/2*d*x+1/2*c)-1)-1/3/d/a/(tan(1/2*d*x+1/2*c)+1)^3+1/2/a/d/(tan(1/2*d*x+1/2*c)+1)^2+1/2/d/a^2/(tan(1/2*d*x+1/2*c)+1)^2*b-1/a/d/(tan(1/2*d*x+1/2*c)+1)-1/2/d/a^2/(tan(1/2*d*x+1/2*c)+1)*b-1/d/a^3/(tan(1/2*d*x+1/2*c)+1)*b^2-1/2/d*b/a^2*ln(tan(1/2*d*x+1/2*c)+1)-1/d*b^3/a^4*ln(tan(1/2*d*x+1/2*c)+1)","B"
459,1,504,253,0.071000," ","int(cos(d*x+c)^5/(a+b*cos(d*x+c))^2,x)","\frac{2 a^{5} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,b^{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{8 a^{6} \arctan \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 -b \right) \left(a +b \right) \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{10 a^{4} \arctan \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 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{2}}{d \,b^{4} \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) a}{d \,b^{3} \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)}{d \,b^{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) a^{2}}{d \,b^{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 \,b^{2} \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 \,b^{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) a}{d \,b^{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 \,b^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}-\frac{8 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{3}}{d \,b^{5}}-\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) a}{d \,b^{3}}"," ",0,"2/d*a^5/b^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)+8/d*a^6/b^5/(a-b)/(a+b)/((a-b)*(a+b))^(1/2)*arctan(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))-10/d*a^4/b^3/(a-b)/(a+b)/((a-b)*(a+b))^(1/2)*arctan(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))+6/d/b^4/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)^5*a^2+2/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)^5*a+2/d/b^2/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)^5+12/d/b^4/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)^3*a^2+4/3/d/b^2/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)^3+6/d/b^4/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)*a^2-2/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)*a+2/d/b^2/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)-8/d/b^5*arctan(tan(1/2*d*x+1/2*c))*a^3-2/d/b^3*arctan(tan(1/2*d*x+1/2*c))*a","A"
460,1,358,158,0.063000," ","int(cos(d*x+c)^4/(a+b*cos(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} \arctan \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} \arctan \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 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a}{d \,b^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}-\frac{\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,b^{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) a}{d \,b^{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 \,b^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{6 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{2}}{d \,b^{4}}+\frac{\arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{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)*arctan(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)*arctan(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))-4/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)^3*a-1/d/b^2/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)^3-4/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)*a+1/d/b^2/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)+6/d/b^4*arctan(tan(1/2*d*x+1/2*c))*a^2+1/d/b^2*arctan(tan(1/2*d*x+1/2*c))","B"
461,1,238,146,0.063000," ","int(cos(d*x+c)^3/(a+b*cos(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} \arctan \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} \arctan \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 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,b^{2} \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}{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)*arctan(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)*arctan(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))+2/d/b^2*tan(1/2*d*x+1/2*c)/(1+tan(1/2*d*x+1/2*c)^2)-4/d/b^3*arctan(tan(1/2*d*x+1/2*c))*a","A"
462,1,200,99,0.056000," ","int(cos(d*x+c)^2/(a+b*cos(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} \arctan \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 \arctan \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 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\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)*arctan(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)*arctan(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))+2/d/b^2*arctan(tan(1/2*d*x+1/2*c))","B"
463,1,116,76,0.048000," ","int(cos(d*x+c)/(a+b*cos(d*x+c))^2,x)","\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \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 \arctan \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)}}"," ",0,"2/d*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/d*b/(a-b)/(a+b)/((a-b)*(a+b))^(1/2)*arctan(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))","A"
464,1,116,77,0.041000," ","int(1/(a+b*cos(d*x+c))^2,x)","-\frac{2 b \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \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 \arctan \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)}}"," ",0,"-2/d*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/(a-b)/(a+b)/((a-b)*(a+b))^(1/2)*arctan(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))","A"
465,1,221,109,0.088000," ","int(sec(d*x+c)/(a+b*cos(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 \arctan \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} \arctan \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{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}{d \,a^{2}}+\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\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)*arctan(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)*arctan(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))-1/d/a^2*ln(tan(1/2*d*x+1/2*c)-1)+1/d/a^2*ln(tan(1/2*d*x+1/2*c)+1)","B"
466,1,271,146,0.094000," ","int(sec(d*x+c)^2/(a+b*cos(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} \arctan \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} \arctan \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 b \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}{d \,a^{3}}-\frac{1}{d \,a^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{1}{d \,a^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}-\frac{2 b \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\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)*arctan(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)*arctan(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))+2/d*b/a^3*ln(tan(1/2*d*x+1/2*c)-1)-1/d/a^2/(tan(1/2*d*x+1/2*c)-1)-1/d/a^2/(tan(1/2*d*x+1/2*c)+1)-2/d*b/a^3*ln(tan(1/2*d*x+1/2*c)+1)","A"
467,1,401,204,0.128000," ","int(sec(d*x+c)^3/(a+b*cos(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} \arctan \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} \arctan \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{1}{2 d \,a^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}+\frac{1}{2 d \,a^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{2 b}{d \,a^{3} \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)}{2 d \,a^{2}}-\frac{3 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right) b^{2}}{d \,a^{4}}-\frac{1}{2 d \,a^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}+\frac{1}{2 d \,a^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}+\frac{2 b}{d \,a^{3} \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)}{2 d \,a^{2}}+\frac{3 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\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)*arctan(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)*arctan(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))+1/2/d/a^2/(tan(1/2*d*x+1/2*c)-1)^2+1/2/d/a^2/(tan(1/2*d*x+1/2*c)-1)+2/d/a^3/(tan(1/2*d*x+1/2*c)-1)*b-1/2/d/a^2*ln(tan(1/2*d*x+1/2*c)-1)-3/d/a^4*ln(tan(1/2*d*x+1/2*c)-1)*b^2-1/2/d/a^2/(tan(1/2*d*x+1/2*c)+1)^2+1/2/d/a^2/(tan(1/2*d*x+1/2*c)+1)+2/d/a^3/(tan(1/2*d*x+1/2*c)+1)*b+1/2/d/a^2*ln(tan(1/2*d*x+1/2*c)+1)+3/d/a^4*ln(tan(1/2*d*x+1/2*c)+1)*b^2","A"
468,1,535,257,0.124000," ","int(sec(d*x+c)^4/(a+b*cos(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} \arctan \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} \arctan \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{1}{3 d \,a^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{3}}-\frac{1}{2 d \,a^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}-\frac{b}{d \,a^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}-\frac{1}{d \,a^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{b}{d \,a^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{3 b^{2}}{d \,a^{4} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{b \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}{d \,a^{3}}+\frac{4 b^{3} \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}{d \,a^{5}}-\frac{1}{3 d \,a^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}+\frac{1}{2 d \,a^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}+\frac{b}{d \,a^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}-\frac{1}{d \,a^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}-\frac{b}{d \,a^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}-\frac{3 b^{2}}{d \,a^{4} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}-\frac{b \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{d \,a^{3}}-\frac{4 b^{3} \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{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)*arctan(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)*arctan(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))-1/3/d/a^2/(tan(1/2*d*x+1/2*c)-1)^3-1/2/d/a^2/(tan(1/2*d*x+1/2*c)-1)^2-1/d/a^3/(tan(1/2*d*x+1/2*c)-1)^2*b-1/d/a^2/(tan(1/2*d*x+1/2*c)-1)-1/d/a^3/(tan(1/2*d*x+1/2*c)-1)*b-3/d/a^4/(tan(1/2*d*x+1/2*c)-1)*b^2+1/d*b/a^3*ln(tan(1/2*d*x+1/2*c)-1)+4/d*b^3/a^5*ln(tan(1/2*d*x+1/2*c)-1)-1/3/d/a^2/(tan(1/2*d*x+1/2*c)+1)^3+1/2/d/a^2/(tan(1/2*d*x+1/2*c)+1)^2+1/d/a^3/(tan(1/2*d*x+1/2*c)+1)^2*b-1/d/a^2/(tan(1/2*d*x+1/2*c)+1)-1/d/a^3/(tan(1/2*d*x+1/2*c)+1)*b-3/d/a^4/(tan(1/2*d*x+1/2*c)+1)*b^2-1/d*b/a^3*ln(tan(1/2*d*x+1/2*c)+1)-4/d*b^3/a^5*ln(tan(1/2*d*x+1/2*c)+1)","B"
469,1,802,281,0.069000," ","int(cos(d*x+c)^5/(a+b*cos(d*x+c))^3,x)","-\frac{6 a^{6} \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)^{2} \left(a -b \right) \left(a^{2}+2 a b +b^{2}\right)}+\frac{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{10 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{6 a^{6} \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)^{2} \left(a +b \right) \left(a^{2}-2 a b +b^{2}\right)}-\frac{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{10 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{12 a^{7} \arctan \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^{4}-2 a^{2} b^{2}+b^{4}\right) \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{29 a^{5} \arctan \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{20 a^{3} \arctan \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 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a}{d \,b^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}-\frac{\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,b^{3} \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) a}{d \,b^{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 \,b^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{12 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{2}}{d \,b^{5}}+\frac{\arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,b^{3}}"," ",0,"-6/d*a^6/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*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+10/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)^3-6/d*a^6/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*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)+10/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)-12/d*a^7/b^5/(a^4-2*a^2*b^2+b^4)/((a-b)*(a+b))^(1/2)*arctan(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))+29/d*a^5/b^3/(a^4-2*a^2*b^2+b^4)/((a-b)*(a+b))^(1/2)*arctan(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))-20/d*a^3/b/(a^4-2*a^2*b^2+b^4)/((a-b)*(a+b))^(1/2)*arctan(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))-6/d/b^4/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)^3*a-1/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)^3-6/d/b^4/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)*a+1/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)+12/d/b^5*arctan(tan(1/2*d*x+1/2*c))*a^2+1/d/b^3*arctan(tan(1/2*d*x+1/2*c))","B"
470,1,679,206,0.071000," ","int(cos(d*x+c)^4/(a+b*cos(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} \arctan \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} \arctan \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} \arctan \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{2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,b^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}-\frac{6 a \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\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)*arctan(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)*arctan(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)*arctan(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))+2/d/b^3*tan(1/2*d*x+1/2*c)/(1+tan(1/2*d*x+1/2*c)^2)-6/d/b^4*a*arctan(tan(1/2*d*x+1/2*c))","B"
471,1,639,166,0.063000," ","int(cos(d*x+c)^3/(a+b*cos(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} \arctan \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} \arctan \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 \arctan \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{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\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)*arctan(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)*arctan(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)*arctan(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))+2/d/b^3*arctan(tan(1/2*d*x+1/2*c))","B"
472,1,400,136,0.051000," ","int(cos(d*x+c)^2/(a+b*cos(d*x+c))^3,x)","-\frac{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{4 a \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b}{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{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{4 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b}{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{a^{2} \arctan \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{2 \arctan \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) b^{2}}{d \left(a^{4}-2 a^{2} b^{2}+b^{4}\right) \sqrt{\left(a -b \right) \left(a +b \right)}}"," ",0,"-1/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)^3-4/d/(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^2+2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3*b+1/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)-4/d/(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^2-2*a*b+b^2)*tan(1/2*d*x+1/2*c)*b+1/d*a^2/(a^4-2*a^2*b^2+b^4)/((a-b)*(a+b))^(1/2)*arctan(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))+2/d/(a^4-2*a^2*b^2+b^4)/((a-b)*(a+b))^(1/2)*arctan(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))*b^2","B"
473,1,475,121,0.051000," ","int(cos(d*x+c)/(a+b*cos(d*x+c))^3,x)","\frac{2 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{a \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b}{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 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{2}}{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^{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{a \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b}{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 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b^{2}}{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{3 a b \arctan \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)}}"," ",0,"2/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+1/d/(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^2+2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3*b+2/d/(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*b^2+2/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)-1/d/(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^2-2*a*b+b^2)*tan(1/2*d*x+1/2*c)*b+2/d/(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)*b^2-3/d*a*b/(a^4-2*a^2*b^2+b^4)/((a-b)*(a+b))^(1/2)*arctan(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))","B"
474,1,400,120,0.047000," ","int(1/(a+b*cos(d*x+c))^3,x)","-\frac{4 a \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b}{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{\left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{2}}{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{4 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b}{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{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) b^{2}}{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^{2} \arctan \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{\arctan \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) b^{2}}{d \left(a^{4}-2 a^{2} b^{2}+b^{4}\right) \sqrt{\left(a -b \right) \left(a +b \right)}}"," ",0,"-4/d/(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^2+2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3*b-1/d/(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*b^2-4/d/(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^2-2*a*b+b^2)*tan(1/2*d*x+1/2*c)*b+1/d/(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)*b^2+2/d*a^2/(a^4-2*a^2*b^2+b^4)/((a-b)*(a+b))^(1/2)*arctan(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))+1/d/(a^4-2*a^2*b^2+b^4)/((a-b)*(a+b))^(1/2)*arctan(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))*b^2","B"
475,1,660,169,0.096000," ","int(sec(d*x+c)/(a+b*cos(d*x+c))^3,x)","\frac{6 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{2}}{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 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b^{2}}{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 \arctan \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} \arctan \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} \arctan \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{\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,"6/d/(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*b^2+1/d*b^3/a/(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*b^4/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+6/d/(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)*b^2-1/d*b^3/a/(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*b^4/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)-6/d*a*b/(a^4-2*a^2*b^2+b^4)/((a-b)*(a+b))^(1/2)*arctan(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))+5/d*b^3/a/(a^4-2*a^2*b^2+b^4)/((a-b)*(a+b))^(1/2)*arctan(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))-2/d*b^5/a^3/(a^4-2*a^2*b^2+b^4)/((a-b)*(a+b))^(1/2)*arctan(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))-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)","B"
476,1,712,217,0.105000," ","int(sec(d*x+c)^2/(a+b*cos(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 \arctan \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) b^{2}}{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} \arctan \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} \arctan \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{1}{d \,a^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{3 b \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}{d \,a^{4}}-\frac{1}{d \,a^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}-\frac{3 b \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{d \,a^{4}}"," ",0,"-8/d*b^3/a/(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^4/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+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*b^3/a/(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^4/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)+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/(a^4-2*a^2*b^2+b^4)/((a-b)*(a+b))^(1/2)*arctan(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))*b^2-15/d*b^4/a^2/(a^4-2*a^2*b^2+b^4)/((a-b)*(a+b))^(1/2)*arctan(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)*arctan(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))-1/d/a^3/(tan(1/2*d*x+1/2*c)-1)+3/d*b/a^4*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*b/a^4*ln(tan(1/2*d*x+1/2*c)+1)","B"
477,1,845,286,0.136000," ","int(sec(d*x+c)^3/(a+b*cos(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} \arctan \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} \arctan \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} \arctan \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{1}{2 d \,a^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}+\frac{1}{2 d \,a^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{3 b}{d \,a^{4} \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)}{2 d \,a^{3}}-\frac{6 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right) b^{2}}{d \,a^{5}}-\frac{1}{2 d \,a^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}+\frac{1}{2 d \,a^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}+\frac{3 b}{d \,a^{4} \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)}{2 d \,a^{3}}+\frac{6 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right) b^{2}}{d \,a^{5}}"," ",0,"10/d*b^4/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+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*b^4/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)-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*b^3/a/(a^4-2*a^2*b^2+b^4)/((a-b)*(a+b))^(1/2)*arctan(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))+29/d*b^5/a^3/(a^4-2*a^2*b^2+b^4)/((a-b)*(a+b))^(1/2)*arctan(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)*arctan(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))+1/2/d/a^3/(tan(1/2*d*x+1/2*c)-1)^2+1/2/d/a^3/(tan(1/2*d*x+1/2*c)-1)+3/d/a^4/(tan(1/2*d*x+1/2*c)-1)*b-1/2/d/a^3*ln(tan(1/2*d*x+1/2*c)-1)-6/d/a^5*ln(tan(1/2*d*x+1/2*c)-1)*b^2-1/2/d/a^3/(tan(1/2*d*x+1/2*c)+1)^2+1/2/d/a^3/(tan(1/2*d*x+1/2*c)+1)+3/d/a^4/(tan(1/2*d*x+1/2*c)+1)*b+1/2/d/a^3*ln(tan(1/2*d*x+1/2*c)+1)+6/d/a^5*ln(tan(1/2*d*x+1/2*c)+1)*b^2","B"
478,1,1396,290,0.075000," ","int(cos(d*x+c)^5/(a+b*cos(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} \arctan \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 b^{2} a^{4}+3 b^{4} a^{2}-b^{6}\right) \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{28 a^{6} \arctan \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 b^{2} a^{4}+3 b^{4} a^{2}-b^{6}\right) \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{35 a^{4} \arctan \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 b^{2} a^{4}+3 b^{4} a^{2}-b^{6}\right) \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{20 a^{2} b \arctan \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 b^{2} a^{4}+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 \,b^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}-\frac{8 a \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\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)*arctan(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)*arctan(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)*arctan(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)*arctan(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))+2/d/b^4*tan(1/2*d*x+1/2*c)/(1+tan(1/2*d*x+1/2*c)^2)-8/d/b^5*a*arctan(tan(1/2*d*x+1/2*c))","B"
479,1,1356,235,0.075000," ","int(cos(d*x+c)^4/(a+b*cos(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} \arctan \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 b^{2} a^{4}+3 b^{4} a^{2}-b^{6}\right) \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{7 a^{5} \arctan \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 b^{2} a^{4}+3 b^{4} a^{2}-b^{6}\right) \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{8 a^{3} \arctan \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 b^{2} a^{4}+3 b^{4} a^{2}-b^{6}\right) \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{8 a \,b^{2} \arctan \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 b^{2} a^{4}+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 \,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)*arctan(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)*arctan(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)*arctan(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)*arctan(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))+2/d/b^4*arctan(tan(1/2*d*x+1/2*c))","B"
480,1,776,207,0.063000," ","int(cos(d*x+c)^3/(a+b*cos(d*x+c))^4,x)","\frac{2 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{3 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{6 a \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{2}}{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^{3} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 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{12 a \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{2}}{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^{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{3 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{6 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b^{2}}{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{3 a^{2} b \arctan \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 b^{2} a^{4}+3 b^{4} a^{2}-b^{6}\right) \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{2 b^{3} \arctan \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 b^{2} a^{4}+3 b^{4} a^{2}-b^{6}\right) \sqrt{\left(a -b \right) \left(a +b \right)}}"," ",0,"2/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+3/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+6/d/(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-b)/(a^3+3*a^2*b+3*a*b^2+b^3)*tan(1/2*d*x+1/2*c)^5*b^2+4/3/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+12/d/(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^2-2*a*b+b^2)/(a^2+2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3*b^2+2/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)-3/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)+6/d/(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+b)/(a^3-3*a^2*b+3*a*b^2-b^3)*tan(1/2*d*x+1/2*c)*b^2-3/d*a^2*b/(a^6-3*a^4*b^2+3*a^2*b^4-b^6)/((a-b)*(a+b))^(1/2)*arctan(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))-2/d*b^3/(a^6-3*a^4*b^2+3*a^2*b^4-b^6)/((a-b)*(a+b))^(1/2)*arctan(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))","B"
481,1,930,191,0.054000," ","int(cos(d*x+c)^2/(a+b*cos(d*x+c))^4,x)","-\frac{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{6 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{2 a \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{2}}{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 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{3}}{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{28 a^{2} b \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 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{4 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{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{6 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 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b^{2}}{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 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b^{3}}{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{a^{3} \arctan \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 b^{2} a^{4}+3 b^{4} a^{2}-b^{6}\right) \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{4 a \,b^{2} \arctan \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 b^{2} a^{4}+3 b^{4} a^{2}-b^{6}\right) \sqrt{\left(a -b \right) \left(a +b \right)}}"," ",0,"-1/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)^5-6/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)^5-2/d/(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-b)/(a^3+3*a^2*b+3*a*b^2+b^3)*tan(1/2*d*x+1/2*c)^5*b^2-2/d/(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*b^3-28/3/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)^3-4/d/(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*a*b+b^2)/(a^2+2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3+1/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)-6/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*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b+a+b)^3*a/(a+b)/(a^3-3*a^2*b+3*a*b^2-b^3)*tan(1/2*d*x+1/2*c)*b^2-2/d/(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)*b^3+1/d*a^3/(a^6-3*a^4*b^2+3*a^2*b^4-b^6)/((a-b)*(a+b))^(1/2)*arctan(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))+4/d*a*b^2/(a^6-3*a^4*b^2+3*a^2*b^4-b^6)/((a-b)*(a+b))^(1/2)*arctan(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))","B"
482,1,931,177,0.054000," ","int(cos(d*x+c)/(a+b*cos(d*x+c))^4,x)","\frac{2 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{2 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{6 a \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{2}}{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{\left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{3}}{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^{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{28 a \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{2}}{3 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^{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{2 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{6 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b^{2}}{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{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) b^{3}}{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^{2} b \arctan \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 b^{2} a^{4}+3 b^{4} a^{2}-b^{6}\right) \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{b^{3} \arctan \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 b^{2} a^{4}+3 b^{4} a^{2}-b^{6}\right) \sqrt{\left(a -b \right) \left(a +b \right)}}"," ",0,"2/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+2/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+6/d/(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-b)/(a^3+3*a^2*b+3*a*b^2+b^3)*tan(1/2*d*x+1/2*c)^5*b^2+1/d/(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*b^3+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^2-2*a*b+b^2)/(a^2+2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3+28/3/d/(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^2-2*a*b+b^2)/(a^2+2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3*b^2+2/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)-2/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)+6/d/(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+b)/(a^3-3*a^2*b+3*a*b^2-b^3)*tan(1/2*d*x+1/2*c)*b^2-1/d/(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)*b^3-4/d*a^2*b/(a^6-3*a^4*b^2+3*a^2*b^4-b^6)/((a-b)*(a+b))^(1/2)*arctan(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))-1/d*b^3/(a^6-3*a^4*b^2+3*a^2*b^4-b^6)/((a-b)*(a+b))^(1/2)*arctan(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))","B"
483,1,776,169,0.054000," ","int(1/(a+b*cos(d*x+c))^4,x)","-\frac{6 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{3 a \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{2}}{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 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{3}}{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^{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{4 b^{3} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 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^{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{3 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b^{2}}{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 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b^{3}}{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^{3} \arctan \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 b^{2} a^{4}+3 b^{4} a^{2}-b^{6}\right) \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{3 a \,b^{2} \arctan \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 b^{2} a^{4}+3 b^{4} a^{2}-b^{6}\right) \sqrt{\left(a -b \right) \left(a +b \right)}}"," ",0,"-6/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)^5-3/d/(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-b)/(a^3+3*a^2*b+3*a*b^2+b^3)*tan(1/2*d*x+1/2*c)^5*b^2-2/d/(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*b^3-12/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^2-2*a*b+b^2)/(a^2+2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3-4/3/d/(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*a*b+b^2)/(a^2+2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3-6/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)+3/d/(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+b)/(a^3-3*a^2*b+3*a*b^2-b^3)*tan(1/2*d*x+1/2*c)*b^2-2/d/(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)*b^3+2/d*a^3/(a^6-3*a^4*b^2+3*a^2*b^4-b^6)/((a-b)*(a+b))^(1/2)*arctan(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))+3/d*a*b^2/(a^6-3*a^4*b^2+3*a^2*b^4-b^6)/((a-b)*(a+b))^(1/2)*arctan(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))","B"
484,1,1377,236,0.102000," ","int(sec(d*x+c)/(a+b*cos(d*x+c))^4,x)","\frac{12 a \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{2}}{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 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{3}}{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 a \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{2}}{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 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b^{2}}{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 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b^{3}}{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 \arctan \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 b^{2} a^{4}+3 b^{4} a^{2}-b^{6}\right) \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{8 b^{3} \arctan \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 b^{2} a^{4}+3 b^{4} a^{2}-b^{6}\right) \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{7 b^{5} \arctan \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 b^{2} a^{4}+3 b^{4} a^{2}-b^{6}\right) \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{2 b^{7} \arctan \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 b^{2} a^{4}+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 \,a^{4}}+\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{d \,a^{4}}"," ",0,"12/d/(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-b)/(a^3+3*a^2*b+3*a*b^2+b^3)*tan(1/2*d*x+1/2*c)^5*b^2+4/d/(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*b^3-6/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/(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^2-2*a*b+b^2)/(a^2+2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3*b^2-44/3/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/(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+b)/(a^3-3*a^2*b+3*a*b^2-b^3)*tan(1/2*d*x+1/2*c)*b^2-4/d/(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)*b^3-6/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)*arctan(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)*arctan(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)*arctan(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)*arctan(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))-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)","B"
485,1,1429,291,0.121000," ","int(sec(d*x+c)^2/(a+b*cos(d*x+c))^4,x)","-\frac{20 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{3}}{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 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b^{3}}{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} \arctan \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 b^{2} a^{4}+3 b^{4} a^{2}-b^{6}\right) \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{35 b^{4} \arctan \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 b^{2} a^{4}+3 b^{4} a^{2}-b^{6}\right) \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{28 b^{6} \arctan \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 b^{2} a^{4}+3 b^{4} a^{2}-b^{6}\right) \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{8 b^{8} \arctan \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 b^{2} a^{4}+3 b^{4} a^{2}-b^{6}\right) \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{1}{d \,a^{4} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{4 b \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}{d \,a^{5}}-\frac{1}{d \,a^{4} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}-\frac{4 b \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{d \,a^{5}}"," ",0,"-20/d/(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*b^3-5/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/(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*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/(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)*b^3+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)*arctan(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)*arctan(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)*arctan(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)*arctan(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))-1/d/a^4/(tan(1/2*d*x+1/2*c)-1)+4/d*b/a^5*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*b/a^5*ln(tan(1/2*d*x+1/2*c)+1)","B"
486,1,827,298,1.088000," ","int(cos(d*x+c)^3*(a+b*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) b +a -b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(240 \left(\cos^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{4}+144 \left(\cos^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a \,b^{3}-600 \left(\cos^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{4}-4 \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{2} b^{2}-288 \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a \,b^{3}+640 \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{4}-8 \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{3} b +6 \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{2} b^{2}+230 \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a \,b^{3}-360 \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{4}-8 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{4}-17 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{2} b^{2}+25 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) b^{4}+8 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{4}-8 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{3} b +19 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{2} b^{2}-19 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a \,b^{3}+8 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) a^{3} b -2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) a^{2} b^{2}-86 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) a \,b^{3}+80 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) b^{4}\right)}{105 b^{3} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(a +b \right) \left(\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(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a +b}\, d}"," ",0,"-2/105*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(240*cos(1/2*d*x+1/2*c)^9*b^4+144*cos(1/2*d*x+1/2*c)^7*a*b^3-600*cos(1/2*d*x+1/2*c)^7*b^4-4*cos(1/2*d*x+1/2*c)^5*a^2*b^2-288*cos(1/2*d*x+1/2*c)^5*a*b^3+640*cos(1/2*d*x+1/2*c)^5*b^4-8*cos(1/2*d*x+1/2*c)^3*a^3*b+6*cos(1/2*d*x+1/2*c)^3*a^2*b^2+230*cos(1/2*d*x+1/2*c)^3*a*b^3-360*cos(1/2*d*x+1/2*c)^3*b^4-8*(sin(1/2*d*x+1/2*c)^2)^(1/2)*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)/(a-b))^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a^4-17*(sin(1/2*d*x+1/2*c)^2)^(1/2)*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)/(a-b))^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a^2*b^2+25*(sin(1/2*d*x+1/2*c)^2)^(1/2)*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)/(a-b))^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*b^4+8*(sin(1/2*d*x+1/2*c)^2)^(1/2)*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)/(a-b))^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a^4-8*(sin(1/2*d*x+1/2*c)^2)^(1/2)*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)/(a-b))^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a^3*b+19*(sin(1/2*d*x+1/2*c)^2)^(1/2)*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)/(a-b))^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a^2*b^2-19*(sin(1/2*d*x+1/2*c)^2)^(1/2)*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)/(a-b))^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a*b^3+8*cos(1/2*d*x+1/2*c)*a^3*b-2*cos(1/2*d*x+1/2*c)*a^2*b^2-86*cos(1/2*d*x+1/2*c)*a*b^3+80*cos(1/2*d*x+1/2*c)*b^4)/b^3/(-2*sin(1/2*d*x+1/2*c)^4*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*b+a+b)^(1/2)/d","B"
487,1,665,245,0.825000," ","int(cos(d*x+c)^2*(a+b*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) b +a -b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(24 \left(\cos^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{3}+16 \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a \,b^{2}-48 \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{3}+2 \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{2} b -24 \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a \,b^{2}+30 \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{3}+2 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{3}-2 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a \,b^{2}-2 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{3}+2 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{2} b +9 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a \,b^{2}-9 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) b^{3}-2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) a^{2} b +8 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) a \,b^{2}-6 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) b^{3}\right)}{15 b^{2} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(a +b \right) \left(\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(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a +b}\, d}"," ",0,"-2/15*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(24*cos(1/2*d*x+1/2*c)^7*b^3+16*cos(1/2*d*x+1/2*c)^5*a*b^2-48*cos(1/2*d*x+1/2*c)^5*b^3+2*cos(1/2*d*x+1/2*c)^3*a^2*b-24*cos(1/2*d*x+1/2*c)^3*a*b^2+30*cos(1/2*d*x+1/2*c)^3*b^3+2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)/(a-b))^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a^3-2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)/(a-b))^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a*b^2-2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)/(a-b))^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a^3+2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)/(a-b))^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a^2*b+9*(sin(1/2*d*x+1/2*c)^2)^(1/2)*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)/(a-b))^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a*b^2-9*(sin(1/2*d*x+1/2*c)^2)^(1/2)*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)/(a-b))^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*b^3-2*cos(1/2*d*x+1/2*c)*a^2*b+8*cos(1/2*d*x+1/2*c)*a*b^2-6*cos(1/2*d*x+1/2*c)*b^3)/b^2/(-2*sin(1/2*d*x+1/2*c)^4*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*b+a+b)^(1/2)/d","B"
488,1,452,204,0.740000," ","int(cos(d*x+c)*(a+b*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) b +a -b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(4 \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{2}+2 \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a b -6 \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{2}-\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{2}+\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) b^{2}+\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{2}-\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a b -2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) a b +2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) b^{2}\right)}{3 b \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(a +b \right) \left(\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(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a +b}\, d}"," ",0,"-2/3*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(4*cos(1/2*d*x+1/2*c)^5*b^2+2*cos(1/2*d*x+1/2*c)^3*a*b-6*cos(1/2*d*x+1/2*c)^3*b^2-(sin(1/2*d*x+1/2*c)^2)^(1/2)*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)/(a-b))^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a^2+(sin(1/2*d*x+1/2*c)^2)^(1/2)*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)/(a-b))^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*b^2+(sin(1/2*d*x+1/2*c)^2)^(1/2)*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)/(a-b))^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a^2-(sin(1/2*d*x+1/2*c)^2)^(1/2)*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)/(a-b))^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a*b-2*cos(1/2*d*x+1/2*c)*a*b+2*cos(1/2*d*x+1/2*c)*b^2)/b/(-2*sin(1/2*d*x+1/2*c)^4*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*b+a+b)^(1/2)/d","B"
489,1,170,82,0.000000," ","int((a+b*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) b +a -b \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{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) \left(a -b \right)}{\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(a +b \right) \left(\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(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a +b}\, d}"," ",0,"-2*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)*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*b+a-b)/(a-b))^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*(a-b)/(-2*sin(1/2*d*x+1/2*c)^4*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*b+a+b)^(1/2)/d","B"
490,1,194,168,1.089000," ","int(sec(d*x+c)*(a+b*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) b +a -b \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{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, \left(\EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) b -\EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), 2, \sqrt{-\frac{2 b}{a -b}}\right) a \right)}{\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(a +b \right) \left(\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(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a +b}\, d}"," ",0,"-2*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)*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*b+a-b)/(a-b))^(1/2)*(EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*b-EllipticPi(cos(1/2*d*x+1/2*c),2,(-2*b/(a-b))^(1/2))*a)/(-2*sin(1/2*d*x+1/2*c)^4*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*b+a+b)^(1/2)/d","A"
491,1,622,270,0.826000," ","int(sec(d*x+c)^2*(a+b*cos(d*x+c))^(1/2),x)","-\frac{\sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(4 b \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 -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)-2 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-\frac{2 b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a -b}+\frac{a +b}{a -b}}\, \left(\EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a -\EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a +\EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) b -\EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), 2, \sqrt{-\frac{2 b}{a -b}}\right) b \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{-\frac{2 b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a -b}+\frac{a +b}{a -b}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a -\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-\frac{2 b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a -b}+\frac{a +b}{a -b}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a +\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-\frac{2 b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a -b}+\frac{a +b}{a -b}}\, b \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right)-b \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-\frac{2 b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a -b}+\frac{a +b}{a -b}}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), 2, \sqrt{-\frac{2 b}{a -b}}\right)\right)}{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(a +b \right) \left(\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(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a +b}\, d}"," ",0,"-((2*cos(1/2*d*x+1/2*c)^2*b+a-b)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(4*b*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4+(-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)^2)^(1/2)*(-2*b/(a-b)*sin(1/2*d*x+1/2*c)^2+(a+b)/(a-b))^(1/2)*(EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a-EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a+EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*b-EllipticPi(cos(1/2*d*x+1/2*c),2,(-2*b/(a-b))^(1/2))*b)*sin(1/2*d*x+1/2*c)^2+(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*b/(a-b)*sin(1/2*d*x+1/2*c)^2+(a+b)/(a-b))^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a-(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*b/(a-b)*sin(1/2*d*x+1/2*c)^2+(a+b)/(a-b))^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a+(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*b/(a-b)*sin(1/2*d*x+1/2*c)^2+(a+b)/(a-b))^(1/2)*b*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))-b*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*b/(a-b)*sin(1/2*d*x+1/2*c)^2+(a+b)/(a-b))^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2,(-2*b/(a-b))^(1/2)))/(2*cos(1/2*d*x+1/2*c)^2-1)/(-2*sin(1/2*d*x+1/2*c)^4*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*b+a+b)^(1/2)/d","B"
492,1,977,323,0.908000," ","int(sec(d*x+c)^3*(a+b*cos(d*x+c))^(1/2),x)","-\frac{\sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(-8 b^{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(12 a b +8 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(-4 a^{2}-6 a b -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)+4 \sqrt{-\frac{2 b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a -b}+\frac{a +b}{a -b}}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(3 \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a b -\EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a b +\EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) b^{2}-4 \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), 2, \sqrt{-\frac{2 b}{a -b}}\right) a^{2}+\EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), 2, \sqrt{-\frac{2 b}{a -b}}\right) b^{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-4 \sqrt{-\frac{2 b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a -b}+\frac{a +b}{a -b}}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(3 \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a b -\EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a b +\EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) b^{2}-4 \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), 2, \sqrt{-\frac{2 b}{a -b}}\right) a^{2}+\EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), 2, \sqrt{-\frac{2 b}{a -b}}\right) b^{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+3 b \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-\frac{2 b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a -b}+\frac{a +b}{a -b}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a -\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-\frac{2 b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a -b}+\frac{a +b}{a -b}}\, b \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a +b^{2} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-\frac{2 b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a -b}+\frac{a +b}{a -b}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right)-4 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-\frac{2 b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a -b}+\frac{a +b}{a -b}}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), 2, \sqrt{-\frac{2 b}{a -b}}\right) a^{2}+\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-\frac{2 b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a -b}+\frac{a +b}{a -b}}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), 2, \sqrt{-\frac{2 b}{a -b}}\right) b^{2}\right)}{4 a \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)^{2} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(a +b \right) \left(\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(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a +b}\, d}"," ",0,"-1/4*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(-8*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6+(12*a*b+8*b^2)*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+(-4*a^2-6*a*b-2*b^2)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+4*(-2*b/(a-b)*sin(1/2*d*x+1/2*c)^2+(a+b)/(a-b))^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(3*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a*b-EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a*b+EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*b^2-4*EllipticPi(cos(1/2*d*x+1/2*c),2,(-2*b/(a-b))^(1/2))*a^2+EllipticPi(cos(1/2*d*x+1/2*c),2,(-2*b/(a-b))^(1/2))*b^2)*sin(1/2*d*x+1/2*c)^4-4*(-2*b/(a-b)*sin(1/2*d*x+1/2*c)^2+(a+b)/(a-b))^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(3*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a*b-EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a*b+EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*b^2-4*EllipticPi(cos(1/2*d*x+1/2*c),2,(-2*b/(a-b))^(1/2))*a^2+EllipticPi(cos(1/2*d*x+1/2*c),2,(-2*b/(a-b))^(1/2))*b^2)*sin(1/2*d*x+1/2*c)^2+3*b*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*b/(a-b)*sin(1/2*d*x+1/2*c)^2+(a+b)/(a-b))^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a-(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*b/(a-b)*sin(1/2*d*x+1/2*c)^2+(a+b)/(a-b))^(1/2)*b*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a+b^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*b/(a-b)*sin(1/2*d*x+1/2*c)^2+(a+b)/(a-b))^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))-4*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*b/(a-b)*sin(1/2*d*x+1/2*c)^2+(a+b)/(a-b))^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2,(-2*b/(a-b))^(1/2))*a^2+(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*b/(a-b)*sin(1/2*d*x+1/2*c)^2+(a+b)/(a-b))^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2,(-2*b/(a-b))^(1/2))*b^2)/a/(2*cos(1/2*d*x+1/2*c)^2-1)^2/(-2*sin(1/2*d*x+1/2*c)^4*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*b+a+b)^(1/2)/d","B"
493,1,995,344,0.875000," ","int(cos(d*x+c)^3*(a+b*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) b +a -b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(-1120 b^{5} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{10}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(1360 a \,b^{4}+2240 b^{5}\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(-424 a^{2} b^{3}-2040 a \,b^{4}-2072 b^{5}\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(-4 a^{3} b^{2}+424 a^{2} b^{3}+1568 a \,b^{4}+952 b^{5}\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(8 a^{4} b +2 a^{3} b^{2}-282 a^{2} b^{3}-444 a \,b^{4}-168 b^{5}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-8 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-\frac{2 b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a -b}+\frac{a +b}{a -b}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{5}-31 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-\frac{2 b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a -b}+\frac{a +b}{a -b}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{3} b^{2}+39 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-\frac{2 b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a -b}+\frac{a +b}{a -b}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a \,b^{4}+8 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-\frac{2 b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a -b}+\frac{a +b}{a -b}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{5}-8 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-\frac{2 b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a -b}+\frac{a +b}{a -b}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{4} b +33 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-\frac{2 b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a -b}+\frac{a +b}{a -b}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{3} b^{2}-33 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-\frac{2 b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a -b}+\frac{a +b}{a -b}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{2} b^{3}+147 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-\frac{2 b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a -b}+\frac{a +b}{a -b}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a \,b^{4}-147 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-\frac{2 b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a -b}+\frac{a +b}{a -b}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) b^{5}\right)}{315 b^{3} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(a +b \right) \left(\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(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a +b}\, d}"," ",0,"-2/315*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(-1120*b^5*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^10+(1360*a*b^4+2240*b^5)*sin(1/2*d*x+1/2*c)^8*cos(1/2*d*x+1/2*c)+(-424*a^2*b^3-2040*a*b^4-2072*b^5)*sin(1/2*d*x+1/2*c)^6*cos(1/2*d*x+1/2*c)+(-4*a^3*b^2+424*a^2*b^3+1568*a*b^4+952*b^5)*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+(8*a^4*b+2*a^3*b^2-282*a^2*b^3-444*a*b^4-168*b^5)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)-8*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*b/(a-b)*sin(1/2*d*x+1/2*c)^2+(a+b)/(a-b))^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a^5-31*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*b/(a-b)*sin(1/2*d*x+1/2*c)^2+(a+b)/(a-b))^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a^3*b^2+39*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*b/(a-b)*sin(1/2*d*x+1/2*c)^2+(a+b)/(a-b))^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a*b^4+8*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*b/(a-b)*sin(1/2*d*x+1/2*c)^2+(a+b)/(a-b))^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a^5-8*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*b/(a-b)*sin(1/2*d*x+1/2*c)^2+(a+b)/(a-b))^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a^4*b+33*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*b/(a-b)*sin(1/2*d*x+1/2*c)^2+(a+b)/(a-b))^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a^3*b^2-33*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*b/(a-b)*sin(1/2*d*x+1/2*c)^2+(a+b)/(a-b))^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a^2*b^3+147*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*b/(a-b)*sin(1/2*d*x+1/2*c)^2+(a+b)/(a-b))^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a*b^4-147*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*b/(a-b)*sin(1/2*d*x+1/2*c)^2+(a+b)/(a-b))^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*b^5)/b^3/(-2*sin(1/2*d*x+1/2*c)^4*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*b+a+b)^(1/2)/d","B"
494,1,827,292,0.701000," ","int(cos(d*x+c)^2*(a+b*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) b +a -b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(240 \left(\cos^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{4}+312 \left(\cos^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a \,b^{3}-600 \left(\cos^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{4}+108 \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{2} b^{2}-624 \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a \,b^{3}+640 \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{4}+6 \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{3} b -162 \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{2} b^{2}+440 \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a \,b^{3}-360 \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{4}+6 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{4}-31 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{2} b^{2}+25 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) b^{4}-6 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{4}+6 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{3} b +82 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{2} b^{2}-82 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a \,b^{3}-6 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) a^{3} b +54 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) a^{2} b^{2}-128 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) a \,b^{3}+80 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) b^{4}\right)}{105 b^{2} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(a +b \right) \left(\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(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a +b}\, d}"," ",0,"-2/105*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(240*cos(1/2*d*x+1/2*c)^9*b^4+312*cos(1/2*d*x+1/2*c)^7*a*b^3-600*cos(1/2*d*x+1/2*c)^7*b^4+108*cos(1/2*d*x+1/2*c)^5*a^2*b^2-624*cos(1/2*d*x+1/2*c)^5*a*b^3+640*cos(1/2*d*x+1/2*c)^5*b^4+6*cos(1/2*d*x+1/2*c)^3*a^3*b-162*cos(1/2*d*x+1/2*c)^3*a^2*b^2+440*cos(1/2*d*x+1/2*c)^3*a*b^3-360*cos(1/2*d*x+1/2*c)^3*b^4+6*(sin(1/2*d*x+1/2*c)^2)^(1/2)*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)/(a-b))^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a^4-31*(sin(1/2*d*x+1/2*c)^2)^(1/2)*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)/(a-b))^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a^2*b^2+25*(sin(1/2*d*x+1/2*c)^2)^(1/2)*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)/(a-b))^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*b^4-6*(sin(1/2*d*x+1/2*c)^2)^(1/2)*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)/(a-b))^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a^4+6*(sin(1/2*d*x+1/2*c)^2)^(1/2)*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)/(a-b))^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a^3*b+82*(sin(1/2*d*x+1/2*c)^2)^(1/2)*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)/(a-b))^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a^2*b^2-82*(sin(1/2*d*x+1/2*c)^2)^(1/2)*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)/(a-b))^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a*b^3-6*cos(1/2*d*x+1/2*c)*a^3*b+54*cos(1/2*d*x+1/2*c)*a^2*b^2-128*cos(1/2*d*x+1/2*c)*a*b^3+80*cos(1/2*d*x+1/2*c)*b^4)/b^2/(-2*sin(1/2*d*x+1/2*c)^4*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*b+a+b)^(1/2)/d","B"
495,1,663,237,0.756000," ","int(cos(d*x+c)*(a+b*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) b +a -b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(8 \left(\cos^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{3}+12 \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a \,b^{2}-16 \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{3}+4 \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{2} b -18 \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a \,b^{2}+10 \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{3}-\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{3}+\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a \,b^{2}+\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{3}-\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{2} b +3 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a \,b^{2}-3 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) b^{3}-4 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) a^{2} b +6 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) a \,b^{2}-2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) b^{3}\right)}{5 b \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(a +b \right) \left(\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(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a +b}\, d}"," ",0,"-2/5*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(8*cos(1/2*d*x+1/2*c)^7*b^3+12*cos(1/2*d*x+1/2*c)^5*a*b^2-16*cos(1/2*d*x+1/2*c)^5*b^3+4*cos(1/2*d*x+1/2*c)^3*a^2*b-18*cos(1/2*d*x+1/2*c)^3*a*b^2+10*cos(1/2*d*x+1/2*c)^3*b^3-(sin(1/2*d*x+1/2*c)^2)^(1/2)*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)/(a-b))^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a^3+(sin(1/2*d*x+1/2*c)^2)^(1/2)*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)/(a-b))^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a*b^2+(sin(1/2*d*x+1/2*c)^2)^(1/2)*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)/(a-b))^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a^3-(sin(1/2*d*x+1/2*c)^2)^(1/2)*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)/(a-b))^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a^2*b+3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)/(a-b))^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a*b^2-3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)/(a-b))^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*b^3-4*cos(1/2*d*x+1/2*c)*a^2*b+6*cos(1/2*d*x+1/2*c)*a*b^2-2*cos(1/2*d*x+1/2*c)*b^3)/b/(-2*sin(1/2*d*x+1/2*c)^4*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*b+a+b)^(1/2)/d","B"
496,1,450,199,0.000000," ","int((a+b*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) b +a -b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(4 \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{2}+2 \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a b -6 \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{2}-\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{2}+\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) b^{2}+4 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{2}-4 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a b -2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) a b +2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) b^{2}\right)}{3 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(a +b \right) \left(\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(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a +b}\, d}"," ",0,"-2/3*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(4*cos(1/2*d*x+1/2*c)^5*b^2+2*cos(1/2*d*x+1/2*c)^3*a*b-6*cos(1/2*d*x+1/2*c)^3*b^2-(sin(1/2*d*x+1/2*c)^2)^(1/2)*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)/(a-b))^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a^2+(sin(1/2*d*x+1/2*c)^2)^(1/2)*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)/(a-b))^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*b^2+4*(sin(1/2*d*x+1/2*c)^2)^(1/2)*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)/(a-b))^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a^2-4*(sin(1/2*d*x+1/2*c)^2)^(1/2)*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)/(a-b))^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a*b-2*cos(1/2*d*x+1/2*c)*a*b+2*cos(1/2*d*x+1/2*c)*b^2)/(-2*sin(1/2*d*x+1/2*c)^4*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*b+a+b)^(1/2)/d","B"
497,1,249,254,0.716000," ","int((a+b*cos(d*x+c))^(3/2)*sec(d*x+c),x)","-\frac{2 \sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b \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{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, \left(\EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a b +\EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a b -\EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) b^{2}-\EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), 2, \sqrt{-\frac{2 b}{a -b}}\right) a^{2}\right)}{\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(a +b \right) \left(\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(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a +b}\, d}"," ",0,"-2*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)*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*b+a-b)/(a-b))^(1/2)*(EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a*b+EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a*b-EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*b^2-EllipticPi(cos(1/2*d*x+1/2*c),2,(-2*b/(a-b))^(1/2))*a^2)/(-2*sin(1/2*d*x+1/2*c)^4*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*b+a+b)^(1/2)/d","A"
498,1,740,282,0.776000," ","int((a+b*cos(d*x+c))^(3/2)*sec(d*x+c)^2,x)","-\frac{\sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(4 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)+\left(-2 a^{2}-2 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)-2 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-\frac{2 b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a -b}+\frac{a +b}{a -b}}\, \left(\EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{2}+2 \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) b^{2}-\EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{2}+\EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a b -3 \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), 2, \sqrt{-\frac{2 b}{a -b}}\right) a b \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{-\frac{2 b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a -b}+\frac{a +b}{a -b}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{2}+2 b^{2} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-\frac{2 b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a -b}+\frac{a +b}{a -b}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right)-\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-\frac{2 b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a -b}+\frac{a +b}{a -b}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{2}+\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-\frac{2 b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a -b}+\frac{a +b}{a -b}}\, b \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a -3 a b \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-\frac{2 b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a -b}+\frac{a +b}{a -b}}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), 2, \sqrt{-\frac{2 b}{a -b}}\right)\right)}{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(a +b \right) \left(\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(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a +b}\, d}"," ",0,"-((2*cos(1/2*d*x+1/2*c)^2*b+a-b)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(4*a*b*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4+(-2*a^2-2*a*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)^2)^(1/2)*(-2*b/(a-b)*sin(1/2*d*x+1/2*c)^2+(a+b)/(a-b))^(1/2)*(EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a^2+2*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*b^2-EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a^2+EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a*b-3*EllipticPi(cos(1/2*d*x+1/2*c),2,(-2*b/(a-b))^(1/2))*a*b)*sin(1/2*d*x+1/2*c)^2+(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*b/(a-b)*sin(1/2*d*x+1/2*c)^2+(a+b)/(a-b))^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a^2+2*b^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*b/(a-b)*sin(1/2*d*x+1/2*c)^2+(a+b)/(a-b))^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))-(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*b/(a-b)*sin(1/2*d*x+1/2*c)^2+(a+b)/(a-b))^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a^2+(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*b/(a-b)*sin(1/2*d*x+1/2*c)^2+(a+b)/(a-b))^(1/2)*b*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a-3*a*b*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*b/(a-b)*sin(1/2*d*x+1/2*c)^2+(a+b)/(a-b))^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2,(-2*b/(a-b))^(1/2)))/(2*cos(1/2*d*x+1/2*c)^2-1)/(-2*sin(1/2*d*x+1/2*c)^4*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*b+a+b)^(1/2)/d","B"
499,1,980,316,0.867000," ","int((a+b*cos(d*x+c))^(3/2)*sec(d*x+c)^3,x)","-\frac{\sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(-40 b^{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(28 a b +40 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(-4 a^{2}-14 a b -10 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)+4 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-\frac{2 b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a -b}+\frac{a +b}{a -b}}\, \left(7 \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a b -5 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a b +5 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) b^{2}-4 \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), 2, \sqrt{-\frac{2 b}{a -b}}\right) a^{2}-3 \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), 2, \sqrt{-\frac{2 b}{a -b}}\right) b^{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{-\frac{2 b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a -b}+\frac{a +b}{a -b}}\, \left(7 \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a b -5 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a b +5 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) b^{2}-4 \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), 2, \sqrt{-\frac{2 b}{a -b}}\right) a^{2}-3 \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), 2, \sqrt{-\frac{2 b}{a -b}}\right) b^{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+7 b \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-\frac{2 b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a -b}+\frac{a +b}{a -b}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a -5 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-\frac{2 b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a -b}+\frac{a +b}{a -b}}\, b \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a +5 b^{2} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-\frac{2 b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a -b}+\frac{a +b}{a -b}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right)-4 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-\frac{2 b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a -b}+\frac{a +b}{a -b}}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), 2, \sqrt{-\frac{2 b}{a -b}}\right) a^{2}-3 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-\frac{2 b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a -b}+\frac{a +b}{a -b}}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), 2, \sqrt{-\frac{2 b}{a -b}}\right) b^{2}\right)}{4 \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)^{2} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(a +b \right) \left(\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(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a +b}\, d}"," ",0,"-1/4*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(-40*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6+(28*a*b+40*b^2)*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+(-4*a^2-14*a*b-10*b^2)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+4*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*b/(a-b)*sin(1/2*d*x+1/2*c)^2+(a+b)/(a-b))^(1/2)*(7*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a*b-5*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a*b+5*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*b^2-4*EllipticPi(cos(1/2*d*x+1/2*c),2,(-2*b/(a-b))^(1/2))*a^2-3*EllipticPi(cos(1/2*d*x+1/2*c),2,(-2*b/(a-b))^(1/2))*b^2)*sin(1/2*d*x+1/2*c)^4-4*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*b/(a-b)*sin(1/2*d*x+1/2*c)^2+(a+b)/(a-b))^(1/2)*(7*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a*b-5*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a*b+5*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*b^2-4*EllipticPi(cos(1/2*d*x+1/2*c),2,(-2*b/(a-b))^(1/2))*a^2-3*EllipticPi(cos(1/2*d*x+1/2*c),2,(-2*b/(a-b))^(1/2))*b^2)*sin(1/2*d*x+1/2*c)^2+7*b*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*b/(a-b)*sin(1/2*d*x+1/2*c)^2+(a+b)/(a-b))^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a-5*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*b/(a-b)*sin(1/2*d*x+1/2*c)^2+(a+b)/(a-b))^(1/2)*b*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a+5*b^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*b/(a-b)*sin(1/2*d*x+1/2*c)^2+(a+b)/(a-b))^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))-4*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*b/(a-b)*sin(1/2*d*x+1/2*c)^2+(a+b)/(a-b))^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2,(-2*b/(a-b))^(1/2))*a^2-3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*b/(a-b)*sin(1/2*d*x+1/2*c)^2+(a+b)/(a-b))^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2,(-2*b/(a-b))^(1/2))*b^2)/(2*cos(1/2*d*x+1/2*c)^2-1)^2/(-2*sin(1/2*d*x+1/2*c)^4*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*b+a+b)^(1/2)/d","B"
500,1,1140,397,0.993000," ","int(cos(d*x+c)^3*(a+b*cos(d*x+c))^(5/2),x)","-\frac{2 \sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(4032 b^{6} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{12}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(-7168 a \,b^{5}-10080 b^{6}\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(4384 b^{4} a^{2}+14336 a \,b^{5}+11376 b^{6}\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(-928 a^{3} b^{3}-6576 b^{4} a^{2}-13232 a \,b^{5}-6984 b^{6}\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(-4 b^{2} a^{4}+928 a^{3} b^{3}+5024 b^{4} a^{2}+6064 a \,b^{5}+2772 b^{6}\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(8 a^{5} b +2 b^{2} a^{4}-642 a^{3} b^{3}-1416 b^{4} a^{2}-1338 a \,b^{5}-558 b^{6}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+8 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-\frac{2 b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a -b}+\frac{a +b}{a -b}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{6}-8 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-\frac{2 b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a -b}+\frac{a +b}{a -b}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{5} b +51 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-\frac{2 b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a -b}+\frac{a +b}{a -b}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{4} b^{2}-51 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-\frac{2 b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a -b}+\frac{a +b}{a -b}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{3} b^{3}+741 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-\frac{2 b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a -b}+\frac{a +b}{a -b}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{2} b^{4}-741 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-\frac{2 b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a -b}+\frac{a +b}{a -b}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a \,b^{5}-8 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-\frac{2 b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a -b}+\frac{a +b}{a -b}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{6}-49 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-\frac{2 b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a -b}+\frac{a +b}{a -b}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{4} b^{2}-78 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-\frac{2 b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a -b}+\frac{a +b}{a -b}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{2} b^{4}+135 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-\frac{2 b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a -b}+\frac{a +b}{a -b}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) b^{6}\right)}{693 b^{3} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(a +b \right) \left(\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(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a +b}\, d}"," ",0,"-2/693*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(4032*b^6*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^12+(-7168*a*b^5-10080*b^6)*sin(1/2*d*x+1/2*c)^10*cos(1/2*d*x+1/2*c)+(4384*a^2*b^4+14336*a*b^5+11376*b^6)*sin(1/2*d*x+1/2*c)^8*cos(1/2*d*x+1/2*c)+(-928*a^3*b^3-6576*a^2*b^4-13232*a*b^5-6984*b^6)*sin(1/2*d*x+1/2*c)^6*cos(1/2*d*x+1/2*c)+(-4*a^4*b^2+928*a^3*b^3+5024*a^2*b^4+6064*a*b^5+2772*b^6)*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+(8*a^5*b+2*a^4*b^2-642*a^3*b^3-1416*a^2*b^4-1338*a*b^5-558*b^6)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+8*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*b/(a-b)*sin(1/2*d*x+1/2*c)^2+(a+b)/(a-b))^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a^6-8*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*b/(a-b)*sin(1/2*d*x+1/2*c)^2+(a+b)/(a-b))^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a^5*b+51*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*b/(a-b)*sin(1/2*d*x+1/2*c)^2+(a+b)/(a-b))^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a^4*b^2-51*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*b/(a-b)*sin(1/2*d*x+1/2*c)^2+(a+b)/(a-b))^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a^3*b^3+741*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*b/(a-b)*sin(1/2*d*x+1/2*c)^2+(a+b)/(a-b))^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a^2*b^4-741*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*b/(a-b)*sin(1/2*d*x+1/2*c)^2+(a+b)/(a-b))^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a*b^5-8*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*b/(a-b)*sin(1/2*d*x+1/2*c)^2+(a+b)/(a-b))^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a^6-49*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*b/(a-b)*sin(1/2*d*x+1/2*c)^2+(a+b)/(a-b))^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a^4*b^2-78*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*b/(a-b)*sin(1/2*d*x+1/2*c)^2+(a+b)/(a-b))^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a^2*b^4+135*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*b/(a-b)*sin(1/2*d*x+1/2*c)^2+(a+b)/(a-b))^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*b^6)/b^3/(-2*sin(1/2*d*x+1/2*c)^4*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*b+a+b)^(1/2)/d","B"
501,1,995,338,0.946000," ","int(cos(d*x+c)^2*(a+b*cos(d*x+c))^(5/2),x)","-\frac{2 \sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(-1120 b^{5} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{10}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(2080 a \,b^{4}+2240 b^{5}\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(-1360 a^{2} b^{3}-3120 a \,b^{4}-2072 b^{5}\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(320 a^{3} b^{2}+1360 a^{2} b^{3}+2408 a \,b^{4}+952 b^{5}\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(-10 a^{4} b -160 a^{3} b^{2}-666 a^{2} b^{3}-684 a \,b^{4}-168 b^{5}\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 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-\frac{2 b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a -b}+\frac{a +b}{a -b}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{5}-124 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-\frac{2 b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a -b}+\frac{a +b}{a -b}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{3} b^{2}+114 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-\frac{2 b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a -b}+\frac{a +b}{a -b}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a \,b^{4}-10 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-\frac{2 b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a -b}+\frac{a +b}{a -b}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{5}+10 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-\frac{2 b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a -b}+\frac{a +b}{a -b}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{4} b +279 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-\frac{2 b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a -b}+\frac{a +b}{a -b}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{3} b^{2}-279 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-\frac{2 b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a -b}+\frac{a +b}{a -b}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{2} b^{3}+147 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-\frac{2 b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a -b}+\frac{a +b}{a -b}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a \,b^{4}-147 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-\frac{2 b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a -b}+\frac{a +b}{a -b}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) b^{5}\right)}{315 b^{2} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(a +b \right) \left(\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(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a +b}\, d}"," ",0,"-2/315*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(-1120*b^5*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^10+(2080*a*b^4+2240*b^5)*sin(1/2*d*x+1/2*c)^8*cos(1/2*d*x+1/2*c)+(-1360*a^2*b^3-3120*a*b^4-2072*b^5)*sin(1/2*d*x+1/2*c)^6*cos(1/2*d*x+1/2*c)+(320*a^3*b^2+1360*a^2*b^3+2408*a*b^4+952*b^5)*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+(-10*a^4*b-160*a^3*b^2-666*a^2*b^3-684*a*b^4-168*b^5)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+10*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*b/(a-b)*sin(1/2*d*x+1/2*c)^2+(a+b)/(a-b))^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a^5-124*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*b/(a-b)*sin(1/2*d*x+1/2*c)^2+(a+b)/(a-b))^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a^3*b^2+114*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*b/(a-b)*sin(1/2*d*x+1/2*c)^2+(a+b)/(a-b))^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a*b^4-10*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*b/(a-b)*sin(1/2*d*x+1/2*c)^2+(a+b)/(a-b))^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a^5+10*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*b/(a-b)*sin(1/2*d*x+1/2*c)^2+(a+b)/(a-b))^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a^4*b+279*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*b/(a-b)*sin(1/2*d*x+1/2*c)^2+(a+b)/(a-b))^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a^3*b^2-279*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*b/(a-b)*sin(1/2*d*x+1/2*c)^2+(a+b)/(a-b))^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a^2*b^3+147*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*b/(a-b)*sin(1/2*d*x+1/2*c)^2+(a+b)/(a-b))^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a*b^4-147*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*b/(a-b)*sin(1/2*d*x+1/2*c)^2+(a+b)/(a-b))^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*b^5)/b^2/(-2*sin(1/2*d*x+1/2*c)^4*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*b+a+b)^(1/2)/d","B"
502,1,827,283,0.853000," ","int(cos(d*x+c)*(a+b*cos(d*x+c))^(5/2),x)","-\frac{2 \sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(48 \left(\cos^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{4}+96 \left(\cos^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a \,b^{3}-120 \left(\cos^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{4}+72 \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{2} b^{2}-192 \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a \,b^{3}+128 \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{4}+18 \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{3} b -108 \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{2} b^{2}+130 \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a \,b^{3}-72 \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{4}-3 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{4}-2 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{2} b^{2}+5 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) b^{4}+3 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{4}-3 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{3} b +29 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{2} b^{2}-29 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a \,b^{3}-18 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) a^{3} b +36 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) a^{2} b^{2}-34 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) a \,b^{3}+16 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) b^{4}\right)}{21 b \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(a +b \right) \left(\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(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a +b}\, d}"," ",0,"-2/21*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(48*cos(1/2*d*x+1/2*c)^9*b^4+96*cos(1/2*d*x+1/2*c)^7*a*b^3-120*cos(1/2*d*x+1/2*c)^7*b^4+72*cos(1/2*d*x+1/2*c)^5*a^2*b^2-192*cos(1/2*d*x+1/2*c)^5*a*b^3+128*cos(1/2*d*x+1/2*c)^5*b^4+18*cos(1/2*d*x+1/2*c)^3*a^3*b-108*cos(1/2*d*x+1/2*c)^3*a^2*b^2+130*cos(1/2*d*x+1/2*c)^3*a*b^3-72*cos(1/2*d*x+1/2*c)^3*b^4-3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)/(a-b))^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a^4-2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)/(a-b))^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a^2*b^2+5*(sin(1/2*d*x+1/2*c)^2)^(1/2)*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)/(a-b))^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*b^4+3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)/(a-b))^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a^4-3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)/(a-b))^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a^3*b+29*(sin(1/2*d*x+1/2*c)^2)^(1/2)*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)/(a-b))^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a^2*b^2-29*(sin(1/2*d*x+1/2*c)^2)^(1/2)*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)/(a-b))^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a*b^3-18*cos(1/2*d*x+1/2*c)*a^3*b+36*cos(1/2*d*x+1/2*c)*a^2*b^2-34*cos(1/2*d*x+1/2*c)*a*b^3+16*cos(1/2*d*x+1/2*c)*b^4)/b/(-2*sin(1/2*d*x+1/2*c)^4*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*b+a+b)^(1/2)/d","B"
503,1,662,235,0.856000," ","int((a+b*cos(d*x+c))^(5/2),x)","-\frac{2 \sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(24 \left(\cos^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{3}+56 \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a \,b^{2}-48 \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{3}+22 \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{2} b -84 \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a \,b^{2}+30 \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{3}-8 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{3}+8 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a \,b^{2}+23 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{3}-23 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{2} b +9 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a \,b^{2}-9 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) b^{3}-22 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) a^{2} b +28 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) a \,b^{2}-6 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) b^{3}\right)}{15 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(a +b \right) \left(\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(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a +b}\, d}"," ",0,"-2/15*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(24*cos(1/2*d*x+1/2*c)^7*b^3+56*cos(1/2*d*x+1/2*c)^5*a*b^2-48*cos(1/2*d*x+1/2*c)^5*b^3+22*cos(1/2*d*x+1/2*c)^3*a^2*b-84*cos(1/2*d*x+1/2*c)^3*a*b^2+30*cos(1/2*d*x+1/2*c)^3*b^3-8*(sin(1/2*d*x+1/2*c)^2)^(1/2)*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)/(a-b))^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a^3+8*(sin(1/2*d*x+1/2*c)^2)^(1/2)*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)/(a-b))^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a*b^2+23*(sin(1/2*d*x+1/2*c)^2)^(1/2)*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)/(a-b))^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a^3-23*(sin(1/2*d*x+1/2*c)^2)^(1/2)*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)/(a-b))^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a^2*b+9*(sin(1/2*d*x+1/2*c)^2)^(1/2)*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)/(a-b))^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a*b^2-9*(sin(1/2*d*x+1/2*c)^2)^(1/2)*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)/(a-b))^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*b^3-22*cos(1/2*d*x+1/2*c)*a^2*b+28*cos(1/2*d*x+1/2*c)*a*b^2-6*cos(1/2*d*x+1/2*c)*b^3)/(-2*sin(1/2*d*x+1/2*c)^4*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*b+a+b)^(1/2)/d","B"
504,1,528,289,0.768000," ","int((a+b*cos(d*x+c))^(5/2)*sec(d*x+c),x)","-\frac{2 \sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(4 \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{3}+2 \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a \,b^{2}-6 \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{3}+2 a^{2} b \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right)+b^{3} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right)+7 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{2} b -7 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a \,b^{2}-3 a^{3} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), 2, \sqrt{-\frac{2 b}{a -b}}\right)-2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) a \,b^{2}+2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) b^{3}\right)}{3 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(a +b \right) \left(\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(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a +b}\, d}"," ",0,"-2/3*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(4*cos(1/2*d*x+1/2*c)^5*b^3+2*cos(1/2*d*x+1/2*c)^3*a*b^2-6*cos(1/2*d*x+1/2*c)^3*b^3+2*a^2*b*(sin(1/2*d*x+1/2*c)^2)^(1/2)*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)/(a-b))^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))+b^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)/(a-b))^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))+7*(sin(1/2*d*x+1/2*c)^2)^(1/2)*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)/(a-b))^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a^2*b-7*(sin(1/2*d*x+1/2*c)^2)^(1/2)*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)/(a-b))^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a*b^2-3*a^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)/(a-b))^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2,(-2*b/(a-b))^(1/2))-2*cos(1/2*d*x+1/2*c)*a*b^2+2*cos(1/2*d*x+1/2*c)*b^3)/(-2*sin(1/2*d*x+1/2*c)^4*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*b+a+b)^(1/2)/d","A"
505,1,960,295,0.845000," ","int((a+b*cos(d*x+c))^(5/2)*sec(d*x+c)^2,x)","-\frac{\sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(4 a^{2} b \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)-2 \sqrt{-\frac{2 b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a -b}+\frac{a +b}{a -b}}\, \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{-\frac{2 b}{a -b}}\right) a^{3}+4 \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a \,b^{2}-\EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{3}+\EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{2} b +2 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a \,b^{2}-2 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) b^{3}-5 \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), 2, \sqrt{-\frac{2 b}{a -b}}\right) a^{2} b \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{-\frac{2 b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a -b}+\frac{a +b}{a -b}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{3}+4 b^{2} a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-\frac{2 b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a -b}+\frac{a +b}{a -b}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right)-\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-\frac{2 b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a -b}+\frac{a +b}{a -b}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{3}+\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-\frac{2 b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a -b}+\frac{a +b}{a -b}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{2} b +2 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-\frac{2 b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a -b}+\frac{a +b}{a -b}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a \,b^{2}-2 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-\frac{2 b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a -b}+\frac{a +b}{a -b}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) b^{3}-5 a^{2} b \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-\frac{2 b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a -b}+\frac{a +b}{a -b}}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), 2, \sqrt{-\frac{2 b}{a -b}}\right)\right)}{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(a +b \right) \left(\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(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a +b}\, d}"," ",0,"-((2*cos(1/2*d*x+1/2*c)^2*b+a-b)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(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)-2*(-2*b/(a-b)*sin(1/2*d*x+1/2*c)^2+(a+b)/(a-b))^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a^3+4*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a*b^2-EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a^3+EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a^2*b+2*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a*b^2-2*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*b^3-5*EllipticPi(cos(1/2*d*x+1/2*c),2,(-2*b/(a-b))^(1/2))*a^2*b)*sin(1/2*d*x+1/2*c)^2+(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*b/(a-b)*sin(1/2*d*x+1/2*c)^2+(a+b)/(a-b))^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a^3+4*b^2*a*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*b/(a-b)*sin(1/2*d*x+1/2*c)^2+(a+b)/(a-b))^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))-(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*b/(a-b)*sin(1/2*d*x+1/2*c)^2+(a+b)/(a-b))^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a^3+(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*b/(a-b)*sin(1/2*d*x+1/2*c)^2+(a+b)/(a-b))^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a^2*b+2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*b/(a-b)*sin(1/2*d*x+1/2*c)^2+(a+b)/(a-b))^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a*b^2-2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*b/(a-b)*sin(1/2*d*x+1/2*c)^2+(a+b)/(a-b))^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*b^3-5*a^2*b*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*b/(a-b)*sin(1/2*d*x+1/2*c)^2+(a+b)/(a-b))^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2,(-2*b/(a-b))^(1/2)))/(2*cos(1/2*d*x+1/2*c)^2-1)/(-2*sin(1/2*d*x+1/2*c)^4*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*b+a+b)^(1/2)/d","B"
506,1,1134,331,0.962000," ","int((a+b*cos(d*x+c))^(5/2)*sec(d*x+c)^3,x)","-\frac{\sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(-72 a \,b^{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(44 a^{2} b +72 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(-4 a^{3}-22 a^{2} b -18 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)+4 \sqrt{-\frac{2 b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a -b}+\frac{a +b}{a -b}}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(11 \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{2} b +8 \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) b^{3}-4 \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), 2, \sqrt{-\frac{2 b}{a -b}}\right) a^{3}-15 \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), 2, \sqrt{-\frac{2 b}{a -b}}\right) a \,b^{2}-9 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{2} b +9 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a \,b^{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-4 \sqrt{-\frac{2 b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a -b}+\frac{a +b}{a -b}}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(11 \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{2} b +8 \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) b^{3}-4 \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), 2, \sqrt{-\frac{2 b}{a -b}}\right) a^{3}-15 \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), 2, \sqrt{-\frac{2 b}{a -b}}\right) a \,b^{2}-9 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{2} b +9 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a \,b^{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+11 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-\frac{2 b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a -b}+\frac{a +b}{a -b}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{2} b +8 b^{3} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-\frac{2 b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a -b}+\frac{a +b}{a -b}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right)-4 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-\frac{2 b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a -b}+\frac{a +b}{a -b}}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), 2, \sqrt{-\frac{2 b}{a -b}}\right) a^{3}-15 b^{2} a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-\frac{2 b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a -b}+\frac{a +b}{a -b}}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), 2, \sqrt{-\frac{2 b}{a -b}}\right)-9 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-\frac{2 b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a -b}+\frac{a +b}{a -b}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{2} b +9 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-\frac{2 b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a -b}+\frac{a +b}{a -b}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a \,b^{2}\right)}{4 \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)^{2} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(a +b \right) \left(\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(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a +b}\, d}"," ",0,"-1/4*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(-72*a*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6+(44*a^2*b+72*a*b^2)*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+(-4*a^3-22*a^2*b-18*a*b^2)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+4*(-2*b/(a-b)*sin(1/2*d*x+1/2*c)^2+(a+b)/(a-b))^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(11*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a^2*b+8*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*b^3-4*EllipticPi(cos(1/2*d*x+1/2*c),2,(-2*b/(a-b))^(1/2))*a^3-15*EllipticPi(cos(1/2*d*x+1/2*c),2,(-2*b/(a-b))^(1/2))*a*b^2-9*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a^2*b+9*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a*b^2)*sin(1/2*d*x+1/2*c)^4-4*(-2*b/(a-b)*sin(1/2*d*x+1/2*c)^2+(a+b)/(a-b))^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(11*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a^2*b+8*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*b^3-4*EllipticPi(cos(1/2*d*x+1/2*c),2,(-2*b/(a-b))^(1/2))*a^3-15*EllipticPi(cos(1/2*d*x+1/2*c),2,(-2*b/(a-b))^(1/2))*a*b^2-9*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a^2*b+9*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a*b^2)*sin(1/2*d*x+1/2*c)^2+11*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*b/(a-b)*sin(1/2*d*x+1/2*c)^2+(a+b)/(a-b))^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a^2*b+8*b^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*b/(a-b)*sin(1/2*d*x+1/2*c)^2+(a+b)/(a-b))^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))-4*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*b/(a-b)*sin(1/2*d*x+1/2*c)^2+(a+b)/(a-b))^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2,(-2*b/(a-b))^(1/2))*a^3-15*b^2*a*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*b/(a-b)*sin(1/2*d*x+1/2*c)^2+(a+b)/(a-b))^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2,(-2*b/(a-b))^(1/2))-9*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*b/(a-b)*sin(1/2*d*x+1/2*c)^2+(a+b)/(a-b))^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a^2*b+9*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*b/(a-b)*sin(1/2*d*x+1/2*c)^2+(a+b)/(a-b))^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a*b^2)/(2*cos(1/2*d*x+1/2*c)^2-1)^2/(-2*sin(1/2*d*x+1/2*c)^4*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*b+a+b)^(1/2)/d","B"
507,1,1742,380,1.110000," ","int((a+b*cos(d*x+c))^(5/2)*sec(d*x+c)^4,x)","-\frac{\sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(\left(256 a^{2} b +528 b^{3}\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(-128 a^{3}-384 a^{2} b -472 b^{2} a -792 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(128 a^{3}+328 a^{2} b +472 b^{2} a +396 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(-48 a^{3}-100 a^{2} b -118 b^{2} a -66 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)-8 \sqrt{-\frac{2 b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a -b}+\frac{a +b}{a -b}}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(16 \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{3}+59 \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a \,b^{2}-16 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{3}+16 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{2} b -33 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a \,b^{2}+33 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) b^{3}-60 \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), 2, \sqrt{-\frac{2 b}{a -b}}\right) a^{2} b -15 \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), 2, \sqrt{-\frac{2 b}{a -b}}\right) b^{3}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+12 \sqrt{-\frac{2 b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a -b}+\frac{a +b}{a -b}}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(16 \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{3}+59 \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a \,b^{2}-16 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{3}+16 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{2} b -33 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a \,b^{2}+33 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) b^{3}-60 \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), 2, \sqrt{-\frac{2 b}{a -b}}\right) a^{2} b -15 \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), 2, \sqrt{-\frac{2 b}{a -b}}\right) b^{3}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-6 \sqrt{-\frac{2 b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a -b}+\frac{a +b}{a -b}}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(16 \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{3}+59 \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a \,b^{2}-16 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{3}+16 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{2} b -33 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a \,b^{2}+33 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) b^{3}-60 \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), 2, \sqrt{-\frac{2 b}{a -b}}\right) a^{2} b -15 \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), 2, \sqrt{-\frac{2 b}{a -b}}\right) b^{3}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+16 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-\frac{2 b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a -b}+\frac{a +b}{a -b}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{3}+59 b^{2} a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-\frac{2 b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a -b}+\frac{a +b}{a -b}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right)-16 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-\frac{2 b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a -b}+\frac{a +b}{a -b}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{3}+16 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-\frac{2 b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a -b}+\frac{a +b}{a -b}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{2} b -33 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-\frac{2 b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a -b}+\frac{a +b}{a -b}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a \,b^{2}+33 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-\frac{2 b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a -b}+\frac{a +b}{a -b}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) b^{3}-60 a^{2} b \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-\frac{2 b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a -b}+\frac{a +b}{a -b}}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), 2, \sqrt{-\frac{2 b}{a -b}}\right)-15 b^{3} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-\frac{2 b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a -b}+\frac{a +b}{a -b}}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), 2, \sqrt{-\frac{2 b}{a -b}}\right)\right)}{24 \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)^{3} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(a +b \right) \left(\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(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a +b}\, d}"," ",0,"-1/24*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)*sin(1/2*d*x+1/2*c)^2)^(1/2)*((256*a^2*b+528*b^3)*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^8+(-128*a^3-384*a^2*b-472*a*b^2-792*b^3)*sin(1/2*d*x+1/2*c)^6*cos(1/2*d*x+1/2*c)+(128*a^3+328*a^2*b+472*a*b^2+396*b^3)*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+(-48*a^3-100*a^2*b-118*a*b^2-66*b^3)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)-8*(-2*b/(a-b)*sin(1/2*d*x+1/2*c)^2+(a+b)/(a-b))^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(16*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a^3+59*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a*b^2-16*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a^3+16*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a^2*b-33*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a*b^2+33*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*b^3-60*EllipticPi(cos(1/2*d*x+1/2*c),2,(-2*b/(a-b))^(1/2))*a^2*b-15*EllipticPi(cos(1/2*d*x+1/2*c),2,(-2*b/(a-b))^(1/2))*b^3)*sin(1/2*d*x+1/2*c)^6+12*(-2*b/(a-b)*sin(1/2*d*x+1/2*c)^2+(a+b)/(a-b))^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(16*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a^3+59*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a*b^2-16*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a^3+16*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a^2*b-33*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a*b^2+33*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*b^3-60*EllipticPi(cos(1/2*d*x+1/2*c),2,(-2*b/(a-b))^(1/2))*a^2*b-15*EllipticPi(cos(1/2*d*x+1/2*c),2,(-2*b/(a-b))^(1/2))*b^3)*sin(1/2*d*x+1/2*c)^4-6*(-2*b/(a-b)*sin(1/2*d*x+1/2*c)^2+(a+b)/(a-b))^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(16*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a^3+59*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a*b^2-16*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a^3+16*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a^2*b-33*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a*b^2+33*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*b^3-60*EllipticPi(cos(1/2*d*x+1/2*c),2,(-2*b/(a-b))^(1/2))*a^2*b-15*EllipticPi(cos(1/2*d*x+1/2*c),2,(-2*b/(a-b))^(1/2))*b^3)*sin(1/2*d*x+1/2*c)^2+16*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*b/(a-b)*sin(1/2*d*x+1/2*c)^2+(a+b)/(a-b))^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a^3+59*b^2*a*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*b/(a-b)*sin(1/2*d*x+1/2*c)^2+(a+b)/(a-b))^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))-16*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*b/(a-b)*sin(1/2*d*x+1/2*c)^2+(a+b)/(a-b))^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a^3+16*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*b/(a-b)*sin(1/2*d*x+1/2*c)^2+(a+b)/(a-b))^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a^2*b-33*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*b/(a-b)*sin(1/2*d*x+1/2*c)^2+(a+b)/(a-b))^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a*b^2+33*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*b/(a-b)*sin(1/2*d*x+1/2*c)^2+(a+b)/(a-b))^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*b^3-60*a^2*b*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*b/(a-b)*sin(1/2*d*x+1/2*c)^2+(a+b)/(a-b))^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2,(-2*b/(a-b))^(1/2))-15*b^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*b/(a-b)*sin(1/2*d*x+1/2*c)^2+(a+b)/(a-b))^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2,(-2*b/(a-b))^(1/2)))/(2*cos(1/2*d*x+1/2*c)^2-1)^3/(-2*sin(1/2*d*x+1/2*c)^4*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*b+a+b)^(1/2)/d","B"
508,1,824,280,0.915000," ","int((a+b*cos(d*x+c))^(7/2),x)","-\frac{2 \sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(240 \left(\cos^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{4}+648 \left(\cos^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a \,b^{3}-600 \left(\cos^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{4}+752 \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{2} b^{2}-1296 \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a \,b^{3}+640 \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{4}+244 \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{3} b -1128 \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{2} b^{2}+860 \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a \,b^{3}-360 \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{4}-71 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{4}+46 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{2} b^{2}+25 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) b^{4}+176 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{4}-176 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{3} b +208 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{2} b^{2}-208 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a \,b^{3}-244 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) a^{3} b +376 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) a^{2} b^{2}-212 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) a \,b^{3}+80 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) b^{4}\right)}{105 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(a +b \right) \left(\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(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a +b}\, d}"," ",0,"-2/105*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(240*cos(1/2*d*x+1/2*c)^9*b^4+648*cos(1/2*d*x+1/2*c)^7*a*b^3-600*cos(1/2*d*x+1/2*c)^7*b^4+752*cos(1/2*d*x+1/2*c)^5*a^2*b^2-1296*cos(1/2*d*x+1/2*c)^5*a*b^3+640*cos(1/2*d*x+1/2*c)^5*b^4+244*cos(1/2*d*x+1/2*c)^3*a^3*b-1128*cos(1/2*d*x+1/2*c)^3*a^2*b^2+860*cos(1/2*d*x+1/2*c)^3*a*b^3-360*cos(1/2*d*x+1/2*c)^3*b^4-71*(sin(1/2*d*x+1/2*c)^2)^(1/2)*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)/(a-b))^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a^4+46*(sin(1/2*d*x+1/2*c)^2)^(1/2)*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)/(a-b))^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a^2*b^2+25*(sin(1/2*d*x+1/2*c)^2)^(1/2)*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)/(a-b))^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*b^4+176*(sin(1/2*d*x+1/2*c)^2)^(1/2)*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)/(a-b))^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a^4-176*(sin(1/2*d*x+1/2*c)^2)^(1/2)*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)/(a-b))^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a^3*b+208*(sin(1/2*d*x+1/2*c)^2)^(1/2)*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)/(a-b))^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a^2*b^2-208*(sin(1/2*d*x+1/2*c)^2)^(1/2)*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)/(a-b))^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a*b^3-244*cos(1/2*d*x+1/2*c)*a^3*b+376*cos(1/2*d*x+1/2*c)*a^2*b^2-212*cos(1/2*d*x+1/2*c)*a*b^3+80*cos(1/2*d*x+1/2*c)*b^4)/(-2*sin(1/2*d*x+1/2*c)^4*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*b+a+b)^(1/2)/d","B"
509,1,275,170,0.648000," ","int(cos(d*x+c)^3*(3+4*cos(d*x+c))^(1/2),x)","-\frac{\sqrt{\left(8 \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(7680 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-14976 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+12344 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+413 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{8 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-7}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), 2 \sqrt{2}\right)-141 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{8 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-7}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), 2 \sqrt{2}\right)-4480 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{420 \sqrt{-8 \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)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{8 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-1/420*((8*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(7680*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^8-14976*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6+12344*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+413*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(8*sin(1/2*d*x+1/2*c)^2-7)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2*2^(1/2))-141*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(8*sin(1/2*d*x+1/2*c)^2-7)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2*2^(1/2))-4480*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c))/(-8*sin(1/2*d*x+1/2*c)^4+7*sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(8*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
510,1,253,141,0.657000," ","int(cos(d*x+c)^2*(3+4*cos(d*x+c))^(1/2),x)","-\frac{\sqrt{\left(8 \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(-256 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+384 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-7 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{8 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-7}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), 2 \sqrt{2}\right)-21 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{8 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-7}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), 2 \sqrt{2}\right)-140 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{20 \sqrt{-8 \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)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{8 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-1/20*((8*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(-256*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6+384*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)-7*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(8*sin(1/2*d*x+1/2*c)^2-7)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2*2^(1/2))-21*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(8*sin(1/2*d*x+1/2*c)^2-7)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2*2^(1/2))-140*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c))/(-8*sin(1/2*d*x+1/2*c)^4+7*sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(8*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
511,1,231,118,0.617000," ","int(cos(d*x+c)*(3+4*cos(d*x+c))^(1/2),x)","-\frac{\sqrt{\left(8 \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(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+7 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{8 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-7}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), 2 \sqrt{2}\right)-3 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{8 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-7}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), 2 \sqrt{2}\right)-56 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{6 \sqrt{-8 \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)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{8 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-1/6*((8*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(64*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+7*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(8*sin(1/2*d*x+1/2*c)^2-7)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2*2^(1/2))-3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(8*sin(1/2*d*x+1/2*c)^2-7)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2*2^(1/2))-56*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c))/(-8*sin(1/2*d*x+1/2*c)^4+7*sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(8*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
512,1,137,47,0.415000," ","int((3+4*cos(d*x+c))^(1/2),x)","\frac{2 \sqrt{\left(8 \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{-8 \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), 2 \sqrt{2}\right)}{\sqrt{-8 \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)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{8 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"2*((8*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)*(-8*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2*2^(1/2))/(-8*sin(1/2*d*x+1/2*c)^4+7*sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(8*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
513,1,158,96,0.549000," ","int(sec(d*x+c)*(3+4*cos(d*x+c))^(1/2),x)","-\frac{2 \sqrt{\left(8 \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{-8 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \left(4 \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), 2 \sqrt{2}\right)-3 \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), 2, 2 \sqrt{2}\right)\right)}{\sqrt{-8 \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)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{8 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-2*((8*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)*(-8*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*(4*EllipticF(cos(1/2*d*x+1/2*c),2*2^(1/2))-3*EllipticPi(cos(1/2*d*x+1/2*c),2,2*2^(1/2)))/(-8*sin(1/2*d*x+1/2*c)^4+7*sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(8*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
514,1,350,165,0.795000," ","int(sec(d*x+c)^2*(3+4*cos(d*x+c))^(1/2),x)","-\frac{\sqrt{-\left(-8 \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 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-8 \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)}}{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}+\frac{3 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-8 \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), 2 \sqrt{2}\right)}{\sqrt{-8 \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)}}+\frac{\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-8 \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), 2 \sqrt{2}\right)}{\sqrt{-8 \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)}}-\frac{4 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-8 \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), 2, 2 \sqrt{2}\right)}{\sqrt{-8 \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)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{8 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-(-(-8*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)*(-8*sin(1/2*d*x+1/2*c)^4+7*sin(1/2*d*x+1/2*c)^2)^(1/2)/(2*cos(1/2*d*x+1/2*c)^2-1)+3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-8*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-8*sin(1/2*d*x+1/2*c)^4+7*sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2*2^(1/2))+(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-8*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-8*sin(1/2*d*x+1/2*c)^4+7*sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2*2^(1/2))-4*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-8*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-8*sin(1/2*d*x+1/2*c)^4+7*sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2,2*2^(1/2)))/sin(1/2*d*x+1/2*c)/(8*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
515,1,408,195,0.954000," ","int(sec(d*x+c)^3*(3+4*cos(d*x+c))^(1/2),x)","-\frac{\sqrt{-\left(-8 \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{-8 \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)}}{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)^{2}}-\frac{2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-8 \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)}}{3 \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}+\frac{3 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-8 \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), 2 \sqrt{2}\right)}{\sqrt{-8 \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)}}+\frac{\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-8 \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), 2 \sqrt{2}\right)}{3 \sqrt{-8 \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)}}-\frac{5 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-8 \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), 2, 2 \sqrt{2}\right)}{3 \sqrt{-8 \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)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{8 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-(-(-8*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)*(-8*sin(1/2*d*x+1/2*c)^4+7*sin(1/2*d*x+1/2*c)^2)^(1/2)/(2*cos(1/2*d*x+1/2*c)^2-1)^2-2/3*cos(1/2*d*x+1/2*c)*(-8*sin(1/2*d*x+1/2*c)^4+7*sin(1/2*d*x+1/2*c)^2)^(1/2)/(2*cos(1/2*d*x+1/2*c)^2-1)+3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-8*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-8*sin(1/2*d*x+1/2*c)^4+7*sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2*2^(1/2))+1/3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-8*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-8*sin(1/2*d*x+1/2*c)^4+7*sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2*2^(1/2))-5/3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-8*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-8*sin(1/2*d*x+1/2*c)^4+7*sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2,2*2^(1/2)))/sin(1/2*d*x+1/2*c)/(8*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
516,1,276,170,0.754000," ","int(cos(d*x+c)^3*(3-4*cos(d*x+c))^(1/2),x)","\frac{\sqrt{-\left(8 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-7\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(7680 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-8064 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+5432 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+59 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{56 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-7}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 \sqrt{14}}{7}\right)+141 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{56 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-7}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 \sqrt{14}}{7}\right)-568 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{420 \sqrt{8 \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)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-8 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+7}\, d}"," ",0,"1/420*(-(8*cos(1/2*d*x+1/2*c)^2-7)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(7680*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^8-8064*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6+5432*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+59*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(56*sin(1/2*d*x+1/2*c)^2-7)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2/7*14^(1/2))+141*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(56*sin(1/2*d*x+1/2*c)^2-7)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2/7*14^(1/2))-568*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c))/(8*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*cos(1/2*d*x+1/2*c)^2+7)^(1/2)/d","A"
517,1,253,141,0.724000," ","int(cos(d*x+c)^2*(3-4*cos(d*x+c))^(1/2),x)","\frac{\sqrt{-\left(8 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-7\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(-256 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+128 \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{56 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-7}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 \sqrt{14}}{7}\right)-21 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{56 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-7}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 \sqrt{14}}{7}\right)-12 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{20 \sqrt{8 \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)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-8 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+7}\, d}"," ",0,"1/20*(-(8*cos(1/2*d*x+1/2*c)^2-7)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(-256*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6+128*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)*(56*sin(1/2*d*x+1/2*c)^2-7)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2/7*14^(1/2))-21*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(56*sin(1/2*d*x+1/2*c)^2-7)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2/7*14^(1/2))-12*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c))/(8*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*cos(1/2*d*x+1/2*c)^2+7)^(1/2)/d","A"
518,1,231,118,0.739000," ","int(cos(d*x+c)*(3-4*cos(d*x+c))^(1/2),x)","\frac{\sqrt{-\left(8 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-7\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(64 \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{56 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-7}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 \sqrt{14}}{7}\right)+3 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{56 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-7}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 \sqrt{14}}{7}\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)}{6 \sqrt{8 \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)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-8 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+7}\, d}"," ",0,"1/6*(-(8*cos(1/2*d*x+1/2*c)^2-7)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(64*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)*(56*sin(1/2*d*x+1/2*c)^2-7)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2/7*14^(1/2))+3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(56*sin(1/2*d*x+1/2*c)^2-7)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2/7*14^(1/2))-8*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c))/(8*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*cos(1/2*d*x+1/2*c)^2+7)^(1/2)/d","A"
519,1,138,47,0.460000," ","int((3-4*cos(d*x+c))^(1/2),x)","-\frac{2 \sqrt{-\left(8 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-7\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{56 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-7}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 \sqrt{14}}{7}\right)}{\sqrt{8 \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)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-8 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+7}\, d}"," ",0,"-2*(-(8*cos(1/2*d*x+1/2*c)^2-7)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(56*sin(1/2*d*x+1/2*c)^2-7)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2/7*14^(1/2))/(8*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*cos(1/2*d*x+1/2*c)^2+7)^(1/2)/d","B"
520,1,159,96,0.796000," ","int(sec(d*x+c)*(3-4*cos(d*x+c))^(1/2),x)","\frac{2 \sqrt{-\left(8 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-7\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{56 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-7}\, \left(4 \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 \sqrt{14}}{7}\right)+3 \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), 2, \frac{2 \sqrt{14}}{7}\right)\right)}{7 \sqrt{8 \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)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-8 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+7}\, d}"," ",0,"2/7*(-(8*cos(1/2*d*x+1/2*c)^2-7)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(56*sin(1/2*d*x+1/2*c)^2-7)^(1/2)*(4*EllipticF(cos(1/2*d*x+1/2*c),2/7*14^(1/2))+3*EllipticPi(cos(1/2*d*x+1/2*c),2,2/7*14^(1/2)))/(8*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*cos(1/2*d*x+1/2*c)^2+7)^(1/2)/d","A"
521,1,351,164,0.877000," ","int(sec(d*x+c)^2*(3-4*cos(d*x+c))^(1/2),x)","-\frac{\sqrt{-\left(8 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-7\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(-\frac{2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{8 \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)}}{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}+\frac{3 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{56 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-7}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 \sqrt{14}}{7}\right)}{7 \sqrt{8 \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)}}-\frac{\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{56 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-7}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 \sqrt{14}}{7}\right)}{\sqrt{8 \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)}}+\frac{4 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{56 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-7}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), 2, \frac{2 \sqrt{14}}{7}\right)}{7 \sqrt{8 \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)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-8 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+7}\, d}"," ",0,"-(-(8*cos(1/2*d*x+1/2*c)^2-7)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)*(8*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)+3/7*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(56*sin(1/2*d*x+1/2*c)^2-7)^(1/2)/(8*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),2/7*14^(1/2))-(sin(1/2*d*x+1/2*c)^2)^(1/2)*(56*sin(1/2*d*x+1/2*c)^2-7)^(1/2)/(8*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),2/7*14^(1/2))+4/7*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(56*sin(1/2*d*x+1/2*c)^2-7)^(1/2)/(8*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),2,2/7*14^(1/2)))/sin(1/2*d*x+1/2*c)/(-8*cos(1/2*d*x+1/2*c)^2+7)^(1/2)/d","B"
522,1,408,195,1.043000," ","int(sec(d*x+c)^3*(3-4*cos(d*x+c))^(1/2),x)","-\frac{\sqrt{-\left(8 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-7\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{8 \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)}}{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)^{2}}+\frac{2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{8 \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)}}{3 \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}-\frac{3 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{56 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-7}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 \sqrt{14}}{7}\right)}{7 \sqrt{8 \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)}}+\frac{\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{56 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-7}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 \sqrt{14}}{7}\right)}{3 \sqrt{8 \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)}}-\frac{5 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{56 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-7}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), 2, \frac{2 \sqrt{14}}{7}\right)}{21 \sqrt{8 \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)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-8 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+7}\, d}"," ",0,"-(-(8*cos(1/2*d*x+1/2*c)^2-7)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(-cos(1/2*d*x+1/2*c)*(8*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)^2+2/3*cos(1/2*d*x+1/2*c)*(8*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)-3/7*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(56*sin(1/2*d*x+1/2*c)^2-7)^(1/2)/(8*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),2/7*14^(1/2))+1/3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(56*sin(1/2*d*x+1/2*c)^2-7)^(1/2)/(8*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),2/7*14^(1/2))-5/21*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(56*sin(1/2*d*x+1/2*c)^2-7)^(1/2)/(8*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),2,2/7*14^(1/2)))/sin(1/2*d*x+1/2*c)/(-8*cos(1/2*d*x+1/2*c)^2+7)^(1/2)/d","B"
523,1,665,253,0.825000," ","int(cos(d*x+c)^3/(a+b*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) b +a -b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(24 \left(\cos^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{3}-4 \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a \,b^{2}-48 \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{3}-8 \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{2} b +6 \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a \,b^{2}+30 \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{3}-8 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{3}-7 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a \,b^{2}+8 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{3}-8 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{2} b +9 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a \,b^{2}-9 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) b^{3}+8 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) a^{2} b -2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) a \,b^{2}-6 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) b^{3}\right)}{15 b^{3} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(a +b \right) \left(\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(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a +b}\, d}"," ",0,"-2/15*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(24*cos(1/2*d*x+1/2*c)^7*b^3-4*cos(1/2*d*x+1/2*c)^5*a*b^2-48*cos(1/2*d*x+1/2*c)^5*b^3-8*cos(1/2*d*x+1/2*c)^3*a^2*b+6*cos(1/2*d*x+1/2*c)^3*a*b^2+30*cos(1/2*d*x+1/2*c)^3*b^3-8*(sin(1/2*d*x+1/2*c)^2)^(1/2)*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)/(a-b))^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a^3-7*(sin(1/2*d*x+1/2*c)^2)^(1/2)*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)/(a-b))^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a*b^2+8*(sin(1/2*d*x+1/2*c)^2)^(1/2)*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)/(a-b))^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a^3-8*(sin(1/2*d*x+1/2*c)^2)^(1/2)*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)/(a-b))^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a^2*b+9*(sin(1/2*d*x+1/2*c)^2)^(1/2)*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)/(a-b))^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a*b^2-9*(sin(1/2*d*x+1/2*c)^2)^(1/2)*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)/(a-b))^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*b^3+8*cos(1/2*d*x+1/2*c)*a^2*b-2*cos(1/2*d*x+1/2*c)*a*b^2-6*cos(1/2*d*x+1/2*c)*b^3)/b^3/(-2*sin(1/2*d*x+1/2*c)^4*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*b+a+b)^(1/2)/d","B"
524,1,453,207,0.944000," ","int(cos(d*x+c)^2/(a+b*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) b +a -b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(4 \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{2}+2 \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a b -6 \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{2}+2 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{2}+\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) b^{2}-2 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{2}+2 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a b -2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) a b +2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) b^{2}\right)}{3 b^{2} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(a +b \right) \left(\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(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a +b}\, d}"," ",0,"-2/3*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(4*cos(1/2*d*x+1/2*c)^5*b^2+2*cos(1/2*d*x+1/2*c)^3*a*b-6*cos(1/2*d*x+1/2*c)^3*b^2+2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)/(a-b))^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a^2+(sin(1/2*d*x+1/2*c)^2)^(1/2)*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)/(a-b))^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*b^2-2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)/(a-b))^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a^2+2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)/(a-b))^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a*b-2*cos(1/2*d*x+1/2*c)*a*b+2*cos(1/2*d*x+1/2*c)*b^2)/b^2/(-2*sin(1/2*d*x+1/2*c)^4*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*b+a+b)^(1/2)/d","B"
525,1,220,172,0.773000," ","int(cos(d*x+c)/(a+b*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) b +a -b \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{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, \left(\EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a -\EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a +\EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) b \right)}{\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(a +b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, b \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a +b}\, d}"," ",0,"2*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)*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*b+a-b)/(a-b))^(1/2)*(EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a-EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a+EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*b)/(-2*sin(1/2*d*x+1/2*c)^4*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)/b/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*b+a+b)^(1/2)/d","A"
526,1,75,82,0.102000," ","int(1/(a+b*cos(d*x+c))^(1/2),x)","\frac{2 \sqrt{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a +b}}\, \mathrm{am}^{-1}\left(\frac{d x}{2}+\frac{c}{2}\bigg| \frac{\sqrt{2}\, \sqrt{b}}{\sqrt{a +b}}\right)}{d \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}}"," ",0,"2/d/(2*cos(1/2*d*x+1/2*c)^2*b+a-b)^(1/2)*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)/(a+b))^(1/2)*InverseJacobiAM(1/2*d*x+1/2*c,2^(1/2)/(a+b)^(1/2)*b^(1/2))","C"
527,1,166,83,0.596000," ","int(sec(d*x+c)/(a+b*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) b +a -b \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{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), 2, \sqrt{-\frac{2 b}{a -b}}\right)}{\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(a +b \right) \left(\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(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a +b}\, d}"," ",0,"2*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)*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*b+a-b)/(a-b))^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2,(-2*b/(a-b))^(1/2))/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*b+a+b)^(1/2)/d","A"
528,1,532,279,1.160000," ","int(sec(d*x+c)^2/(a+b*cos(d*x+c))^(1/2),x)","-\frac{\sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a +b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(-\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) b +\left(a +b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}}{a \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}+\frac{\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right)}{\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(a +b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}}-\frac{\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right)}{\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(a +b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}}+\frac{\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, b \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right)}{a \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(a +b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}}+\frac{b \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), 2, \sqrt{-\frac{2 b}{a -b}}\right)}{a \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(a +b \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(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a +b}\, d}"," ",0,"-(-(-2*cos(1/2*d*x+1/2*c)^2*b-a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2/a*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)/(2*cos(1/2*d*x+1/2*c)^2-1)+(sin(1/2*d*x+1/2*c)^2)^(1/2)*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)/(a-b))^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))-(sin(1/2*d*x+1/2*c)^2)^(1/2)*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)/(a-b))^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))+1/a*(sin(1/2*d*x+1/2*c)^2)^(1/2)*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)/(a-b))^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)*b*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))+1/a*b*(sin(1/2*d*x+1/2*c)^2)^(1/2)*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)/(a-b))^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2,(-2*b/(a-b))^(1/2)))/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*b+a+b)^(1/2)/d","A"
529,1,710,329,0.989000," ","int(sec(d*x+c)^3/(a+b*cos(d*x+c))^(1/2),x)","-\frac{\sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a +b \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) b +\left(a +b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}}{a \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)^{2}}+\frac{3 b \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) b +\left(a +b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}}{2 a^{2} \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}-\frac{b \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right)}{4 a \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(a +b \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{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, b \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right)}{4 a \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(a +b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}}-\frac{3 b^{2} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right)}{4 a^{2} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(a +b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}}-\frac{\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), 2, \sqrt{-\frac{2 b}{a -b}}\right)}{\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(a +b \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{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), 2, \sqrt{-\frac{2 b}{a -b}}\right) b^{2}}{4 a^{2} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(a +b \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(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a +b}\, d}"," ",0,"-(-(-2*cos(1/2*d*x+1/2*c)^2*b-a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(-1/a*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)/(2*cos(1/2*d*x+1/2*c)^2-1)^2+3/2*b/a^2*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)/(2*cos(1/2*d*x+1/2*c)^2-1)-1/4*b/a*(sin(1/2*d*x+1/2*c)^2)^(1/2)*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)/(a-b))^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))+3/4/a*(sin(1/2*d*x+1/2*c)^2)^(1/2)*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)/(a-b))^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)*b*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))-3/4*b^2/a^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)/(a-b))^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))-(sin(1/2*d*x+1/2*c)^2)^(1/2)*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)/(a-b))^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2,(-2*b/(a-b))^(1/2))-3/4/a^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)/(a-b))^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2,(-2*b/(a-b))^(1/2))*b^2)/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*b+a+b)^(1/2)/d","B"
530,1,1285,362,1.132000," ","int(cos(d*x+c)^4/(a+b*cos(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) b +\left(a +b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, b^{3} \left(a^{2}-b^{2}\right) \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) b +\left(a +b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, b^{2} \left(a^{3}-a^{2} b -b^{2} 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)+2 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(a +b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, b \left(8 a^{4}+2 a^{3} b -4 a^{2} b^{2}-2 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)-16 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(a +b \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{-\frac{2 b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a -b}+\frac{a +b}{a -b}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{5}+12 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(a +b \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{-\frac{2 b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a -b}+\frac{a +b}{a -b}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{3} b^{2}+4 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(a +b \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{-\frac{2 b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a -b}+\frac{a +b}{a -b}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a \,b^{4}+16 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(a +b \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{-\frac{2 b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a -b}+\frac{a +b}{a -b}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{5}-16 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(a +b \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{-\frac{2 b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a -b}+\frac{a +b}{a -b}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{4} b -8 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(a +b \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{-\frac{2 b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a -b}+\frac{a +b}{a -b}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{3} b^{2}+8 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(a +b \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{-\frac{2 b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a -b}+\frac{a +b}{a -b}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{2} b^{3}-3 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(a +b \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{-\frac{2 b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a -b}+\frac{a +b}{a -b}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a \,b^{4}+3 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(a +b \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{-\frac{2 b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a -b}+\frac{a +b}{a -b}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) b^{5}\right)}{5 b^{4} \left(a -b \right) \left(a +b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(a +b \right) \left(\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(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a +b}\, d}"," ",0,"-2/5*(-8*(-2*sin(1/2*d*x+1/2*c)^4*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)*b^3*(a^2-b^2)*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*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)*b^2*(a^3-a^2*b-a*b^2+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*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)*b*(8*a^4+2*a^3*b-4*a^2*b^2-2*a*b^3+b^4)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)-16*(-2*sin(1/2*d*x+1/2*c)^4*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*b/(a-b)*sin(1/2*d*x+1/2*c)^2+(a+b)/(a-b))^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a^5+12*(-2*sin(1/2*d*x+1/2*c)^4*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*b/(a-b)*sin(1/2*d*x+1/2*c)^2+(a+b)/(a-b))^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a^3*b^2+4*(-2*sin(1/2*d*x+1/2*c)^4*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*b/(a-b)*sin(1/2*d*x+1/2*c)^2+(a+b)/(a-b))^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a*b^4+16*(-2*sin(1/2*d*x+1/2*c)^4*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*b/(a-b)*sin(1/2*d*x+1/2*c)^2+(a+b)/(a-b))^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a^5-16*(-2*sin(1/2*d*x+1/2*c)^4*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*b/(a-b)*sin(1/2*d*x+1/2*c)^2+(a+b)/(a-b))^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a^4*b-8*(-2*sin(1/2*d*x+1/2*c)^4*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*b/(a-b)*sin(1/2*d*x+1/2*c)^2+(a+b)/(a-b))^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a^3*b^2+8*(-2*sin(1/2*d*x+1/2*c)^4*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*b/(a-b)*sin(1/2*d*x+1/2*c)^2+(a+b)/(a-b))^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a^2*b^3-3*(-2*sin(1/2*d*x+1/2*c)^4*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*b/(a-b)*sin(1/2*d*x+1/2*c)^2+(a+b)/(a-b))^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a*b^4+3*(-2*sin(1/2*d*x+1/2*c)^4*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*b/(a-b)*sin(1/2*d*x+1/2*c)^2+(a+b)/(a-b))^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*b^5)/b^4/(a-b)/(a+b)/(-2*sin(1/2*d*x+1/2*c)^4*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*b+a+b)^(1/2)/d","B"
531,1,984,297,1.003000," ","int(cos(d*x+c)^3/(a+b*cos(d*x+c))^(3/2),x)","-\frac{2 \left(4 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(a +b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, b^{2} \left(a^{2}-b^{2}\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{4}\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) b +\left(a +b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, b \left(4 a^{3}+a^{2} b -b^{2} 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)+8 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(a +b \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{-\frac{2 b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a -b}+\frac{a +b}{a -b}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{4}-7 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(a +b \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{-\frac{2 b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a -b}+\frac{a +b}{a -b}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{2} b^{2}-\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(a +b \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{-\frac{2 b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a -b}+\frac{a +b}{a -b}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) b^{4}-8 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(a +b \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{-\frac{2 b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a -b}+\frac{a +b}{a -b}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{4}+8 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(a +b \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{-\frac{2 b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a -b}+\frac{a +b}{a -b}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{3} b +5 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(a +b \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{-\frac{2 b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a -b}+\frac{a +b}{a -b}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{2} b^{2}-5 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(a +b \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{-\frac{2 b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a -b}+\frac{a +b}{a -b}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a \,b^{3}\right)}{3 b^{3} \left(a -b \right) \left(a +b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(a +b \right) \left(\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(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a +b}\, d}"," ",0,"-2/3*(4*(-2*sin(1/2*d*x+1/2*c)^4*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)*b^2*(a^2-b^2)*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4-2*(-2*sin(1/2*d*x+1/2*c)^4*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)*b*(4*a^3+a^2*b-a*b^2-b^3)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+8*(-2*sin(1/2*d*x+1/2*c)^4*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*b/(a-b)*sin(1/2*d*x+1/2*c)^2+(a+b)/(a-b))^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a^4-7*(-2*sin(1/2*d*x+1/2*c)^4*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*b/(a-b)*sin(1/2*d*x+1/2*c)^2+(a+b)/(a-b))^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a^2*b^2-(-2*sin(1/2*d*x+1/2*c)^4*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*b/(a-b)*sin(1/2*d*x+1/2*c)^2+(a+b)/(a-b))^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*b^4-8*(-2*sin(1/2*d*x+1/2*c)^4*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*b/(a-b)*sin(1/2*d*x+1/2*c)^2+(a+b)/(a-b))^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a^4+8*(-2*sin(1/2*d*x+1/2*c)^4*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*b/(a-b)*sin(1/2*d*x+1/2*c)^2+(a+b)/(a-b))^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a^3*b+5*(-2*sin(1/2*d*x+1/2*c)^4*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*b/(a-b)*sin(1/2*d*x+1/2*c)^2+(a+b)/(a-b))^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a^2*b^2-5*(-2*sin(1/2*d*x+1/2*c)^4*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*b/(a-b)*sin(1/2*d*x+1/2*c)^2+(a+b)/(a-b))^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a*b^3)/b^3/(a-b)/(a+b)/(-2*sin(1/2*d*x+1/2*c)^4*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*b+a+b)^(1/2)/d","B"
532,1,530,234,0.939000," ","int(cos(d*x+c)^2/(a+b*cos(d*x+c))^(3/2),x)","\frac{4 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-\frac{2 b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a -b}+\frac{a +b}{a -b}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{3}-4 b^{2} a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-\frac{2 b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a -b}+\frac{a +b}{a -b}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right)-4 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-\frac{2 b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a -b}+\frac{a +b}{a -b}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{3}+4 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-\frac{2 b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a -b}+\frac{a +b}{a -b}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{2} b +2 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-\frac{2 b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a -b}+\frac{a +b}{a -b}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a \,b^{2}-2 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-\frac{2 b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a -b}+\frac{a +b}{a -b}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) b^{3}-4 a^{2} b \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} \left(a -b \right) \left(a +b \right) \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a +b}\, d}"," ",0,"2*(2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*b/(a-b)*sin(1/2*d*x+1/2*c)^2+(a+b)/(a-b))^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a^3-2*b^2*a*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*b/(a-b)*sin(1/2*d*x+1/2*c)^2+(a+b)/(a-b))^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))-2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*b/(a-b)*sin(1/2*d*x+1/2*c)^2+(a+b)/(a-b))^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a^3+2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*b/(a-b)*sin(1/2*d*x+1/2*c)^2+(a+b)/(a-b))^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a^2*b+(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*b/(a-b)*sin(1/2*d*x+1/2*c)^2+(a+b)/(a-b))^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a*b^2-(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*b/(a-b)*sin(1/2*d*x+1/2*c)^2+(a+b)/(a-b))^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*b^3-2*a^2*b*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2)/b^2/(a-b)/(a+b)/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*b+a+b)^(1/2)/d","B"
533,1,373,218,0.982000," ","int(cos(d*x+c)/(a+b*cos(d*x+c))^(3/2),x)","-\frac{2 \left(\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-\frac{2 b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a -b}+\frac{a +b}{a -b}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{2}-b^{2} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-\frac{2 b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a -b}+\frac{a +b}{a -b}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right)-\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-\frac{2 b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a -b}+\frac{a +b}{a -b}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{2}+\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-\frac{2 b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a -b}+\frac{a +b}{a -b}}\, b \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a -2 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)\right)}{b \left(a -b \right) \left(a +b \right) \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a +b}\, d}"," ",0,"-2*((sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*b/(a-b)*sin(1/2*d*x+1/2*c)^2+(a+b)/(a-b))^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a^2-b^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*b/(a-b)*sin(1/2*d*x+1/2*c)^2+(a+b)/(a-b))^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))-(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*b/(a-b)*sin(1/2*d*x+1/2*c)^2+(a+b)/(a-b))^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a^2+(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*b/(a-b)*sin(1/2*d*x+1/2*c)^2+(a+b)/(a-b))^(1/2)*b*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a-2*a*b*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2)/b/(a-b)/(a+b)/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*b+a+b)^(1/2)/d","A"
534,1,217,129,0.793000," ","int(1/(a+b*cos(d*x+c))^(3/2),x)","-\frac{2 \left(\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-\frac{2 b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a -b}+\frac{a +b}{a -b}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a -\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-\frac{2 b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a -b}+\frac{a +b}{a -b}}\, b \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right)+2 b \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}{\left(a -b \right) \left(a +b \right) \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a +b}\, d}"," ",0,"-2*((sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*b/(a-b)*sin(1/2*d*x+1/2*c)^2+(a+b)/(a-b))^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a-(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*b/(a-b)*sin(1/2*d*x+1/2*c)^2+(a+b)/(a-b))^(1/2)*b*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))+2*b*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2)/(a-b)/(a+b)/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*b+a+b)^(1/2)/d","A"
535,1,376,224,0.922000," ","int(sec(d*x+c)/(a+b*cos(d*x+c))^(3/2),x)","\frac{2 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-\frac{2 b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a -b}+\frac{a +b}{a -b}}\, b \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a -2 b^{2} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-\frac{2 b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a -b}+\frac{a +b}{a -b}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right)+2 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-\frac{2 b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a -b}+\frac{a +b}{a -b}}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), 2, \sqrt{-\frac{2 b}{a -b}}\right) a^{2}-2 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-\frac{2 b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a -b}+\frac{a +b}{a -b}}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), 2, \sqrt{-\frac{2 b}{a -b}}\right) b^{2}+4 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 \left(a -b \right) \left(a +b \right) \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a +b}\, d}"," ",0,"2*((sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*b/(a-b)*sin(1/2*d*x+1/2*c)^2+(a+b)/(a-b))^(1/2)*b*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a-b^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*b/(a-b)*sin(1/2*d*x+1/2*c)^2+(a+b)/(a-b))^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))+(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*b/(a-b)*sin(1/2*d*x+1/2*c)^2+(a+b)/(a-b))^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2,(-2*b/(a-b))^(1/2))*a^2-(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*b/(a-b)*sin(1/2*d*x+1/2*c)^2+(a+b)/(a-b))^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2,(-2*b/(a-b))^(1/2))*b^2+2*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2)/a/(a-b)/(a+b)/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*b+a+b)^(1/2)/d","A"
536,1,894,348,2.025000," ","int(sec(d*x+c)^2/(a+b*cos(d*x+c))^(3/2),x)","-\frac{\sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a +b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(\frac{2 b^{2} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(a +b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-\frac{2 b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a -b}+\frac{a +b}{a -b}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a -\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-\frac{2 b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a -b}+\frac{a +b}{a -b}}\, b \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right)+2 b \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}{a^{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) b +a +b \right) \left(a^{2}-b^{2}\right)}+\frac{2 b \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), 2, \sqrt{-\frac{2 b}{a -b}}\right)}{a^{2} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(a +b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}}+\frac{-\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) b +\left(a +b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}}{a \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}+\frac{\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right)}{\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(a +b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}}-\frac{\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right)}{\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(a +b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}}+\frac{\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, b \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right)}{a \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(a +b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}}+\frac{b \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), 2, \sqrt{-\frac{2 b}{a -b}}\right)}{a \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(a +b \right) \left(\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(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a +b}\, d}"," ",0,"-(-(-2*cos(1/2*d*x+1/2*c)^2*b-a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*b^2/a^2/sin(1/2*d*x+1/2*c)^2/(-2*sin(1/2*d*x+1/2*c)^2*b+a+b)/(a^2-b^2)*(-2*sin(1/2*d*x+1/2*c)^4*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)*((sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*b/(a-b)*sin(1/2*d*x+1/2*c)^2+(a+b)/(a-b))^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a-(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*b/(a-b)*sin(1/2*d*x+1/2*c)^2+(a+b)/(a-b))^(1/2)*b*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))+2*b*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2)+2/a^2*b*(sin(1/2*d*x+1/2*c)^2)^(1/2)*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)/(a-b))^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2,(-2*b/(a-b))^(1/2))+2/a*(-1/a*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4*b+(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*(sin(1/2*d*x+1/2*c)^2)^(1/2)*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)/(a-b))^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))-1/2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)/(a-b))^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))+1/2/a*(sin(1/2*d*x+1/2*c)^2)^(1/2)*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)/(a-b))^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)*b*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))+1/2/a*b*(sin(1/2*d*x+1/2*c)^2)^(1/2)*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)/(a-b))^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2,(-2*b/(a-b))^(1/2))))/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*b+a+b)^(1/2)/d","B"
537,1,1542,402,2.392000," ","int(sec(d*x+c)^3/(a+b*cos(d*x+c))^(3/2),x)","-\frac{\sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a +b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(\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) b +\left(a +b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}}{a \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)^{2}}+\frac{3 b \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) b +\left(a +b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}}{2 a^{2} \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}-\frac{b \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right)}{4 a \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(a +b \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{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, b \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right)}{4 a \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(a +b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}}-\frac{3 b^{2} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right)}{4 a^{2} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(a +b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}}-\frac{\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), 2, \sqrt{-\frac{2 b}{a -b}}\right)}{\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(a +b \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{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), 2, \sqrt{-\frac{2 b}{a -b}}\right) b^{2}}{4 a^{2} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(a +b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}}}{a}-\frac{2 b^{3} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(a +b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-\frac{2 b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a -b}+\frac{a +b}{a -b}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a -\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-\frac{2 b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a -b}+\frac{a +b}{a -b}}\, b \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right)+2 b \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}{a^{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) b +a +b \right) \left(a^{2}-b^{2}\right)}-\frac{2 b^{2} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), 2, \sqrt{-\frac{2 b}{a -b}}\right)}{a^{3} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(a +b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}}-\frac{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) b +\left(a +b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}}{a \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}+\frac{\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right)}{2 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(a +b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}}-\frac{\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right)}{2 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(a +b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}}+\frac{\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, b \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right)}{2 a \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(a +b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}}+\frac{b \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), 2, \sqrt{-\frac{2 b}{a -b}}\right)}{2 a \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(a +b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}}\right)}{a^{2}}\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a +b}\, d}"," ",0,"-(-(-2*cos(1/2*d*x+1/2*c)^2*b-a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(2/a*(-1/2/a*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)/(2*cos(1/2*d*x+1/2*c)^2-1)^2+3/4*b/a^2*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)/(2*cos(1/2*d*x+1/2*c)^2-1)-1/8*b/a*(sin(1/2*d*x+1/2*c)^2)^(1/2)*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)/(a-b))^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))+3/8/a*(sin(1/2*d*x+1/2*c)^2)^(1/2)*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)/(a-b))^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)*b*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))-3/8*b^2/a^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)/(a-b))^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))-1/2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)/(a-b))^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2,(-2*b/(a-b))^(1/2))-3/8/a^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)/(a-b))^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2,(-2*b/(a-b))^(1/2))*b^2)-2/a^3*b^3/sin(1/2*d*x+1/2*c)^2/(-2*sin(1/2*d*x+1/2*c)^2*b+a+b)/(a^2-b^2)*(-2*sin(1/2*d*x+1/2*c)^4*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)*((sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*b/(a-b)*sin(1/2*d*x+1/2*c)^2+(a+b)/(a-b))^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a-(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*b/(a-b)*sin(1/2*d*x+1/2*c)^2+(a+b)/(a-b))^(1/2)*b*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))+2*b*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2)-2*b^2/a^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)/(a-b))^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2,(-2*b/(a-b))^(1/2))-2/a^2*b*(-1/a*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4*b+(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*(sin(1/2*d*x+1/2*c)^2)^(1/2)*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)/(a-b))^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))-1/2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)/(a-b))^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))+1/2/a*(sin(1/2*d*x+1/2*c)^2)^(1/2)*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)/(a-b))^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)*b*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))+1/2/a*b*(sin(1/2*d*x+1/2*c)^2)^(1/2)*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)/(a-b))^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2,(-2*b/(a-b))^(1/2))))/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*b+a+b)^(1/2)/d","B"
538,1,1684,466,4.373000," ","int(cos(d*x+c)^5/(a+b*cos(d*x+c))^(5/2),x)","-\frac{\sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a +b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(\frac{-\frac{8 \left(\cos^{3}\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) b +\left(a +b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}}{5 b}-\frac{4 \left(-4 a +12 b \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) b +\left(a +b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}}{15 b^{2}}+\frac{4 \left(-4 a +12 b \right) \left(a -b \right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right)}{15 b^{2} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(a +b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}}-\frac{4 \left(4 a^{2}-15 a b +27 b^{2}\right) \left(a -b \right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, \left(\EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right)-\EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right)\right)}{15 b^{3} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(a +b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}}}{b^{2}}-\frac{8 \left(2 a +3 b \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) b +\left(a +b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}}{6 b}+\frac{\left(a -b \right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right)}{6 b \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(a +b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}}-\frac{\left(-2 a +6 b \right) \left(a -b \right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, \left(\EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right)-\EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right)\right)}{12 b^{2} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(a +b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}}\right)}{b^{3}}-\frac{2 \left(3 a^{2}+4 a b +3 b^{2}\right) \left(a -b \right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, \left(\EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right)-\EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right)\right)}{b^{5} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(a +b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}}-\frac{2 \left(4 a^{3}+3 a^{2} b +2 b^{2} a +b^{3}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right)}{b^{5} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(a +b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}}+\frac{10 a^{4} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(a +b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-\frac{2 b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a -b}+\frac{a +b}{a -b}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a -\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-\frac{2 b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a -b}+\frac{a +b}{a -b}}\, b \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right)+2 b \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^{5} \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) b +a +b \right) \left(a^{2}-b^{2}\right)}-\frac{2 a^{5} \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) b +\left(a +b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}}{6 b \left(a -b \right) \left(a +b \right) \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)+\frac{a -b}{2 b}\right)^{2}}+\frac{8 b \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 \left(a -b \right)^{2} \left(a +b \right)^{2} \sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a +b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}}+\frac{\left(3 a -b \right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right)}{\left(3 a^{3}+3 a^{2} b -3 b^{2} a -3 b^{3}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(a +b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}}-\frac{4 a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, \left(\EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right)-\EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right)\right)}{3 \left(a -b \right) \left(a +b \right)^{2} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(a +b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}}\right)}{b^{5}}\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a +b}\, d}"," ",0,"-(-(-2*cos(1/2*d*x+1/2*c)^2*b-a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(16/b^2*(-1/10/b*cos(1/2*d*x+1/2*c)^3*(-2*sin(1/2*d*x+1/2*c)^4*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)-1/60/b^2*(-4*a+12*b)*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)+1/60/b^2*(-4*a+12*b)*(a-b)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)/(a-b))^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))-1/60*(4*a^2-15*a*b+27*b^2)/b^3*(a-b)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)/(a-b))^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))-EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))))-8/b^3*(2*a+3*b)*(-1/6/b*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)+1/6/b*(a-b)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)/(a-b))^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))-1/12/b^2*(-2*a+6*b)*(a-b)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)/(a-b))^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))-EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))))-2/b^5*(3*a^2+4*a*b+3*b^2)*(a-b)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)/(a-b))^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))-EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2)))-2*(4*a^3+3*a^2*b+2*a*b^2+b^3)/b^5*(sin(1/2*d*x+1/2*c)^2)^(1/2)*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)/(a-b))^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))+10*a^4/b^5/sin(1/2*d*x+1/2*c)^2/(-2*sin(1/2*d*x+1/2*c)^2*b+a+b)/(a^2-b^2)*(-2*sin(1/2*d*x+1/2*c)^4*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)*((sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*b/(a-b)*sin(1/2*d*x+1/2*c)^2+(a+b)/(a-b))^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a-(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*b/(a-b)*sin(1/2*d*x+1/2*c)^2+(a+b)/(a-b))^(1/2)*b*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))+2*b*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2)-2/b^5*a^5*(1/6/b/(a-b)/(a+b)*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)/(cos(1/2*d*x+1/2*c)^2+1/2/b*(a-b))^2+8/3*b*sin(1/2*d*x+1/2*c)^2/(a-b)^2/(a+b)^2*cos(1/2*d*x+1/2*c)*a/(-(-2*cos(1/2*d*x+1/2*c)^2*b-a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)+(3*a-b)/(3*a^3+3*a^2*b-3*a*b^2-3*b^3)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)/(a-b))^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))-4/3*a/(a-b)/(a+b)^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)/(a-b))^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))-EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2)))))/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*b+a+b)^(1/2)/d","B"
539,1,1291,379,3.383000," ","int(cos(d*x+c)^4/(a+b*cos(d*x+c))^(5/2),x)","-\frac{\sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a +b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(\frac{-\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) b +\left(a +b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}}{3 b}+\frac{4 \left(a -b \right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right)}{3 b \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(a +b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}}-\frac{2 \left(-2 a +6 b \right) \left(a -b \right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, \left(\EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right)-\EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right)\right)}{3 b^{2} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(a +b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}}}{b^{2}}+\frac{4 \left(a +b \right) \left(a -b \right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, \left(\EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right)-\EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right)\right)}{b^{4} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(a +b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}}+\frac{2 \left(3 a^{2}+2 a b +b^{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right)}{b^{4} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(a +b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}}-\frac{8 a^{3} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(a +b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-\frac{2 b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a -b}+\frac{a +b}{a -b}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a -\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-\frac{2 b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a -b}+\frac{a +b}{a -b}}\, b \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right)+2 b \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^{4} \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) b +a +b \right) \left(a^{2}-b^{2}\right)}+\frac{2 a^{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) b +\left(a +b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}}{6 b \left(a -b \right) \left(a +b \right) \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)+\frac{a -b}{2 b}\right)^{2}}+\frac{8 b \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 \left(a -b \right)^{2} \left(a +b \right)^{2} \sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a +b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}}+\frac{\left(3 a -b \right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right)}{\left(3 a^{3}+3 a^{2} b -3 b^{2} a -3 b^{3}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(a +b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}}-\frac{4 a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, \left(\EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right)-\EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right)\right)}{3 \left(a -b \right) \left(a +b \right)^{2} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(a +b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}}\right)}{b^{4}}\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a +b}\, d}"," ",0,"-(-(-2*cos(1/2*d*x+1/2*c)^2*b-a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(8/b^2*(-1/6/b*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)+1/6/b*(a-b)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)/(a-b))^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))-1/12/b^2*(-2*a+6*b)*(a-b)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)/(a-b))^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))-EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))))+4/b^4*(a+b)*(a-b)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)/(a-b))^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))-EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2)))+2*(3*a^2+2*a*b+b^2)/b^4*(sin(1/2*d*x+1/2*c)^2)^(1/2)*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)/(a-b))^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))-8*a^3/b^4/sin(1/2*d*x+1/2*c)^2/(-2*sin(1/2*d*x+1/2*c)^2*b+a+b)/(a^2-b^2)*(-2*sin(1/2*d*x+1/2*c)^4*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)*((sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*b/(a-b)*sin(1/2*d*x+1/2*c)^2+(a+b)/(a-b))^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a-(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*b/(a-b)*sin(1/2*d*x+1/2*c)^2+(a+b)/(a-b))^(1/2)*b*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))+2*b*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2)+2/b^4*a^4*(1/6/b/(a-b)/(a+b)*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)/(cos(1/2*d*x+1/2*c)^2+1/2/b*(a-b))^2+8/3*b*sin(1/2*d*x+1/2*c)^2/(a-b)^2/(a+b)^2*cos(1/2*d*x+1/2*c)*a/(-(-2*cos(1/2*d*x+1/2*c)^2*b-a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)+(3*a-b)/(3*a^3+3*a^2*b-3*a*b^2-3*b^3)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)/(a-b))^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))-4/3*a/(a-b)/(a+b)^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)/(a-b))^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))-EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2)))))/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*b+a+b)^(1/2)/d","B"
540,1,907,319,2.878000," ","int(cos(d*x+c)^3/(a+b*cos(d*x+c))^(5/2),x)","-\frac{\sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a +b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(-\frac{2 \sqrt{-\frac{2 b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a -b}+\frac{a +b}{a -b}}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(3 \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a -\EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a +\EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) b \right)}{b^{3} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(a +b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}}+\frac{6 a^{2} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(a +b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-\frac{2 b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a -b}+\frac{a +b}{a -b}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a -\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-\frac{2 b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a -b}+\frac{a +b}{a -b}}\, b \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right)+2 b \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) b +a +b \right) \left(a^{2}-b^{2}\right)}-\frac{2 a^{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) b +\left(a +b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}}{6 b \left(a -b \right) \left(a +b \right) \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)+\frac{a -b}{2 b}\right)^{2}}+\frac{8 b \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 \left(a -b \right)^{2} \left(a +b \right)^{2} \sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a +b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}}+\frac{\left(3 a -b \right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right)}{\left(3 a^{3}+3 a^{2} b -3 b^{2} a -3 b^{3}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(a +b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}}-\frac{4 a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, \left(\EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right)-\EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right)\right)}{3 \left(a -b \right) \left(a +b \right)^{2} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(a +b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}}\right)}{b^{3}}\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a +b}\, d}"," ",0,"-(-(-2*cos(1/2*d*x+1/2*c)^2*b-a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2/b^3/(-2*sin(1/2*d*x+1/2*c)^4*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*b/(a-b)*sin(1/2*d*x+1/2*c)^2+(a+b)/(a-b))^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(3*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a-EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a+EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*b)+6*a^2/b^3/sin(1/2*d*x+1/2*c)^2/(-2*sin(1/2*d*x+1/2*c)^2*b+a+b)/(a^2-b^2)*(-2*sin(1/2*d*x+1/2*c)^4*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)*((sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*b/(a-b)*sin(1/2*d*x+1/2*c)^2+(a+b)/(a-b))^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a-(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*b/(a-b)*sin(1/2*d*x+1/2*c)^2+(a+b)/(a-b))^(1/2)*b*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))+2*b*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2)-2/b^3*a^3*(1/6/b/(a-b)/(a+b)*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)/(cos(1/2*d*x+1/2*c)^2+1/2/b*(a-b))^2+8/3*b*sin(1/2*d*x+1/2*c)^2/(a-b)^2/(a+b)^2*cos(1/2*d*x+1/2*c)*a/(-(-2*cos(1/2*d*x+1/2*c)^2*b-a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)+(3*a-b)/(3*a^3+3*a^2*b-3*a*b^2-3*b^3)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)/(a-b))^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))-4/3*a/(a-b)/(a+b)^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)/(a-b))^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))-EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2)))))/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*b+a+b)^(1/2)/d","B"
541,1,846,301,2.853000," ","int(cos(d*x+c)^2/(a+b*cos(d*x+c))^(5/2),x)","-\frac{\sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a +b \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{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right)}{b^{2} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(a +b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}}-\frac{4 a \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(a +b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-\frac{2 b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a -b}+\frac{a +b}{a -b}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a -\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-\frac{2 b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a -b}+\frac{a +b}{a -b}}\, b \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right)+2 b \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) b +a +b \right) \left(a^{2}-b^{2}\right)}+\frac{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) b +\left(a +b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}}{6 b \left(a -b \right) \left(a +b \right) \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)+\frac{a -b}{2 b}\right)^{2}}+\frac{8 b \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 \left(a -b \right)^{2} \left(a +b \right)^{2} \sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a +b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}}+\frac{\left(3 a -b \right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right)}{\left(3 a^{3}+3 a^{2} b -3 b^{2} a -3 b^{3}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(a +b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}}-\frac{4 a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, \left(\EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right)-\EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right)\right)}{3 \left(a -b \right) \left(a +b \right)^{2} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(a +b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}}\right)}{b^{2}}\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a +b}\, d}"," ",0,"-(-(-2*cos(1/2*d*x+1/2*c)^2*b-a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(2/b^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)/(a-b))^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))-4/b^2*a/sin(1/2*d*x+1/2*c)^2/(-2*sin(1/2*d*x+1/2*c)^2*b+a+b)/(a^2-b^2)*(-2*sin(1/2*d*x+1/2*c)^4*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)*((sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*b/(a-b)*sin(1/2*d*x+1/2*c)^2+(a+b)/(a-b))^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a-(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*b/(a-b)*sin(1/2*d*x+1/2*c)^2+(a+b)/(a-b))^(1/2)*b*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))+2*b*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2)+2/b^2*a^2*(1/6/b/(a-b)/(a+b)*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)/(cos(1/2*d*x+1/2*c)^2+1/2/b*(a-b))^2+8/3*b*sin(1/2*d*x+1/2*c)^2/(a-b)^2/(a+b)^2*cos(1/2*d*x+1/2*c)*a/(-(-2*cos(1/2*d*x+1/2*c)^2*b-a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)+(3*a-b)/(3*a^3+3*a^2*b-3*a*b^2-3*b^3)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)/(a-b))^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))-4/3*a/(a-b)/(a+b)^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)/(a-b))^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))-EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2)))))/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*b+a+b)^(1/2)/d","B"
542,1,742,281,2.727000," ","int(cos(d*x+c)/(a+b*cos(d*x+c))^(5/2),x)","-\frac{\sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a +b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(\frac{2 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(a +b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-\frac{2 b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a -b}+\frac{a +b}{a -b}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a -\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-\frac{2 b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a -b}+\frac{a +b}{a -b}}\, b \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right)+2 b \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 \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) b +a +b \right) \left(a^{2}-b^{2}\right)}-\frac{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) b +\left(a +b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}}{6 b \left(a -b \right) \left(a +b \right) \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)+\frac{a -b}{2 b}\right)^{2}}+\frac{8 b \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 \left(a -b \right)^{2} \left(a +b \right)^{2} \sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a +b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}}+\frac{\left(3 a -b \right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right)}{\left(3 a^{3}+3 a^{2} b -3 b^{2} a -3 b^{3}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(a +b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}}-\frac{4 a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, \left(\EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right)-\EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right)\right)}{3 \left(a -b \right) \left(a +b \right)^{2} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(a +b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}}\right)}{b}\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a +b}\, d}"," ",0,"-(-(-2*cos(1/2*d*x+1/2*c)^2*b-a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(2/b/sin(1/2*d*x+1/2*c)^2/(-2*sin(1/2*d*x+1/2*c)^2*b+a+b)/(a^2-b^2)*(-2*sin(1/2*d*x+1/2*c)^4*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)*((sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*b/(a-b)*sin(1/2*d*x+1/2*c)^2+(a+b)/(a-b))^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a-(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*b/(a-b)*sin(1/2*d*x+1/2*c)^2+(a+b)/(a-b))^(1/2)*b*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))+2*b*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2)-2*a/b*(1/6/b/(a-b)/(a+b)*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)/(cos(1/2*d*x+1/2*c)^2+1/2/b*(a-b))^2+8/3*b*sin(1/2*d*x+1/2*c)^2/(a-b)^2/(a+b)^2*cos(1/2*d*x+1/2*c)*a/(-(-2*cos(1/2*d*x+1/2*c)^2*b-a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)+(3*a-b)/(3*a^3+3*a^2*b-3*a*b^2-3*b^3)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)/(a-b))^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))-4/3*a/(a-b)/(a+b)^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)/(a-b))^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))-EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2)))))/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*b+a+b)^(1/2)/d","B"
543,1,489,259,1.655000," ","int(1/(a+b*cos(d*x+c))^(5/2),x)","-\frac{\sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a +b \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) b +\left(a +b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}}{3 b \left(a -b \right) \left(a +b \right) \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)+\frac{a -b}{2 b}\right)^{2}}+\frac{16 b \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 \left(a -b \right)^{2} \left(a +b \right)^{2} \sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a +b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}}+\frac{2 \left(3 a -b \right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right)}{\left(3 a^{3}+3 a^{2} b -3 b^{2} a -3 b^{3}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(a +b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}}-\frac{8 a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, \left(\EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right)-\EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right)\right)}{3 \left(a -b \right) \left(a +b \right)^{2} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(a +b \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(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a +b}\, d}"," ",0,"-(-(-2*cos(1/2*d*x+1/2*c)^2*b-a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(1/3/b/(a-b)/(a+b)*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)/(cos(1/2*d*x+1/2*c)^2+1/2/b*(a-b))^2+16/3*b*sin(1/2*d*x+1/2*c)^2/(a-b)^2/(a+b)^2*cos(1/2*d*x+1/2*c)*a/(-(-2*cos(1/2*d*x+1/2*c)^2*b-a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)+2*(3*a-b)/(3*a^3+3*a^2*b-3*a*b^2-3*b^3)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)/(a-b))^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))-8/3*a/(a-b)/(a+b)^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)/(a-b))^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))-EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))))/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*b+a+b)^(1/2)/d","A"
544,1,845,383,2.718000," ","int(sec(d*x+c)/(a+b*cos(d*x+c))^(5/2),x)","-\frac{\sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a +b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(-\frac{2 b \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(a +b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-\frac{2 b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a -b}+\frac{a +b}{a -b}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a -\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-\frac{2 b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a -b}+\frac{a +b}{a -b}}\, b \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right)+2 b \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}{a^{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) b +a +b \right) \left(a^{2}-b^{2}\right)}-\frac{2 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), 2, \sqrt{-\frac{2 b}{a -b}}\right)}{a^{2} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(a +b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}}-\frac{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) b +\left(a +b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}}{6 b \left(a -b \right) \left(a +b \right) \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)+\frac{a -b}{2 b}\right)^{2}}+\frac{8 b \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 \left(a -b \right)^{2} \left(a +b \right)^{2} \sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a +b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}}+\frac{\left(3 a -b \right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right)}{\left(3 a^{3}+3 a^{2} b -3 b^{2} a -3 b^{3}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(a +b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}}-\frac{4 a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, \left(\EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right)-\EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right)\right)}{3 \left(a -b \right) \left(a +b \right)^{2} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(a +b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}}\right)}{a}\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a +b}\, d}"," ",0,"-(-(-2*cos(1/2*d*x+1/2*c)^2*b-a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2/a^2*b/sin(1/2*d*x+1/2*c)^2/(-2*sin(1/2*d*x+1/2*c)^2*b+a+b)/(a^2-b^2)*(-2*sin(1/2*d*x+1/2*c)^4*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)*((sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*b/(a-b)*sin(1/2*d*x+1/2*c)^2+(a+b)/(a-b))^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a-(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*b/(a-b)*sin(1/2*d*x+1/2*c)^2+(a+b)/(a-b))^(1/2)*b*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))+2*b*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^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*b+a-b)/(a-b))^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2,(-2*b/(a-b))^(1/2))-2/a*b*(1/6/b/(a-b)/(a+b)*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)/(cos(1/2*d*x+1/2*c)^2+1/2/b*(a-b))^2+8/3*b*sin(1/2*d*x+1/2*c)^2/(a-b)^2/(a+b)^2*cos(1/2*d*x+1/2*c)*a/(-(-2*cos(1/2*d*x+1/2*c)^2*b-a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)+(3*a-b)/(3*a^3+3*a^2*b-3*a*b^2-3*b^3)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)/(a-b))^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))-4/3*a/(a-b)/(a+b)^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)/(a-b))^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))-EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2)))))/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*b+a+b)^(1/2)/d","B"
545,1,1320,441,3.606000," ","int(sec(d*x+c)^2/(a+b*cos(d*x+c))^(5/2),x)","-\frac{\sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a +b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(\frac{4 b^{2} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(a +b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-\frac{2 b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a -b}+\frac{a +b}{a -b}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a -\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-\frac{2 b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a -b}+\frac{a +b}{a -b}}\, b \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right)+2 b \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}{a^{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) b +a +b \right) \left(a^{2}-b^{2}\right)}+\frac{4 b \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), 2, \sqrt{-\frac{2 b}{a -b}}\right)}{a^{3} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(a +b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}}+\frac{-\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) b +\left(a +b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}}{a \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}+\frac{\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right)}{\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(a +b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}}-\frac{\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right)}{\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(a +b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}}+\frac{\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, b \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right)}{a \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(a +b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}}+\frac{b \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), 2, \sqrt{-\frac{2 b}{a -b}}\right)}{a \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(a +b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}}}{a^{2}}+\frac{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) b +\left(a +b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}}{6 b \left(a -b \right) \left(a +b \right) \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)+\frac{a -b}{2 b}\right)^{2}}+\frac{8 b \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 \left(a -b \right)^{2} \left(a +b \right)^{2} \sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a +b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}}+\frac{\left(3 a -b \right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right)}{\left(3 a^{3}+3 a^{2} b -3 b^{2} a -3 b^{3}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(a +b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}}-\frac{4 a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, \left(\EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right)-\EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right)\right)}{3 \left(a -b \right) \left(a +b \right)^{2} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(a +b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}}\right)}{a^{2}}\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a +b}\, d}"," ",0,"-(-(-2*cos(1/2*d*x+1/2*c)^2*b-a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(4*b^2/a^3/sin(1/2*d*x+1/2*c)^2/(-2*sin(1/2*d*x+1/2*c)^2*b+a+b)/(a^2-b^2)*(-2*sin(1/2*d*x+1/2*c)^4*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)*((sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*b/(a-b)*sin(1/2*d*x+1/2*c)^2+(a+b)/(a-b))^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a-(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*b/(a-b)*sin(1/2*d*x+1/2*c)^2+(a+b)/(a-b))^(1/2)*b*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))+2*b*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2)+4/a^3*b*(sin(1/2*d*x+1/2*c)^2)^(1/2)*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)/(a-b))^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2,(-2*b/(a-b))^(1/2))+2/a^2*(-1/a*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4*b+(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*(sin(1/2*d*x+1/2*c)^2)^(1/2)*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)/(a-b))^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))-1/2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)/(a-b))^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))+1/2/a*(sin(1/2*d*x+1/2*c)^2)^(1/2)*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)/(a-b))^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)*b*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))+1/2/a*b*(sin(1/2*d*x+1/2*c)^2)^(1/2)*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)/(a-b))^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2,(-2*b/(a-b))^(1/2)))+2*b^2/a^2*(1/6/b/(a-b)/(a+b)*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)/(cos(1/2*d*x+1/2*c)^2+1/2/b*(a-b))^2+8/3*b*sin(1/2*d*x+1/2*c)^2/(a-b)^2/(a+b)^2*cos(1/2*d*x+1/2*c)*a/(-(-2*cos(1/2*d*x+1/2*c)^2*b-a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)+(3*a-b)/(3*a^3+3*a^2*b-3*a*b^2-3*b^3)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)/(a-b))^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))-4/3*a/(a-b)/(a+b)^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)/(a-b))^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))-EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2)))))/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*b+a+b)^(1/2)/d","B"
546,1,616,316,2.355000," ","int(1/(a+b*cos(d*x+c))^(7/2),x)","-\frac{\sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a +b \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) b +\left(a +b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}}{10 b^{2} \left(a -b \right) \left(a +b \right) \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)+\frac{a -b}{2 b}\right)^{3}}+\frac{8 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) b +\left(a +b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}}{15 b \left(a -b \right)^{2} \left(a +b \right)^{2} \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)+\frac{a -b}{2 b}\right)^{2}}+\frac{4 b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(23 a^{2}+9 b^{2}\right)}{15 \left(a -b \right)^{3} \left(a +b \right)^{3} \sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a +b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}}+\frac{2 \left(15 a^{2}-8 a b +9 b^{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right)}{\left(15 a^{5}+15 a^{4} b -30 a^{3} b^{2}-30 a^{2} b^{3}+15 a \,b^{4}+15 b^{5}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(a +b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}}-\frac{2 \left(23 a^{2}+9 b^{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, \left(\EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right)-\EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right)\right)}{15 \left(a -b \right)^{2} \left(a +b \right)^{3} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(a +b \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(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a +b}\, d}"," ",0,"-(-(-2*cos(1/2*d*x+1/2*c)^2*b-a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(1/10/b^2/(a-b)/(a+b)*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)/(cos(1/2*d*x+1/2*c)^2+1/2/b*(a-b))^3+8/15*a/b/(a-b)^2/(a+b)^2*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)/(cos(1/2*d*x+1/2*c)^2+1/2/b*(a-b))^2+4/15*b*sin(1/2*d*x+1/2*c)^2/(a-b)^3/(a+b)^3*cos(1/2*d*x+1/2*c)*(23*a^2+9*b^2)/(-(-2*cos(1/2*d*x+1/2*c)^2*b-a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)+2*(15*a^2-8*a*b+9*b^2)/(15*a^5+15*a^4*b-30*a^3*b^2-30*a^2*b^3+15*a*b^4+15*b^5)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)/(a-b))^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))-2/15*(23*a^2+9*b^2)/(a-b)^2/(a+b)^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)/(a-b))^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))-EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))))/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*b+a+b)^(1/2)/d","A"
547,1,231,147,0.757000," ","int(cos(d*x+c)^3/(3+4*cos(d*x+c))^(1/2),x)","-\frac{\sqrt{\left(8 \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 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+56 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-23 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{8 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-7}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), 2 \sqrt{2}\right)-9 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{8 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-7}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), 2 \sqrt{2}\right)\right)}{20 \sqrt{-8 \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)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{8 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-1/20*((8*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)*sin(1/2*d*x+1/2*c)^6+56*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)-23*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(8*sin(1/2*d*x+1/2*c)^2-7)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2*2^(1/2))-9*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(8*sin(1/2*d*x+1/2*c)^2-7)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2*2^(1/2)))/(-8*sin(1/2*d*x+1/2*c)^4+7*sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(8*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
548,1,231,118,0.594000," ","int(cos(d*x+c)^2/(3+4*cos(d*x+c))^(1/2),x)","-\frac{\sqrt{\left(8 \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(32 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+17 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{8 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-7}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), 2 \sqrt{2}\right)+3 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{8 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-7}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), 2 \sqrt{2}\right)-28 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{12 \sqrt{-8 \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)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{8 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-1/12*((8*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(32*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+17*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(8*sin(1/2*d*x+1/2*c)^2-7)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2*2^(1/2))+3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(8*sin(1/2*d*x+1/2*c)^2-7)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2*2^(1/2))-28*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c))/(-8*sin(1/2*d*x+1/2*c)^4+7*sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(8*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
549,1,155,95,0.609000," ","int(cos(d*x+c)/(3+4*cos(d*x+c))^(1/2),x)","\frac{\sqrt{\left(8 \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{-8 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \left(3 \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), 2 \sqrt{2}\right)+\EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), 2 \sqrt{2}\right)\right)}{2 \sqrt{-8 \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)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{8 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"1/2*((8*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)*(-8*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*(3*EllipticF(cos(1/2*d*x+1/2*c),2*2^(1/2))+EllipticE(cos(1/2*d*x+1/2*c),2*2^(1/2)))/(-8*sin(1/2*d*x+1/2*c)^4+7*sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(8*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
550,1,23,47,0.017000," ","int(1/(3+4*cos(d*x+c))^(1/2),x)","\frac{2 \sqrt{7}\, \mathrm{am}^{-1}\left(\frac{d x}{2}+\frac{c}{2}\bigg| \frac{2 \sqrt{14}}{7}\right)}{7 d}"," ",0,"2/7/d*7^(1/2)*InverseJacobiAM(1/2*d*x+1/2*c,2/7*14^(1/2))","C"
551,1,138,48,0.483000," ","int(sec(d*x+c)/(3+4*cos(d*x+c))^(1/2),x)","\frac{2 \sqrt{\left(8 \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{-8 \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), 2, 2 \sqrt{2}\right)}{\sqrt{-8 \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)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{8 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"2*((8*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)*(-8*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-8*sin(1/2*d*x+1/2*c)^4+7*sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2,2*2^(1/2))/sin(1/2*d*x+1/2*c)/(8*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
552,1,350,166,0.839000," ","int(sec(d*x+c)^2/(3+4*cos(d*x+c))^(1/2),x)","-\frac{\sqrt{-\left(-8 \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 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-8 \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)}}{3 \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}+\frac{\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-8 \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), 2 \sqrt{2}\right)}{\sqrt{-8 \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)}}+\frac{\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-8 \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), 2 \sqrt{2}\right)}{3 \sqrt{-8 \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)}}+\frac{4 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-8 \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), 2, 2 \sqrt{2}\right)}{3 \sqrt{-8 \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)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{8 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-(-(-8*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)*(-8*sin(1/2*d*x+1/2*c)^4+7*sin(1/2*d*x+1/2*c)^2)^(1/2)/(2*cos(1/2*d*x+1/2*c)^2-1)+(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-8*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-8*sin(1/2*d*x+1/2*c)^4+7*sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2*2^(1/2))+1/3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-8*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-8*sin(1/2*d*x+1/2*c)^4+7*sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2*2^(1/2))+4/3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-8*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-8*sin(1/2*d*x+1/2*c)^4+7*sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2,2*2^(1/2)))/sin(1/2*d*x+1/2*c)/(8*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
553,1,408,195,0.839000," ","int(sec(d*x+c)^3/(3+4*cos(d*x+c))^(1/2),x)","-\frac{\sqrt{-\left(-8 \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{-8 \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)}}{3 \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)^{2}}+\frac{2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-8 \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)}}{3 \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}-\frac{\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-8 \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), 2 \sqrt{2}\right)}{3 \sqrt{-8 \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)}}-\frac{\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-8 \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), 2 \sqrt{2}\right)}{3 \sqrt{-8 \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)}}-\frac{7 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-8 \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), 2, 2 \sqrt{2}\right)}{3 \sqrt{-8 \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)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{8 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-(-(-8*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(-1/3*cos(1/2*d*x+1/2*c)*(-8*sin(1/2*d*x+1/2*c)^4+7*sin(1/2*d*x+1/2*c)^2)^(1/2)/(2*cos(1/2*d*x+1/2*c)^2-1)^2+2/3*cos(1/2*d*x+1/2*c)*(-8*sin(1/2*d*x+1/2*c)^4+7*sin(1/2*d*x+1/2*c)^2)^(1/2)/(2*cos(1/2*d*x+1/2*c)^2-1)-1/3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-8*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-8*sin(1/2*d*x+1/2*c)^4+7*sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2*2^(1/2))-1/3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-8*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-8*sin(1/2*d*x+1/2*c)^4+7*sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2*2^(1/2))-7/3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-8*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-8*sin(1/2*d*x+1/2*c)^4+7*sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2,2*2^(1/2)))/sin(1/2*d*x+1/2*c)/(8*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
554,1,254,147,0.633000," ","int(cos(d*x+c)^3/(3-4*cos(d*x+c))^(1/2),x)","-\frac{\sqrt{-\left(8 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-7\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(-448 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+504 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+23 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{56 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-7}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 \sqrt{14}}{7}\right)-63 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{56 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-7}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 \sqrt{14}}{7}\right)-56 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{140 \sqrt{8 \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)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-8 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+7}\, d}"," ",0,"-1/140*(-(8*cos(1/2*d*x+1/2*c)^2-7)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(-448*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6+504*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+23*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(56*sin(1/2*d*x+1/2*c)^2-7)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2/7*14^(1/2))-63*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(56*sin(1/2*d*x+1/2*c)^2-7)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2/7*14^(1/2))-56*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c))/(8*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*cos(1/2*d*x+1/2*c)^2+7)^(1/2)/d","A"
555,1,232,118,0.677000," ","int(cos(d*x+c)^2/(3-4*cos(d*x+c))^(1/2),x)","-\frac{\sqrt{-\left(8 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-7\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(224 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+17 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{56 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-7}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 \sqrt{14}}{7}\right)-21 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{56 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-7}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 \sqrt{14}}{7}\right)-28 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{84 \sqrt{8 \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)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-8 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+7}\, d}"," ",0,"-1/84*(-(8*cos(1/2*d*x+1/2*c)^2-7)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(224*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+17*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(56*sin(1/2*d*x+1/2*c)^2-7)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2/7*14^(1/2))-21*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(56*sin(1/2*d*x+1/2*c)^2-7)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2/7*14^(1/2))-28*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c))/(8*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*cos(1/2*d*x+1/2*c)^2+7)^(1/2)/d","A"
556,1,158,95,0.729000," ","int(cos(d*x+c)/(3-4*cos(d*x+c))^(1/2),x)","-\frac{\sqrt{-\left(8 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-7\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{56 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-7}\, \left(3 \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 \sqrt{14}}{7}\right)-7 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 \sqrt{14}}{7}\right)\right)}{14 \sqrt{8 \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)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-8 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+7}\, d}"," ",0,"-1/14*(-(8*cos(1/2*d*x+1/2*c)^2-7)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(56*sin(1/2*d*x+1/2*c)^2-7)^(1/2)*(3*EllipticF(cos(1/2*d*x+1/2*c),2/7*14^(1/2))-7*EllipticE(cos(1/2*d*x+1/2*c),2/7*14^(1/2)))/(8*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*cos(1/2*d*x+1/2*c)^2+7)^(1/2)/d","A"
557,1,54,47,0.066000," ","int(1/(3-4*cos(d*x+c))^(1/2),x)","\frac{2 \sqrt{8 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-7}\, \mathrm{am}^{-1}\left(\frac{d x}{2}+\frac{c}{2}| 2 \sqrt{2}\right)}{d \sqrt{-8 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+7}}"," ",0,"2/d/(-8*cos(1/2*d*x+1/2*c)^2+7)^(1/2)*(8*cos(1/2*d*x+1/2*c)^2-7)^(1/2)*InverseJacobiAM(1/2*d*x+1/2*c,2*2^(1/2))","C"
558,1,139,48,0.593000," ","int(sec(d*x+c)/(3-4*cos(d*x+c))^(1/2),x)","\frac{2 \sqrt{-\left(8 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-7\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{56 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-7}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), 2, \frac{2 \sqrt{14}}{7}\right)}{7 \sqrt{8 \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)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-8 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+7}\, d}"," ",0,"2/7*(-(8*cos(1/2*d*x+1/2*c)^2-7)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(56*sin(1/2*d*x+1/2*c)^2-7)^(1/2)/(8*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),2,2/7*14^(1/2))/sin(1/2*d*x+1/2*c)/(-8*cos(1/2*d*x+1/2*c)^2+7)^(1/2)/d","B"
559,1,351,166,0.828000," ","int(sec(d*x+c)^2/(3-4*cos(d*x+c))^(1/2),x)","-\frac{\sqrt{-\left(8 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-7\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(-\frac{2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{8 \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)}}{3 \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}+\frac{\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{56 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-7}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 \sqrt{14}}{7}\right)}{7 \sqrt{8 \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)}}-\frac{\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{56 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-7}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 \sqrt{14}}{7}\right)}{3 \sqrt{8 \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)}}-\frac{4 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{56 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-7}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), 2, \frac{2 \sqrt{14}}{7}\right)}{21 \sqrt{8 \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)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-8 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+7}\, d}"," ",0,"-(-(8*cos(1/2*d*x+1/2*c)^2-7)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2/3*cos(1/2*d*x+1/2*c)*(8*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)+1/7*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(56*sin(1/2*d*x+1/2*c)^2-7)^(1/2)/(8*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),2/7*14^(1/2))-1/3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(56*sin(1/2*d*x+1/2*c)^2-7)^(1/2)/(8*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),2/7*14^(1/2))-4/21*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(56*sin(1/2*d*x+1/2*c)^2-7)^(1/2)/(8*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),2,2/7*14^(1/2)))/sin(1/2*d*x+1/2*c)/(-8*cos(1/2*d*x+1/2*c)^2+7)^(1/2)/d","B"
560,1,408,195,1.058000," ","int(sec(d*x+c)^3/(3-4*cos(d*x+c))^(1/2),x)","-\frac{\sqrt{-\left(8 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-7\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{8 \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)}}{3 \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)^{2}}-\frac{2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{8 \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)}}{3 \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}+\frac{\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{56 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-7}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 \sqrt{14}}{7}\right)}{21 \sqrt{8 \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)}}-\frac{\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{56 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-7}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 \sqrt{14}}{7}\right)}{3 \sqrt{8 \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)}}-\frac{\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{56 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-7}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), 2, \frac{2 \sqrt{14}}{7}\right)}{3 \sqrt{8 \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)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-8 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+7}\, d}"," ",0,"-(-(8*cos(1/2*d*x+1/2*c)^2-7)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(-1/3*cos(1/2*d*x+1/2*c)*(8*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)^2-2/3*cos(1/2*d*x+1/2*c)*(8*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)+1/21*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(56*sin(1/2*d*x+1/2*c)^2-7)^(1/2)/(8*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),2/7*14^(1/2))-1/3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(56*sin(1/2*d*x+1/2*c)^2-7)^(1/2)/(8*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),2/7*14^(1/2))-1/3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(56*sin(1/2*d*x+1/2*c)^2-7)^(1/2)/(8*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),2,2/7*14^(1/2)))/sin(1/2*d*x+1/2*c)/(-8*cos(1/2*d*x+1/2*c)^2+7)^(1/2)/d","B"
561,1,290,147,0.713000," ","int(cos(d*x+c)^(5/2)*(A+B*cos(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 B \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(-168 A -360 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(168 A +280 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(-42 A -80 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)-63 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}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+25 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)\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*B*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^8+(-168*A-360*B)*sin(1/2*d*x+1/2*c)^6*cos(1/2*d*x+1/2*c)+(168*A+280*B)*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+(-42*A-80*B)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)-63*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)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+25*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)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
562,1,262,127,0.738000," ","int(cos(d*x+c)^(3/2)*(A+B*cos(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 B \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(20 A +24 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(-10 A -6 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 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 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)\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*B*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6+(20*A+24*B)*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+(-10*A-6*B)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+5*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*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)))/(-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"
563,1,229,107,0.641000," ","int((A+B*cos(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)}\, \left(-4 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 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}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\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)+2 B \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*B*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4+3*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)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-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))+2*B*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"
564,1,152,87,0.689000," ","int((A+B*cos(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(A \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-B \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)*(A*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-B*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"
565,1,148,107,0.735000," ","int((A+B*cos(d*x+c))/cos(d*x+c)^(3/2),x)","-\frac{2 \left(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}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-2 A \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\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)\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)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-2*A*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^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)))/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
566,1,397,127,1.594000," ","int((A+B*cos(d*x+c))/cos(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(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) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+6 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) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-12 B \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{4}\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}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+2 A \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-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}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+6 B \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*(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+6*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))*sin(1/2*d*x+1/2*c)^2-12*B*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4-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))+2*A*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2-3*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)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+6*B*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"
567,1,502,147,1.830000," ","int((A+B*cos(d*x+c))/cos(d*x+c)^(7/2),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 \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}}+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)\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)*(-2/5*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*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"
568,1,398,192,0.797000," ","int(cos(d*x+c)^(5/2)*(a+b*cos(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 b^{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(1440 a b +2240 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(-504 a^{2}-2160 a b -2072 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(504 a^{2}+1680 a b +952 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(-126 a^{2}-480 a b -168 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)-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) a^{2}-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) b^{2}+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)\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*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^10+(1440*a*b+2240*b^2)*sin(1/2*d*x+1/2*c)^8*cos(1/2*d*x+1/2*c)+(-504*a^2-2160*a*b-2072*b^2)*sin(1/2*d*x+1/2*c)^6*cos(1/2*d*x+1/2*c)+(504*a^2+1680*a*b+952*b^2)*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+(-126*a^2-480*a*b-168*b^2)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)-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^2-147*(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))*b^2+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)))/(-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"
569,1,362,171,0.746000," ","int(cos(d*x+c)^(3/2)*(a+b*cos(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 b^{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(-336 a b -360 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(140 a^{2}+336 a b +280 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(-70 a^{2}-84 a b -80 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)+35 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}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+25 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)-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*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^8+(-336*a*b-360*b^2)*sin(1/2*d*x+1/2*c)^6*cos(1/2*d*x+1/2*c)+(140*a^2+336*a*b+280*b^2)*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+(-70*a^2-84*a*b-80*b^2)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+35*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))+25*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"
570,1,321,141,0.694000," ","int(cos(d*x+c)^(1/2)*(a+b*cos(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 b^{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(40 a b +24 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(-20 a b -6 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)+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)-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}-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) 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*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6+(40*a*b+24*b^2)*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+(-20*a*b-6*b^2)*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))-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^2-9*(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))*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"
571,1,283,118,0.797000," ","int((a+b*cos(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(4 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 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}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+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)-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 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)}{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*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4+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))-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*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)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
572,1,202,118,0.692000," ","int((a+b*cos(d*x+c))^2/cos(d*x+c)^(3/2),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 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)}{\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*a^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"
573,1,514,139,1.580000," ","int((a+b*cos(d*x+c))^2/cos(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(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^{2} \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}}\, b^{2} \left(\sin^{2}\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}}\, 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)-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}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-3 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)-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)+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)\right) \sqrt{-2 \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))*(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+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)*b^2*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)*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-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+12*a*b*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"
574,1,660,171,2.086000," ","int((a+b*cos(d*x+c))^2/cos(d*x+c)^(7/2),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(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 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)}+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)*(-2/5*a^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*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)+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"
575,1,470,226,0.749000," ","int(cos(d*x+c)^(3/2)*(a+b*cos(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 b^{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(2160 b^{2} a +2240 b^{3}\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(-1512 a^{2} b -3240 b^{2} a -2072 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(420 a^{3}+1512 a^{2} b +2520 b^{2} a +952 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(-210 a^{3}-378 a^{2} b -720 b^{2} a -168 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)+105 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)+225 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)-567 \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 -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) b^{3}\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*b^3*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^10+(2160*a*b^2+2240*b^3)*sin(1/2*d*x+1/2*c)^8*cos(1/2*d*x+1/2*c)+(-1512*a^2*b-3240*a*b^2-2072*b^3)*sin(1/2*d*x+1/2*c)^6*cos(1/2*d*x+1/2*c)+(420*a^3+1512*a^2*b+2520*a*b^2+952*b^3)*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+(-210*a^3-378*a^2*b-720*a*b^2-168*b^3)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+105*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))+225*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))-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^2*b-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))*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"
576,1,421,195,0.744000," ","int(cos(d*x+c)^(1/2)*(a+b*cos(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 b^{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(-504 b^{2} a -360 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(420 a^{2} b +504 b^{2} a +280 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(-210 a^{2} b -126 b^{2} a -80 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)+105 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}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+25 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)-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) a^{3}-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) a \,b^{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)}\, \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*b^3*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^8+(-504*a*b^2-360*b^3)*sin(1/2*d*x+1/2*c)^6*cos(1/2*d*x+1/2*c)+(420*a^2*b+504*a*b^2+280*b^3)*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+(-210*a^2*b-126*a*b^2-80*b^3)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+105*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))+25*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))-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))*a^3-189*(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*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"
577,1,376,158,0.685000," ","int((a+b*cos(d*x+c))^3/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(-8 b^{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(20 b^{2} a +8 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(-10 b^{2} a -2 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)+5 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)+5 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)-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 -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}\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*b^3*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6+(20*a*b^2+8*b^3)*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+(-10*a*b^2-2*b^3)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+5*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))+5*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))-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-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*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"
578,1,303,168,0.800000," ","int((a+b*cos(d*x+c))^3/cos(d*x+c)^(3/2),x)","-\frac{2 \left(4 b^{3} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\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}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+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)+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^{3}-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 \,b^{2}-6 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)-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)}{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*b^3*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4+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))+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^2-6*a^3*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)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
579,1,631,162,1.642000," ","int((a+b*cos(d*x+c))^3/cos(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(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^{3} \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{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^{2} \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{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} 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{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^{3} \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-36 a^{2} b \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 \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 +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)+18 a^{2} b \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*(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^3*sin(1/2*d*x+1/2*c)^2+18*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^2*sin(1/2*d*x+1/2*c)^2+18*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*b*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)*b^3*sin(1/2*d*x+1/2*c)^2-36*a^2*b*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+18*a^2*b*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"
580,1,738,187,2.068000," ","int((a+b*cos(d*x+c))^3/cos(d*x+c)^(7/2),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 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}\, \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 a^{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 b^{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)}{\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)}+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)\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*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+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*a^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*b^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))+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)+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))))/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
581,1,847,226,2.599000," ","int((a+b*cos(d*x+c))^3/cos(d*x+c)^(9/2),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{6 a^{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}}+\frac{2 b^{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)}+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)+2 a^{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)\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)*(-6/5*a^2*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^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)+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*a^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))))/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
582,1,516,184,0.866000," ","int(cos(d*x+c)^(5/2)/(a+b*cos(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 b^{2} a -4 b^{3}\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 b^{2} a +2 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)+3 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)-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}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+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)-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)+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^{2} 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}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a \,b^{2}-3 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}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), -\frac{2 b}{a -b}, \sqrt{2}\right)\right)}{3 b^{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*b^2-4*b^3)*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4+(-2*a*b^2+2*b^3)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+3*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))-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)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+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))-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*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)*EllipticPi(cos(1/2*d*x+1/2*c),-2*b/(a-b),2^(1/2)))/b^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"
583,1,227,153,0.790000," ","int(cos(d*x+c)^(3/2)/(a+b*cos(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^{2}-\EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a b +\EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a b -\EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) b^{2}-a^{2} \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), -\frac{2 b}{a -b}, \sqrt{2}\right)\right)}{b^{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^2-EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*a*b+EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a*b-EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*b^2-a^2*EllipticPi(cos(1/2*d*x+1/2*c),-2*b/(a-b),2^(1/2)))/b^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"
584,1,188,105,0.675000," ","int(cos(d*x+c)^(1/2)/(a+b*cos(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 -\EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) b -a \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), -\frac{2 b}{a -b}, \sqrt{2}\right)\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)}\, \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-EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*b-a*EllipticPi(cos(1/2*d*x+1/2*c),-2*b/(a-b),2^(1/2)))/(a-b)/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"
585,1,150,55,0.631000," ","int(1/cos(d*x+c)^(1/2)/(a+b*cos(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 b}{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*b/(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"
586,1,354,127,0.944000," ","int(1/cos(d*x+c)^(3/2)/(a+b*cos(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)-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}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), -\frac{2 b}{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)}{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*(-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-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)*EllipticPi(cos(1/2*d*x+1/2*c),-2*b/(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)/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","B"
587,1,452,198,1.959000," ","int(1/cos(d*x+c)^(5/2)/(a+b*cos(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{4 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 b}{a -b}, \sqrt{2}\right)}{a^{2} \left(-2 a b +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{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)}{a^{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)}}}{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)*(-4*b^3/a^2/(-2*a*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)*EllipticPi(cos(1/2*d*x+1/2*c),-2*b/(a-b),2^(1/2))-2/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)+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))))/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
588,1,1070,315,2.591000," ","int(cos(d*x+c)^(7/2)/(a+b*cos(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}}{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{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)}{b^{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(3 a^{2}+2 a b +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)}{b^{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{16 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 b}{a -b}, \sqrt{2}\right)}{b^{3} \left(-2 a b +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{2 a^{4} \left(-\frac{b^{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)}}{a \left(a^{2}-b^{2}\right) \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +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) 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)}}-\frac{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)}{2 a \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{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}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{2 a \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 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 b}{a -b}, \sqrt{2}\right)}{\left(a^{2}-b^{2}\right) \left(-2 a b +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{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 b}{a -b}, \sqrt{2}\right)}{a \left(a^{2}-b^{2}\right) \left(-2 a b +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)}}\right)}{b^{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/b^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/b^3*(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)*(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*(3*a^2+2*a*b+b^2)/b^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))+16*a^3/b^3/(-2*a*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)*EllipticPi(cos(1/2*d*x+1/2*c),-2*b/(a-b),2^(1/2))+2/b^4*a^4*(-b^2/a/(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*cos(1/2*d*x+1/2*c)^2*b+a-b)-1/2/(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)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-1/2*b/a/(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*b/a/(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))-3*a/(a^2-b^2)/(-2*a*b+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)*EllipticPi(cos(1/2*d*x+1/2*c),-2*b/(a-b),2^(1/2))+1/a/(a^2-b^2)/(-2*a*b+2*b^2)*b^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*b/(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"
589,1,815,261,2.239000," ","int(cos(d*x+c)^(5/2)/(a+b*cos(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{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(2 \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) b \right)}{b^{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{12 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 b}{a -b}, \sqrt{2}\right)}{b^{2} \left(-2 a b +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{2 a^{3} \left(-\frac{b^{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)}}{a \left(a^{2}-b^{2}\right) \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +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) 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)}}-\frac{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)}{2 a \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{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}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{2 a \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 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 b}{a -b}, \sqrt{2}\right)}{\left(a^{2}-b^{2}\right) \left(-2 a b +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{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 b}{a -b}, \sqrt{2}\right)}{a \left(a^{2}-b^{2}\right) \left(-2 a b +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)}}\right)}{b^{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/b^3/(-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)*(2*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))*b)-12*a^2/b^2/(-2*a*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)*EllipticPi(cos(1/2*d*x+1/2*c),-2*b/(a-b),2^(1/2))-2/b^3*a^3*(-b^2/a/(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*cos(1/2*d*x+1/2*c)^2*b+a-b)-1/2/(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)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-1/2*b/a/(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*b/a/(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))-3*a/(a^2-b^2)/(-2*a*b+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)*EllipticPi(cos(1/2*d*x+1/2*c),-2*b/(a-b),2^(1/2))+1/a/(a^2-b^2)/(-2*a*b+2*b^2)*b^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*b/(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"
590,1,794,239,1.808000," ","int(cos(d*x+c)^(3/2)/(a+b*cos(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)}{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{8 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 b}{a -b}, \sqrt{2}\right)}{b \left(-2 a b +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{2 a^{2} \left(-\frac{b^{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)}}{a \left(a^{2}-b^{2}\right) \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +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) 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)}}-\frac{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)}{2 a \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{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}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{2 a \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 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 b}{a -b}, \sqrt{2}\right)}{\left(a^{2}-b^{2}\right) \left(-2 a b +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{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 b}{a -b}, \sqrt{2}\right)}{a \left(a^{2}-b^{2}\right) \left(-2 a b +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)}}\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)*(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))+8/b*a/(-2*a*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)*EllipticPi(cos(1/2*d*x+1/2*c),-2*b/(a-b),2^(1/2))+2/b^2*a^2*(-b^2/a/(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*cos(1/2*d*x+1/2*c)^2*b+a-b)-1/2/(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)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-1/2*b/a/(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*b/a/(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))-3*a/(a^2-b^2)/(-2*a*b+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)*EllipticPi(cos(1/2*d*x+1/2*c),-2*b/(a-b),2^(1/2))+1/a/(a^2-b^2)/(-2*a*b+2*b^2)*b^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*b/(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"
591,1,713,224,1.912000," ","int(cos(d*x+c)^(1/2)/(a+b*cos(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 \sqrt{\frac{1}{2}-\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 b}{a -b}, \sqrt{2}\right)}{\left(-2 a b +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{2 a \left(-\frac{b^{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)}}{a \left(a^{2}-b^{2}\right) \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +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) 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)}}-\frac{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)}{2 a \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{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}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{2 a \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 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 b}{a -b}, \sqrt{2}\right)}{\left(a^{2}-b^{2}\right) \left(-2 a b +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{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 b}{a -b}, \sqrt{2}\right)}{a \left(a^{2}-b^{2}\right) \left(-2 a b +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)}}\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)*(-4/(-2*a*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)*EllipticPi(cos(1/2*d*x+1/2*c),-2*b/(a-b),2^(1/2))-2/b*a*(-b^2/a/(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*cos(1/2*d*x+1/2*c)^2*b+a-b)-1/2/(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)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-1/2*b/a/(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*b/a/(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))-3*a/(a^2-b^2)/(-2*a*b+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)*EllipticPi(cos(1/2*d*x+1/2*c),-2*b/(a-b),2^(1/2))+1/a/(a^2-b^2)/(-2*a*b+2*b^2)*b^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*b/(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"
592,1,612,233,1.361000," ","int(1/cos(d*x+c)^(1/2)/(a+b*cos(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 b^{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)}}{a \left(a^{2}-b^{2}\right) \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +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) 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)}}-\frac{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)}{a \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{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}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{a \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{6 a 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 b}{a -b}, \sqrt{2}\right)}{\left(a^{2}-b^{2}\right) \left(-2 a b +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{2 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 b}{a -b}, \sqrt{2}\right)}{a \left(a^{2}-b^{2}\right) \left(-2 a b +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)}}\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/(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*cos(1/2*d*x+1/2*c)^2*b+a-b)-1/(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)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-b/a/(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))+b/a/(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))-6*a/(a^2-b^2)/(-2*a*b+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)*EllipticPi(cos(1/2*d*x+1/2*c),-2*b/(a-b),2^(1/2))+2/a/(a^2-b^2)/(-2*a*b+2*b^2)*b^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*b/(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"
593,1,874,291,2.492000," ","int(1/cos(d*x+c)^(3/2)/(a+b*cos(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 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 b}{a -b}, \sqrt{2}\right)}{a^{2} \left(-2 a b +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{-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)}{a^{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 b \left(-\frac{b^{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)}}{a \left(a^{2}-b^{2}\right) \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +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) 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)}}-\frac{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)}{2 a \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{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}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{2 a \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 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 b}{a -b}, \sqrt{2}\right)}{\left(a^{2}-b^{2}\right) \left(-2 a b +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{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 b}{a -b}, \sqrt{2}\right)}{a \left(a^{2}-b^{2}\right) \left(-2 a b +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)}}\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)*(4/a^2*b^2/(-2*a*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)*EllipticPi(cos(1/2*d*x+1/2*c),-2*b/(a-b),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/a*b*(-b^2/a/(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*cos(1/2*d*x+1/2*c)^2*b+a-b)-1/2/(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)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-1/2*b/a/(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*b/a/(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))-3*a/(a^2-b^2)/(-2*a*b+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)*EllipticPi(cos(1/2*d*x+1/2*c),-2*b/(a-b),2^(1/2))+1/a/(a^2-b^2)/(-2*a*b+2*b^2)*b^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*b/(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"
594,1,1008,349,3.361000," ","int(1/cos(d*x+c)^(5/2)/(a+b*cos(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{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 b}{a -b}, \sqrt{2}\right)}{a^{3} \left(-2 a b +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{4 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)}{a^{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{-\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)}}}{a^{2}}+\frac{2 b^{2} \left(-\frac{b^{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)}}{a \left(a^{2}-b^{2}\right) \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +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) 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)}}-\frac{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)}{2 a \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{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}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{2 a \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 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 b}{a -b}, \sqrt{2}\right)}{\left(a^{2}-b^{2}\right) \left(-2 a b +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{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 b}{a -b}, \sqrt{2}\right)}{a \left(a^{2}-b^{2}\right) \left(-2 a b +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)}}\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)*(-8*b^3/a^3/(-2*a*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)*EllipticPi(cos(1/2*d*x+1/2*c),-2*b/(a-b),2^(1/2))-4/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)+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)))+2*b^2/a^2*(-b^2/a/(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*cos(1/2*d*x+1/2*c)^2*b+a-b)-1/2/(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)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-1/2*b/a/(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*b/a/(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))-3*a/(a^2-b^2)/(-2*a*b+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)*EllipticPi(cos(1/2*d*x+1/2*c),-2*b/(a-b),2^(1/2))+1/a/(a^2-b^2)/(-2*a*b+2*b^2)*b^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*b/(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"
595,1,2194,406,3.687000," ","int(cos(d*x+c)^(9/2)/(a+b*cos(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/b^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/b^4*(3*a+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))-EllipticE(cos(1/2*d*x+1/2*c),2^(1/2)))+2*(6*a^2+3*a*b+b^2)/b^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))-2/b^5*a^5*(-1/2*b^2/a/(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*cos(1/2*d*x+1/2*c)^2*b+a-b)^2-3/4*b^2*(3*a^2-b^2)/a^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*cos(1/2*d*x+1/2*c)^2*b+a-b)-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))+1/4/(a+b)/(a^2-b^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))*b+3/8/(a+b)/(a^2-b^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))*b^2-9/8*b/(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*b^3/a^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*b/(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*b^3/a^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))-15/4*a^2/(a^2-b^2)^2/(-2*a*b+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)*EllipticPi(cos(1/2*d*x+1/2*c),-2*b/(a-b),2^(1/2))+3/2/(a^2-b^2)^2/(-2*a*b+2*b^2)*b^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*b/(a-b),2^(1/2))-3/4/a^2/(a^2-b^2)^2/(-2*a*b+2*b^2)*b^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*b/(a-b),2^(1/2)))+40/b^4*a^3/(-2*a*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)*EllipticPi(cos(1/2*d*x+1/2*c),-2*b/(a-b),2^(1/2))+10/b^5*a^4*(-b^2/a/(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*cos(1/2*d*x+1/2*c)^2*b+a-b)-1/2/(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)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-1/2*b/a/(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*b/a/(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))-3*a/(a^2-b^2)/(-2*a*b+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)*EllipticPi(cos(1/2*d*x+1/2*c),-2*b/(a-b),2^(1/2))+1/a/(a^2-b^2)/(-2*a*b+2*b^2)*b^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*b/(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"
596,1,1935,346,3.520000," ","int(cos(d*x+c)^(7/2)/(a+b*cos(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/b^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*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))*b)+2/b^4*a^4*(-1/2*b^2/a/(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*cos(1/2*d*x+1/2*c)^2*b+a-b)^2-3/4*b^2*(3*a^2-b^2)/a^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*cos(1/2*d*x+1/2*c)^2*b+a-b)-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))+1/4/(a+b)/(a^2-b^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))*b+3/8/(a+b)/(a^2-b^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))*b^2-9/8*b/(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*b^3/a^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*b/(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*b^3/a^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))-15/4*a^2/(a^2-b^2)^2/(-2*a*b+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)*EllipticPi(cos(1/2*d*x+1/2*c),-2*b/(a-b),2^(1/2))+3/2/(a^2-b^2)^2/(-2*a*b+2*b^2)*b^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*b/(a-b),2^(1/2))-3/4/a^2/(a^2-b^2)^2/(-2*a*b+2*b^2)*b^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*b/(a-b),2^(1/2)))-24*a^2/b^3/(-2*a*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)*EllipticPi(cos(1/2*d*x+1/2*c),-2*b/(a-b),2^(1/2))-8/b^4*a^3*(-b^2/a/(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*cos(1/2*d*x+1/2*c)^2*b+a-b)-1/2/(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)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-1/2*b/a/(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*b/a/(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))-3*a/(a^2-b^2)/(-2*a*b+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)*EllipticPi(cos(1/2*d*x+1/2*c),-2*b/(a-b),2^(1/2))+1/a/(a^2-b^2)/(-2*a*b+2*b^2)*b^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*b/(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"
597,1,1914,328,3.079000," ","int(cos(d*x+c)^(5/2)/(a+b*cos(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/b^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^3*a^3*(-1/2*b^2/a/(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*cos(1/2*d*x+1/2*c)^2*b+a-b)^2-3/4*b^2*(3*a^2-b^2)/a^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*cos(1/2*d*x+1/2*c)^2*b+a-b)-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))+1/4/(a+b)/(a^2-b^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))*b+3/8/(a+b)/(a^2-b^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))*b^2-9/8*b/(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*b^3/a^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*b/(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*b^3/a^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))-15/4*a^2/(a^2-b^2)^2/(-2*a*b+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)*EllipticPi(cos(1/2*d*x+1/2*c),-2*b/(a-b),2^(1/2))+3/2/(a^2-b^2)^2/(-2*a*b+2*b^2)*b^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*b/(a-b),2^(1/2))-3/4/a^2/(a^2-b^2)^2/(-2*a*b+2*b^2)*b^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*b/(a-b),2^(1/2)))+12/b^2*a/(-2*a*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)*EllipticPi(cos(1/2*d*x+1/2*c),-2*b/(a-b),2^(1/2))+6/b^3*a^2*(-b^2/a/(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*cos(1/2*d*x+1/2*c)^2*b+a-b)-1/2/(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)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-1/2*b/a/(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*b/a/(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))-3*a/(a^2-b^2)/(-2*a*b+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)*EllipticPi(cos(1/2*d*x+1/2*c),-2*b/(a-b),2^(1/2))+1/a/(a^2-b^2)/(-2*a*b+2*b^2)*b^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*b/(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"
598,1,1836,308,3.046000," ","int(cos(d*x+c)^(3/2)/(a+b*cos(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^{2} \left(-\frac{b^{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 a \left(a^{2}-b^{2}\right) \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b \right)^{2}}-\frac{3 b^{2} \left(3 a^{2}-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 a^{2} \left(a^{2}-b^{2}\right)^{2} \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b \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{\sqrt{\frac{1}{2}-\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}{4 \left(a +b \right) \left(a^{2}-b^{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)}}+\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) b^{2}}{8 \left(a +b \right) \left(a^{2}-b^{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{9 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)}{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 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}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{8 a^{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 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}\, \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 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}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{8 a^{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{15 a^{2} 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 b}{a -b}, \sqrt{2}\right)}{4 \left(a^{2}-b^{2}\right)^{2} \left(-2 a b +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 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 b}{a -b}, \sqrt{2}\right)}{2 \left(a^{2}-b^{2}\right)^{2} \left(-2 a b +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 b^{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 b}{a -b}, \sqrt{2}\right)}{4 a^{2} \left(a^{2}-b^{2}\right)^{2} \left(-2 a b +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)}}\right)}{b^{2}}-\frac{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}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), -\frac{2 b}{a -b}, \sqrt{2}\right)}{b \left(-2 a b +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{4 a \left(-\frac{b^{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)}}{a \left(a^{2}-b^{2}\right) \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +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) 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)}}-\frac{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)}{2 a \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{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}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{2 a \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 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 b}{a -b}, \sqrt{2}\right)}{\left(a^{2}-b^{2}\right) \left(-2 a b +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{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 b}{a -b}, \sqrt{2}\right)}{a \left(a^{2}-b^{2}\right) \left(-2 a b +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)}}\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)*(2/b^2*a^2*(-1/2*b^2/a/(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*cos(1/2*d*x+1/2*c)^2*b+a-b)^2-3/4*b^2*(3*a^2-b^2)/a^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*cos(1/2*d*x+1/2*c)^2*b+a-b)-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))+1/4/(a+b)/(a^2-b^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))*b+3/8/(a+b)/(a^2-b^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))*b^2-9/8*b/(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*b^3/a^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*b/(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*b^3/a^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))-15/4*a^2/(a^2-b^2)^2/(-2*a*b+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)*EllipticPi(cos(1/2*d*x+1/2*c),-2*b/(a-b),2^(1/2))+3/2/(a^2-b^2)^2/(-2*a*b+2*b^2)*b^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*b/(a-b),2^(1/2))-3/4/a^2/(a^2-b^2)^2/(-2*a*b+2*b^2)*b^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*b/(a-b),2^(1/2)))-4/b/(-2*a*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)*EllipticPi(cos(1/2*d*x+1/2*c),-2*b/(a-b),2^(1/2))-4/b^2*a*(-b^2/a/(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*cos(1/2*d*x+1/2*c)^2*b+a-b)-1/2/(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)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-1/2*b/a/(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*b/a/(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))-3*a/(a^2-b^2)/(-2*a*b+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)*EllipticPi(cos(1/2*d*x+1/2*c),-2*b/(a-b),2^(1/2))+1/a/(a^2-b^2)/(-2*a*b+2*b^2)*b^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*b/(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"
599,1,1736,314,2.955000," ","int(cos(d*x+c)^(1/2)/(a+b*cos(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 \left(-\frac{b^{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 a \left(a^{2}-b^{2}\right) \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b \right)^{2}}-\frac{3 b^{2} \left(3 a^{2}-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 a^{2} \left(a^{2}-b^{2}\right)^{2} \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b \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{\sqrt{\frac{1}{2}-\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}{4 \left(a +b \right) \left(a^{2}-b^{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)}}+\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) b^{2}}{8 \left(a +b \right) \left(a^{2}-b^{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{9 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)}{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 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}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{8 a^{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 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}\, \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 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}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{8 a^{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{15 a^{2} 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 b}{a -b}, \sqrt{2}\right)}{4 \left(a^{2}-b^{2}\right)^{2} \left(-2 a b +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 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 b}{a -b}, \sqrt{2}\right)}{2 \left(a^{2}-b^{2}\right)^{2} \left(-2 a b +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 b^{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 b}{a -b}, \sqrt{2}\right)}{4 a^{2} \left(a^{2}-b^{2}\right)^{2} \left(-2 a b +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)}}\right)}{b}+\frac{-\frac{2 b^{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)}}{a \left(a^{2}-b^{2}\right) \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +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) 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)}}-\frac{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)}{a \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{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}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{a \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{6 a 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 b}{a -b}, \sqrt{2}\right)}{\left(a^{2}-b^{2}\right) \left(-2 a b +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{2 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 b}{a -b}, \sqrt{2}\right)}{a \left(a^{2}-b^{2}\right) \left(-2 a b +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)}}}{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*a*(-1/2*b^2/a/(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*cos(1/2*d*x+1/2*c)^2*b+a-b)^2-3/4*b^2*(3*a^2-b^2)/a^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*cos(1/2*d*x+1/2*c)^2*b+a-b)-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))+1/4/(a+b)/(a^2-b^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))*b+3/8/(a+b)/(a^2-b^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))*b^2-9/8*b/(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*b^3/a^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*b/(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*b^3/a^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))-15/4*a^2/(a^2-b^2)^2/(-2*a*b+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)*EllipticPi(cos(1/2*d*x+1/2*c),-2*b/(a-b),2^(1/2))+3/2/(a^2-b^2)^2/(-2*a*b+2*b^2)*b^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*b/(a-b),2^(1/2))-3/4/a^2/(a^2-b^2)^2/(-2*a*b+2*b^2)*b^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*b/(a-b),2^(1/2)))+2/b*(-b^2/a/(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*cos(1/2*d*x+1/2*c)^2*b+a-b)-1/2/(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)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-1/2*b/a/(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*b/a/(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))-3*a/(a^2-b^2)/(-2*a*b+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)*EllipticPi(cos(1/2*d*x+1/2*c),-2*b/(a-b),2^(1/2))+1/a/(a^2-b^2)/(-2*a*b+2*b^2)*b^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*b/(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"
600,1,1176,325,1.915000," ","int(1/cos(d*x+c)^(1/2)/(a+b*cos(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{b^{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)}}{a \left(a^{2}-b^{2}\right) \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b \right)^{2}}-\frac{3 b^{2} \left(3 a^{2}-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 a^{2} \left(a^{2}-b^{2}\right)^{2} \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b \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{\sqrt{\frac{1}{2}-\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}{2 \left(a +b \right) \left(a^{2}-b^{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)}}+\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) b^{2}}{4 \left(a +b \right) \left(a^{2}-b^{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{9 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)}{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 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}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{4 a^{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 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}\, \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 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}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{4 a^{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{15 a^{2} 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 b}{a -b}, \sqrt{2}\right)}{2 \left(a^{2}-b^{2}\right)^{2} \left(-2 a b +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 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 b}{a -b}, \sqrt{2}\right)}{\left(a^{2}-b^{2}\right)^{2} \left(-2 a b +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 b^{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 b}{a -b}, \sqrt{2}\right)}{2 a^{2} \left(a^{2}-b^{2}\right)^{2} \left(-2 a b +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)}}\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)*(-b^2/a/(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*cos(1/2*d*x+1/2*c)^2*b+a-b)^2-3/2*b^2*(3*a^2-b^2)/a^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*cos(1/2*d*x+1/2*c)^2*b+a-b)-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))+1/2/(a+b)/(a^2-b^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))*b+3/4/(a+b)/(a^2-b^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))*b^2-9/4*b/(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*b^3/a^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*b/(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*b^3/a^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))-15/2*a^2/(a^2-b^2)^2/(-2*a*b+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)*EllipticPi(cos(1/2*d*x+1/2*c),-2*b/(a-b),2^(1/2))+3/(a^2-b^2)^2/(-2*a*b+2*b^2)*b^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*b/(a-b),2^(1/2))-3/2/a^2/(a^2-b^2)^2/(-2*a*b+2*b^2)*b^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*b/(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"
601,1,1992,388,3.708000," ","int(1/cos(d*x+c)^(3/2)/(a+b*cos(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*b*(-1/2*b^2/a/(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*cos(1/2*d*x+1/2*c)^2*b+a-b)^2-3/4*b^2*(3*a^2-b^2)/a^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*cos(1/2*d*x+1/2*c)^2*b+a-b)-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))+1/4/(a+b)/(a^2-b^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))*b+3/8/(a+b)/(a^2-b^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))*b^2-9/8*b/(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*b^3/a^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*b/(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*b^3/a^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))-15/4*a^2/(a^2-b^2)^2/(-2*a*b+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)*EllipticPi(cos(1/2*d*x+1/2*c),-2*b/(a-b),2^(1/2))+3/2/(a^2-b^2)^2/(-2*a*b+2*b^2)*b^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*b/(a-b),2^(1/2))-3/4/a^2/(a^2-b^2)^2/(-2*a*b+2*b^2)*b^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*b/(a-b),2^(1/2)))+4*b^2/a^3/(-2*a*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)*EllipticPi(cos(1/2*d*x+1/2*c),-2*b/(a-b),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)-2/a^2*b*(-b^2/a/(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*cos(1/2*d*x+1/2*c)^2*b+a-b)-1/2/(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)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-1/2*b/a/(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*b/a/(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))-3*a/(a^2-b^2)/(-2*a*b+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)*EllipticPi(cos(1/2*d*x+1/2*c),-2*b/(a-b),2^(1/2))+1/a/(a^2-b^2)/(-2*a*b+2*b^2)*b^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*b/(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"
602,1,2128,451,5.452000," ","int(1/cos(d*x+c)^(5/2)/(a+b*cos(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*b^2/a^2*(-1/2*b^2/a/(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*cos(1/2*d*x+1/2*c)^2*b+a-b)^2-3/4*b^2*(3*a^2-b^2)/a^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*cos(1/2*d*x+1/2*c)^2*b+a-b)-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))+1/4/(a+b)/(a^2-b^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))*b+3/8/(a+b)/(a^2-b^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))*b^2-9/8*b/(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*b^3/a^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*b/(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*b^3/a^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))-15/4*a^2/(a^2-b^2)^2/(-2*a*b+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)*EllipticPi(cos(1/2*d*x+1/2*c),-2*b/(a-b),2^(1/2))+3/2/(a^2-b^2)^2/(-2*a*b+2*b^2)*b^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*b/(a-b),2^(1/2))-3/4/a^2/(a^2-b^2)^2/(-2*a*b+2*b^2)*b^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*b/(a-b),2^(1/2)))-12*b^3/a^4/(-2*a*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)*EllipticPi(cos(1/2*d*x+1/2*c),-2*b/(a-b),2^(1/2))-6/a^4*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)+2/a^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)))+4*b^2/a^3*(-b^2/a/(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*cos(1/2*d*x+1/2*c)^2*b+a-b)-1/2/(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)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-1/2*b/a/(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*b/a/(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))-3*a/(a^2-b^2)/(-2*a*b+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)*EllipticPi(cos(1/2*d*x+1/2*c),-2*b/(a-b),2^(1/2))+1/a/(a^2-b^2)/(-2*a*b+2*b^2)*b^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*b/(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"
603,1,1233,396,0.274000," ","int(cos(d*x+c)^(3/2)*(a+b*cos(d*x+c))^(1/2),x)","-\frac{-2 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}+8 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}+2 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 -4 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}+\cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}+\cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 \left(\cos^{4}\left(d x +c \right)\right) b^{2}-2 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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} \sin \left(d x +c \right)+8 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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)-4 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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{a +b \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)+\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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)+3 \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 -2 \left(\cos^{2}\left(d x +c \right)\right) b^{2}-a^{2} \cos \left(d x +c \right)-2 a b \cos \left(d x +c \right)}{4 d \sqrt{a +b \cos \left(d x +c \right)}\, \sqrt{\cos \left(d x +c \right)}\, \sin \left(d x +c \right) b}"," ",0,"-1/4/d*(-2*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+8*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+2*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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-4*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*cos(d*x+c)^4*b^2-2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*sin(d*x+c)+8*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)/(1+cos(d*x+c)))^(1/2)*((a+b*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)-4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)*((a+b*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)/(1+cos(d*x+c)))^(1/2)*((a+b*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)+3*cos(d*x+c)^3*a*b+cos(d*x+c)^2*a^2-cos(d*x+c)^2*a*b-2*cos(d*x+c)^2*b^2-a^2*cos(d*x+c)-2*a*b*cos(d*x+c))/(a+b*cos(d*x+c))^(1/2)/cos(d*x+c)^(1/2)/sin(d*x+c)/b","B"
604,1,801,343,0.269000," ","int(cos(d*x+c)^(1/2)*(a+b*cos(d*x+c))^(1/2),x)","-\frac{-2 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \sin \left(d x +c \right) a +\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \sin \left(d x +c \right) a +\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \sin \left(d x +c \right) b +2 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \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{a +b \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{a +b \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{a +b \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)+2 a \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \sin \left(d x +c \right)+\left(\cos^{3}\left(d x +c \right)\right) b +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)}{d \sqrt{a +b \cos \left(d x +c \right)}\, \sqrt{\cos \left(d x +c \right)}\, \sin \left(d x +c \right)}"," ",0,"-1/d*(-2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)*sin(d*x+c)*a+(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)*b+2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)*sin(d*x+c)*a-2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)*((a+b*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)*((a+b*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)+2*a*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)+cos(d*x+c)^3*b+a*cos(d*x+c)^2-cos(d*x+c)^2*b-a*cos(d*x+c))/(a+b*cos(d*x+c))^(1/2)/cos(d*x+c)^(1/2)/sin(d*x+c)","B"
605,1,197,123,0.219000," ","int((a+b*cos(d*x+c))^(1/2)/cos(d*x+c)^(1/2),x)","-\frac{2 \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{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 b \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) \sqrt{\frac{a +b \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \left(\sin^{4}\left(d x +c \right)\right)}{d \sqrt{a +b \cos \left(d x +c \right)}\, \cos \left(d x +c \right)^{\frac{3}{2}} \left(-1+\cos \left(d x +c \right)\right)^{2}}"," ",0,"-2/d*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)/(a+b*cos(d*x+c))^(1/2)*(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*b*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,(-(a-b)/(a+b))^(1/2)))*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)^4/cos(d*x+c)^(3/2)/(-1+cos(d*x+c))^2","A"
606,1,789,213,0.248000," ","int((a+b*cos(d*x+c))^(1/2)/cos(d*x+c)^(3/2),x)","-\frac{2 \left(\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \sin \left(d x +c \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) \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, b -\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \sin \left(d x +c \right) a -\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \sin \left(d x +c \right) b +\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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{a +b \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{a +b \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{a +b \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) b +a \cos \left(d x +c \right)-b \cos \left(d x +c \right)-a \right)}{d \sqrt{a +b \cos \left(d x +c \right)}\, \sin \left(d x +c \right) \sqrt{\cos \left(d x +c \right)}}"," ",0,"-2/d*((cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)*sin(d*x+c)*a+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)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*b-(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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-(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)*b+(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)*((a+b*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)*((a+b*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)*((a+b*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*b+a*cos(d*x+c)-b*cos(d*x+c)-a)/(a+b*cos(d*x+c))^(1/2)/sin(d*x+c)/cos(d*x+c)^(1/2)","B"
607,1,880,245,0.298000," ","int((a+b*cos(d*x+c))^(1/2)/cos(d*x+c)^(5/2),x)","-\frac{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) \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, a^{2}+\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) a b -\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \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) \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, b^{2}+\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) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 -\cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) a b +\left(\cos^{3}\left(d x +c \right)\right) 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)-a^{2}\right)}{3 d \sqrt{a +b \cos \left(d x +c \right)}\, \sin \left(d x +c \right) \cos \left(d x +c \right)^{\frac{3}{2}} a}"," ",0,"-2/3/d*(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)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^2+(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^2*sin(d*x+c)*a*b-(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^2*sin(d*x+c)*a*b-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)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*b^2+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)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^2+cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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-cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*b^2+cos(d*x+c)^3*a*b+cos(d*x+c)^3*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)-a^2)/(a+b*cos(d*x+c))^(1/2)/sin(d*x+c)/cos(d*x+c)^(3/2)/a","B"
608,1,1555,297,0.265000," ","int((a+b*cos(d*x+c))^(1/2)/cos(d*x+c)^(7/2),x)","-\frac{2 \left(-3 a^{3}-9 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}-9 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}+\left(\cos^{2}\left(d x +c \right)\right) a \,b^{2}-4 \cos \left(d x +c \right) a^{2} b -2 \left(\cos^{4}\left(d x +c \right)\right) b^{3}+2 \left(\cos^{3}\left(d x +c \right)\right) b^{3}-6 \left(\cos^{2}\left(d x +c \right)\right) a^{3}+9 \left(\cos^{3}\left(d x +c \right)\right) a^{3}+7 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 +9 \left(\cos^{4}\left(d x +c \right)\right) a^{2} b -5 \left(\cos^{3}\left(d x +c \right)\right) a^{2} b -2 \left(\cos^{3}\left(d x +c \right)\right) a \,b^{2}+\left(\cos^{4}\left(d x +c \right)\right) a \,b^{2}-9 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}+9 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}+9 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}\right)}{15 d \sqrt{a +b \cos \left(d x +c \right)}\, \sin \left(d x +c \right) \cos \left(d x +c \right)^{\frac{5}{2}} a^{2}}"," ",0,"-2/15/d*(cos(d*x+c)^2*a*b^2-9*cos(d*x+c)^3*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^3-3*a^3+2*cos(d*x+c)^3*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*cos(d*x+c)^3*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*cos(d*x+c)^3*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^2-9*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*cos(d*x+c)^4*b^3+9*cos(d*x+c)^3*a^3-4*cos(d*x+c)*a^2*b+9*cos(d*x+c)^4*a^2*b+cos(d*x+c)^4*a*b^2-5*cos(d*x+c)^3*a^2*b-2*cos(d*x+c)^3*a*b^2+2*cos(d*x+c)^3*b^3-6*cos(d*x+c)^2*a^3-9*cos(d*x+c)^3*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*cos(d*x+c)^3*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+9*cos(d*x+c)^3*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+9*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)/(a+b*cos(d*x+c))^(1/2)/sin(d*x+c)/cos(d*x+c)^(5/2)/a^2","B"
609,1,1826,351,0.309000," ","int((a+b*cos(d*x+c))^(1/2)/cos(d*x+c)^(9/2),x)","-\frac{2 \left(-15 a^{4}-26 \left(\cos^{3}\left(d x +c \right)\right) a^{3} b -20 \left(\cos^{4}\left(d x +c \right)\right) a^{2} b^{2}-4 \left(\cos^{5}\left(d x +c \right)\right) a \,b^{3}-4 \left(\cos^{3}\left(d x +c \right)\right) a \,b^{3}+8 \left(\cos^{4}\left(d x +c \right)\right) a \,b^{3}+19 \left(\cos^{5}\left(d x +c \right)\right) a^{2} b^{2}+19 \left(\cos^{4}\left(d x +c \right)\right) a^{3} b +19 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) a^{3} b +2 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) a^{2} b^{2}+8 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) a \,b^{3}-19 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) a^{3} b -19 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) a^{2} b^{2}-8 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) a \,b^{3}+25 \left(\cos^{5}\left(d x +c \right)\right) a^{3} b -18 \cos \left(d x +c \right) a^{3} b +19 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \left(\cos^{4}\left(d x +c \right)\right) \sin \left(d x +c \right) a^{3} b +2 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \left(\cos^{4}\left(d x +c \right)\right) \sin \left(d x +c \right) a^{2} b^{2}+8 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \left(\cos^{4}\left(d x +c \right)\right) \sin \left(d x +c \right) a \,b^{3}-19 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \left(\cos^{4}\left(d x +c \right)\right) \sin \left(d x +c \right) a^{3} b -19 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \left(\cos^{4}\left(d x +c \right)\right) \sin \left(d x +c \right) a^{2} b^{2}-10 \left(\cos^{2}\left(d x +c \right)\right) a^{4}+8 \left(\cos^{5}\left(d x +c \right)\right) b^{4}-8 \left(\cos^{4}\left(d x +c \right)\right) b^{4}+25 \left(\cos^{4}\left(d x +c \right)\right) a^{4}+25 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \left(\cos^{4}\left(d x +c \right)\right) \sin \left(d x +c \right) a^{4}-8 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \left(\cos^{4}\left(d x +c \right)\right) \sin \left(d x +c \right) b^{4}+25 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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^{4}-8 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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^{4}+\left(\cos^{2}\left(d x +c \right)\right) a^{2} b^{2}-8 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \left(\cos^{4}\left(d x +c \right)\right) \sin \left(d x +c \right) a \,b^{3}\right)}{105 d \sqrt{a +b \cos \left(d x +c \right)}\, \sin \left(d x +c \right) \cos \left(d x +c \right)^{\frac{7}{2}} a^{3}}"," ",0,"-2/105/d*(25*cos(d*x+c)^5*a^3*b+25*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^4*sin(d*x+c)*a^4-15*a^4+19*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^4*sin(d*x+c)*a^3*b+2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^4*sin(d*x+c)*a^2*b^2+8*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^4*sin(d*x+c)*a*b^3-19*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^4*sin(d*x+c)*a^3*b-19*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^4*sin(d*x+c)*a^2*b^2-8*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^4*sin(d*x+c)*a*b^3+19*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^3*sin(d*x+c)*a^3*b+2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^3*sin(d*x+c)*a^2*b^2+8*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^3*sin(d*x+c)*a*b^3-19*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^3*sin(d*x+c)*a^3*b-19*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^3*sin(d*x+c)*a^2*b^2-8*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^3*sin(d*x+c)*a*b^3-8*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^4*sin(d*x+c)*b^4+25*cos(d*x+c)^3*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^4-8*cos(d*x+c)^3*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+19*cos(d*x+c)^5*a^2*b^2-4*cos(d*x+c)^5*a*b^3+19*cos(d*x+c)^4*a^3*b-20*cos(d*x+c)^4*a^2*b^2+8*cos(d*x+c)^4*a*b^3-26*cos(d*x+c)^3*a^3*b-4*cos(d*x+c)^3*a*b^3+cos(d*x+c)^2*a^2*b^2-18*cos(d*x+c)*a^3*b+25*cos(d*x+c)^4*a^4-10*cos(d*x+c)^2*a^4+8*cos(d*x+c)^5*b^4-8*cos(d*x+c)^4*b^4)/(a+b*cos(d*x+c))^(1/2)/sin(d*x+c)/cos(d*x+c)^(7/2)/a^3","B"
610,1,1683,460,0.259000," ","int(cos(d*x+c)^(3/2)*(a+b*cos(d*x+c))^(3/2),x)","\frac{6 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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} \sin \left(d x +c \right)-3 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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)-16 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 a^{3} \cos \left(d x +c \right)+3 \left(\cos^{2}\left(d x +c \right)\right) a^{2} b +16 \cos \left(d x +c \right) a \,b^{2}+6 \left(\cos^{2}\left(d x +c \right)\right) a \,b^{2}+14 \cos \left(d x +c \right) a^{2} b -8 \left(\cos^{5}\left(d x +c \right)\right) b^{3}-8 \left(\cos^{3}\left(d x +c \right)\right) b^{3}-3 \left(\cos^{2}\left(d x +c \right)\right) a^{3}+16 \left(\cos^{2}\left(d x +c \right)\right) b^{3}-17 \left(\cos^{3}\left(d x +c \right)\right) a^{2} b -22 \left(\cos^{4}\left(d x +c \right)\right) a \,b^{2}+6 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}-3 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}-16 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}-72 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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} \sin \left(d x +c \right)-3 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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)-16 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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)-14 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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)+52 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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)-72 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}-3 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 -16 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}-14 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 +52 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}}{24 d \sqrt{a +b \cos \left(d x +c \right)}\, \sin \left(d x +c \right) \sqrt{\cos \left(d x +c \right)}\, b}"," ",0,"1/24/d*(6*cos(d*x+c)^2*a*b^2+6*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+6*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*sin(d*x+c)-3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*a^3*cos(d*x+c)+16*cos(d*x+c)*a*b^2+3*cos(d*x+c)^2*a^2*b-8*cos(d*x+c)^5*b^3+16*cos(d*x+c)^2*b^3+14*cos(d*x+c)*a^2*b-22*cos(d*x+c)^4*a*b^2-17*cos(d*x+c)^3*a^2*b-8*cos(d*x+c)^3*b^3-3*cos(d*x+c)^2*a^3-3*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^3-16*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^3-72*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*sin(d*x+c)-3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)-16*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)-14*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)+52*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)-72*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^2-3*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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-16*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^2-14*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+52*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)/(a+b*cos(d*x+c))^(1/2)/sin(d*x+c)/cos(d*x+c)^(1/2)/b","B"
611,1,1421,391,0.186000," ","int(cos(d*x+c)^(1/2)*(a+b*cos(d*x+c))^(3/2),x)","\frac{8 \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) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 +4 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}-5 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}-5 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}-8 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}+8 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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)+4 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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)-5 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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)-5 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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)-6 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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} \sin \left(d x +c \right)-8 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) b^{2}-7 \left(\cos^{3}\left(d x +c \right)\right) a b -5 \left(\cos^{2}\left(d x +c \right)\right) a^{2}+5 \left(\cos^{2}\left(d x +c \right)\right) a b +2 \left(\cos^{2}\left(d x +c \right)\right) b^{2}+5 a^{2} \cos \left(d x +c \right)+2 a b \cos \left(d x +c \right)}{4 d \sqrt{a +b \cos \left(d x +c \right)}\, \sqrt{\cos \left(d x +c \right)}\, \sin \left(d x +c \right)}"," ",0,"1/4/d*(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)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^2-2*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+4*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^2-5*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^2-5*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^2-8*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+8*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)+4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)-5*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)-5*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)-6*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*sin(d*x+c)-8*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*b^2-7*cos(d*x+c)^3*a*b-5*cos(d*x+c)^2*a^2+5*cos(d*x+c)^2*a*b+2*cos(d*x+c)^2*b^2+5*a^2*cos(d*x+c)+2*a*b*cos(d*x+c))/(a+b*cos(d*x+c))^(1/2)/cos(d*x+c)^(1/2)/sin(d*x+c)","B"
612,1,1003,347,0.270000," ","int((a+b*cos(d*x+c))^(3/2)/cos(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) \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 +\cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, b^{2}+6 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \sin \left(d x +c \right) a b +2 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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)-4 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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)+\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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)+\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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)+6 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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)+\left(\cos^{3}\left(d x +c \right)\right) b^{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)}{d \sqrt{a +b \cos \left(d x +c \right)}\, \sqrt{\cos \left(d x +c \right)}\, \sin \left(d x +c \right)}"," ",0,"-1/d/(a+b*cos(d*x+c))^(1/2)*(2*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)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^2-4*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*b^2+6*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)*sin(d*x+c)*a*b+2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)-4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)/(1+cos(d*x+c)))^(1/2)*((a+b*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)/(1+cos(d*x+c)))^(1/2)*((a+b*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)+6*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)+cos(d*x+c)^3*b^2+cos(d*x+c)^2*a*b-cos(d*x+c)^2*b^2-a*b*cos(d*x+c))/cos(d*x+c)^(1/2)/sin(d*x+c)","B"
613,1,1183,313,0.225000," ","int((a+b*cos(d*x+c))^(3/2)/cos(d*x+c)^(3/2),x)","-\frac{2 \left(2 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}+\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) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 -\cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}-\cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}-\cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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)+\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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)-\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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{a +b \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)-\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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)+\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)-a^{2}\right)}{d \sqrt{a +b \cos \left(d x +c \right)}\, \sin \left(d x +c \right) \sqrt{\cos \left(d x +c \right)}}"," ",0,"-2/d*(2*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+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)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^2+2*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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-cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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-cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)/(1+cos(d*x+c)))^(1/2)*((a+b*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*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)/(1+cos(d*x+c)))^(1/2)*((a+b*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)*((a+b*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)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^2*a*b+a^2*cos(d*x+c)-a*b*cos(d*x+c)-a^2)/(a+b*cos(d*x+c))^(1/2)/sin(d*x+c)/cos(d*x+c)^(1/2)","B"
614,1,1075,251,0.264000," ","int((a+b*cos(d*x+c))^(3/2)/cos(d*x+c)^(5/2),x)","-\frac{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) \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, a^{2}+4 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \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{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) a b -4 \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) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, b^{2}+\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) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 \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) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) a b +4 \left(\cos^{3}\left(d x +c \right)\right) b^{2}+\left(\cos^{2}\left(d x +c \right)\right) a^{2}+4 \left(\cos^{2}\left(d x +c \right)\right) a b -4 \left(\cos^{2}\left(d x +c \right)\right) b^{2}-5 a b \cos \left(d x +c \right)-a^{2}\right)}{3 d \sqrt{a +b \cos \left(d x +c \right)}\, \sin \left(d x +c \right) \cos \left(d x +c \right)^{\frac{3}{2}}}"," ",0,"-2/3/d*(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)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^2+4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^2*sin(d*x+c)*a*b+3*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^2*sin(d*x+c)*a*b-4*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)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*b^2+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)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^2+4*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*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)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*b^2+cos(d*x+c)^3*a*b+4*cos(d*x+c)^3*b^2+cos(d*x+c)^2*a^2+4*cos(d*x+c)^2*a*b-4*cos(d*x+c)^2*b^2-5*a*b*cos(d*x+c)-a^2)/(a+b*cos(d*x+c))^(1/2)/sin(d*x+c)/cos(d*x+c)^(3/2)","B"
615,1,1539,293,0.217000," ","int((a+b*cos(d*x+c))^(3/2)/cos(d*x+c)^(7/2),x)","-\frac{2 \left(3 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}+4 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 +\left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}-3 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 -\left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}-\left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}+4 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 +\left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}-3 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 -\left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}-\left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 \left(\cos^{4}\left(d x +c \right)\right) a^{2} b +2 \left(\cos^{4}\left(d x +c \right)\right) a \,b^{2}+\left(\cos^{4}\left(d x +c \right)\right) b^{3}+3 \left(\cos^{3}\left(d x +c \right)\right) a^{3}+\left(\cos^{3}\left(d x +c \right)\right) a \,b^{2}-\left(\cos^{3}\left(d x +c \right)\right) b^{3}-2 \left(\cos^{2}\left(d x +c \right)\right) a^{3}-3 \left(\cos^{2}\left(d x +c \right)\right) a \,b^{2}-3 \cos \left(d x +c \right) a^{2} b -a^{3}\right)}{5 d \sqrt{a +b \cos \left(d x +c \right)}\, \sin \left(d x +c \right) \cos \left(d x +c \right)^{\frac{5}{2}} a}"," ",0,"-2/5/d*(3*cos(d*x+c)^3*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+4*cos(d*x+c)^3*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+cos(d*x+c)^3*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^3*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^3-3*cos(d*x+c)^3*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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-cos(d*x+c)^3*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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-cos(d*x+c)^3*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+3*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+4*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^3-3*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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-cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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-cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+3*cos(d*x+c)^4*a^2*b+2*cos(d*x+c)^4*a*b^2+cos(d*x+c)^4*b^3+3*cos(d*x+c)^3*a^3+cos(d*x+c)^3*a*b^2-cos(d*x+c)^3*b^3-2*cos(d*x+c)^2*a^3-3*cos(d*x+c)^2*a*b^2-3*cos(d*x+c)*a^2*b-a^3)/(a+b*cos(d*x+c))^(1/2)/sin(d*x+c)/cos(d*x+c)^(5/2)/a","B"
616,1,1827,349,0.272000," ","int((a+b*cos(d*x+c))^(3/2)/cos(d*x+c)^(9/2),x)","-\frac{2 \left(-15 a^{4}-68 \left(\cos^{3}\left(d x +c \right)\right) a^{3} b -55 \left(\cos^{4}\left(d x +c \right)\right) a^{2} b^{2}+3 \left(\cos^{5}\left(d x +c \right)\right) a \,b^{3}+3 \left(\cos^{3}\left(d x +c \right)\right) a \,b^{3}-6 \left(\cos^{4}\left(d x +c \right)\right) a \,b^{3}+82 \left(\cos^{5}\left(d x +c \right)\right) a^{2} b^{2}+82 \left(\cos^{4}\left(d x +c \right)\right) a^{3} b +82 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) a^{3} b +51 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) a^{2} b^{2}-6 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) a \,b^{3}-82 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) a^{3} b -82 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) a^{2} b^{2}+6 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) a \,b^{3}+25 \left(\cos^{5}\left(d x +c \right)\right) a^{3} b -39 \cos \left(d x +c \right) a^{3} b +82 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \left(\cos^{4}\left(d x +c \right)\right) \sin \left(d x +c \right) a^{3} b +51 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \left(\cos^{4}\left(d x +c \right)\right) \sin \left(d x +c \right) a^{2} b^{2}-6 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \left(\cos^{4}\left(d x +c \right)\right) \sin \left(d x +c \right) a \,b^{3}-82 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \left(\cos^{4}\left(d x +c \right)\right) \sin \left(d x +c \right) a^{3} b -82 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \left(\cos^{4}\left(d x +c \right)\right) \sin \left(d x +c \right) a^{2} b^{2}-10 \left(\cos^{2}\left(d x +c \right)\right) a^{4}-6 \left(\cos^{5}\left(d x +c \right)\right) b^{4}+6 \left(\cos^{4}\left(d x +c \right)\right) b^{4}+25 \left(\cos^{4}\left(d x +c \right)\right) a^{4}+25 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \left(\cos^{4}\left(d x +c \right)\right) \sin \left(d x +c \right) a^{4}+6 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \left(\cos^{4}\left(d x +c \right)\right) \sin \left(d x +c \right) b^{4}+25 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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^{4}+6 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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^{4}-27 \left(\cos^{2}\left(d x +c \right)\right) a^{2} b^{2}+6 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \left(\cos^{4}\left(d x +c \right)\right) \sin \left(d x +c \right) a \,b^{3}\right)}{105 d \sqrt{a +b \cos \left(d x +c \right)}\, \sin \left(d x +c \right) \cos \left(d x +c \right)^{\frac{7}{2}} a^{2}}"," ",0,"-2/105/d*(25*cos(d*x+c)^5*a^3*b+25*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^4*sin(d*x+c)*a^4-15*a^4+82*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^4*sin(d*x+c)*a^3*b+51*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^4*sin(d*x+c)*a^2*b^2-6*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^4*sin(d*x+c)*a*b^3-82*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^4*sin(d*x+c)*a^3*b-82*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^4*sin(d*x+c)*a^2*b^2+6*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^4*sin(d*x+c)*a*b^3+82*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^3*sin(d*x+c)*a^3*b+51*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^3*sin(d*x+c)*a^2*b^2-6*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^3*sin(d*x+c)*a*b^3-82*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^3*sin(d*x+c)*a^3*b-82*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^3*sin(d*x+c)*a^2*b^2+6*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^3*sin(d*x+c)*a*b^3+6*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^4*sin(d*x+c)*b^4+25*cos(d*x+c)^3*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+6*cos(d*x+c)^3*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+82*cos(d*x+c)^5*a^2*b^2+3*cos(d*x+c)^5*a*b^3+82*cos(d*x+c)^4*a^3*b-55*cos(d*x+c)^4*a^2*b^2-6*cos(d*x+c)^4*a*b^3-68*cos(d*x+c)^3*a^3*b+3*cos(d*x+c)^3*a*b^3-27*cos(d*x+c)^2*a^2*b^2-39*cos(d*x+c)*a^3*b+25*cos(d*x+c)^4*a^4-10*cos(d*x+c)^2*a^4-6*cos(d*x+c)^5*b^4+6*cos(d*x+c)^4*b^4)/(a+b*cos(d*x+c))^(1/2)/sin(d*x+c)/cos(d*x+c)^(7/2)/a^2","B"
617,1,2503,410,0.415000," ","int((a+b*cos(d*x+c))^(3/2)/cos(d*x+c)^(11/2),x)","\text{Expression too large to display}"," ",0,"-2/315/d*(cos(d*x+c)^3*a^2*b^3+147*cos(d*x+c)^5*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^5-10*cos(d*x+c)^5*a^4*b+33*cos(d*x+c)^5*a^3*b^2-34*cos(d*x+c)^5*a^2*b^3+8*cos(d*x+c)^5*a*b^4-68*cos(d*x+c)^4*a^3*b^2-4*cos(d*x+c)^4*a*b^4-52*cos(d*x+c)^3*a^4*b-53*cos(d*x+c)^2*a^3*b^2-85*cos(d*x+c)*a^4*b+147*cos(d*x+c)^6*a^4*b+88*cos(d*x+c)^6*a^3*b^2+33*cos(d*x+c)^6*a^2*b^3-4*cos(d*x+c)^6*a*b^4-35*a^5+8*cos(d*x+c)^6*b^5+147*cos(d*x+c)^5*a^5-8*cos(d*x+c)^5*b^5-98*cos(d*x+c)^4*a^5-14*cos(d*x+c)^2*a^5+8*cos(d*x+c)^5*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^4-147*cos(d*x+c)^5*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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-33*cos(d*x+c)^5*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^2-33*cos(d*x+c)^5*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^3-8*cos(d*x+c)^5*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+186*cos(d*x+c)^4*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+33*cos(d*x+c)^4*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+2*cos(d*x+c)^4*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^3+8*cos(d*x+c)^4*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^4-147*cos(d*x+c)^4*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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-33*cos(d*x+c)^4*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^2-33*cos(d*x+c)^4*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^3-8*cos(d*x+c)^4*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+186*cos(d*x+c)^5*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+33*cos(d*x+c)^5*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+2*cos(d*x+c)^5*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^3-147*cos(d*x+c)^5*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^5-8*cos(d*x+c)^5*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^5+147*cos(d*x+c)^4*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^5-147*cos(d*x+c)^4*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^5-8*cos(d*x+c)^4*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^5)/(a+b*cos(d*x+c))^(1/2)/sin(d*x+c)/cos(d*x+c)^(9/2)/a^3","B"
618,1,1866,458,0.247000," ","int(cos(d*x+c)^(1/2)*(a+b*cos(d*x+c))^(5/2),x)","-\frac{30 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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} \sin \left(d x +c \right)+33 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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)+16 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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)-33 a^{3} \cos \left(d x +c \right)-33 \left(\cos^{2}\left(d x +c \right)\right) a^{2} b -16 \cos \left(d x +c \right) a \,b^{2}-18 \left(\cos^{2}\left(d x +c \right)\right) a \,b^{2}-26 \cos \left(d x +c \right) a^{2} b +8 \left(\cos^{5}\left(d x +c \right)\right) b^{3}-48 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}+8 \left(\cos^{3}\left(d x +c \right)\right) b^{3}+33 \left(\cos^{2}\left(d x +c \right)\right) a^{3}-16 \left(\cos^{2}\left(d x +c \right)\right) b^{3}+59 \left(\cos^{3}\left(d x +c \right)\right) a^{2} b +34 \left(\cos^{4}\left(d x +c \right)\right) a \,b^{2}+30 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}+33 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}+16 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}+120 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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} \sin \left(d x +c \right)+33 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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)+16 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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)+26 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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)-76 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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)-48 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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)+120 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}+33 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 +16 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}+26 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 -76 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}}{24 d \sqrt{a +b \cos \left(d x +c \right)}\, \sqrt{\cos \left(d x +c \right)}\, \sin \left(d x +c \right)}"," ",0,"-1/24/d*(-18*cos(d*x+c)^2*a*b^2-48*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+30*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*sin(d*x+c)+33*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)-33*a^3*cos(d*x+c)-16*cos(d*x+c)*a*b^2-33*cos(d*x+c)^2*a^2*b+8*cos(d*x+c)^5*b^3-16*cos(d*x+c)^2*b^3-26*cos(d*x+c)*a^2*b+34*cos(d*x+c)^4*a*b^2+59*cos(d*x+c)^3*a^2*b+8*cos(d*x+c)^3*b^3+33*cos(d*x+c)^2*a^3+33*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+16*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+120*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*sin(d*x+c)+33*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)+16*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)+26*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)-76*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)-48*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)+120*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+33*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+16*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+26*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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-76*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)/(a+b*cos(d*x+c))^(1/2)/cos(d*x+c)^(1/2)/sin(d*x+c)","B"
619,1,1629,401,0.209000," ","int((a+b*cos(d*x+c))^(5/2)/cos(d*x+c)^(1/2),x)","-\frac{30 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 +8 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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^{3}+8 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}-24 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}-4 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}+9 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 \left(\cos^{4}\left(d x +c \right)\right) b^{3}+30 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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)+8 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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^{3} \sin \left(d x +c \right)+8 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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)-24 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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{a +b \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 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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} \sin \left(d x +c \right)+9 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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)+9 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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)+11 \left(\cos^{3}\left(d x +c \right)\right) a \,b^{2}+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 \left(\cos^{2}\left(d x +c \right)\right) b^{3}-9 \cos \left(d x +c \right) a^{2} b -2 \cos \left(d x +c \right) a \,b^{2}}{4 d \sqrt{a +b \cos \left(d x +c \right)}\, \sqrt{\cos \left(d x +c \right)}\, \sin \left(d x +c \right)}"," ",0,"-1/4/d/(a+b*cos(d*x+c))^(1/2)*(30*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+8*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^3+8*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^3-24*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^2-4*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+9*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*cos(d*x+c)^4*b^3+30*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)/(1+cos(d*x+c)))^(1/2)*((a+b*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^3*sin(d*x+c)+8*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)-24*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)*((a+b*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)/(1+cos(d*x+c)))^(1/2)*((a+b*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*sin(d*x+c)+9*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)+9*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)+11*cos(d*x+c)^3*a*b^2+9*cos(d*x+c)^2*a^2*b-9*cos(d*x+c)^2*a*b^2-2*cos(d*x+c)^2*b^3-9*cos(d*x+c)*a^2*b-2*cos(d*x+c)*a*b^2)/cos(d*x+c)^(1/2)/sin(d*x+c)","B"
620,1,1626,413,0.195000," ","int((a+b*cos(d*x+c))^(5/2)/cos(d*x+c)^(3/2),x)","\frac{2 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 -\cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}-\cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}-10 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}-2 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}-6 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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)-\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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)-\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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)-10 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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} \sin \left(d x +c \right)-2 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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)-6 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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{a +b \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)-\left(\cos^{3}\left(d x +c \right)\right) b^{3}-2 \left(\cos^{2}\left(d x +c \right)\right) a^{2} b -\left(\cos^{2}\left(d x +c \right)\right) a \,b^{2}+\left(\cos^{2}\left(d x +c \right)\right) b^{3}-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}+2 a^{3}}{d \sqrt{a +b \cos \left(d x +c \right)}\, \sin \left(d x +c \right) \sqrt{\cos \left(d x +c \right)}}"," ",0,"1/d*(2*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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-cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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-cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^3-10*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^2-2*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^3-6*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)/(1+cos(d*x+c)))^(1/2)*((a+b*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)/(1+cos(d*x+c)))^(1/2)*((a+b*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)-10*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*sin(d*x+c)-2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)-6*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)*((a+b*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)^3*b^3-2*cos(d*x+c)^2*a^2*b-cos(d*x+c)^2*a*b^2+cos(d*x+c)^2*b^3-2*a^3*cos(d*x+c)+2*cos(d*x+c)*a^2*b+cos(d*x+c)*a*b^2+2*a^3)/(a+b*cos(d*x+c))^(1/2)/sin(d*x+c)/cos(d*x+c)^(1/2)","B"
621,1,1485,358,0.283000," ","int((a+b*cos(d*x+c))^(5/2)/cos(d*x+c)^(5/2),x)","-\frac{2 \left(\left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}+7 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 +9 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \left(\cos^{2}\left(d x +c \right)\right) \sin \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{a +b \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) \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) b^{3}-7 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}+\cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}+7 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 +9 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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^{3}-7 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}+\left(\cos^{3}\left(d x +c \right)\right) a^{2} b +7 \left(\cos^{3}\left(d x +c \right)\right) a \,b^{2}+\left(\cos^{2}\left(d x +c \right)\right) a^{3}+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}-8 \cos \left(d x +c \right) a^{2} b -a^{3}\right)}{3 d \sqrt{a +b \cos \left(d x +c \right)}\, \sin \left(d x +c \right) \cos \left(d x +c \right)^{\frac{3}{2}}}"," ",0,"-2/3/d*(cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+7*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+9*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^2*sin(d*x+c)*b^3+6*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^2*sin(d*x+c)*b^3-7*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+7*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+9*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^3-7*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+cos(d*x+c)^3*a^2*b+7*cos(d*x+c)^3*a*b^2+cos(d*x+c)^2*a^3+7*cos(d*x+c)^2*a^2*b-7*cos(d*x+c)^2*a*b^2-8*cos(d*x+c)*a^2*b-a^3)/(a+b*cos(d*x+c))^(1/2)/sin(d*x+c)/cos(d*x+c)^(3/2)","B"
622,1,1750,306,0.223000," ","int((a+b*cos(d*x+c))^(5/2)/cos(d*x+c)^(7/2),x)","-\frac{2 \left(-3 a^{3}-9 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 +23 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}-9 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 -23 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}-23 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}+17 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 +23 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}-34 \left(\cos^{2}\left(d x +c \right)\right) a \,b^{2}-14 \cos \left(d x +c \right) a^{2} b +23 \left(\cos^{4}\left(d x +c \right)\right) b^{3}-23 \left(\cos^{3}\left(d x +c \right)\right) b^{3}-6 \left(\cos^{2}\left(d x +c \right)\right) a^{3}+9 \left(\cos^{3}\left(d x +c \right)\right) a^{3}+17 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 +9 \left(\cos^{4}\left(d x +c \right)\right) a^{2} b +5 \left(\cos^{3}\left(d x +c \right)\right) a^{2} b +23 \left(\cos^{3}\left(d x +c \right)\right) a \,b^{2}+11 \left(\cos^{4}\left(d x +c \right)\right) a \,b^{2}+15 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) b^{3}+15 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) b^{3}-9 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}-23 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}+9 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}-23 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}+9 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}\right)}{15 d \sqrt{a +b \cos \left(d x +c \right)}\, \sin \left(d x +c \right) \cos \left(d x +c \right)^{\frac{5}{2}}}"," ",0,"-2/15/d*(-34*cos(d*x+c)^2*a*b^2+15*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^3*sin(d*x+c)*b^3-9*cos(d*x+c)^3*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^3-3*a^3-23*cos(d*x+c)^3*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+17*cos(d*x+c)^3*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+23*cos(d*x+c)^3*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^2-9*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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-23*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+23*cos(d*x+c)^4*b^3+9*cos(d*x+c)^3*a^3-14*cos(d*x+c)*a^2*b+9*cos(d*x+c)^4*a^2*b+11*cos(d*x+c)^4*a*b^2+5*cos(d*x+c)^3*a^2*b+23*cos(d*x+c)^3*a*b^2-23*cos(d*x+c)^3*b^3-6*cos(d*x+c)^2*a^3+15*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^2*sin(d*x+c)*b^3-9*cos(d*x+c)^3*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+17*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+23*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^2-23*cos(d*x+c)^3*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+9*cos(d*x+c)^3*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^3-23*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+9*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)/(a+b*cos(d*x+c))^(1/2)/sin(d*x+c)/cos(d*x+c)^(5/2)","B"
623,1,1827,349,0.275000," ","int((a+b*cos(d*x+c))^(5/2)/cos(d*x+c)^(9/2),x)","-\frac{2 \left(-3 a^{4}-22 \left(\cos^{3}\left(d x +c \right)\right) a^{3} b -11 \left(\cos^{4}\left(d x +c \right)\right) a^{2} b^{2}+9 \left(\cos^{5}\left(d x +c \right)\right) a \,b^{3}-12 \left(\cos^{3}\left(d x +c \right)\right) a \,b^{3}+3 \left(\cos^{4}\left(d x +c \right)\right) a \,b^{3}+29 \left(\cos^{5}\left(d x +c \right)\right) a^{2} b^{2}+29 \left(\cos^{4}\left(d x +c \right)\right) a^{3} b +29 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) a^{3} b +27 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) a^{2} b^{2}+3 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) a \,b^{3}-29 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) a^{3} b -29 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) a^{2} b^{2}-3 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) a \,b^{3}+5 \left(\cos^{5}\left(d x +c \right)\right) a^{3} b -12 \cos \left(d x +c \right) a^{3} b +29 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \left(\cos^{4}\left(d x +c \right)\right) \sin \left(d x +c \right) a^{3} b +27 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \left(\cos^{4}\left(d x +c \right)\right) \sin \left(d x +c \right) a^{2} b^{2}+3 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \left(\cos^{4}\left(d x +c \right)\right) \sin \left(d x +c \right) a \,b^{3}-29 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \left(\cos^{4}\left(d x +c \right)\right) \sin \left(d x +c \right) a^{3} b -29 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \left(\cos^{4}\left(d x +c \right)\right) \sin \left(d x +c \right) a^{2} b^{2}-2 \left(\cos^{2}\left(d x +c \right)\right) a^{4}+3 \left(\cos^{5}\left(d x +c \right)\right) b^{4}-3 \left(\cos^{4}\left(d x +c \right)\right) b^{4}+5 \left(\cos^{4}\left(d x +c \right)\right) a^{4}+5 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \left(\cos^{4}\left(d x +c \right)\right) \sin \left(d x +c \right) a^{4}-3 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \left(\cos^{4}\left(d x +c \right)\right) \sin \left(d x +c \right) b^{4}+5 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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^{4}-3 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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^{4}-18 \left(\cos^{2}\left(d x +c \right)\right) a^{2} b^{2}-3 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \left(\cos^{4}\left(d x +c \right)\right) \sin \left(d x +c \right) a \,b^{3}\right)}{21 d \sqrt{a +b \cos \left(d x +c \right)}\, \sin \left(d x +c \right) \cos \left(d x +c \right)^{\frac{7}{2}} a}"," ",0,"-2/21/d*(5*cos(d*x+c)^5*a^3*b+5*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^4*sin(d*x+c)*a^4-3*a^4+29*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^4*sin(d*x+c)*a^3*b+27*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^4*sin(d*x+c)*a^2*b^2+3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^4*sin(d*x+c)*a*b^3-29*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^4*sin(d*x+c)*a^3*b-29*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^4*sin(d*x+c)*a^2*b^2-3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^4*sin(d*x+c)*a*b^3+29*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^3*sin(d*x+c)*a^3*b+27*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^3*sin(d*x+c)*a^2*b^2+3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^3*sin(d*x+c)*a*b^3-29*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^3*sin(d*x+c)*a^3*b-29*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^3*sin(d*x+c)*a^2*b^2-3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^3*sin(d*x+c)*a*b^3-3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^4*sin(d*x+c)*b^4+5*cos(d*x+c)^3*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^4-3*cos(d*x+c)^3*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+29*cos(d*x+c)^5*a^2*b^2+9*cos(d*x+c)^5*a*b^3+29*cos(d*x+c)^4*a^3*b-11*cos(d*x+c)^4*a^2*b^2+3*cos(d*x+c)^4*a*b^3-22*cos(d*x+c)^3*a^3*b-12*cos(d*x+c)^3*a*b^3-18*cos(d*x+c)^2*a^2*b^2-12*cos(d*x+c)*a^3*b+5*cos(d*x+c)^4*a^4-2*cos(d*x+c)^2*a^4+3*cos(d*x+c)^5*b^4-3*cos(d*x+c)^4*b^4)/(a+b*cos(d*x+c))^(1/2)/sin(d*x+c)/cos(d*x+c)^(7/2)/a","B"
624,1,2504,410,0.375000," ","int((a+b*cos(d*x+c))^(5/2)/cos(d*x+c)^(11/2),x)","\text{Expression too large to display}"," ",0,"-2/315/d*(-80*cos(d*x+c)^3*a^2*b^3+147*cos(d*x+c)^5*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+65*cos(d*x+c)^5*a^4*b+279*cos(d*x+c)^5*a^3*b^2-199*cos(d*x+c)^5*a^2*b^3-10*cos(d*x+c)^5*a*b^4-272*cos(d*x+c)^4*a^3*b^2+5*cos(d*x+c)^4*a*b^4-82*cos(d*x+c)^3*a^4*b-170*cos(d*x+c)^2*a^3*b^2-130*cos(d*x+c)*a^4*b+147*cos(d*x+c)^6*a^4*b+163*cos(d*x+c)^6*a^3*b^2+279*cos(d*x+c)^6*a^2*b^3+5*cos(d*x+c)^6*a*b^4-35*a^5-10*cos(d*x+c)^6*b^5+147*cos(d*x+c)^5*a^5+10*cos(d*x+c)^5*b^5-98*cos(d*x+c)^4*a^5-14*cos(d*x+c)^2*a^5-10*cos(d*x+c)^5*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^4-147*cos(d*x+c)^5*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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-279*cos(d*x+c)^5*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^2-279*cos(d*x+c)^5*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+10*cos(d*x+c)^5*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+261*cos(d*x+c)^4*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+279*cos(d*x+c)^4*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+155*cos(d*x+c)^4*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^3-10*cos(d*x+c)^4*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^4-147*cos(d*x+c)^4*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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-279*cos(d*x+c)^4*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^2-279*cos(d*x+c)^4*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+10*cos(d*x+c)^4*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+261*cos(d*x+c)^5*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+279*cos(d*x+c)^5*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+155*cos(d*x+c)^5*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^3-147*cos(d*x+c)^5*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^5+10*cos(d*x+c)^5*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^5+147*cos(d*x+c)^4*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^5-147*cos(d*x+c)^4*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^5+10*cos(d*x+c)^4*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^5)/(a+b*cos(d*x+c))^(1/2)/sin(d*x+c)/cos(d*x+c)^(9/2)/a^2","B"
625,1,2789,472,0.594000," ","int((a+b*cos(d*x+c))^(5/2)/cos(d*x+c)^(13/2),x)","\text{Expression too large to display}"," ",0,"-2/693/d*(-4*cos(d*x+c)^7*a*b^5+741*cos(d*x+c)^6*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+663*cos(d*x+c)^6*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^2+51*cos(d*x+c)^6*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^3+2*cos(d*x+c)^6*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^4+8*cos(d*x+c)^6*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^5-741*cos(d*x+c)^6*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^5*b-741*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^6*sin(d*x+c)*a^4*b^2-51*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^6*sin(d*x+c)*a^3*b^3-51*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^6*sin(d*x+c)*a^2*b^4-8*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^6*sin(d*x+c)*a*b^5+741*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^5*sin(d*x+c)*a^5*b+8*cos(d*x+c)^7*b^6-8*cos(d*x+c)^6*b^6+135*cos(d*x+c)^6*a^6-54*cos(d*x+c)^4*a^6-18*cos(d*x+c)^2*a^6+135*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^6*sin(d*x+c)*a^6-63*a^6+663*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^5*sin(d*x+c)*a^4*b^2+51*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^5*sin(d*x+c)*a^3*b^3+2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^5*sin(d*x+c)*a^2*b^4+8*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^5*sin(d*x+c)*a*b^5-741*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^5*sin(d*x+c)*a^5*b-741*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^5*sin(d*x+c)*a^4*b^2-51*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^5*sin(d*x+c)*a^3*b^3-51*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^5*sin(d*x+c)*a^2*b^4-8*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^5*sin(d*x+c)*a*b^5+741*cos(d*x+c)^6*a^5*b-307*cos(d*x+c)^6*a^4*b^2+51*cos(d*x+c)^6*a^3*b^3-52*cos(d*x+c)^6*a^2*b^4+8*cos(d*x+c)^6*a*b^5-566*cos(d*x+c)^5*a^5*b-140*cos(d*x+c)^5*a^3*b^3-4*cos(d*x+c)^5*a*b^5-160*cos(d*x+c)^4*a^4*b^2+cos(d*x+c)^4*a^2*b^4-86*cos(d*x+c)^3*a^5*b-116*cos(d*x+c)^3*a^3*b^3-274*cos(d*x+c)^2*a^4*b^2-224*cos(d*x+c)*a^5*b+135*cos(d*x+c)^7*a^5*b+741*cos(d*x+c)^7*a^4*b^2+205*cos(d*x+c)^7*a^3*b^3+51*cos(d*x+c)^7*a^2*b^4-8*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^6*sin(d*x+c)*b^6+135*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^5*sin(d*x+c)*a^6-8*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^5*sin(d*x+c)*b^6)/(a+b*cos(d*x+c))^(1/2)/sin(d*x+c)/cos(d*x+c)^(11/2)/a^3","B"
626,1,622,351,0.252000," ","int(cos(d*x+c)^(3/2)/(a+b*cos(d*x+c))^(1/2),x)","-\frac{\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \sin \left(d x +c \right) a +\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \sin \left(d x +c \right) b -2 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \sin \left(d x +c \right) a +\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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{a +b \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)-2 a \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \sin \left(d x +c \right)+\left(\cos^{3}\left(d x +c \right)\right) b +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)}{d \sqrt{a +b \cos \left(d x +c \right)}\, \sin \left(d x +c \right) \sqrt{\cos \left(d x +c \right)}\, b}"," ",0,"-1/d*((cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)*b-2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)*sin(d*x+c)*a+(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)*((a+b*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)-2*a*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)+cos(d*x+c)^3*b+a*cos(d*x+c)^2-cos(d*x+c)^2*b-a*cos(d*x+c))/(a+b*cos(d*x+c))^(1/2)/sin(d*x+c)/cos(d*x+c)^(1/2)/b","A"
627,1,159,108,0.246000," ","int(cos(d*x+c)^(1/2)/(a+b*cos(d*x+c))^(1/2),x)","-\frac{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(\sin^{2}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}}{d \sqrt{a +b \cos \left(d x +c \right)}\, \left(-1+\cos \left(d x +c \right)\right) \sqrt{\cos \left(d x +c \right)}}"," ",0,"-2/d*(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)))/(a+b*cos(d*x+c))^(1/2)*sin(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)/(-1+cos(d*x+c))/cos(d*x+c)^(1/2)","A"
628,1,123,101,0.214000," ","int(1/cos(d*x+c)^(1/2)/(a+b*cos(d*x+c))^(1/2),x)","-\frac{2 \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{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{a +b \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \left(\sin^{4}\left(d x +c \right)\right)}{d \sqrt{a +b \cos \left(d x +c \right)}\, \cos \left(d x +c \right)^{\frac{3}{2}} \left(-1+\cos \left(d x +c \right)\right)^{2}}"," ",0,"-2/d*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)/(a+b*cos(d*x+c))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)^4/cos(d*x+c)^(3/2)/(-1+cos(d*x+c))^2","A"
629,1,612,208,0.235000," ","int(1/cos(d*x+c)^(3/2)/(a+b*cos(d*x+c))^(1/2),x)","-\frac{2 \left(\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \sin \left(d x +c \right) a -\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \sin \left(d x +c \right) a -\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \sin \left(d x +c \right) b +\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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{a +b \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{a +b \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) b +a \cos \left(d x +c \right)-b \cos \left(d x +c \right)-a \right)}{d \sqrt{a +b \cos \left(d x +c \right)}\, \sin \left(d x +c \right) \sqrt{\cos \left(d x +c \right)}\, a}"," ",0,"-2/d*((cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)*sin(d*x+c)*a-(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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-(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)*b+(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)*((a+b*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)*((a+b*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*b+a*cos(d*x+c)-b*cos(d*x+c)-a)/(a+b*cos(d*x+c))^(1/2)/sin(d*x+c)/cos(d*x+c)^(1/2)/a","B"
630,1,883,248,0.325000," ","int(1/cos(d*x+c)^(5/2)/(a+b*cos(d*x+c))^(1/2),x)","-\frac{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) \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, a^{2}-2 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) a b +2 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) a b +2 \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) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, b^{2}+\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) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 \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) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) a b -2 \left(\cos^{3}\left(d x +c \right)\right) 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 +2 \left(\cos^{2}\left(d x +c \right)\right) b^{2}+a b \cos \left(d x +c \right)-a^{2}\right)}{3 d \sqrt{a +b \cos \left(d x +c \right)}\, \sin \left(d x +c \right) \cos \left(d x +c \right)^{\frac{3}{2}} a^{2}}"," ",0,"-2/3/d*(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)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^2-2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^2*sin(d*x+c)*a*b+2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^2*sin(d*x+c)*a*b+2*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)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*b^2+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)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^2-2*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*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)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*b^2+cos(d*x+c)^3*a*b-2*cos(d*x+c)^3*b^2+cos(d*x+c)^2*a^2-2*cos(d*x+c)^2*a*b+2*cos(d*x+c)^2*b^2+a*b*cos(d*x+c)-a^2)/(a+b*cos(d*x+c))^(1/2)/sin(d*x+c)/cos(d*x+c)^(3/2)/a^2","B"
631,1,1661,433,0.220000," ","int(cos(d*x+c)^(5/2)/(a+b*cos(d*x+c))^(3/2),x)","\frac{6 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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} \sin \left(d x +c \right)-3 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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)+\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 a^{3} \cos \left(d x +c \right)+3 \left(\cos^{2}\left(d x +c \right)\right) a^{2} b -\cos \left(d x +c \right) a \,b^{2}+\left(\cos^{2}\left(d x +c \right)\right) a \,b^{2}-2 \cos \left(d x +c \right) a^{2} b +\left(\cos^{3}\left(d x +c \right)\right) b^{3}-3 \left(\cos^{2}\left(d x +c \right)\right) a^{3}-\left(\cos^{2}\left(d x +c \right)\right) b^{3}-\left(\cos^{3}\left(d x +c \right)\right) a^{2} b +6 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}-3 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}+\cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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} \sin \left(d x +c \right)-3 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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)+\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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)+2 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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{a +b \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)-6 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}-3 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 +\cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}}{d \sqrt{a +b \cos \left(d x +c \right)}\, \sin \left(d x +c \right) \sqrt{\cos \left(d x +c \right)}\, b^{2} \left(a -b \right) \left(a +b \right)}"," ",0,"1/d*(cos(d*x+c)^2*a*b^2+6*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+6*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*sin(d*x+c)-3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)/(1+cos(d*x+c)))^(1/2)*((a+b*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*a^3*cos(d*x+c)-cos(d*x+c)*a*b^2+3*cos(d*x+c)^2*a^2*b-cos(d*x+c)^2*b^3-2*cos(d*x+c)*a^2*b-cos(d*x+c)^3*a^2*b+cos(d*x+c)^3*b^3-3*cos(d*x+c)^2*a^3-3*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*sin(d*x+c)-3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)/(1+cos(d*x+c)))^(1/2)*((a+b*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)+2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)*((a+b*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)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^2-3*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)/(a+b*cos(d*x+c))^(1/2)/sin(d*x+c)/cos(d*x+c)^(1/2)/b^2/(a-b)/(a+b)","B"
632,1,1206,359,0.249000," ","int(cos(d*x+c)^(3/2)/(a+b*cos(d*x+c))^(3/2),x)","\frac{-2 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}+4 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}-2 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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)-2 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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)+2 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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)+2 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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)-4 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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} \sin \left(d x +c \right)+4 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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^{2}\left(d x +c \right)\right) a^{2}-2 \left(\cos^{2}\left(d x +c \right)\right) a b -2 a^{2} \cos \left(d x +c \right)+2 a b \cos \left(d x +c \right)}{d \sqrt{a +b \cos \left(d x +c \right)}\, \sin \left(d x +c \right) \sqrt{\cos \left(d x +c \right)}\, b \left(a -b \right) \left(a +b \right)}"," ",0,"2/d*(-cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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-cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+2*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)*((a+b*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)/(1+cos(d*x+c)))^(1/2)*((a+b*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)*((a+b*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)/(1+cos(d*x+c)))^(1/2)*((a+b*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)-2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*sin(d*x+c)+2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^2-cos(d*x+c)^2*a*b-a^2*cos(d*x+c)+a*b*cos(d*x+c))/(a+b*cos(d*x+c))^(1/2)/sin(d*x+c)/cos(d*x+c)^(1/2)/b/(a-b)/(a+b)","B"
633,1,809,246,0.211000," ","int(cos(d*x+c)^(1/2)/(a+b*cos(d*x+c))^(3/2),x)","\frac{2 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \sin \left(d x +c \right) a +2 \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) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, b -2 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \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{a +b \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) \sin \left(d x +c \right) b +2 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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)+2 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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{a +b \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)-2 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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)-2 a \left(\cos^{2}\left(d x +c \right)\right)+2 \left(\cos^{2}\left(d x +c \right)\right) b +2 a \cos \left(d x +c \right)-2 b \cos \left(d x +c \right)}{d \sqrt{a +b \cos \left(d x +c \right)}\, \sqrt{\cos \left(d x +c \right)}\, \sin \left(d x +c \right) \left(a -b \right) \left(a +b \right)}"," ",0,"2/d*((cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)*sin(d*x+c)*a+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)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*b-(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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-(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)*b+(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)*((a+b*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)*((a+b*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)*((a+b*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)-a*cos(d*x+c)^2+cos(d*x+c)^2*b+a*cos(d*x+c)-b*cos(d*x+c))/(a+b*cos(d*x+c))^(1/2)/cos(d*x+c)^(1/2)/sin(d*x+c)/(a-b)/(a+b)","B"
634,1,830,247,0.230000," ","int(1/cos(d*x+c)^(1/2)/(a+b*cos(d*x+c))^(3/2),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) \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 \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) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, b^{2}-2 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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)+2 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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)+2 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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^{2}\left(d x +c \right)\right) a b -2 \left(\cos^{2}\left(d x +c \right)\right) b^{2}-2 a b \cos \left(d x +c \right)+2 \cos \left(d x +c \right) b^{2}}{d \sqrt{a +b \cos \left(d x +c \right)}\, \sqrt{\cos \left(d x +c \right)}\, \sin \left(d x +c \right) \left(a +b \right) \left(a -b \right) a}"," ",0,"2/d/(a+b*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)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^2-cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*b^2-(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)-(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)/(1+cos(d*x+c)))^(1/2)*((a+b*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)/(1+cos(d*x+c)))^(1/2)*((a+b*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)+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)/cos(d*x+c)^(1/2)/sin(d*x+c)/(a+b)/(a-b)/a","B"
635,1,1452,265,0.250000," ","int(1/cos(d*x+c)^(3/2)/(a+b*cos(d*x+c))^(3/2),x)","-\frac{2 \left(\cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}-\cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}+\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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)-\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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{a +b \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)-\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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)-\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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)+2 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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)+2 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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)+\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 \left(\cos^{2}\left(d x +c \right)\right) b^{3}+a^{3} \cos \left(d x +c \right)-\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}-a^{3}+b^{2} a \right)}{d \sqrt{a +b \cos \left(d x +c \right)}\, \sin \left(d x +c \right) \sqrt{\cos \left(d x +c \right)}\, a^{2} \left(a -b \right) \left(a +b \right)}"," ",0,"-2/d*(cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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-cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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-cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)/(1+cos(d*x+c)))^(1/2)*((a+b*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)*((a+b*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)/(1+cos(d*x+c)))^(1/2)*((a+b*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)/(1+cos(d*x+c)))^(1/2)*((a+b*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)+2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)+2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)+cos(d*x+c)^2*a^2*b+cos(d*x+c)^2*a*b^2-2*cos(d*x+c)^2*b^3+a^3*cos(d*x+c)-cos(d*x+c)*a^2*b-2*cos(d*x+c)*a*b^2+2*cos(d*x+c)*b^3-a^3+b^2*a)/(a+b*cos(d*x+c))^(1/2)/sin(d*x+c)/cos(d*x+c)^(1/2)/a^2/(a-b)/(a+b)","B"
636,1,1781,327,0.222000," ","int(1/cos(d*x+c)^(5/2)/(a+b*cos(d*x+c))^(3/2),x)","-\frac{2 \left(-a^{4}+\left(\cos^{3}\left(d x +c \right)\right) a^{3} b -4 \left(\cos^{3}\left(d x +c \right)\right) a \,b^{3}+8 \left(\cos^{2}\left(d x +c \right)\right) a \,b^{3}-5 \left(\cos^{2}\left(d x +c \right)\right) a^{3} b -5 \left(\cos^{3}\left(d x +c \right)\right) a^{2} b^{2}+5 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}+8 \left(\cos^{3}\left(d x +c \right)\right) b^{4}-4 \cos \left(d x +c \right) a \,b^{3}+a^{2} b^{2}+4 \cos \left(d x +c \right) a^{3} b -8 \left(\cos^{2}\left(d x +c \right)\right) b^{4}+\left(\cos^{2}\left(d x +c \right)\right) a^{4}-8 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}-5 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}+8 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}+4 \left(\cos^{2}\left(d x +c \right)\right) a^{2} b^{2}+5 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}-8 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}-5 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}+8 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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^{4}+\cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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^{4}-8 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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^{4}+\left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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^{4}\right)}{3 d \sqrt{a +b \cos \left(d x +c \right)}\, \sin \left(d x +c \right) \cos \left(d x +c \right)^{\frac{3}{2}} \left(a +b \right) \left(a -b \right) a^{3}}"," ",0,"-2/3/d*(-8*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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-a^4-5*cos(d*x+c)^3*a^2*b^2-5*cos(d*x+c)^2*a^3*b+8*cos(d*x+c)^2*a*b^3-4*cos(d*x+c)*a*b^3+8*cos(d*x+c)^3*b^4-8*cos(d*x+c)^2*b^4+a^2*b^2+cos(d*x+c)^3*a^3*b-4*cos(d*x+c)^3*a*b^3+4*cos(d*x+c)^2*a^2*b^2+4*cos(d*x+c)*a^3*b-8*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^3-5*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+8*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+5*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^2-8*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^3-5*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+8*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+5*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+cos(d*x+c)^2*a^4+cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^4-8*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)/(a+b*cos(d*x+c))^(1/2)/sin(d*x+c)/cos(d*x+c)^(3/2)/(a+b)/(a-b)/a^3","B"
637,1,2478,397,0.267000," ","int(1/cos(d*x+c)^(7/2)/(a+b*cos(d*x+c))^(3/2),x)","\text{Expression too large to display}"," ",0,"-2/5/d*(-6*cos(d*x+c)^3*a^2*b^3+3*cos(d*x+c)^3*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^5-16*cos(d*x+c)^4*b^5+3*cos(d*x+c)^3*a^5+16*cos(d*x+c)^3*b^5+3*cos(d*x+c)^4*a^4*b-3*cos(d*x+c)^4*a^3*b^2+8*cos(d*x+c)^4*a*b^4-5*cos(d*x+c)^3*a^4*b-6*cos(d*x+c)^2*a^3*b^2+2*cos(d*x+c)*a^4*b-a^5+8*cos(d*x+c)^4*a^2*b^3+8*cos(d*x+c)^3*a^3*b^2-16*cos(d*x+c)^3*a*b^4+8*cos(d*x+c)^2*a*b^4-2*cos(d*x+c)*a^2*b^3+a^3*b^2-2*cos(d*x+c)^2*a^5-3*cos(d*x+c)^3*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^5+16*cos(d*x+c)^3*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^5+3*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^5-3*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^5+16*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^5-8*cos(d*x+c)^3*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+16*cos(d*x+c)^3*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+8*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^2-4*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^3-16*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^4-3*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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-8*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^2-8*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+16*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+8*cos(d*x+c)^3*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^2-4*cos(d*x+c)^3*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^3-16*cos(d*x+c)^3*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^4-3*cos(d*x+c)^3*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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-8*cos(d*x+c)^3*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^2)/(a+b*cos(d*x+c))^(1/2)/sin(d*x+c)/cos(d*x+c)^(5/2)/(a+b)/(a-b)/a^4","B"
638,1,3911,457,0.271000," ","int(cos(d*x+c)^(5/2)/(a+b*cos(d*x+c))^(5/2),x)","\text{output too large to display}"," ",0,"-2/3/d*(6*cos(d*x+c)^2*a^4*b+8*cos(d*x+c)^3*a^2*b^3+6*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)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*cos(d*x+c)^2*b^5-14*cos(d*x+c)^2*a^2*b^3-7*cos(d*x+c)*a^3*b^2-4*cos(d*x+c)^3*a^4*b+4*cos(d*x+c)^2*a^3*b^2-2*cos(d*x+c)*a^4*b+3*a^5*cos(d*x+c)+3*cos(d*x+c)^3*a^3*b^2-7*cos(d*x+c)^3*a*b^4+7*cos(d*x+c)^2*a*b^4+6*cos(d*x+c)*a^2*b^3+6*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,(-(a-b)/(a+b))^(1/2))*a^5*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)-3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^5*sin(d*x+c)-3*cos(d*x+c)^2*a^5-3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+6*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)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*cos(d*x+c)*a^5+6*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)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*cos(d*x+c)*b^5-3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)*b^5-3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)*a^5-12*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,(-(a-b)/(a+b))^(1/2))*a^3*b^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)+6*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,(-(a-b)/(a+b))^(1/2))*a*b^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)+2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*sin(d*x+c)-(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)-6*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^3*sin(d*x+c)-3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^4*sin(d*x+c)-3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*sin(d*x+c)+7*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^2*sin(d*x+c)+7*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)-9*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)*a*b^4+4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)*a^3*b^2+7*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)*a*b^4+6*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)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(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)*((a+b*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)*a^4*b+14*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)*a^2*b^3-12*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)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*cos(d*x+c)^2*a^2*b^3+6*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)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*cos(d*x+c)*a^4*b-12*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)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*cos(d*x+c)*a^3*b^2-12*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)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*cos(d*x+c)*a^2*b^3+6*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)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*cos(d*x+c)*a*b^4+2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)*a^4*b+(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)*a^3*b^2+2*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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-cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^3-6*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^4-3*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^2+7*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+7*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^4-7*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)*a^2*b^3)/(a+b*cos(d*x+c))^(3/2)/sin(d*x+c)/cos(d*x+c)^(1/2)/(a-b)^2/(a+b)^2/b^2","B"
639,1,1782,310,0.297000," ","int(cos(d*x+c)^(3/2)/(a+b*cos(d*x+c))^(5/2),x)","-\frac{2 \left(-a^{3} \cos \left(d x +c \right)-4 \left(\cos^{2}\left(d x +c \right)\right) a^{2} b -3 \cos \left(d x +c \right) a \,b^{2}-4 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 \left(\cos^{2}\left(d x +c \right)\right) a \,b^{2}+4 \cos \left(d x +c \right) a^{2} b +\cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}+4 \left(\cos^{3}\left(d x +c \right)\right) b^{3}-4 \left(\cos^{2}\left(d x +c \right)\right) b^{3}+\left(\cos^{3}\left(d x +c \right)\right) a^{3}+\left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 \left(\cos^{3}\left(d x +c \right)\right) a \,b^{2}+3 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}+3 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) b^{3}-4 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}-4 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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)-4 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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)+4 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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)+3 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}+\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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)-4 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 -8 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}+5 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}\right)}{3 d \left(a +b \cos \left(d x +c \right)\right)^{\frac{3}{2}} \sin \left(d x +c \right) \sqrt{\cos \left(d x +c \right)}\, \left(a -b \right)^{2} \left(a +b \right)^{2}}"," ",0,"-2/3/d*(8*cos(d*x+c)^2*a*b^2+cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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-a^3*cos(d*x+c)-3*cos(d*x+c)*a*b^2-4*cos(d*x+c)^2*a^2*b-4*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*cos(d*x+c)^2*b^3+cos(d*x+c)^3*a^3+4*cos(d*x+c)*a^2*b-5*cos(d*x+c)^3*a*b^2+4*cos(d*x+c)^3*b^3+3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^2*sin(d*x+c)*b^3+3*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+4*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^2-4*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^3-4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)-4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)+4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)+3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)-4*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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-8*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+5*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)/(a+b*cos(d*x+c))^(3/2)/sin(d*x+c)/cos(d*x+c)^(1/2)/(a-b)^2/(a+b)^2","B"
640,1,2417,327,0.212000," ","int(cos(d*x+c)^(1/2)/(a+b*cos(d*x+c))^(5/2),x)","\text{Expression too large to display}"," ",0,"-2/3/d*(cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^4-3*cos(d*x+c)^3*a^2*b^2-6*cos(d*x+c)^2*a^3*b-2*cos(d*x+c)^2*a*b^3-cos(d*x+c)*a^2*b^2-cos(d*x+c)^3*b^4+cos(d*x+c)^2*b^4+2*cos(d*x+c)^3*a^3*b+2*cos(d*x+c)^3*a*b^3+4*cos(d*x+c)^2*a^2*b^2+4*cos(d*x+c)*a^3*b+sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)/(1+cos(d*x+c)))^(1/2)*((a+b*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^3-4*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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-sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+3*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+2*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^3-7*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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-5*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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-cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+3*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^3-3*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)*((a+b*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-cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+6*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+4*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*cos(d*x+c)^2*a^4-3*a^4*cos(d*x+c)+3*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^4-3*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^4-3*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)/(a+b*cos(d*x+c))^(3/2)/cos(d*x+c)^(1/2)/sin(d*x+c)/(a-b)^2/(a+b)^2/a","B"
641,1,2743,349,0.289000," ","int(1/cos(d*x+c)^(1/2)/(a+b*cos(d*x+c))^(5/2),x)","\text{Expression too large to display}"," ",0,"2/3/d/(a+b*cos(d*x+c))^(3/2)*(6*cos(d*x+c)^2*a^4*b-6*cos(d*x+c)^3*a^2*b^3-2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*sin(d*x+c)+2*cos(d*x+c)^3*b^5-3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)*sin(d*x+c)*a^5-2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)*b^5+4*cos(d*x+c)^2*a^2*b^3+7*cos(d*x+c)*a^3*b^2-12*cos(d*x+c)^2*a^3*b^2-6*cos(d*x+c)*a^4*b-3*cos(d*x+c)*a*b^4-2*cos(d*x+c)^2*b^5+5*cos(d*x+c)^3*a^3*b^2-cos(d*x+c)^3*a*b^4+4*cos(d*x+c)^2*a*b^4+2*cos(d*x+c)*a^2*b^3-3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*sin(d*x+c)-6*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*sin(d*x+c)-(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)+2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^3*sin(d*x+c)+6*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*sin(d*x+c)+6*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^2*sin(d*x+c)-2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)+2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)*a*b^4+12*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)*a^3*b^2-4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)*a*b^4+6*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)*a^4*b+4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)*a^2*b^3-9*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)*a^4*b-7*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)*a^3*b^2-2*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^5-3*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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-6*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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-cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^3+2*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^4+6*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^2+6*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^3-2*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)/(1+cos(d*x+c)))^(1/2)*((a+b*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)*a^2*b^3)/cos(d*x+c)^(1/2)/sin(d*x+c)/a^2/(a+b)^2/(a-b)^2","B"
642,1,3693,366,0.272000," ","int(1/cos(d*x+c)^(3/2)/(a+b*cos(d*x+c))^(5/2),x)","\text{output too large to display}"," ",0,"-2/3/d*(-15*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^2*sin(d*x+c)+8*cos(d*x+c)^3*b^6-8*cos(d*x+c)^2*b^6+3*cos(d*x+c)*a^6+6*b^2*a^4-3*b^4*a^2-3*a^6+3*cos(d*x+c)^3*a^4*b^2-15*cos(d*x+c)^3*a^2*b^4-4*cos(d*x+c)^3*a*b^5+6*cos(d*x+c)^2*a^5*b-30*cos(d*x+c)^2*a^3*b^3+10*cos(d*x+c)^2*a^2*b^4+16*cos(d*x+c)^2*a*b^5-15*cos(d*x+c)*a^4*b^2+22*cos(d*x+c)*a^3*b^3+8*cos(d*x+c)*a^2*b^4-12*cos(d*x+c)*a*b^5+3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*sin(d*x+c)-3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*sin(d*x+c)+8*cos(d*x+c)^3*a^3*b^3+6*cos(d*x+c)^2*a^4*b^2-6*cos(d*x+c)*a^5*b+2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^3*sin(d*x+c)+8*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^4*sin(d*x+c)-3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+15*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+15*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^3-8*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)-8*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^2*sin(d*x+c)*b^6+3*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^6-3*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^6-8*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^6-6*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*sin(d*x+c)+7*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^4-16*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*b^5-3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)*sin(d*x+c)*a^5*b-21*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)*sin(d*x+c)*a^4*b^2-13*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^3+10*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)*sin(d*x+c)*a^2*b^4+8*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)*sin(d*x+c)*a*b^5-6*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^5*b+12*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^2+30*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^3*b^3+3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^2*sin(d*x+c)*a^5*b-6*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^2*sin(d*x+c)*a^4*b^2-15*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^2*sin(d*x+c)*a^3*b^3+2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^2*sin(d*x+c)*a^2*b^4+8*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^2*sin(d*x+c)*a*b^5-3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^2*sin(d*x+c)*a^5*b-3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^2*sin(d*x+c)*a^4*b^2+15*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^2*sin(d*x+c)*a^3*b^3+15*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^2*sin(d*x+c)*a^2*b^4-8*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^2*sin(d*x+c)*a*b^5)/(a+b*cos(d*x+c))^(3/2)/sin(d*x+c)/cos(d*x+c)^(1/2)/a^3/(a+b)^2/(a-b)^2","B"
643,1,4189,435,0.319000," ","int(1/cos(d*x+c)^(5/2)/(a+b*cos(d*x+c))^(5/2),x)","\text{output too large to display}"," ",0,"-2/3/d*(16*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^3*sin(d*x+c)*b^7+cos(d*x+c)^4*a^5*b^2-16*cos(d*x+c)^2*a^2*b^5+24*cos(d*x+c)^2*a*b^6+6*cos(d*x+c)*a^6*b-12*cos(d*x+c)*a^4*b^3+6*cos(d*x+c)*a^2*b^5-8*cos(d*x+c)^4*a^4*b^3-13*cos(d*x+c)^4*a^3*b^4+28*cos(d*x+c)^4*a^2*b^5+8*cos(d*x+c)^4*a*b^6+2*cos(d*x+c)^3*a^6*b-16*cos(d*x+c)^3*a^5*b^2-8*cos(d*x+c)^3*a^4*b^3+56*cos(d*x+c)^3*a^3*b^4-18*cos(d*x+c)^3*a^2*b^5-32*cos(d*x+c)^3*a*b^6-8*cos(d*x+c)^2*a^6*b+13*cos(d*x+c)^2*a^5*b^2+28*cos(d*x+c)^2*a^4*b^3-42*cos(d*x+c)^2*a^3*b^4+cos(d*x+c)^2*a^7-16*cos(d*x+c)^4*b^7+16*cos(d*x+c)^3*b^7-a^7+2*a^5*b^2-a^3*b^4+(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^2*sin(d*x+c)*a^7+16*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^2*sin(d*x+c)*b^7+(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)*sin(d*x+c)*a^7+(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^3*sin(d*x+c)*a^6*b-8*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^3*sin(d*x+c)*a^5*b^2+7*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^3*sin(d*x+c)*a^4*b^3+28*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^3*sin(d*x+c)*a^3*b^4-4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^3*sin(d*x+c)*a^2*b^5-16*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^3*sin(d*x+c)*a*b^6+8*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^3*sin(d*x+c)*a^5*b^2+8*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^3*sin(d*x+c)*a^4*b^3-28*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^3*sin(d*x+c)*a^3*b^4-28*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^3*sin(d*x+c)*a^2*b^5+16*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^3*sin(d*x+c)*a*b^6-7*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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-cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+35*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+24*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^4-20*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^5-16*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+8*cos(d*x+c)^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)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^6*b+16*cos(d*x+c)^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)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^5*b^2-20*cos(d*x+c)^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)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^4*b^3-56*cos(d*x+c)^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)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^3*b^4-12*cos(d*x+c)^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)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^2*b^5+32*cos(d*x+c)^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)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a*b^6-8*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)*sin(d*x+c)*a^6*b+7*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)*sin(d*x+c)*a^5*b^2+28*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^3-4*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^4-16*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)*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)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^6*b+8*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^5*b^2-28*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)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^4*b^3-28*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^3*b^4+16*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)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^2*b^5+16*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)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a*b^6)/(a+b*cos(d*x+c))^(3/2)/sin(d*x+c)/cos(d*x+c)^(3/2)/(a-b)^2/(a+b)^2/a^4","B"
644,1,115,31,0.202000," ","int(1/cos(d*x+c)^(1/2)/(2+3*cos(d*x+c))^(1/2),x)","-\frac{\sqrt{2}\, \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \left(\sin^{4}\left(d x +c \right)\right) \sqrt{10}\, \sqrt{\frac{2+3 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \frac{\sqrt{5}}{5}\right)}{5 d \sqrt{2+3 \cos \left(d x +c \right)}\, \cos \left(d x +c \right)^{\frac{3}{2}} \left(-1+\cos \left(d x +c \right)\right)^{2}}"," ",0,"-1/5/d*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)/(2+3*cos(d*x+c))^(1/2)*sin(d*x+c)^4*10^(1/2)*((2+3*cos(d*x+c))/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),1/5*5^(1/2))/cos(d*x+c)^(3/2)/(-1+cos(d*x+c))^2","B"
645,1,107,26,0.187000," ","int(1/cos(d*x+c)^(1/2)/(-2+3*cos(d*x+c))^(1/2),x)","-\frac{2 \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \left(\sin^{4}\left(d x +c \right)\right) \sqrt{\frac{-2+3 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{5}\right)}{d \sqrt{-2+3 \cos \left(d x +c \right)}\, \cos \left(d x +c \right)^{\frac{3}{2}} \left(-1+\cos \left(d x +c \right)\right)^{2}}"," ",0,"-2/d*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)/(-2+3*cos(d*x+c))^(1/2)*sin(d*x+c)^4*((-2+3*cos(d*x+c))/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),5^(1/2))/cos(d*x+c)^(3/2)/(-1+cos(d*x+c))^2","B"
646,1,119,51,0.184000," ","int(1/(2-3*cos(d*x+c))^(1/2)/cos(d*x+c)^(1/2),x)","\frac{2 \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sqrt{2-3 \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{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{5}\right) \left(\sin^{4}\left(d x +c \right)\right)}{d \cos \left(d x +c \right)^{\frac{3}{2}} \left(-2+3 \cos \left(d x +c \right)\right) \left(-1+\cos \left(d x +c \right)\right)^{2}}"," ",0,"2/d*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*(2-3*cos(d*x+c))^(1/2)*((-2+3*cos(d*x+c))/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),5^(1/2))*sin(d*x+c)^4/cos(d*x+c)^(3/2)/(-2+3*cos(d*x+c))/(-1+cos(d*x+c))^2","B"
647,1,132,46,0.192000," ","int(1/(-2-3*cos(d*x+c))^(1/2)/cos(d*x+c)^(1/2),x)","\frac{\sqrt{2}\, \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sqrt{-2-3 \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{\sqrt{5}\, \left(-1+\cos \left(d x +c \right)\right)}{5 \sin \left(d x +c \right)}, \sqrt{5}\right) \left(\sin^{4}\left(d x +c \right)\right) \sqrt{5}}{5 d \cos \left(d x +c \right)^{\frac{3}{2}} \left(2+3 \cos \left(d x +c \right)\right) \left(-1+\cos \left(d x +c \right)\right)^{2}}"," ",0,"1/5/d*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*(-2-3*cos(d*x+c))^(1/2)*10^(1/2)*((2+3*cos(d*x+c))/(1+cos(d*x+c)))^(1/2)*EllipticF(1/5*5^(1/2)*(-1+cos(d*x+c))/sin(d*x+c),5^(1/2))*sin(d*x+c)^4/cos(d*x+c)^(3/2)/(2+3*cos(d*x+c))/(-1+cos(d*x+c))^2*5^(1/2)","B"
648,1,116,55,0.215000," ","int(1/cos(d*x+c)^(1/2)/(3+2*cos(d*x+c))^(1/2),x)","-\frac{\sqrt{2}\, \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sqrt{10}\, \sqrt{\frac{3+2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \frac{i \sqrt{5}}{5}\right) \left(\sin^{4}\left(d x +c \right)\right)}{5 d \sqrt{3+2 \cos \left(d x +c \right)}\, \cos \left(d x +c \right)^{\frac{3}{2}} \left(-1+\cos \left(d x +c \right)\right)^{2}}"," ",0,"-1/5/d*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)/(3+2*cos(d*x+c))^(1/2)*10^(1/2)*((3+2*cos(d*x+c))/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),1/5*I*5^(1/2))*sin(d*x+c)^4/cos(d*x+c)^(3/2)/(-1+cos(d*x+c))^2","B"
649,1,125,54,0.194000," ","int(1/(3-2*cos(d*x+c))^(1/2)/cos(d*x+c)^(1/2),x)","\frac{\sqrt{2}\, \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sqrt{3-2 \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)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, i \sqrt{5}\right) \left(\sin^{4}\left(d x +c \right)\right)}{d \cos \left(d x +c \right)^{\frac{3}{2}} \left(-3+2 \cos \left(d x +c \right)\right) \left(-1+\cos \left(d x +c \right)\right)^{2}}"," ",0,"1/d*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*(3-2*cos(d*x+c))^(1/2)*(-2*(-3+2*cos(d*x+c))/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),I*5^(1/2))*sin(d*x+c)^4/cos(d*x+c)^(3/2)/(-3+2*cos(d*x+c))/(-1+cos(d*x+c))^2","B"
650,1,123,74,0.198000," ","int(1/cos(d*x+c)^(1/2)/(-3+2*cos(d*x+c))^(1/2),x)","\frac{i \sqrt{2}\, \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \left(\sin^{4}\left(d x +c \right)\right) \sqrt{-\frac{2 \left(-3+2 \cos \left(d x +c \right)\right)}{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{i \sqrt{5}}{5}\right) \sqrt{5}}{5 d \sqrt{-3+2 \cos \left(d x +c \right)}\, \cos \left(d x +c \right)^{\frac{3}{2}} \left(-1+\cos \left(d x +c \right)\right)^{2}}"," ",0,"1/5*I/d*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)/(-3+2*cos(d*x+c))^(1/2)*sin(d*x+c)^4*(-2*(-3+2*cos(d*x+c))/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))*5^(1/2)/sin(d*x+c),1/5*I*5^(1/2))/cos(d*x+c)^(3/2)/(-1+cos(d*x+c))^2*5^(1/2)","A"
651,1,137,75,0.201000," ","int(1/(-3-2*cos(d*x+c))^(1/2)/cos(d*x+c)^(1/2),x)","-\frac{i \sqrt{2}\, \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sqrt{-3-2 \cos \left(d x +c \right)}\, \left(\sin^{4}\left(d x +c \right)\right) \sqrt{10}\, \sqrt{\frac{3+2 \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) \sqrt{5}}{5 \sin \left(d x +c \right)}, i \sqrt{5}\right) \sqrt{5}}{5 d \cos \left(d x +c \right)^{\frac{3}{2}} \left(3+2 \cos \left(d x +c \right)\right) \left(-1+\cos \left(d x +c \right)\right)^{2}}"," ",0,"-1/5*I/d*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*(-3-2*cos(d*x+c))^(1/2)*sin(d*x+c)^4*10^(1/2)*((3+2*cos(d*x+c))/(1+cos(d*x+c)))^(1/2)*EllipticF(1/5*I*(-1+cos(d*x+c))*5^(1/2)/sin(d*x+c),I*5^(1/2))/cos(d*x+c)^(3/2)/(3+2*cos(d*x+c))/(-1+cos(d*x+c))^2*5^(1/2)","A"
652,1,122,49,0.187000," ","int(1/(-cos(d*x+c))^(1/2)/(2+3*cos(d*x+c))^(1/2),x)","\frac{\EllipticF \left(\frac{\sqrt{5}\, \left(-1+\cos \left(d x +c \right)\right)}{5 \sin \left(d x +c \right)}, \sqrt{5}\right) \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{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)}}\, \left(\sin^{2}\left(d x +c \right)\right) \sqrt{5}}{5 d \sqrt{2+3 \cos \left(d x +c \right)}\, \left(-1+\cos \left(d x +c \right)\right) \sqrt{-\cos \left(d x +c \right)}}"," ",0,"1/5/d*EllipticF(1/5*5^(1/2)*(-1+cos(d*x+c))/sin(d*x+c),5^(1/2))*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*10^(1/2)*((2+3*cos(d*x+c))/(1+cos(d*x+c)))^(1/2)/(2+3*cos(d*x+c))^(1/2)*sin(d*x+c)^2/(-1+cos(d*x+c))/(-cos(d*x+c))^(1/2)*5^(1/2)","B"
653,1,109,44,0.190000," ","int(1/(-cos(d*x+c))^(1/2)/(-2+3*cos(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{5}\right) \sqrt{\frac{-2+3 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \left(\sin^{2}\left(d x +c \right)\right)}{d \sqrt{-2+3 \cos \left(d x +c \right)}\, \left(-1+\cos \left(d x +c \right)\right) \sqrt{-\cos \left(d x +c \right)}}"," ",0,"2/d*EllipticF((-1+cos(d*x+c))/sin(d*x+c),5^(1/2))*((-2+3*cos(d*x+c))/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)/(-2+3*cos(d*x+c))^(1/2)*sin(d*x+c)^2/(-1+cos(d*x+c))/(-cos(d*x+c))^(1/2)","B"
654,1,121,33,0.165000," ","int(1/(2-3*cos(d*x+c))^(1/2)/(-cos(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{5}\right) \sqrt{\frac{-2+3 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2-3 \cos \left(d x +c \right)}\, \left(\sin^{2}\left(d x +c \right)\right)}{d \left(3 \left(\cos^{2}\left(d x +c \right)\right)-5 \cos \left(d x +c \right)+2\right) \sqrt{-\cos \left(d x +c \right)}}"," ",0,"-2/d*EllipticF((-1+cos(d*x+c))/sin(d*x+c),5^(1/2))*((-2+3*cos(d*x+c))/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*(2-3*cos(d*x+c))^(1/2)*sin(d*x+c)^2/(3*cos(d*x+c)^2-5*cos(d*x+c)+2)/(-cos(d*x+c))^(1/2)","B"
655,1,129,28,0.181000," ","int(1/(-2-3*cos(d*x+c))^(1/2)/(-cos(d*x+c))^(1/2),x)","-\frac{\EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \frac{\sqrt{5}}{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{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{-2-3 \cos \left(d x +c \right)}\, \left(\sin^{2}\left(d x +c \right)\right)}{5 d \left(3 \left(\cos^{2}\left(d x +c \right)\right)-\cos \left(d x +c \right)-2\right) \sqrt{-\cos \left(d x +c \right)}}"," ",0,"-1/5/d*EllipticF((-1+cos(d*x+c))/sin(d*x+c),1/5*5^(1/2))*10^(1/2)*((2+3*cos(d*x+c))/(1+cos(d*x+c)))^(1/2)*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*(-2-3*cos(d*x+c))^(1/2)*sin(d*x+c)^2/(3*cos(d*x+c)^2-cos(d*x+c)-2)/(-cos(d*x+c))^(1/2)","B"
656,1,127,73,0.160000," ","int(1/(-cos(d*x+c))^(1/2)/(3+2*cos(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)}, i \sqrt{5}\right) \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{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)}}\, \left(\sin^{2}\left(d x +c \right)\right) \sqrt{5}}{5 d \sqrt{3+2 \cos \left(d x +c \right)}\, \left(-1+\cos \left(d x +c \right)\right) \sqrt{-\cos \left(d x +c \right)}}"," ",0,"-1/5*I/d*EllipticF(1/5*I*(-1+cos(d*x+c))*5^(1/2)/sin(d*x+c),I*5^(1/2))*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*10^(1/2)*((3+2*cos(d*x+c))/(1+cos(d*x+c)))^(1/2)/(3+2*cos(d*x+c))^(1/2)*sin(d*x+c)^2/(-1+cos(d*x+c))/(-cos(d*x+c))^(1/2)*5^(1/2)","A"
657,1,107,72,0.126000," ","int(1/(3-2*cos(d*x+c))^(1/2)/(-cos(d*x+c))^(1/2),x)","\frac{2 i \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right) \sqrt{5}}{\sin \left(d x +c \right)}, \frac{i \sqrt{5}}{5}\right) \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{3-2 \cos \left(d x +c \right)}\, \sqrt{5}}{5 d \sqrt{-\frac{2 \left(-3+2 \cos \left(d x +c \right)\right)}{1+\cos \left(d x +c \right)}}\, \sqrt{-\cos \left(d x +c \right)}}"," ",0,"2/5*I/d*EllipticF(I*(-1+cos(d*x+c))*5^(1/2)/sin(d*x+c),1/5*I*5^(1/2))*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)/(-2*(-3+2*cos(d*x+c))/(1+cos(d*x+c)))^(1/2)*(3-2*cos(d*x+c))^(1/2)/(-cos(d*x+c))^(1/2)*5^(1/2)","A"
658,1,98,56,0.120000," ","int(1/(-cos(d*x+c))^(1/2)/(-3+2*cos(d*x+c))^(1/2),x)","\frac{2 \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, i \sqrt{5}\right) \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{-3+2 \cos \left(d x +c \right)}}{d \sqrt{-\frac{2 \left(-3+2 \cos \left(d x +c \right)\right)}{1+\cos \left(d x +c \right)}}\, \sqrt{-\cos \left(d x +c \right)}}"," ",0,"2/d*EllipticF((-1+cos(d*x+c))/sin(d*x+c),I*5^(1/2))/(-2*(-3+2*cos(d*x+c))/(1+cos(d*x+c)))^(1/2)*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*(-3+2*cos(d*x+c))^(1/2)/(-cos(d*x+c))^(1/2)","A"
659,1,128,57,0.168000," ","int(1/(-3-2*cos(d*x+c))^(1/2)/(-cos(d*x+c))^(1/2),x)","-\frac{\EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \frac{i \sqrt{5}}{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{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{-3-2 \cos \left(d x +c \right)}\, \left(\sin^{2}\left(d x +c \right)\right)}{5 d \left(2 \left(\cos^{2}\left(d x +c \right)\right)+\cos \left(d x +c \right)-3\right) \sqrt{-\cos \left(d x +c \right)}}"," ",0,"-1/5/d*EllipticF((-1+cos(d*x+c))/sin(d*x+c),1/5*I*5^(1/2))*10^(1/2)*((3+2*cos(d*x+c))/(1+cos(d*x+c)))^(1/2)*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*(-3-2*cos(d*x+c))^(1/2)*sin(d*x+c)^2/(2*cos(d*x+c)^2+cos(d*x+c)-3)/(-cos(d*x+c))^(1/2)","B"
660,1,142,65,0.209000," ","int(cos(d*x+c)^(1/2)/(2+3*cos(d*x+c))^(1/2),x)","-\frac{\sqrt{10}\, \sqrt{2}\, \left(\EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \frac{\sqrt{5}}{5}\right)-2 \EllipticPi \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, -1, \frac{\sqrt{5}}{5}\right)\right) \left(\sin^{2}\left(d x +c \right)\right) \sqrt{\frac{2+3 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}{5 d \sqrt{2+3 \cos \left(d x +c \right)}\, \left(-1+\cos \left(d x +c \right)\right) \sqrt{\cos \left(d x +c \right)}}"," ",0,"-1/5/d*10^(1/2)*2^(1/2)*(EllipticF((-1+cos(d*x+c))/sin(d*x+c),1/5*5^(1/2))-2*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,1/5*5^(1/2)))*sin(d*x+c)^2*((2+3*cos(d*x+c))/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)/(2+3*cos(d*x+c))^(1/2)/(-1+cos(d*x+c))/cos(d*x+c)^(1/2)","B"
661,1,132,62,0.182000," ","int(cos(d*x+c)^(1/2)/(-2+3*cos(d*x+c))^(1/2),x)","-\frac{2 \left(\EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{5}\right)-2 \EllipticPi \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, -1, \sqrt{5}\right)\right) \sqrt{\frac{-2+3 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \left(\sin^{2}\left(d x +c \right)\right)}{d \sqrt{-2+3 \cos \left(d x +c \right)}\, \left(-1+\cos \left(d x +c \right)\right) \sqrt{\cos \left(d x +c \right)}}"," ",0,"-2/d*(EllipticF((-1+cos(d*x+c))/sin(d*x+c),5^(1/2))-2*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,5^(1/2)))*((-2+3*cos(d*x+c))/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)/(-2+3*cos(d*x+c))^(1/2)*sin(d*x+c)^2/(-1+cos(d*x+c))/cos(d*x+c)^(1/2)","B"
662,1,144,82,0.192000," ","int(cos(d*x+c)^(1/2)/(2-3*cos(d*x+c))^(1/2),x)","\frac{2 \left(\EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{5}\right)-2 \EllipticPi \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, -1, \sqrt{5}\right)\right) \sqrt{\frac{-2+3 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2-3 \cos \left(d x +c \right)}\, \left(\sin^{2}\left(d x +c \right)\right)}{d \left(3 \left(\cos^{2}\left(d x +c \right)\right)-5 \cos \left(d x +c \right)+2\right) \sqrt{\cos \left(d x +c \right)}}"," ",0,"2/d*(EllipticF((-1+cos(d*x+c))/sin(d*x+c),5^(1/2))-2*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,5^(1/2)))*((-2+3*cos(d*x+c))/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*(2-3*cos(d*x+c))^(1/2)*sin(d*x+c)^2/(3*cos(d*x+c)^2-5*cos(d*x+c)+2)/cos(d*x+c)^(1/2)","A"
663,1,161,85,0.185000," ","int(cos(d*x+c)^(1/2)/(-2-3*cos(d*x+c))^(1/2),x)","\frac{\sqrt{2}\, \sqrt{10}\, \left(\EllipticF \left(\frac{\sqrt{5}\, \left(-1+\cos \left(d x +c \right)\right)}{5 \sin \left(d x +c \right)}, \sqrt{5}\right)-2 \EllipticPi \left(\frac{\sqrt{5}\, \left(-1+\cos \left(d x +c \right)\right)}{5 \sin \left(d x +c \right)}, -5, \sqrt{5}\right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{2+3 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{-2-3 \cos \left(d x +c \right)}\, \left(\sin^{2}\left(d x +c \right)\right) \sqrt{5}}{5 d \left(3 \left(\cos^{2}\left(d x +c \right)\right)-\cos \left(d x +c \right)-2\right) \sqrt{\cos \left(d x +c \right)}}"," ",0,"1/5/d*2^(1/2)*10^(1/2)*(EllipticF(1/5*5^(1/2)*(-1+cos(d*x+c))/sin(d*x+c),5^(1/2))-2*EllipticPi(1/5*5^(1/2)*(-1+cos(d*x+c))/sin(d*x+c),-5,5^(1/2)))*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((2+3*cos(d*x+c))/(1+cos(d*x+c)))^(1/2)*(-2-3*cos(d*x+c))^(1/2)*sin(d*x+c)^2/(3*cos(d*x+c)^2-cos(d*x+c)-2)/cos(d*x+c)^(1/2)*5^(1/2)","A"
664,1,144,66,0.178000," ","int(cos(d*x+c)^(1/2)/(3+2*cos(d*x+c))^(1/2),x)","-\frac{\sqrt{10}\, \sqrt{2}\, \left(\EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \frac{i \sqrt{5}}{5}\right)-2 \EllipticPi \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, -1, \frac{i \sqrt{5}}{5}\right)\right) \sqrt{\frac{3+2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \left(\sin^{2}\left(d x +c \right)\right)}{5 d \sqrt{3+2 \cos \left(d x +c \right)}\, \left(-1+\cos \left(d x +c \right)\right) \sqrt{\cos \left(d x +c \right)}}"," ",0,"-1/5/d*10^(1/2)*2^(1/2)*(EllipticF((-1+cos(d*x+c))/sin(d*x+c),1/5*I*5^(1/2))-2*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,1/5*I*5^(1/2)))*((3+2*cos(d*x+c))/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)/(3+2*cos(d*x+c))^(1/2)*sin(d*x+c)^2/(-1+cos(d*x+c))/cos(d*x+c)^(1/2)","B"
665,1,153,65,0.175000," ","int(cos(d*x+c)^(1/2)/(3-2*cos(d*x+c))^(1/2),x)","\frac{\sqrt{2}\, \left(\EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, i \sqrt{5}\right)-2 \EllipticPi \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, -1, i \sqrt{5}\right)\right) \sqrt{-\frac{2 \left(-3+2 \cos \left(d x +c \right)\right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{3-2 \cos \left(d x +c \right)}\, \left(\sin^{2}\left(d x +c \right)\right)}{d \left(2 \left(\cos^{2}\left(d x +c \right)\right)-5 \cos \left(d x +c \right)+3\right) \sqrt{\cos \left(d x +c \right)}}"," ",0,"1/d*2^(1/2)*(EllipticF((-1+cos(d*x+c))/sin(d*x+c),I*5^(1/2))-2*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,I*5^(1/2)))*(-2*(-3+2*cos(d*x+c))/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*(3-2*cos(d*x+c))^(1/2)*sin(d*x+c)^2/(2*cos(d*x+c)^2-5*cos(d*x+c)+3)/cos(d*x+c)^(1/2)","B"
666,1,158,85,0.179000," ","int(cos(d*x+c)^(1/2)/(-3+2*cos(d*x+c))^(1/2),x)","-\frac{i \sqrt{2}\, \left(2 \EllipticPi \left(\frac{i \left(-1+\cos \left(d x +c \right)\right) \sqrt{5}}{\sin \left(d x +c \right)}, \frac{1}{5}, \frac{i \sqrt{5}}{5}\right)-\EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right) \sqrt{5}}{\sin \left(d x +c \right)}, \frac{i \sqrt{5}}{5}\right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{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)}}\, \left(\sin^{2}\left(d x +c \right)\right) \sqrt{5}}{5 d \sqrt{-3+2 \cos \left(d x +c \right)}\, \left(-1+\cos \left(d x +c \right)\right) \sqrt{\cos \left(d x +c \right)}}"," ",0,"-1/5*I/d*2^(1/2)*(2*EllipticPi(I*(-1+cos(d*x+c))*5^(1/2)/sin(d*x+c),1/5,1/5*I*5^(1/2))-EllipticF(I*(-1+cos(d*x+c))*5^(1/2)/sin(d*x+c),1/5*I*5^(1/2)))*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*(-2*(-3+2*cos(d*x+c))/(1+cos(d*x+c)))^(1/2)/(-3+2*cos(d*x+c))^(1/2)*sin(d*x+c)^2/(-1+cos(d*x+c))/cos(d*x+c)^(1/2)*5^(1/2)","A"
667,1,168,86,0.175000," ","int(cos(d*x+c)^(1/2)/(-3-2*cos(d*x+c))^(1/2),x)","-\frac{i \sqrt{2}\, \sqrt{10}\, \left(\EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right) \sqrt{5}}{5 \sin \left(d x +c \right)}, i \sqrt{5}\right)-2 \EllipticPi \left(\frac{i \left(-1+\cos \left(d x +c \right)\right) \sqrt{5}}{5 \sin \left(d x +c \right)}, 5, i \sqrt{5}\right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{3+2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{-3-2 \cos \left(d x +c \right)}\, \left(\sin^{2}\left(d x +c \right)\right) \sqrt{5}}{5 d \left(2 \left(\cos^{2}\left(d x +c \right)\right)+\cos \left(d x +c \right)-3\right) \sqrt{\cos \left(d x +c \right)}}"," ",0,"-1/5*I/d*2^(1/2)*10^(1/2)*(EllipticF(1/5*I*(-1+cos(d*x+c))*5^(1/2)/sin(d*x+c),I*5^(1/2))-2*EllipticPi(1/5*I*(-1+cos(d*x+c))*5^(1/2)/sin(d*x+c),5,I*5^(1/2)))*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((3+2*cos(d*x+c))/(1+cos(d*x+c)))^(1/2)*(-3-2*cos(d*x+c))^(1/2)*sin(d*x+c)^2/(2*cos(d*x+c)^2+cos(d*x+c)-3)/cos(d*x+c)^(1/2)*5^(1/2)","A"
668,1,159,83,0.171000," ","int((-cos(d*x+c))^(1/2)/(2+3*cos(d*x+c))^(1/2),x)","-\frac{\sqrt{2}\, \sqrt{10}\, \left(\EllipticF \left(\frac{\sqrt{5}\, \left(-1+\cos \left(d x +c \right)\right)}{5 \sin \left(d x +c \right)}, \sqrt{5}\right)-2 \EllipticPi \left(\frac{\sqrt{5}\, \left(-1+\cos \left(d x +c \right)\right)}{5 \sin \left(d x +c \right)}, -5, \sqrt{5}\right)\right) \sqrt{-\cos \left(d x +c \right)}\, \left(\sin^{2}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{2+3 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{5}}{5 d \sqrt{2+3 \cos \left(d x +c \right)}\, \left(-1+\cos \left(d x +c \right)\right) \cos \left(d x +c \right)}"," ",0,"-1/5/d*2^(1/2)*10^(1/2)*(EllipticF(1/5*5^(1/2)*(-1+cos(d*x+c))/sin(d*x+c),5^(1/2))-2*EllipticPi(1/5*5^(1/2)*(-1+cos(d*x+c))/sin(d*x+c),-5,5^(1/2)))/(2+3*cos(d*x+c))^(1/2)*(-cos(d*x+c))^(1/2)*sin(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((2+3*cos(d*x+c))/(1+cos(d*x+c)))^(1/2)/(-1+cos(d*x+c))/cos(d*x+c)*5^(1/2)","A"
669,1,142,80,0.187000," ","int((-cos(d*x+c))^(1/2)/(-2+3*cos(d*x+c))^(1/2),x)","-\frac{2 \left(\EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{5}\right)-2 \EllipticPi \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, -1, \sqrt{5}\right)\right) \left(\sin^{2}\left(d x +c \right)\right) \sqrt{-\cos \left(d x +c \right)}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{-2+3 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}{d \sqrt{-2+3 \cos \left(d x +c \right)}\, \left(-1+\cos \left(d x +c \right)\right) \cos \left(d x +c \right)}"," ",0,"-2/d*(EllipticF((-1+cos(d*x+c))/sin(d*x+c),5^(1/2))-2*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,5^(1/2)))*sin(d*x+c)^2*(-cos(d*x+c))^(1/2)/(-2+3*cos(d*x+c))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((-2+3*cos(d*x+c))/(1+cos(d*x+c)))^(1/2)/(-1+cos(d*x+c))/cos(d*x+c)","A"
670,1,154,64,0.172000," ","int((-cos(d*x+c))^(1/2)/(2-3*cos(d*x+c))^(1/2),x)","\frac{2 \left(\EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{5}\right)-2 \EllipticPi \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, -1, \sqrt{5}\right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{-2+3 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \left(\sin^{2}\left(d x +c \right)\right) \sqrt{-\cos \left(d x +c \right)}\, \sqrt{2-3 \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) \cos \left(d x +c \right)}"," ",0,"2/d*(EllipticF((-1+cos(d*x+c))/sin(d*x+c),5^(1/2))-2*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,5^(1/2)))*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((-2+3*cos(d*x+c))/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)^2*(-cos(d*x+c))^(1/2)*(2-3*cos(d*x+c))^(1/2)/(3*cos(d*x+c)^2-5*cos(d*x+c)+2)/cos(d*x+c)","B"
671,1,164,67,0.184000," ","int((-cos(d*x+c))^(1/2)/(-2-3*cos(d*x+c))^(1/2),x)","\frac{\sqrt{10}\, \sqrt{2}\, \left(\EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \frac{\sqrt{5}}{5}\right)-2 \EllipticPi \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, -1, \frac{\sqrt{5}}{5}\right)\right) \sqrt{\frac{2+3 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{-2-3 \cos \left(d x +c \right)}\, \sqrt{-\cos \left(d x +c \right)}\, \left(\sin^{2}\left(d x +c \right)\right)}{5 d \left(3 \left(\cos^{2}\left(d x +c \right)\right)-\cos \left(d x +c \right)-2\right) \cos \left(d x +c \right)}"," ",0,"1/5/d*10^(1/2)*2^(1/2)*(EllipticF((-1+cos(d*x+c))/sin(d*x+c),1/5*5^(1/2))-2*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,1/5*5^(1/2)))*((2+3*cos(d*x+c))/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*(-2-3*cos(d*x+c))^(1/2)*(-cos(d*x+c))^(1/2)*sin(d*x+c)^2/(3*cos(d*x+c)^2-cos(d*x+c)-2)/cos(d*x+c)","B"
672,1,168,84,0.175000," ","int((-cos(d*x+c))^(1/2)/(3+2*cos(d*x+c))^(1/2),x)","\frac{i \sqrt{2}\, \sqrt{10}\, \left(\EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right) \sqrt{5}}{5 \sin \left(d x +c \right)}, i \sqrt{5}\right)-2 \EllipticPi \left(\frac{i \left(-1+\cos \left(d x +c \right)\right) \sqrt{5}}{5 \sin \left(d x +c \right)}, 5, i \sqrt{5}\right)\right) \sqrt{-\cos \left(d x +c \right)}\, \left(\sin^{2}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{3+2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{5}}{5 d \sqrt{3+2 \cos \left(d x +c \right)}\, \left(-1+\cos \left(d x +c \right)\right) \cos \left(d x +c \right)}"," ",0,"1/5*I/d*2^(1/2)*10^(1/2)*(EllipticF(1/5*I*(-1+cos(d*x+c))*5^(1/2)/sin(d*x+c),I*5^(1/2))-2*EllipticPi(1/5*I*(-1+cos(d*x+c))*5^(1/2)/sin(d*x+c),5,I*5^(1/2)))/(3+2*cos(d*x+c))^(1/2)*(-cos(d*x+c))^(1/2)*sin(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((3+2*cos(d*x+c))/(1+cos(d*x+c)))^(1/2)/(-1+cos(d*x+c))/cos(d*x+c)*5^(1/2)","A"
673,1,180,83,0.171000," ","int((-cos(d*x+c))^(1/2)/(3-2*cos(d*x+c))^(1/2),x)","\frac{i \sqrt{2}\, \left(2 \EllipticPi \left(\frac{i \left(-1+\cos \left(d x +c \right)\right) \sqrt{5}}{\sin \left(d x +c \right)}, \frac{1}{5}, \frac{i \sqrt{5}}{5}\right)-\EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right) \sqrt{5}}{\sin \left(d x +c \right)}, \frac{i \sqrt{5}}{5}\right)\right) \sqrt{3-2 \cos \left(d x +c \right)}\, \sqrt{-\cos \left(d x +c \right)}\, \left(\sin^{2}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{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)}}\, \sqrt{5}}{5 d \left(2 \left(\cos^{2}\left(d x +c \right)\right)-5 \cos \left(d x +c \right)+3\right) \cos \left(d x +c \right)}"," ",0,"1/5*I/d*2^(1/2)*(2*EllipticPi(I*(-1+cos(d*x+c))*5^(1/2)/sin(d*x+c),1/5,1/5*I*5^(1/2))-EllipticF(I*(-1+cos(d*x+c))*5^(1/2)/sin(d*x+c),1/5*I*5^(1/2)))*(3-2*cos(d*x+c))^(1/2)*(-cos(d*x+c))^(1/2)*sin(d*x+c)^2*(cos(d*x+c)/(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)/cos(d*x+c)*5^(1/2)","B"
674,1,152,67,0.171000," ","int((-cos(d*x+c))^(1/2)/(-3+2*cos(d*x+c))^(1/2),x)","-\frac{\sqrt{2}\, \left(\EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, i \sqrt{5}\right)-2 \EllipticPi \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, -1, i \sqrt{5}\right)\right) \sqrt{-\frac{2 \left(-3+2 \cos \left(d x +c \right)\right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{-\cos \left(d x +c \right)}\, \left(\sin^{2}\left(d x +c \right)\right)}{d \sqrt{-3+2 \cos \left(d x +c \right)}\, \left(-1+\cos \left(d x +c \right)\right) \cos \left(d x +c \right)}"," ",0,"-1/d*2^(1/2)*(EllipticF((-1+cos(d*x+c))/sin(d*x+c),I*5^(1/2))-2*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,I*5^(1/2)))*(-2*(-3+2*cos(d*x+c))/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)/(-3+2*cos(d*x+c))^(1/2)*(-cos(d*x+c))^(1/2)*sin(d*x+c)^2/(-1+cos(d*x+c))/cos(d*x+c)","B"
675,1,164,68,0.175000," ","int((-cos(d*x+c))^(1/2)/(-3-2*cos(d*x+c))^(1/2),x)","\frac{\sqrt{10}\, \sqrt{2}\, \left(\EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \frac{i \sqrt{5}}{5}\right)-2 \EllipticPi \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, -1, \frac{i \sqrt{5}}{5}\right)\right) \sqrt{\frac{3+2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{-3-2 \cos \left(d x +c \right)}\, \sqrt{-\cos \left(d x +c \right)}\, \left(\sin^{2}\left(d x +c \right)\right)}{5 d \left(2 \left(\cos^{2}\left(d x +c \right)\right)+\cos \left(d x +c \right)-3\right) \cos \left(d x +c \right)}"," ",0,"1/5/d*10^(1/2)*2^(1/2)*(EllipticF((-1+cos(d*x+c))/sin(d*x+c),1/5*I*5^(1/2))-2*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,1/5*I*5^(1/2)))*((3+2*cos(d*x+c))/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*(-3-2*cos(d*x+c))^(1/2)*(-cos(d*x+c))^(1/2)*sin(d*x+c)^2/(2*cos(d*x+c)^2+cos(d*x+c)-3)/cos(d*x+c)","B"
676,0,0,156,0.087000," ","int(cos(d*x+c)^(2/3)/(a+b*cos(d*x+c)),x)","\int \frac{\cos^{\frac{2}{3}}\left(d x +c \right)}{a +b \cos \left(d x +c \right)}\, dx"," ",0,"int(cos(d*x+c)^(2/3)/(a+b*cos(d*x+c)),x)","F"
677,0,0,156,0.088000," ","int(cos(d*x+c)^(1/3)/(a+b*cos(d*x+c)),x)","\int \frac{\cos^{\frac{1}{3}}\left(d x +c \right)}{a +b \cos \left(d x +c \right)}\, dx"," ",0,"int(cos(d*x+c)^(1/3)/(a+b*cos(d*x+c)),x)","F"
678,0,0,156,0.147000," ","int(1/cos(d*x+c)^(1/3)/(a+b*cos(d*x+c)),x)","\int \frac{1}{\cos \left(d x +c \right)^{\frac{1}{3}} \left(a +b \cos \left(d x +c \right)\right)}\, dx"," ",0,"int(1/cos(d*x+c)^(1/3)/(a+b*cos(d*x+c)),x)","F"
679,0,0,156,0.161000," ","int(1/cos(d*x+c)^(2/3)/(a+b*cos(d*x+c)),x)","\int \frac{1}{\cos \left(d x +c \right)^{\frac{2}{3}} \left(a +b \cos \left(d x +c \right)\right)}\, dx"," ",0,"int(1/cos(d*x+c)^(2/3)/(a+b*cos(d*x+c)),x)","F"
680,0,0,23,0.204000," ","int(cos(d*x+c)^(7/3)/(a+b*cos(d*x+c))^(1/2),x)","\int \frac{\cos^{\frac{7}{3}}\left(d x +c \right)}{\sqrt{a +b \cos \left(d x +c \right)}}\, dx"," ",0,"int(cos(d*x+c)^(7/3)/(a+b*cos(d*x+c))^(1/2),x)","F"
681,0,0,23,0.199000," ","int(cos(d*x+c)^(5/3)/(a+b*cos(d*x+c))^(1/2),x)","\int \frac{\cos^{\frac{5}{3}}\left(d x +c \right)}{\sqrt{a +b \cos \left(d x +c \right)}}\, dx"," ",0,"int(cos(d*x+c)^(5/3)/(a+b*cos(d*x+c))^(1/2),x)","F"
682,0,0,23,0.166000," ","int(cos(d*x+c)^(4/3)/(a+b*cos(d*x+c))^(1/2),x)","\int \frac{\cos^{\frac{4}{3}}\left(d x +c \right)}{\sqrt{a +b \cos \left(d x +c \right)}}\, dx"," ",0,"int(cos(d*x+c)^(4/3)/(a+b*cos(d*x+c))^(1/2),x)","F"
683,0,0,23,0.156000," ","int(cos(d*x+c)^(2/3)/(a+b*cos(d*x+c))^(1/2),x)","\int \frac{\cos^{\frac{2}{3}}\left(d x +c \right)}{\sqrt{a +b \cos \left(d x +c \right)}}\, dx"," ",0,"int(cos(d*x+c)^(2/3)/(a+b*cos(d*x+c))^(1/2),x)","F"
684,0,0,23,0.167000," ","int(cos(d*x+c)^(1/3)/(a+b*cos(d*x+c))^(1/2),x)","\int \frac{\cos^{\frac{1}{3}}\left(d x +c \right)}{\sqrt{a +b \cos \left(d x +c \right)}}\, dx"," ",0,"int(cos(d*x+c)^(1/3)/(a+b*cos(d*x+c))^(1/2),x)","F"
685,0,0,23,0.157000," ","int(1/cos(d*x+c)^(1/3)/(a+b*cos(d*x+c))^(1/2),x)","\int \frac{1}{\cos \left(d x +c \right)^{\frac{1}{3}} \sqrt{a +b \cos \left(d x +c \right)}}\, dx"," ",0,"int(1/cos(d*x+c)^(1/3)/(a+b*cos(d*x+c))^(1/2),x)","F"
686,0,0,23,0.161000," ","int(1/cos(d*x+c)^(2/3)/(a+b*cos(d*x+c))^(1/2),x)","\int \frac{1}{\cos \left(d x +c \right)^{\frac{2}{3}} \sqrt{a +b \cos \left(d x +c \right)}}\, dx"," ",0,"int(1/cos(d*x+c)^(2/3)/(a+b*cos(d*x+c))^(1/2),x)","F"
687,0,0,23,0.151000," ","int(1/cos(d*x+c)^(4/3)/(a+b*cos(d*x+c))^(1/2),x)","\int \frac{1}{\cos \left(d x +c \right)^{\frac{4}{3}} \sqrt{a +b \cos \left(d x +c \right)}}\, dx"," ",0,"int(1/cos(d*x+c)^(4/3)/(a+b*cos(d*x+c))^(1/2),x)","F"
688,0,0,23,0.153000," ","int(1/cos(d*x+c)^(5/3)/(a+b*cos(d*x+c))^(1/2),x)","\int \frac{1}{\cos \left(d x +c \right)^{\frac{5}{3}} \sqrt{a +b \cos \left(d x +c \right)}}\, dx"," ",0,"int(1/cos(d*x+c)^(5/3)/(a+b*cos(d*x+c))^(1/2),x)","F"
689,0,0,23,0.146000," ","int(1/cos(d*x+c)^(7/3)/(a+b*cos(d*x+c))^(1/2),x)","\int \frac{1}{\cos \left(d x +c \right)^{\frac{7}{3}} \sqrt{a +b \cos \left(d x +c \right)}}\, dx"," ",0,"int(1/cos(d*x+c)^(7/3)/(a+b*cos(d*x+c))^(1/2),x)","F"
690,1,502,179,2.184000," ","int((A+B*cos(d*x+c))*sec(d*x+c)^(7/2),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 \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}}+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)\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)*(-2/5*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*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"
691,1,397,159,1.912000," ","int((A+B*cos(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(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) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+6 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) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-12 B \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{4}\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}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+2 A \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-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}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+6 B \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*(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+6*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))*sin(1/2*d*x+1/2*c)^2-12*B*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4-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))+2*A*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2-3*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)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+6*B*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"
692,1,148,139,0.744000," ","int((A+B*cos(d*x+c))*sec(d*x+c)^(3/2),x)","-\frac{2 \left(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}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-2 A \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\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)\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)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-2*A*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^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)))/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
693,1,152,119,0.774000," ","int((A+B*cos(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(A \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-B \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)*(A*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-B*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"
694,1,229,139,0.738000," ","int((A+B*cos(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)}\, \left(-4 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 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}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\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)+2 B \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*B*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4+3*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)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-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))+2*B*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"
695,1,262,159,0.862000," ","int((A+B*cos(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(-24 B \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(20 A +24 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(-10 A -6 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 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 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)\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*B*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6+(20*A+24*B)*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+(-10*A-6*B)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+5*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*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)))/(-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"
696,1,290,179,0.740000," ","int((A+B*cos(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(240 B \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(-168 A -360 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(168 A +280 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(-42 A -80 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)-63 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}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+25 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)\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*B*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^8+(-168*A-360*B)*sin(1/2*d*x+1/2*c)^6*cos(1/2*d*x+1/2*c)+(168*A+280*B)*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+(-42*A-80*B)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)-63*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)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+25*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)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
697,1,689,224,2.776000," ","int((a+b*cos(d*x+c))^2*sec(d*x+c)^(9/2),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 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}}+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)}}{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 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)*(-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*a^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*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"
698,1,660,203,2.471000," ","int((a+b*cos(d*x+c))^2*sec(d*x+c)^(7/2),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(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 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)}+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)*(-2/5*a^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*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)+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"
699,1,514,171,1.935000," ","int((a+b*cos(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(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^{2} \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}}\, b^{2} \left(\sin^{2}\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}}\, 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)-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}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-3 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)-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)+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)\right) \sqrt{-2 \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))*(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+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)*b^2*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)*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-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+12*a*b*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"
700,1,202,150,0.909000," ","int((a+b*cos(d*x+c))^2*sec(d*x+c)^(3/2),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 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)}{\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*a^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"
701,1,283,150,0.806000," ","int((a+b*cos(d*x+c))^2*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(4 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 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}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+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)-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 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)}{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*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4+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))-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*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)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
702,1,321,173,0.784000," ","int((a+b*cos(d*x+c))^2/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(-24 b^{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(40 a b +24 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(-20 a b -6 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)+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)-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}-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) 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*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6+(40*a*b+24*b^2)*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+(-20*a*b-6*b^2)*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))-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^2-9*(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))*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"
703,1,362,203,0.895000," ","int((a+b*cos(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(240 b^{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(-336 a b -360 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(140 a^{2}+336 a b +280 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(-70 a^{2}-84 a b -80 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)+35 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}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+25 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)-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*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^8+(-336*a*b-360*b^2)*sin(1/2*d*x+1/2*c)^6*cos(1/2*d*x+1/2*c)+(140*a^2+336*a*b+280*b^2)*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+(-70*a^2-84*a*b-80*b^2)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+35*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))+25*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","A"
704,1,398,224,1.176000," ","int((a+b*cos(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(-1120 b^{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(1440 a b +2240 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(-504 a^{2}-2160 a b -2072 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(504 a^{2}+1680 a b +952 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(-126 a^{2}-480 a b -168 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)-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) a^{2}-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) b^{2}+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)\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*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^10+(1440*a*b+2240*b^2)*sin(1/2*d*x+1/2*c)^8*cos(1/2*d*x+1/2*c)+(-504*a^2-2160*a*b-2072*b^2)*sin(1/2*d*x+1/2*c)^6*cos(1/2*d*x+1/2*c)+(504*a^2+1680*a*b+952*b^2)*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+(-126*a^2-480*a*b-168*b^2)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)-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^2-147*(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))*b^2+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)))/(-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"
705,1,847,258,3.344000," ","int((a+b*cos(d*x+c))^3*sec(d*x+c)^(9/2),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{6 a^{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}}+\frac{2 b^{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)}+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)+2 a^{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)\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)*(-6/5*a^2*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^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)+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*a^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))))/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
706,1,738,219,2.566000," ","int((a+b*cos(d*x+c))^3*sec(d*x+c)^(7/2),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 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}\, \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 a^{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 b^{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)}{\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)}+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)\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*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+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*a^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*b^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))+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)+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))))/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
707,1,631,194,2.233000," ","int((a+b*cos(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(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^{3} \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{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^{2} \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{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} 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{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^{3} \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-36 a^{2} b \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 \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 +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)+18 a^{2} b \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*(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^3*sin(1/2*d*x+1/2*c)^2+18*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^2*sin(1/2*d*x+1/2*c)^2+18*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*b*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)*b^3*sin(1/2*d*x+1/2*c)^2-36*a^2*b*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+18*a^2*b*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"
708,1,303,200,0.955000," ","int((a+b*cos(d*x+c))^3*sec(d*x+c)^(3/2),x)","-\frac{2 \left(4 b^{3} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\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}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+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)+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^{3}-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 \,b^{2}-6 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)-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)}{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*b^3*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4+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))+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^2-6*a^3*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)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
709,1,376,190,1.094000," ","int((a+b*cos(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(-8 b^{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(20 b^{2} a +8 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(-10 b^{2} a -2 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)+5 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)+5 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)-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 -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}\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*b^3*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6+(20*a*b^2+8*b^3)*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+(-10*a*b^2-2*b^3)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+5*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))+5*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))-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-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*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"
710,1,421,227,0.928000," ","int((a+b*cos(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(240 b^{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(-504 b^{2} a -360 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(420 a^{2} b +504 b^{2} a +280 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(-210 a^{2} b -126 b^{2} a -80 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)+105 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}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+25 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)-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) a^{3}-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) a \,b^{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)}\, \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*b^3*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^8+(-504*a*b^2-360*b^3)*sin(1/2*d*x+1/2*c)^6*cos(1/2*d*x+1/2*c)+(420*a^2*b+504*a*b^2+280*b^3)*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+(-210*a^2*b-126*a*b^2-80*b^3)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+105*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))+25*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))-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))*a^3-189*(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*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"
711,1,470,258,1.018000," ","int((a+b*cos(d*x+c))^3/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(-1120 b^{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(2160 b^{2} a +2240 b^{3}\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(-1512 a^{2} b -3240 b^{2} a -2072 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(420 a^{3}+1512 a^{2} b +2520 b^{2} a +952 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(-210 a^{3}-378 a^{2} b -720 b^{2} a -168 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)+105 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)+225 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)-567 \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 -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) b^{3}\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*b^3*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^10+(2160*a*b^2+2240*b^3)*sin(1/2*d*x+1/2*c)^8*cos(1/2*d*x+1/2*c)+(-1512*a^2*b-3240*a*b^2-2072*b^3)*sin(1/2*d*x+1/2*c)^6*cos(1/2*d*x+1/2*c)+(420*a^3+1512*a^2*b+2520*a*b^2+952*b^3)*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+(-210*a^3-378*a^2*b-720*a*b^2-168*b^3)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+105*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))+225*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))-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^2*b-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))*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"
712,1,452,246,2.224000," ","int(sec(d*x+c)^(5/2)/(a+b*cos(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{4 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 b}{a -b}, \sqrt{2}\right)}{a^{2} \left(-2 a b +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{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)}{a^{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)}}}{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)*(-4*b^3/a^2/(-2*a*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)*EllipticPi(cos(1/2*d*x+1/2*c),-2*b/(a-b),2^(1/2))-2/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)+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))))/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
713,1,354,159,1.051000," ","int(sec(d*x+c)^(3/2)/(a+b*cos(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)-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}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), -\frac{2 b}{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)}{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*(-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-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)*EllipticPi(cos(1/2*d*x+1/2*c),-2*b/(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)/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","B"
714,1,150,71,0.828000," ","int(sec(d*x+c)^(1/2)/(a+b*cos(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 b}{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*b/(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"
715,1,188,137,0.902000," ","int(1/(a+b*cos(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 -\EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) b -a \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), -\frac{2 b}{a -b}, \sqrt{2}\right)\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)}\, \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-EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*b-a*EllipticPi(cos(1/2*d*x+1/2*c),-2*b/(a-b),2^(1/2)))/(a-b)/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"
716,1,227,201,1.203000," ","int(1/(a+b*cos(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)}\, \sqrt{\frac{1}{2}-\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^{2}-\EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a b +\EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a b -\EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) b^{2}-a^{2} \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), -\frac{2 b}{a -b}, \sqrt{2}\right)\right)}{b^{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^2-EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*a*b+EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a*b-EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*b^2-a^2*EllipticPi(cos(1/2*d*x+1/2*c),-2*b/(a-b),2^(1/2)))/b^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"
717,1,516,232,1.026000," ","int(1/(a+b*cos(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(\left(4 b^{2} a -4 b^{3}\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 b^{2} a +2 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)+3 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)-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}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+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)-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)+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^{2} 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}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a \,b^{2}-3 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}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), -\frac{2 b}{a -b}, \sqrt{2}\right)\right)}{3 b^{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*b^2-4*b^3)*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4+(-2*a*b^2+2*b^3)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+3*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))-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)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+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))-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*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)*EllipticPi(cos(1/2*d*x+1/2*c),-2*b/(a-b),2^(1/2)))/b^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"
718,1,1008,397,3.864000," ","int(sec(d*x+c)^(5/2)/(a+b*cos(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{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 b}{a -b}, \sqrt{2}\right)}{a^{3} \left(-2 a b +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{4 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)}{a^{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{-\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)}}}{a^{2}}+\frac{2 b^{2} \left(-\frac{b^{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)}}{a \left(a^{2}-b^{2}\right) \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +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) 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)}}-\frac{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)}{2 a \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{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}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{2 a \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 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 b}{a -b}, \sqrt{2}\right)}{\left(a^{2}-b^{2}\right) \left(-2 a b +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{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 b}{a -b}, \sqrt{2}\right)}{a \left(a^{2}-b^{2}\right) \left(-2 a b +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)}}\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)*(-8*b^3/a^3/(-2*a*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)*EllipticPi(cos(1/2*d*x+1/2*c),-2*b/(a-b),2^(1/2))-4/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)+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)))+2*b^2/a^2*(-b^2/a/(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*cos(1/2*d*x+1/2*c)^2*b+a-b)-1/2/(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)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-1/2*b/a/(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*b/a/(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))-3*a/(a^2-b^2)/(-2*a*b+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)*EllipticPi(cos(1/2*d*x+1/2*c),-2*b/(a-b),2^(1/2))+1/a/(a^2-b^2)/(-2*a*b+2*b^2)*b^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*b/(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"
719,1,874,339,2.563000," ","int(sec(d*x+c)^(3/2)/(a+b*cos(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 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 b}{a -b}, \sqrt{2}\right)}{a^{2} \left(-2 a b +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{-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)}{a^{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 b \left(-\frac{b^{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)}}{a \left(a^{2}-b^{2}\right) \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +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) 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)}}-\frac{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)}{2 a \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{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}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{2 a \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 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 b}{a -b}, \sqrt{2}\right)}{\left(a^{2}-b^{2}\right) \left(-2 a b +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{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 b}{a -b}, \sqrt{2}\right)}{a \left(a^{2}-b^{2}\right) \left(-2 a b +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)}}\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)*(4/a^2*b^2/(-2*a*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)*EllipticPi(cos(1/2*d*x+1/2*c),-2*b/(a-b),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/a*b*(-b^2/a/(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*cos(1/2*d*x+1/2*c)^2*b+a-b)-1/2/(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)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-1/2*b/a/(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*b/a/(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))-3*a/(a^2-b^2)/(-2*a*b+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)*EllipticPi(cos(1/2*d*x+1/2*c),-2*b/(a-b),2^(1/2))+1/a/(a^2-b^2)/(-2*a*b+2*b^2)*b^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*b/(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"
720,1,612,281,1.681000," ","int(sec(d*x+c)^(1/2)/(a+b*cos(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 b^{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)}}{a \left(a^{2}-b^{2}\right) \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +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) 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)}}-\frac{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)}{a \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{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}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{a \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{6 a 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 b}{a -b}, \sqrt{2}\right)}{\left(a^{2}-b^{2}\right) \left(-2 a b +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{2 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 b}{a -b}, \sqrt{2}\right)}{a \left(a^{2}-b^{2}\right) \left(-2 a b +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)}}\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/(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*cos(1/2*d*x+1/2*c)^2*b+a-b)-1/(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)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-b/a/(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))+b/a/(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))-6*a/(a^2-b^2)/(-2*a*b+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)*EllipticPi(cos(1/2*d*x+1/2*c),-2*b/(a-b),2^(1/2))+2/a/(a^2-b^2)/(-2*a*b+2*b^2)*b^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*b/(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"
721,1,713,272,2.306000," ","int(1/(a+b*cos(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{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}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), -\frac{2 b}{a -b}, \sqrt{2}\right)}{\left(-2 a b +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{2 a \left(-\frac{b^{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)}}{a \left(a^{2}-b^{2}\right) \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +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) 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)}}-\frac{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)}{2 a \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{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}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{2 a \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 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 b}{a -b}, \sqrt{2}\right)}{\left(a^{2}-b^{2}\right) \left(-2 a b +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{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 b}{a -b}, \sqrt{2}\right)}{a \left(a^{2}-b^{2}\right) \left(-2 a b +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)}}\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)*(-4/(-2*a*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)*EllipticPi(cos(1/2*d*x+1/2*c),-2*b/(a-b),2^(1/2))-2/b*a*(-b^2/a/(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*cos(1/2*d*x+1/2*c)^2*b+a-b)-1/2/(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)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-1/2*b/a/(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*b/a/(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))-3*a/(a^2-b^2)/(-2*a*b+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)*EllipticPi(cos(1/2*d*x+1/2*c),-2*b/(a-b),2^(1/2))+1/a/(a^2-b^2)/(-2*a*b+2*b^2)*b^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*b/(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"
722,1,794,287,1.972000," ","int(1/(a+b*cos(d*x+c))^2/sec(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 \sqrt{\frac{1}{2}-\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^{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{8 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 b}{a -b}, \sqrt{2}\right)}{b \left(-2 a b +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{2 a^{2} \left(-\frac{b^{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)}}{a \left(a^{2}-b^{2}\right) \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +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) 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)}}-\frac{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)}{2 a \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{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}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{2 a \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 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 b}{a -b}, \sqrt{2}\right)}{\left(a^{2}-b^{2}\right) \left(-2 a b +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{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 b}{a -b}, \sqrt{2}\right)}{a \left(a^{2}-b^{2}\right) \left(-2 a b +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)}}\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)*(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))+8/b*a/(-2*a*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)*EllipticPi(cos(1/2*d*x+1/2*c),-2*b/(a-b),2^(1/2))+2/b^2*a^2*(-b^2/a/(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*cos(1/2*d*x+1/2*c)^2*b+a-b)-1/2/(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)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-1/2*b/a/(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*b/a/(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))-3*a/(a^2-b^2)/(-2*a*b+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)*EllipticPi(cos(1/2*d*x+1/2*c),-2*b/(a-b),2^(1/2))+1/a/(a^2-b^2)/(-2*a*b+2*b^2)*b^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*b/(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"
723,1,815,309,2.402000," ","int(1/(a+b*cos(d*x+c))^2/sec(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(-\frac{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}}\, \left(2 \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) b \right)}{b^{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{12 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 b}{a -b}, \sqrt{2}\right)}{b^{2} \left(-2 a b +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{2 a^{3} \left(-\frac{b^{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)}}{a \left(a^{2}-b^{2}\right) \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +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) 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)}}-\frac{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)}{2 a \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{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}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{2 a \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 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 b}{a -b}, \sqrt{2}\right)}{\left(a^{2}-b^{2}\right) \left(-2 a b +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{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 b}{a -b}, \sqrt{2}\right)}{a \left(a^{2}-b^{2}\right) \left(-2 a b +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)}}\right)}{b^{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/b^3/(-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)*(2*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))*b)-12*a^2/b^2/(-2*a*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)*EllipticPi(cos(1/2*d*x+1/2*c),-2*b/(a-b),2^(1/2))-2/b^3*a^3*(-b^2/a/(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*cos(1/2*d*x+1/2*c)^2*b+a-b)-1/2/(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)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-1/2*b/a/(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*b/a/(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))-3*a/(a^2-b^2)/(-2*a*b+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)*EllipticPi(cos(1/2*d*x+1/2*c),-2*b/(a-b),2^(1/2))+1/a/(a^2-b^2)/(-2*a*b+2*b^2)*b^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*b/(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"
724,1,2128,499,5.951000," ","int(sec(d*x+c)^(5/2)/(a+b*cos(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*b^2/a^2*(-1/2*b^2/a/(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*cos(1/2*d*x+1/2*c)^2*b+a-b)^2-3/4*b^2*(3*a^2-b^2)/a^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*cos(1/2*d*x+1/2*c)^2*b+a-b)-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))+1/4/(a+b)/(a^2-b^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))*b+3/8/(a+b)/(a^2-b^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))*b^2-9/8*b/(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*b^3/a^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*b/(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*b^3/a^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))-15/4*a^2/(a^2-b^2)^2/(-2*a*b+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)*EllipticPi(cos(1/2*d*x+1/2*c),-2*b/(a-b),2^(1/2))+3/2/(a^2-b^2)^2/(-2*a*b+2*b^2)*b^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*b/(a-b),2^(1/2))-3/4/a^2/(a^2-b^2)^2/(-2*a*b+2*b^2)*b^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*b/(a-b),2^(1/2)))-12*b^3/a^4/(-2*a*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)*EllipticPi(cos(1/2*d*x+1/2*c),-2*b/(a-b),2^(1/2))-6/a^4*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)+2/a^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)))+4*b^2/a^3*(-b^2/a/(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*cos(1/2*d*x+1/2*c)^2*b+a-b)-1/2/(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)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-1/2*b/a/(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*b/a/(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))-3*a/(a^2-b^2)/(-2*a*b+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)*EllipticPi(cos(1/2*d*x+1/2*c),-2*b/(a-b),2^(1/2))+1/a/(a^2-b^2)/(-2*a*b+2*b^2)*b^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*b/(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"
725,1,1992,436,4.537000," ","int(sec(d*x+c)^(3/2)/(a+b*cos(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*b*(-1/2*b^2/a/(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*cos(1/2*d*x+1/2*c)^2*b+a-b)^2-3/4*b^2*(3*a^2-b^2)/a^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*cos(1/2*d*x+1/2*c)^2*b+a-b)-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))+1/4/(a+b)/(a^2-b^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))*b+3/8/(a+b)/(a^2-b^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))*b^2-9/8*b/(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*b^3/a^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*b/(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*b^3/a^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))-15/4*a^2/(a^2-b^2)^2/(-2*a*b+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)*EllipticPi(cos(1/2*d*x+1/2*c),-2*b/(a-b),2^(1/2))+3/2/(a^2-b^2)^2/(-2*a*b+2*b^2)*b^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*b/(a-b),2^(1/2))-3/4/a^2/(a^2-b^2)^2/(-2*a*b+2*b^2)*b^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*b/(a-b),2^(1/2)))+4*b^2/a^3/(-2*a*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)*EllipticPi(cos(1/2*d*x+1/2*c),-2*b/(a-b),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)-2/a^2*b*(-b^2/a/(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*cos(1/2*d*x+1/2*c)^2*b+a-b)-1/2/(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)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-1/2*b/a/(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*b/a/(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))-3*a/(a^2-b^2)/(-2*a*b+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)*EllipticPi(cos(1/2*d*x+1/2*c),-2*b/(a-b),2^(1/2))+1/a/(a^2-b^2)/(-2*a*b+2*b^2)*b^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*b/(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"
726,1,1176,373,2.151000," ","int(sec(d*x+c)^(1/2)/(a+b*cos(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{b^{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)}}{a \left(a^{2}-b^{2}\right) \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b \right)^{2}}-\frac{3 b^{2} \left(3 a^{2}-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 a^{2} \left(a^{2}-b^{2}\right)^{2} \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b \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{\sqrt{\frac{1}{2}-\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}{2 \left(a +b \right) \left(a^{2}-b^{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)}}+\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) b^{2}}{4 \left(a +b \right) \left(a^{2}-b^{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{9 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)}{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 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}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{4 a^{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 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}\, \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 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}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{4 a^{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{15 a^{2} 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 b}{a -b}, \sqrt{2}\right)}{2 \left(a^{2}-b^{2}\right)^{2} \left(-2 a b +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 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 b}{a -b}, \sqrt{2}\right)}{\left(a^{2}-b^{2}\right)^{2} \left(-2 a b +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 b^{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 b}{a -b}, \sqrt{2}\right)}{2 a^{2} \left(a^{2}-b^{2}\right)^{2} \left(-2 a b +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)}}\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)*(-b^2/a/(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*cos(1/2*d*x+1/2*c)^2*b+a-b)^2-3/2*b^2*(3*a^2-b^2)/a^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*cos(1/2*d*x+1/2*c)^2*b+a-b)-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))+1/2/(a+b)/(a^2-b^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))*b+3/4/(a+b)/(a^2-b^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))*b^2-9/4*b/(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*b^3/a^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*b/(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*b^3/a^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))-15/2*a^2/(a^2-b^2)^2/(-2*a*b+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)*EllipticPi(cos(1/2*d*x+1/2*c),-2*b/(a-b),2^(1/2))+3/(a^2-b^2)^2/(-2*a*b+2*b^2)*b^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*b/(a-b),2^(1/2))-3/2/a^2/(a^2-b^2)^2/(-2*a*b+2*b^2)*b^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*b/(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"
727,1,1736,369,3.828000," ","int(1/(a+b*cos(d*x+c))^3/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 \left(-\frac{b^{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 a \left(a^{2}-b^{2}\right) \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b \right)^{2}}-\frac{3 b^{2} \left(3 a^{2}-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 a^{2} \left(a^{2}-b^{2}\right)^{2} \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b \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{\sqrt{\frac{1}{2}-\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}{4 \left(a +b \right) \left(a^{2}-b^{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)}}+\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) b^{2}}{8 \left(a +b \right) \left(a^{2}-b^{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{9 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)}{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 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}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{8 a^{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 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}\, \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 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}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{8 a^{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{15 a^{2} 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 b}{a -b}, \sqrt{2}\right)}{4 \left(a^{2}-b^{2}\right)^{2} \left(-2 a b +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 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 b}{a -b}, \sqrt{2}\right)}{2 \left(a^{2}-b^{2}\right)^{2} \left(-2 a b +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 b^{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 b}{a -b}, \sqrt{2}\right)}{4 a^{2} \left(a^{2}-b^{2}\right)^{2} \left(-2 a b +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)}}\right)}{b}+\frac{-\frac{2 b^{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)}}{a \left(a^{2}-b^{2}\right) \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +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) 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)}}-\frac{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)}{a \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{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}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{a \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{6 a 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 b}{a -b}, \sqrt{2}\right)}{\left(a^{2}-b^{2}\right) \left(-2 a b +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{2 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 b}{a -b}, \sqrt{2}\right)}{a \left(a^{2}-b^{2}\right) \left(-2 a b +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)}}}{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*a*(-1/2*b^2/a/(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*cos(1/2*d*x+1/2*c)^2*b+a-b)^2-3/4*b^2*(3*a^2-b^2)/a^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*cos(1/2*d*x+1/2*c)^2*b+a-b)-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))+1/4/(a+b)/(a^2-b^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))*b+3/8/(a+b)/(a^2-b^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))*b^2-9/8*b/(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*b^3/a^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*b/(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*b^3/a^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))-15/4*a^2/(a^2-b^2)^2/(-2*a*b+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)*EllipticPi(cos(1/2*d*x+1/2*c),-2*b/(a-b),2^(1/2))+3/2/(a^2-b^2)^2/(-2*a*b+2*b^2)*b^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*b/(a-b),2^(1/2))-3/4/a^2/(a^2-b^2)^2/(-2*a*b+2*b^2)*b^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*b/(a-b),2^(1/2)))+2/b*(-b^2/a/(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*cos(1/2*d*x+1/2*c)^2*b+a-b)-1/2/(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)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-1/2*b/a/(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*b/a/(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))-3*a/(a^2-b^2)/(-2*a*b+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)*EllipticPi(cos(1/2*d*x+1/2*c),-2*b/(a-b),2^(1/2))+1/a/(a^2-b^2)/(-2*a*b+2*b^2)*b^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*b/(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"
728,1,1836,354,3.508000," ","int(1/(a+b*cos(d*x+c))^3/sec(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(-\frac{b^{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 a \left(a^{2}-b^{2}\right) \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b \right)^{2}}-\frac{3 b^{2} \left(3 a^{2}-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 a^{2} \left(a^{2}-b^{2}\right)^{2} \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b \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{\sqrt{\frac{1}{2}-\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}{4 \left(a +b \right) \left(a^{2}-b^{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)}}+\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) b^{2}}{8 \left(a +b \right) \left(a^{2}-b^{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{9 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)}{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 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}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{8 a^{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 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}\, \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 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}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{8 a^{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{15 a^{2} 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 b}{a -b}, \sqrt{2}\right)}{4 \left(a^{2}-b^{2}\right)^{2} \left(-2 a b +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 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 b}{a -b}, \sqrt{2}\right)}{2 \left(a^{2}-b^{2}\right)^{2} \left(-2 a b +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 b^{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 b}{a -b}, \sqrt{2}\right)}{4 a^{2} \left(a^{2}-b^{2}\right)^{2} \left(-2 a b +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)}}\right)}{b^{2}}-\frac{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}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), -\frac{2 b}{a -b}, \sqrt{2}\right)}{b \left(-2 a b +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{4 a \left(-\frac{b^{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)}}{a \left(a^{2}-b^{2}\right) \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +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) 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)}}-\frac{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)}{2 a \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{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}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{2 a \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 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 b}{a -b}, \sqrt{2}\right)}{\left(a^{2}-b^{2}\right) \left(-2 a b +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{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 b}{a -b}, \sqrt{2}\right)}{a \left(a^{2}-b^{2}\right) \left(-2 a b +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)}}\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)*(2/b^2*a^2*(-1/2*b^2/a/(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*cos(1/2*d*x+1/2*c)^2*b+a-b)^2-3/4*b^2*(3*a^2-b^2)/a^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*cos(1/2*d*x+1/2*c)^2*b+a-b)-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))+1/4/(a+b)/(a^2-b^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))*b+3/8/(a+b)/(a^2-b^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))*b^2-9/8*b/(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*b^3/a^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*b/(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*b^3/a^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))-15/4*a^2/(a^2-b^2)^2/(-2*a*b+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)*EllipticPi(cos(1/2*d*x+1/2*c),-2*b/(a-b),2^(1/2))+3/2/(a^2-b^2)^2/(-2*a*b+2*b^2)*b^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*b/(a-b),2^(1/2))-3/4/a^2/(a^2-b^2)^2/(-2*a*b+2*b^2)*b^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*b/(a-b),2^(1/2)))-4/b/(-2*a*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)*EllipticPi(cos(1/2*d*x+1/2*c),-2*b/(a-b),2^(1/2))-4/b^2*a*(-b^2/a/(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*cos(1/2*d*x+1/2*c)^2*b+a-b)-1/2/(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)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-1/2*b/a/(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*b/a/(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))-3*a/(a^2-b^2)/(-2*a*b+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)*EllipticPi(cos(1/2*d*x+1/2*c),-2*b/(a-b),2^(1/2))+1/a/(a^2-b^2)/(-2*a*b+2*b^2)*b^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*b/(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"
729,1,1914,371,3.459000," ","int(1/(a+b*cos(d*x+c))^3/sec(d*x+c)^(5/2),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/b^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^3*a^3*(-1/2*b^2/a/(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*cos(1/2*d*x+1/2*c)^2*b+a-b)^2-3/4*b^2*(3*a^2-b^2)/a^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*cos(1/2*d*x+1/2*c)^2*b+a-b)-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))+1/4/(a+b)/(a^2-b^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))*b+3/8/(a+b)/(a^2-b^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))*b^2-9/8*b/(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*b^3/a^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*b/(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*b^3/a^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))-15/4*a^2/(a^2-b^2)^2/(-2*a*b+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)*EllipticPi(cos(1/2*d*x+1/2*c),-2*b/(a-b),2^(1/2))+3/2/(a^2-b^2)^2/(-2*a*b+2*b^2)*b^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*b/(a-b),2^(1/2))-3/4/a^2/(a^2-b^2)^2/(-2*a*b+2*b^2)*b^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*b/(a-b),2^(1/2)))+12/b^2*a/(-2*a*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)*EllipticPi(cos(1/2*d*x+1/2*c),-2*b/(a-b),2^(1/2))+6/b^3*a^2*(-b^2/a/(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*cos(1/2*d*x+1/2*c)^2*b+a-b)-1/2/(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)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-1/2*b/a/(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*b/a/(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))-3*a/(a^2-b^2)/(-2*a*b+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)*EllipticPi(cos(1/2*d*x+1/2*c),-2*b/(a-b),2^(1/2))+1/a/(a^2-b^2)/(-2*a*b+2*b^2)*b^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*b/(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"
730,1,1563,329,0.246000," ","int(sec(d*x+c)^(7/2)*(a+b*cos(d*x+c))^(1/2),x)","-\frac{2 \left(-3 a^{3}-9 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}-9 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}+\left(\cos^{2}\left(d x +c \right)\right) a \,b^{2}-4 \cos \left(d x +c \right) a^{2} b -2 \left(\cos^{4}\left(d x +c \right)\right) b^{3}+2 \left(\cos^{3}\left(d x +c \right)\right) b^{3}-6 \left(\cos^{2}\left(d x +c \right)\right) a^{3}+9 \left(\cos^{3}\left(d x +c \right)\right) a^{3}+7 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 +9 \left(\cos^{4}\left(d x +c \right)\right) a^{2} b -5 \left(\cos^{3}\left(d x +c \right)\right) a^{2} b -2 \left(\cos^{3}\left(d x +c \right)\right) a \,b^{2}+\left(\cos^{4}\left(d x +c \right)\right) a \,b^{2}-9 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}+9 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}+9 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}\right) \cos \left(d x +c \right) \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{7}{2}}}{15 d \sqrt{a +b \cos \left(d x +c \right)}\, \sin \left(d x +c \right) a^{2}}"," ",0,"-2/15/d*(cos(d*x+c)^2*a*b^2-9*cos(d*x+c)^3*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^3-3*a^3+2*cos(d*x+c)^3*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*cos(d*x+c)^3*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*cos(d*x+c)^3*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^2-9*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*cos(d*x+c)^4*b^3+9*cos(d*x+c)^3*a^3-4*cos(d*x+c)*a^2*b+9*cos(d*x+c)^4*a^2*b+cos(d*x+c)^4*a*b^2-5*cos(d*x+c)^3*a^2*b-2*cos(d*x+c)^3*a*b^2+2*cos(d*x+c)^3*b^3-6*cos(d*x+c)^2*a^3-9*cos(d*x+c)^3*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*cos(d*x+c)^3*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+9*cos(d*x+c)^3*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+9*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)*cos(d*x+c)*(1/cos(d*x+c))^(7/2)/(a+b*cos(d*x+c))^(1/2)/sin(d*x+c)/a^2","B"
731,1,888,277,0.286000," ","int(sec(d*x+c)^(5/2)*(a+b*cos(d*x+c))^(1/2),x)","-\frac{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) \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, a^{2}+\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) a b -\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \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) \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, b^{2}+\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) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 -\cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) a b +\left(\cos^{3}\left(d x +c \right)\right) 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)-a^{2}\right) \cos \left(d x +c \right) \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{5}{2}}}{3 d \sqrt{a +b \cos \left(d x +c \right)}\, \sin \left(d x +c \right) a}"," ",0,"-2/3/d*(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)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^2+(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^2*sin(d*x+c)*a*b-(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^2*sin(d*x+c)*a*b-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)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*b^2+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)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^2+cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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-cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*b^2+cos(d*x+c)^3*a*b+cos(d*x+c)^3*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)-a^2)*cos(d*x+c)*(1/cos(d*x+c))^(5/2)/(a+b*cos(d*x+c))^(1/2)/sin(d*x+c)/a","B"
732,1,797,245,0.254000," ","int(sec(d*x+c)^(3/2)*(a+b*cos(d*x+c))^(1/2),x)","-\frac{2 \left(\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \sin \left(d x +c \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) \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, b -\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \sin \left(d x +c \right) a -\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \sin \left(d x +c \right) b +\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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{a +b \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{a +b \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{a +b \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) b +a \cos \left(d x +c \right)-b \cos \left(d x +c \right)-a \right) \cos \left(d x +c \right) \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}}}{d \sqrt{a +b \cos \left(d x +c \right)}\, \sin \left(d x +c \right)}"," ",0,"-2/d*((cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)*sin(d*x+c)*a+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)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*b-(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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-(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)*b+(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)*((a+b*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)*((a+b*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)*((a+b*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*b+a*cos(d*x+c)-b*cos(d*x+c)-a)*cos(d*x+c)*(1/cos(d*x+c))^(3/2)/(a+b*cos(d*x+c))^(1/2)/sin(d*x+c)","B"
733,1,199,139,0.238000," ","int((a+b*cos(d*x+c))^(1/2)*sec(d*x+c)^(1/2),x)","\frac{2 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \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) 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 b \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) \sqrt{\frac{1}{\cos \left(d x +c \right)}}\, \left(\sin^{2}\left(d x +c \right)\right)}{d \sqrt{a +b \cos \left(d x +c \right)}\, \left(-1+\cos \left(d x +c \right)\right)}"," ",0,"2/d*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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-EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*b+2*b*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,(-(a-b)/(a+b))^(1/2)))/(a+b*cos(d*x+c))^(1/2)*(1/cos(d*x+c))^(1/2)*sin(d*x+c)^2/(-1+cos(d*x+c))","A"
734,1,803,391,0.345000," ","int((a+b*cos(d*x+c))^(1/2)/sec(d*x+c)^(1/2),x)","-\frac{\left(-2 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \sin \left(d x +c \right) a +\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \sin \left(d x +c \right) a +\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \sin \left(d x +c \right) b +2 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \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{a +b \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{a +b \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{a +b \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)+2 a \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \sin \left(d x +c \right)+\left(\cos^{3}\left(d x +c \right)\right) b +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)\right) \sqrt{\frac{1}{\cos \left(d x +c \right)}}}{d \sin \left(d x +c \right) \sqrt{a +b \cos \left(d x +c \right)}}"," ",0,"-1/d*(-2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)*sin(d*x+c)*a+(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)*b+2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)*sin(d*x+c)*a-2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)*((a+b*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)*((a+b*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)+2*a*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)+cos(d*x+c)^3*b+a*cos(d*x+c)^2-cos(d*x+c)^2*b-a*cos(d*x+c))*(1/cos(d*x+c))^(1/2)/sin(d*x+c)/(a+b*cos(d*x+c))^(1/2)","B"
735,1,1241,444,0.274000," ","int((a+b*cos(d*x+c))^(1/2)/sec(d*x+c)^(3/2),x)","-\frac{\left(-2 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}+8 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}+2 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 -4 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}+\cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}+\cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 \left(\cos^{4}\left(d x +c \right)\right) b^{2}-2 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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} \sin \left(d x +c \right)+8 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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)-4 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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{a +b \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)+\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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)+3 \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 -2 \left(\cos^{2}\left(d x +c \right)\right) b^{2}-a^{2} \cos \left(d x +c \right)-2 a b \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}}}{4 d \sin \left(d x +c \right) \sqrt{a +b \cos \left(d x +c \right)}\, b}"," ",0,"-1/4/d*(-2*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+8*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+2*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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-4*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*cos(d*x+c)^4*b^2-2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*sin(d*x+c)+8*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)/(1+cos(d*x+c)))^(1/2)*((a+b*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)-4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)*((a+b*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)/(1+cos(d*x+c)))^(1/2)*((a+b*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)+3*cos(d*x+c)^3*a*b+cos(d*x+c)^2*a^2-cos(d*x+c)^2*a*b-2*cos(d*x+c)^2*b^2-a^2*cos(d*x+c)-2*a*b*cos(d*x+c))*cos(d*x+c)*(1/cos(d*x+c))^(3/2)/sin(d*x+c)/(a+b*cos(d*x+c))^(1/2)/b","B"
736,1,1835,381,0.293000," ","int((a+b*cos(d*x+c))^(3/2)*sec(d*x+c)^(9/2),x)","-\frac{2 \left(-15 a^{4}-68 \left(\cos^{3}\left(d x +c \right)\right) a^{3} b -55 \left(\cos^{4}\left(d x +c \right)\right) a^{2} b^{2}+3 \left(\cos^{5}\left(d x +c \right)\right) a \,b^{3}+3 \left(\cos^{3}\left(d x +c \right)\right) a \,b^{3}-6 \left(\cos^{4}\left(d x +c \right)\right) a \,b^{3}+82 \left(\cos^{5}\left(d x +c \right)\right) a^{2} b^{2}+82 \left(\cos^{4}\left(d x +c \right)\right) a^{3} b +82 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) a^{3} b +51 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) a^{2} b^{2}-6 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) a \,b^{3}-82 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) a^{3} b -82 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) a^{2} b^{2}+6 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) a \,b^{3}+25 \left(\cos^{5}\left(d x +c \right)\right) a^{3} b -39 \cos \left(d x +c \right) a^{3} b +82 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \left(\cos^{4}\left(d x +c \right)\right) \sin \left(d x +c \right) a^{3} b +51 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \left(\cos^{4}\left(d x +c \right)\right) \sin \left(d x +c \right) a^{2} b^{2}-6 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \left(\cos^{4}\left(d x +c \right)\right) \sin \left(d x +c \right) a \,b^{3}-82 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \left(\cos^{4}\left(d x +c \right)\right) \sin \left(d x +c \right) a^{3} b -82 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \left(\cos^{4}\left(d x +c \right)\right) \sin \left(d x +c \right) a^{2} b^{2}-10 \left(\cos^{2}\left(d x +c \right)\right) a^{4}-6 \left(\cos^{5}\left(d x +c \right)\right) b^{4}+6 \left(\cos^{4}\left(d x +c \right)\right) b^{4}+25 \left(\cos^{4}\left(d x +c \right)\right) a^{4}+25 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \left(\cos^{4}\left(d x +c \right)\right) \sin \left(d x +c \right) a^{4}+6 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \left(\cos^{4}\left(d x +c \right)\right) \sin \left(d x +c \right) b^{4}+25 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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^{4}+6 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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^{4}-27 \left(\cos^{2}\left(d x +c \right)\right) a^{2} b^{2}+6 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \left(\cos^{4}\left(d x +c \right)\right) \sin \left(d x +c \right) a \,b^{3}\right) \cos \left(d x +c \right) \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{9}{2}}}{105 d \sqrt{a +b \cos \left(d x +c \right)}\, \sin \left(d x +c \right) a^{2}}"," ",0,"-2/105/d*(25*cos(d*x+c)^5*a^3*b+25*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^4*sin(d*x+c)*a^4-15*a^4+82*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^4*sin(d*x+c)*a^3*b+51*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^4*sin(d*x+c)*a^2*b^2-6*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^4*sin(d*x+c)*a*b^3-82*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^4*sin(d*x+c)*a^3*b-82*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^4*sin(d*x+c)*a^2*b^2+6*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^4*sin(d*x+c)*a*b^3+82*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^3*sin(d*x+c)*a^3*b+51*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^3*sin(d*x+c)*a^2*b^2-6*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^3*sin(d*x+c)*a*b^3-82*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^3*sin(d*x+c)*a^3*b-82*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^3*sin(d*x+c)*a^2*b^2+6*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^3*sin(d*x+c)*a*b^3+6*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^4*sin(d*x+c)*b^4+25*cos(d*x+c)^3*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+6*cos(d*x+c)^3*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+82*cos(d*x+c)^5*a^2*b^2+3*cos(d*x+c)^5*a*b^3+82*cos(d*x+c)^4*a^3*b-55*cos(d*x+c)^4*a^2*b^2-6*cos(d*x+c)^4*a*b^3-68*cos(d*x+c)^3*a^3*b+3*cos(d*x+c)^3*a*b^3-27*cos(d*x+c)^2*a^2*b^2-39*cos(d*x+c)*a^3*b+25*cos(d*x+c)^4*a^4-10*cos(d*x+c)^2*a^4-6*cos(d*x+c)^5*b^4+6*cos(d*x+c)^4*b^4)*cos(d*x+c)/(a+b*cos(d*x+c))^(1/2)*(1/cos(d*x+c))^(9/2)/sin(d*x+c)/a^2","B"
737,1,1547,325,0.264000," ","int((a+b*cos(d*x+c))^(3/2)*sec(d*x+c)^(7/2),x)","-\frac{2 \left(3 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}+4 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 +\left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}-3 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 -\left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}-\left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}+4 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 +\left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}-3 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 -\left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}-\left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 \left(\cos^{4}\left(d x +c \right)\right) a^{2} b +2 \left(\cos^{4}\left(d x +c \right)\right) a \,b^{2}+\left(\cos^{4}\left(d x +c \right)\right) b^{3}+3 \left(\cos^{3}\left(d x +c \right)\right) a^{3}+\left(\cos^{3}\left(d x +c \right)\right) a \,b^{2}-\left(\cos^{3}\left(d x +c \right)\right) b^{3}-2 \left(\cos^{2}\left(d x +c \right)\right) a^{3}-3 \left(\cos^{2}\left(d x +c \right)\right) a \,b^{2}-3 \cos \left(d x +c \right) a^{2} b -a^{3}\right) \cos \left(d x +c \right) \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{7}{2}}}{5 d \sqrt{a +b \cos \left(d x +c \right)}\, \sin \left(d x +c \right) a}"," ",0,"-2/5/d*(3*cos(d*x+c)^3*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+4*cos(d*x+c)^3*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+cos(d*x+c)^3*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^3*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^3-3*cos(d*x+c)^3*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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-cos(d*x+c)^3*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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-cos(d*x+c)^3*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+3*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+4*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^3-3*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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-cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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-cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+3*cos(d*x+c)^4*a^2*b+2*cos(d*x+c)^4*a*b^2+cos(d*x+c)^4*b^3+3*cos(d*x+c)^3*a^3+cos(d*x+c)^3*a*b^2-cos(d*x+c)^3*b^3-2*cos(d*x+c)^2*a^3-3*cos(d*x+c)^2*a*b^2-3*cos(d*x+c)*a^2*b-a^3)*cos(d*x+c)/(a+b*cos(d*x+c))^(1/2)*(1/cos(d*x+c))^(7/2)/sin(d*x+c)/a","B"
738,1,1085,283,0.315000," ","int((a+b*cos(d*x+c))^(3/2)*sec(d*x+c)^(5/2),x)","\frac{2 \left(4 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) a b +4 \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) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, b^{2}-\EllipticF \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) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, a^{2}-4 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \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{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 \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) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, b^{2}-\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) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}-\left(\cos^{3}\left(d x +c \right)\right) a b -4 \left(\cos^{3}\left(d x +c \right)\right) b^{2}-\left(\cos^{2}\left(d x +c \right)\right) a^{2}-4 \left(\cos^{2}\left(d x +c \right)\right) a b +4 \left(\cos^{2}\left(d x +c \right)\right) b^{2}+5 a b \cos \left(d x +c \right)+a^{2}\right) \cos \left(d x +c \right) \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{5}{2}}}{3 d \sqrt{a +b \cos \left(d x +c \right)}\, \sin \left(d x +c \right)}"," ",0,"2/3/d*(4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^2*sin(d*x+c)*a*b+4*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)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*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)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^2-4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^2*sin(d*x+c)*a*b-3*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*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)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*b^2-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)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^2-4*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^3*a*b-4*cos(d*x+c)^3*b^2-cos(d*x+c)^2*a^2-4*cos(d*x+c)^2*a*b+4*cos(d*x+c)^2*b^2+5*a*b*cos(d*x+c)+a^2)*cos(d*x+c)/(a+b*cos(d*x+c))^(1/2)*(1/cos(d*x+c))^(5/2)/sin(d*x+c)","B"
739,1,1191,361,0.277000," ","int((a+b*cos(d*x+c))^(3/2)*sec(d*x+c)^(3/2),x)","-\frac{2 \left(2 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}+\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) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 -\cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}-\cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}-\cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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)+\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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)-\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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{a +b \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)-\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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)+\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)-a^{2}\right) \cos \left(d x +c \right) \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}}}{d \sqrt{a +b \cos \left(d x +c \right)}\, \sin \left(d x +c \right)}"," ",0,"-2/d*(2*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+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)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^2+2*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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-cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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-cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)/(1+cos(d*x+c)))^(1/2)*((a+b*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*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)/(1+cos(d*x+c)))^(1/2)*((a+b*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)*((a+b*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)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^2*a*b+a^2*cos(d*x+c)-a*b*cos(d*x+c)-a^2)*cos(d*x+c)/(a+b*cos(d*x+c))^(1/2)*(1/cos(d*x+c))^(3/2)/sin(d*x+c)","B"
740,1,1005,395,0.333000," ","int((a+b*cos(d*x+c))^(3/2)*sec(d*x+c)^(1/2),x)","-\frac{\sqrt{\frac{1}{\cos \left(d x +c \right)}}\, \left(2 \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) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 +\cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, b^{2}+6 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \sin \left(d x +c \right) a b +2 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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)-4 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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)+\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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)+\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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)+6 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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)+\left(\cos^{3}\left(d x +c \right)\right) b^{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)\right)}{d \sqrt{a +b \cos \left(d x +c \right)}\, \sin \left(d x +c \right)}"," ",0,"-1/d*(1/cos(d*x+c))^(1/2)/(a+b*cos(d*x+c))^(1/2)*(2*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)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^2-4*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*b^2+6*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)*sin(d*x+c)*a*b+2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)-4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)/(1+cos(d*x+c)))^(1/2)*((a+b*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)/(1+cos(d*x+c)))^(1/2)*((a+b*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)+6*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)+cos(d*x+c)^3*b^2+cos(d*x+c)^2*a*b-cos(d*x+c)^2*b^2-a*b*cos(d*x+c))/sin(d*x+c)","B"
741,1,1423,439,0.278000," ","int((a+b*cos(d*x+c))^(3/2)/sec(d*x+c)^(1/2),x)","-\frac{\left(-8 \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) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 -4 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}+5 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}+5 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}+8 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}+2 \left(\cos^{4}\left(d x +c \right)\right) b^{2}-8 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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)-4 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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)+5 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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)+5 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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)+6 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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} \sin \left(d x +c \right)+8 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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)+7 \left(\cos^{3}\left(d x +c \right)\right) a b +5 \left(\cos^{2}\left(d x +c \right)\right) a^{2}-5 \left(\cos^{2}\left(d x +c \right)\right) a b -2 \left(\cos^{2}\left(d x +c \right)\right) b^{2}-5 a^{2} \cos \left(d x +c \right)-2 a b \cos \left(d x +c \right)\right) \sqrt{\frac{1}{\cos \left(d x +c \right)}}}{4 d \sin \left(d x +c \right) \sqrt{a +b \cos \left(d x +c \right)}}"," ",0,"-1/4/d*(-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)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^2+2*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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-4*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+5*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+5*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+8*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+2*cos(d*x+c)^4*b^2-8*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)-4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)+5*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)+5*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)+6*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*sin(d*x+c)+8*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)+7*cos(d*x+c)^3*a*b+5*cos(d*x+c)^2*a^2-5*cos(d*x+c)^2*a*b-2*cos(d*x+c)^2*b^2-5*a^2*cos(d*x+c)-2*a*b*cos(d*x+c))*(1/cos(d*x+c))^(1/2)/sin(d*x+c)/(a+b*cos(d*x+c))^(1/2)","B"
742,1,1691,508,0.307000," ","int((a+b*cos(d*x+c))^(3/2)/sec(d*x+c)^(3/2),x)","-\frac{\left(-6 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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} \sin \left(d x +c \right)+3 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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)+16 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 a^{3} \cos \left(d x +c \right)-3 \left(\cos^{2}\left(d x +c \right)\right) a^{2} b -16 \cos \left(d x +c \right) a \,b^{2}-6 \left(\cos^{2}\left(d x +c \right)\right) a \,b^{2}-14 \cos \left(d x +c \right) a^{2} b +8 \left(\cos^{5}\left(d x +c \right)\right) b^{3}+8 \left(\cos^{3}\left(d x +c \right)\right) b^{3}+3 \left(\cos^{2}\left(d x +c \right)\right) a^{3}-16 \left(\cos^{2}\left(d x +c \right)\right) b^{3}+17 \left(\cos^{3}\left(d x +c \right)\right) a^{2} b +22 \left(\cos^{4}\left(d x +c \right)\right) a \,b^{2}-6 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}+3 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}+16 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}+72 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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} \sin \left(d x +c \right)+3 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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)+16 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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)+14 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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)-52 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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)+72 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}+3 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 +16 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}+14 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 -52 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}\right) \cos \left(d x +c \right) \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}}}{24 d \sin \left(d x +c \right) \sqrt{a +b \cos \left(d x +c \right)}\, b}"," ",0,"-1/24/d*(-6*cos(d*x+c)^2*a*b^2-6*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^3-6*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*sin(d*x+c)+3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*a^3*cos(d*x+c)-16*cos(d*x+c)*a*b^2-3*cos(d*x+c)^2*a^2*b+8*cos(d*x+c)^5*b^3-16*cos(d*x+c)^2*b^3-14*cos(d*x+c)*a^2*b+22*cos(d*x+c)^4*a*b^2+17*cos(d*x+c)^3*a^2*b+8*cos(d*x+c)^3*b^3+3*cos(d*x+c)^2*a^3+3*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+16*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+72*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*sin(d*x+c)+3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)+16*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)+14*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)-52*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)+72*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+3*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+16*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+14*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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-52*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)*(1/cos(d*x+c))^(3/2)/sin(d*x+c)/(a+b*cos(d*x+c))^(1/2)/b","B"
743,1,2512,442,0.373000," ","int((a+b*cos(d*x+c))^(5/2)*sec(d*x+c)^(11/2),x)","\text{Expression too large to display}"," ",0,"-2/315/d*(-80*cos(d*x+c)^3*a^2*b^3+147*cos(d*x+c)^5*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+65*cos(d*x+c)^5*a^4*b+279*cos(d*x+c)^5*a^3*b^2-199*cos(d*x+c)^5*a^2*b^3-10*cos(d*x+c)^5*a*b^4-272*cos(d*x+c)^4*a^3*b^2+5*cos(d*x+c)^4*a*b^4-82*cos(d*x+c)^3*a^4*b-170*cos(d*x+c)^2*a^3*b^2-130*cos(d*x+c)*a^4*b+147*cos(d*x+c)^6*a^4*b+163*cos(d*x+c)^6*a^3*b^2+279*cos(d*x+c)^6*a^2*b^3+5*cos(d*x+c)^6*a*b^4-35*a^5-10*cos(d*x+c)^6*b^5+147*cos(d*x+c)^5*a^5+10*cos(d*x+c)^5*b^5-98*cos(d*x+c)^4*a^5-14*cos(d*x+c)^2*a^5-10*cos(d*x+c)^5*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^4-147*cos(d*x+c)^5*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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-279*cos(d*x+c)^5*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^2-279*cos(d*x+c)^5*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+10*cos(d*x+c)^5*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+261*cos(d*x+c)^4*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+279*cos(d*x+c)^4*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+155*cos(d*x+c)^4*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^3-10*cos(d*x+c)^4*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^4-147*cos(d*x+c)^4*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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-279*cos(d*x+c)^4*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^2-279*cos(d*x+c)^4*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+10*cos(d*x+c)^4*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+261*cos(d*x+c)^5*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+279*cos(d*x+c)^5*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+155*cos(d*x+c)^5*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^3-147*cos(d*x+c)^5*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^5+10*cos(d*x+c)^5*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^5+147*cos(d*x+c)^4*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^5-147*cos(d*x+c)^4*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^5+10*cos(d*x+c)^4*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^5)*cos(d*x+c)/(a+b*cos(d*x+c))^(1/2)*(1/cos(d*x+c))^(11/2)/sin(d*x+c)/a^2","B"
744,1,1835,381,0.277000," ","int((a+b*cos(d*x+c))^(5/2)*sec(d*x+c)^(9/2),x)","-\frac{2 \left(-3 a^{4}-22 \left(\cos^{3}\left(d x +c \right)\right) a^{3} b -11 \left(\cos^{4}\left(d x +c \right)\right) a^{2} b^{2}+9 \left(\cos^{5}\left(d x +c \right)\right) a \,b^{3}-12 \left(\cos^{3}\left(d x +c \right)\right) a \,b^{3}+3 \left(\cos^{4}\left(d x +c \right)\right) a \,b^{3}+29 \left(\cos^{5}\left(d x +c \right)\right) a^{2} b^{2}+29 \left(\cos^{4}\left(d x +c \right)\right) a^{3} b +29 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) a^{3} b +27 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) a^{2} b^{2}+3 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) a \,b^{3}-29 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) a^{3} b -29 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) a^{2} b^{2}-3 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) a \,b^{3}+5 \left(\cos^{5}\left(d x +c \right)\right) a^{3} b -12 \cos \left(d x +c \right) a^{3} b +29 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \left(\cos^{4}\left(d x +c \right)\right) \sin \left(d x +c \right) a^{3} b +27 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \left(\cos^{4}\left(d x +c \right)\right) \sin \left(d x +c \right) a^{2} b^{2}+3 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \left(\cos^{4}\left(d x +c \right)\right) \sin \left(d x +c \right) a \,b^{3}-29 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \left(\cos^{4}\left(d x +c \right)\right) \sin \left(d x +c \right) a^{3} b -29 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \left(\cos^{4}\left(d x +c \right)\right) \sin \left(d x +c \right) a^{2} b^{2}-2 \left(\cos^{2}\left(d x +c \right)\right) a^{4}+3 \left(\cos^{5}\left(d x +c \right)\right) b^{4}-3 \left(\cos^{4}\left(d x +c \right)\right) b^{4}+5 \left(\cos^{4}\left(d x +c \right)\right) a^{4}+5 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \left(\cos^{4}\left(d x +c \right)\right) \sin \left(d x +c \right) a^{4}-3 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \left(\cos^{4}\left(d x +c \right)\right) \sin \left(d x +c \right) b^{4}+5 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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^{4}-3 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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^{4}-18 \left(\cos^{2}\left(d x +c \right)\right) a^{2} b^{2}-3 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \left(\cos^{4}\left(d x +c \right)\right) \sin \left(d x +c \right) a \,b^{3}\right) \cos \left(d x +c \right) \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{9}{2}}}{21 d \sqrt{a +b \cos \left(d x +c \right)}\, \sin \left(d x +c \right) a}"," ",0,"-2/21/d*(5*cos(d*x+c)^5*a^3*b+5*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^4*sin(d*x+c)*a^4-3*a^4+29*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^4*sin(d*x+c)*a^3*b+27*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^4*sin(d*x+c)*a^2*b^2+3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^4*sin(d*x+c)*a*b^3-29*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^4*sin(d*x+c)*a^3*b-29*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^4*sin(d*x+c)*a^2*b^2-3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^4*sin(d*x+c)*a*b^3+29*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^3*sin(d*x+c)*a^3*b+27*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^3*sin(d*x+c)*a^2*b^2+3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^3*sin(d*x+c)*a*b^3-29*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^3*sin(d*x+c)*a^3*b-29*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^3*sin(d*x+c)*a^2*b^2-3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^3*sin(d*x+c)*a*b^3-3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^4*sin(d*x+c)*b^4+5*cos(d*x+c)^3*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^4-3*cos(d*x+c)^3*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+29*cos(d*x+c)^5*a^2*b^2+9*cos(d*x+c)^5*a*b^3+29*cos(d*x+c)^4*a^3*b-11*cos(d*x+c)^4*a^2*b^2+3*cos(d*x+c)^4*a*b^3-22*cos(d*x+c)^3*a^3*b-12*cos(d*x+c)^3*a*b^3-18*cos(d*x+c)^2*a^2*b^2-12*cos(d*x+c)*a^3*b+5*cos(d*x+c)^4*a^4-2*cos(d*x+c)^2*a^4+3*cos(d*x+c)^5*b^4-3*cos(d*x+c)^4*b^4)*cos(d*x+c)/(a+b*cos(d*x+c))^(1/2)*(1/cos(d*x+c))^(9/2)/sin(d*x+c)/a","B"
745,1,1758,338,0.290000," ","int((a+b*cos(d*x+c))^(5/2)*sec(d*x+c)^(7/2),x)","-\frac{2 \left(-3 a^{3}-9 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 +23 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}-9 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 -23 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}-23 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}+17 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 +23 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}-34 \left(\cos^{2}\left(d x +c \right)\right) a \,b^{2}-14 \cos \left(d x +c \right) a^{2} b +23 \left(\cos^{4}\left(d x +c \right)\right) b^{3}-23 \left(\cos^{3}\left(d x +c \right)\right) b^{3}-6 \left(\cos^{2}\left(d x +c \right)\right) a^{3}+9 \left(\cos^{3}\left(d x +c \right)\right) a^{3}+17 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 +9 \left(\cos^{4}\left(d x +c \right)\right) a^{2} b +5 \left(\cos^{3}\left(d x +c \right)\right) a^{2} b +23 \left(\cos^{3}\left(d x +c \right)\right) a \,b^{2}+11 \left(\cos^{4}\left(d x +c \right)\right) a \,b^{2}+15 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) b^{3}+15 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) b^{3}-9 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}-23 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}+9 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}-23 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}+9 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}\right) \cos \left(d x +c \right) \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{7}{2}}}{15 d \sqrt{a +b \cos \left(d x +c \right)}\, \sin \left(d x +c \right)}"," ",0,"-2/15/d*(-34*cos(d*x+c)^2*a*b^2-9*cos(d*x+c)^3*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^3-3*a^3-23*cos(d*x+c)^3*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+17*cos(d*x+c)^3*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+23*cos(d*x+c)^3*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^2-9*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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-23*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+23*cos(d*x+c)^4*b^3+9*cos(d*x+c)^3*a^3-14*cos(d*x+c)*a^2*b+9*cos(d*x+c)^4*a^2*b+11*cos(d*x+c)^4*a*b^2+5*cos(d*x+c)^3*a^2*b+23*cos(d*x+c)^3*a*b^2-23*cos(d*x+c)^3*b^3-6*cos(d*x+c)^2*a^3+15*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^2*sin(d*x+c)*b^3-9*cos(d*x+c)^3*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+17*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+23*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^2-23*cos(d*x+c)^3*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+9*cos(d*x+c)^3*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^3-23*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+9*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*cos(d*x+c)^3*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)*cos(d*x+c)/(a+b*cos(d*x+c))^(1/2)*(1/cos(d*x+c))^(7/2)/sin(d*x+c)","B"
746,1,1493,406,0.352000," ","int((a+b*cos(d*x+c))^(5/2)*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) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}+7 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 +9 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \left(\cos^{2}\left(d x +c \right)\right) \sin \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{a +b \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) \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) b^{3}-7 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}+\cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}+7 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 +9 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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^{3}-7 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}+\left(\cos^{3}\left(d x +c \right)\right) a^{2} b +7 \left(\cos^{3}\left(d x +c \right)\right) a \,b^{2}+\left(\cos^{2}\left(d x +c \right)\right) a^{3}+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}-8 \cos \left(d x +c \right) a^{2} b -a^{3}\right) \cos \left(d x +c \right) \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{5}{2}}}{3 d \sqrt{a +b \cos \left(d x +c \right)}\, \sin \left(d x +c \right)}"," ",0,"-2/3/d*(cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+7*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+9*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^2*sin(d*x+c)*b^3+6*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^2*sin(d*x+c)*b^3-7*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+7*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+9*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^3-7*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+cos(d*x+c)^3*a^2*b+7*cos(d*x+c)^3*a*b^2+cos(d*x+c)^2*a^3+7*cos(d*x+c)^2*a^2*b-7*cos(d*x+c)^2*a*b^2-8*cos(d*x+c)*a^2*b-a^3)*cos(d*x+c)/(a+b*cos(d*x+c))^(1/2)*(1/cos(d*x+c))^(5/2)/sin(d*x+c)","B"
747,1,1631,461,0.219000," ","int((a+b*cos(d*x+c))^(5/2)*sec(d*x+c)^(3/2),x)","-\frac{\left(-2 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 +\cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}+\cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}+10 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}+2 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}+6 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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)+\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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)+\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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)+10 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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} \sin \left(d x +c \right)+2 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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)+6 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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{a +b \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)+\left(\cos^{3}\left(d x +c \right)\right) b^{3}+2 \left(\cos^{2}\left(d x +c \right)\right) a^{2} b +\left(\cos^{2}\left(d x +c \right)\right) a \,b^{2}-\left(\cos^{2}\left(d x +c \right)\right) b^{3}+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}-2 a^{3}\right) \cos \left(d x +c \right) \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}}}{d \sqrt{a +b \cos \left(d x +c \right)}\, \sin \left(d x +c \right)}"," ",0,"-1/d*(-2*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+10*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+2*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+6*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)/(1+cos(d*x+c)))^(1/2)*((a+b*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)/(1+cos(d*x+c)))^(1/2)*((a+b*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)+10*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*sin(d*x+c)+2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)+6*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)*((a+b*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)^3*b^3+2*cos(d*x+c)^2*a^2*b+cos(d*x+c)^2*a*b^2-cos(d*x+c)^2*b^3+2*a^3*cos(d*x+c)-2*cos(d*x+c)*a^2*b-cos(d*x+c)*a*b^2-2*a^3)*cos(d*x+c)/(a+b*cos(d*x+c))^(1/2)*(1/cos(d*x+c))^(3/2)/sin(d*x+c)","B"
748,1,1631,449,0.239000," ","int((a+b*cos(d*x+c))^(5/2)*sec(d*x+c)^(1/2),x)","-\frac{\sqrt{\frac{1}{\cos \left(d x +c \right)}}\, \left(30 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 +8 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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^{3}+8 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}-24 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}-4 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}+9 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 \left(\cos^{4}\left(d x +c \right)\right) b^{3}+30 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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)+8 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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^{3} \sin \left(d x +c \right)+8 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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)-24 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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{a +b \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 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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} \sin \left(d x +c \right)+9 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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)+9 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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)+11 \left(\cos^{3}\left(d x +c \right)\right) a \,b^{2}+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 \left(\cos^{2}\left(d x +c \right)\right) b^{3}-9 \cos \left(d x +c \right) a^{2} b -2 \cos \left(d x +c \right) a \,b^{2}\right)}{4 d \sqrt{a +b \cos \left(d x +c \right)}\, \sin \left(d x +c \right)}"," ",0,"-1/4/d*(1/cos(d*x+c))^(1/2)/(a+b*cos(d*x+c))^(1/2)*(30*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+8*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^3+8*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^3-24*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^2-4*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+9*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*cos(d*x+c)^4*b^3+30*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)/(1+cos(d*x+c)))^(1/2)*((a+b*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^3*sin(d*x+c)+8*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)-24*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)*((a+b*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)/(1+cos(d*x+c)))^(1/2)*((a+b*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*sin(d*x+c)+9*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)+9*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)+11*cos(d*x+c)^3*a*b^2+9*cos(d*x+c)^2*a^2*b-9*cos(d*x+c)^2*a*b^2-2*cos(d*x+c)^2*b^3-9*cos(d*x+c)*a^2*b-2*cos(d*x+c)*a*b^2)/sin(d*x+c)","B"
749,1,1868,506,0.299000," ","int((a+b*cos(d*x+c))^(5/2)/sec(d*x+c)^(1/2),x)","\frac{\left(-30 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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} \sin \left(d x +c \right)-33 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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)-16 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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)+33 a^{3} \cos \left(d x +c \right)+33 \left(\cos^{2}\left(d x +c \right)\right) a^{2} b +16 \cos \left(d x +c \right) a \,b^{2}+18 \left(\cos^{2}\left(d x +c \right)\right) a \,b^{2}+26 \cos \left(d x +c \right) a^{2} b -8 \left(\cos^{5}\left(d x +c \right)\right) b^{3}+48 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}-8 \left(\cos^{3}\left(d x +c \right)\right) b^{3}-33 \left(\cos^{2}\left(d x +c \right)\right) a^{3}+16 \left(\cos^{2}\left(d x +c \right)\right) b^{3}-59 \left(\cos^{3}\left(d x +c \right)\right) a^{2} b -34 \left(\cos^{4}\left(d x +c \right)\right) a \,b^{2}-30 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}-33 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}-16 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}-120 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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} \sin \left(d x +c \right)-33 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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)-16 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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)-26 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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)+76 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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)+48 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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)-120 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}-33 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 -16 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}-26 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 +76 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}\right) \sqrt{\frac{1}{\cos \left(d x +c \right)}}}{24 d \sin \left(d x +c \right) \sqrt{a +b \cos \left(d x +c \right)}}"," ",0,"1/24/d*(18*cos(d*x+c)^2*a*b^2+48*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^3-30*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*sin(d*x+c)-33*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)+33*a^3*cos(d*x+c)+16*cos(d*x+c)*a*b^2+33*cos(d*x+c)^2*a^2*b-8*cos(d*x+c)^5*b^3+16*cos(d*x+c)^2*b^3+26*cos(d*x+c)*a^2*b-34*cos(d*x+c)^4*a*b^2-59*cos(d*x+c)^3*a^2*b-8*cos(d*x+c)^3*b^3-33*cos(d*x+c)^2*a^3-33*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^3-16*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^3-120*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*sin(d*x+c)-33*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)-16*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)-26*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)+76*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)+48*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)-120*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^2-33*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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-16*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^2-26*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+76*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)*(1/cos(d*x+c))^(1/2)/sin(d*x+c)/(a+b*cos(d*x+c))^(1/2)","B"
750,1,2327,572,0.437000," ","int((a+b*cos(d*x+c))^(5/2)/sec(d*x+c)^(3/2),x)","\text{Expression too large to display}"," ",0,"-1/192/d*(-30*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+48*cos(d*x+c)^6*b^4-72*cos(d*x+c)*a*b^3-15*cos(d*x+c)^2*a^3*b-284*cos(d*x+c)^2*a*b^3-284*cos(d*x+c)*a^2*b^2-72*cos(d*x+c)^2*b^4+184*cos(d*x+c)^5*a*b^3+254*cos(d*x+c)^4*a^2*b^2+133*cos(d*x+c)^3*a^3*b+172*cos(d*x+c)^3*a*b^3+30*cos(d*x+c)^2*a^2*b^2-118*cos(d*x+c)*a^3*b+284*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+284*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+118*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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-644*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+15*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+15*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+284*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+118*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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-644*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+72*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+15*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+284*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^2-30*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)+288*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)-144*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*sin(d*x+c)+15*cos(d*x+c)^2*a^4+24*cos(d*x+c)^4*b^4+288*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^4-144*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+720*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)+72*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)-15*a^4*cos(d*x+c)+15*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+720*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)*cos(d*x+c)*(1/cos(d*x+c))^(3/2)/sin(d*x+c)/(a+b*cos(d*x+c))^(1/2)/b","B"
751,1,891,280,0.326000," ","int(sec(d*x+c)^(5/2)/(a+b*cos(d*x+c))^(1/2),x)","-\frac{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) \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, a^{2}-2 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) a b +2 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) a b +2 \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) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, b^{2}+\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) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 \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) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) a b -2 \left(\cos^{3}\left(d x +c \right)\right) 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 +2 \left(\cos^{2}\left(d x +c \right)\right) b^{2}+a b \cos \left(d x +c \right)-a^{2}\right) \cos \left(d x +c \right) \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{5}{2}}}{3 d \sqrt{a +b \cos \left(d x +c \right)}\, \sin \left(d x +c \right) a^{2}}"," ",0,"-2/3/d*(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)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^2-2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^2*sin(d*x+c)*a*b+2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^2*sin(d*x+c)*a*b+2*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)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*b^2+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)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^2-2*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*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)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*b^2+cos(d*x+c)^3*a*b-2*cos(d*x+c)^3*b^2+cos(d*x+c)^2*a^2-2*cos(d*x+c)^2*a*b+2*cos(d*x+c)^2*b^2+a*b*cos(d*x+c)-a^2)*cos(d*x+c)*(1/cos(d*x+c))^(5/2)/(a+b*cos(d*x+c))^(1/2)/sin(d*x+c)/a^2","B"
752,1,620,240,0.235000," ","int(sec(d*x+c)^(3/2)/(a+b*cos(d*x+c))^(1/2),x)","-\frac{2 \left(\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \sin \left(d x +c \right) a -\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \sin \left(d x +c \right) a -\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \sin \left(d x +c \right) b +\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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{a +b \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{a +b \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) b +a \cos \left(d x +c \right)-b \cos \left(d x +c \right)-a \right) \cos \left(d x +c \right) \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}}}{d \sqrt{a +b \cos \left(d x +c \right)}\, \sin \left(d x +c \right) a}"," ",0,"-2/d*((cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)*sin(d*x+c)*a-(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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-(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)*b+(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)*((a+b*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)*((a+b*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*b+a*cos(d*x+c)-b*cos(d*x+c)-a)*cos(d*x+c)*(1/cos(d*x+c))^(3/2)/(a+b*cos(d*x+c))^(1/2)/sin(d*x+c)/a","B"
753,1,125,117,0.292000," ","int(sec(d*x+c)^(1/2)/(a+b*cos(d*x+c))^(1/2),x)","\frac{2 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \sqrt{\frac{1}{\cos \left(d x +c \right)}}\, \left(\sin^{2}\left(d x +c \right)\right)}{d \sqrt{a +b \cos \left(d x +c \right)}\, \left(-1+\cos \left(d x +c \right)\right)}"," ",0,"2/d*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*cos(d*x+c))^(1/2)*(1/cos(d*x+c))^(1/2)*sin(d*x+c)^2/(-1+cos(d*x+c))","A"
754,1,143,124,0.221000," ","int(1/(a+b*cos(d*x+c))^(1/2)/sec(d*x+c)^(1/2),x)","\frac{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) \sqrt{\frac{a +b \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}}{d \sqrt{a +b \cos \left(d x +c \right)}\, \sqrt{\frac{1}{\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}"," ",0,"2/d/(a+b*cos(d*x+c))^(1/2)*(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)))*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)/(1/cos(d*x+c))^(1/2)/(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)","A"
755,1,630,430,0.282000," ","int(1/sec(d*x+c)^(3/2)/(a+b*cos(d*x+c))^(1/2),x)","-\frac{\left(\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \sin \left(d x +c \right) a +\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \sin \left(d x +c \right) b -2 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \sin \left(d x +c \right) a +\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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{a +b \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)-2 a \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \sin \left(d x +c \right)+\left(\cos^{3}\left(d x +c \right)\right) b +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)\right) \cos \left(d x +c \right) \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}}}{d \sqrt{a +b \cos \left(d x +c \right)}\, \sin \left(d x +c \right) b}"," ",0,"-1/d*((cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)*b-2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)*sin(d*x+c)*a+(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)*((a+b*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)-2*a*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)+cos(d*x+c)^3*b+a*cos(d*x+c)^2-cos(d*x+c)^2*b-a*cos(d*x+c))*cos(d*x+c)*(1/cos(d*x+c))^(3/2)/(a+b*cos(d*x+c))^(1/2)/sin(d*x+c)/b","A"
756,1,1248,451,0.285000," ","int(1/sec(d*x+c)^(5/2)/(a+b*cos(d*x+c))^(1/2),x)","-\frac{\left(-3 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}-3 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}+8 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}+2 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 -4 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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^{4}\left(d x +c \right)\right) b^{2}-3 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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)-3 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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)+6 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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} \sin \left(d x +c \right)+8 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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)-4 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 b -3 \left(\cos^{2}\left(d x +c \right)\right) a^{2}+3 \left(\cos^{2}\left(d x +c \right)\right) a b -2 \left(\cos^{2}\left(d x +c \right)\right) b^{2}+3 a^{2} \cos \left(d x +c \right)-2 a b \cos \left(d x +c \right)\right) \left(\cos^{2}\left(d x +c \right)\right) \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{5}{2}}}{4 d \sin \left(d x +c \right) \sqrt{a +b \cos \left(d x +c \right)}\, b^{2}}"," ",0,"-1/4/d*(-3*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^2-3*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+8*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+2*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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-4*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^4*b^2-3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)-3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)+6*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*sin(d*x+c)+8*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)/(1+cos(d*x+c)))^(1/2)*((a+b*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)-4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*b-3*cos(d*x+c)^2*a^2+3*cos(d*x+c)^2*a*b-2*cos(d*x+c)^2*b^2+3*a^2*cos(d*x+c)-2*a*b*cos(d*x+c))*cos(d*x+c)^2*(1/cos(d*x+c))^(5/2)/sin(d*x+c)/(a+b*cos(d*x+c))^(1/2)/b^2","B"
757,1,1789,359,0.198000," ","int(sec(d*x+c)^(5/2)/(a+b*cos(d*x+c))^(3/2),x)","-\frac{2 \left(-a^{4}+\left(\cos^{3}\left(d x +c \right)\right) a^{3} b -4 \left(\cos^{3}\left(d x +c \right)\right) a \,b^{3}+8 \left(\cos^{2}\left(d x +c \right)\right) a \,b^{3}-5 \left(\cos^{2}\left(d x +c \right)\right) a^{3} b -5 \left(\cos^{3}\left(d x +c \right)\right) a^{2} b^{2}+5 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}+8 \left(\cos^{3}\left(d x +c \right)\right) b^{4}-4 \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{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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^{4}+a^{2} b^{2}+4 \cos \left(d x +c \right) a^{3} b -8 \left(\cos^{2}\left(d x +c \right)\right) b^{4}+\left(\cos^{2}\left(d x +c \right)\right) a^{4}-8 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}-5 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}+8 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}+4 \left(\cos^{2}\left(d x +c \right)\right) a^{2} b^{2}+5 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}-8 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}-5 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}+8 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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^{4}+\cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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^{4}-8 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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^{4}\right) \cos \left(d x +c \right) \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{5}{2}}}{3 d \sqrt{a +b \cos \left(d x +c \right)}\, \sin \left(d x +c \right) \left(a +b \right) \left(a -b \right) a^{3}}"," ",0,"-2/3/d*(-8*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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-a^4-5*cos(d*x+c)^3*a^2*b^2-4*cos(d*x+c)*a*b^3-5*cos(d*x+c)^2*a^3*b+8*cos(d*x+c)^2*a*b^3+8*cos(d*x+c)^3*b^4-8*cos(d*x+c)^2*b^4+a^2*b^2+cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+cos(d*x+c)^3*a^3*b-4*cos(d*x+c)^3*a*b^3+4*cos(d*x+c)^2*a^2*b^2+4*cos(d*x+c)*a^3*b-8*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^3-5*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+8*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+5*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^2-8*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^3-5*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+8*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+5*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+cos(d*x+c)^2*a^4-8*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)*cos(d*x+c)*(1/cos(d*x+c))^(5/2)/(a+b*cos(d*x+c))^(1/2)/sin(d*x+c)/(a+b)/(a-b)/a^3","B"
758,1,1457,297,0.273000," ","int(sec(d*x+c)^(3/2)/(a+b*cos(d*x+c))^(3/2),x)","\frac{2 \left(\cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}+\cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}-\cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}+\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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)+\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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)-2 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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)-2 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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)-\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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)+\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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{a +b \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)-\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 \left(\cos^{2}\left(d x +c \right)\right) b^{3}-a^{3} \cos \left(d x +c \right)+\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}+a^{3}-b^{2} a \right) \cos \left(d x +c \right) \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}}}{d \sqrt{a +b \cos \left(d x +c \right)}\, \sin \left(d x +c \right) a^{2} \left(a -b \right) \left(a +b \right)}"," ",0,"2/d*(cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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-cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)/(1+cos(d*x+c)))^(1/2)*((a+b*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)/(1+cos(d*x+c)))^(1/2)*((a+b*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)-2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)-2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)-(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)/(1+cos(d*x+c)))^(1/2)*((a+b*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)*((a+b*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)^2*a^2*b-cos(d*x+c)^2*a*b^2+2*cos(d*x+c)^2*b^3-a^3*cos(d*x+c)+cos(d*x+c)*a^2*b+2*cos(d*x+c)*a*b^2-2*cos(d*x+c)*b^3+a^3-b^2*a)*cos(d*x+c)*(1/cos(d*x+c))^(3/2)/(a+b*cos(d*x+c))^(1/2)/sin(d*x+c)/a^2/(a-b)/(a+b)","B"
759,1,832,279,0.314000," ","int(sec(d*x+c)^(1/2)/(a+b*cos(d*x+c))^(3/2),x)","\frac{2 \sqrt{\frac{1}{\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) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 +\cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, b^{2}-\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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)-\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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)+\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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)+\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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)+\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 \sqrt{a +b \cos \left(d x +c \right)}\, \sin \left(d x +c \right) \left(a +b \right) \left(a -b \right) a}"," ",0,"2/d*(1/cos(d*x+c))^(1/2)/(a+b*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)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^2-cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*b^2-(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)-(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)/(1+cos(d*x+c)))^(1/2)*((a+b*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)/(1+cos(d*x+c)))^(1/2)*((a+b*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)+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)/sin(d*x+c)/(a+b)/(a-b)/a","B"
760,1,811,278,0.289000," ","int(1/(a+b*cos(d*x+c))^(3/2)/sec(d*x+c)^(1/2),x)","\frac{2 \left(\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \sin \left(d x +c \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) \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, b -\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \sin \left(d x +c \right) a -\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \sin \left(d x +c \right) b +\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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{a +b \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{a +b \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{a +b \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)-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) \sqrt{\frac{1}{\cos \left(d x +c \right)}}}{d \sin \left(d x +c \right) \sqrt{a +b \cos \left(d x +c \right)}\, \left(a -b \right) \left(a +b \right)}"," ",0,"2/d*((cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)*sin(d*x+c)*a+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)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*b-(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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-(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)*b+(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)*((a+b*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)*((a+b*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)*((a+b*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)-a*cos(d*x+c)^2+cos(d*x+c)^2*b+a*cos(d*x+c)-b*cos(d*x+c))*(1/cos(d*x+c))^(1/2)/sin(d*x+c)/(a+b*cos(d*x+c))^(1/2)/(a-b)/(a+b)","B"
761,1,1214,407,0.367000," ","int(1/(a+b*cos(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{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 -\cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}+\cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}+\cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}+2 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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{a +b \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)-\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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{a +b \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)+\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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)-2 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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} \sin \left(d x +c \right)+2 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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^{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) \cos \left(d x +c \right) \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}}}{d \sin \left(d x +c \right) \sqrt{a +b \cos \left(d x +c \right)}\, \left(a +b \right) \left(a -b \right) b}"," ",0,"2/d*(-cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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-cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+2*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)*((a+b*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)/(1+cos(d*x+c)))^(1/2)*((a+b*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)*((a+b*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)/(1+cos(d*x+c)))^(1/2)*((a+b*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)-2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*sin(d*x+c)+2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^2-cos(d*x+c)^2*a*b-a^2*cos(d*x+c)+a*b*cos(d*x+c))*cos(d*x+c)*(1/cos(d*x+c))^(3/2)/sin(d*x+c)/(a+b*cos(d*x+c))^(1/2)/(a+b)/(a-b)/b","B"
762,1,1675,481,0.249000," ","int(1/(a+b*cos(d*x+c))^(3/2)/sec(d*x+c)^(5/2),x)","-\frac{\left(-6 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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} \sin \left(d x +c \right)+3 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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)-\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 a^{3} \cos \left(d x +c \right)-3 \left(\cos^{2}\left(d x +c \right)\right) a^{2} b +\cos \left(d x +c \right) a \,b^{2}-\left(\cos^{2}\left(d x +c \right)\right) a \,b^{2}+2 \cos \left(d x +c \right) a^{2} b -\left(\cos^{3}\left(d x +c \right)\right) b^{3}+3 \left(\cos^{2}\left(d x +c \right)\right) a^{3}+\left(\cos^{2}\left(d x +c \right)\right) b^{3}+\left(\cos^{3}\left(d x +c \right)\right) a^{2} b -6 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}+3 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}-\cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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} \sin \left(d x +c \right)+3 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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)-\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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)-2 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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{a +b \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)+6 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}+3 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 -\cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}\right) \left(\cos^{2}\left(d x +c \right)\right) \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{5}{2}}}{d \sin \left(d x +c \right) \sqrt{a +b \cos \left(d x +c \right)}\, \left(a +b \right) \left(a -b \right) b^{2}}"," ",0,"-1/d*(-cos(d*x+c)^2*a*b^2-6*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^3-6*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*sin(d*x+c)+3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)/(1+cos(d*x+c)))^(1/2)*((a+b*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*a^3*cos(d*x+c)+cos(d*x+c)*a*b^2-3*cos(d*x+c)^2*a^2*b+cos(d*x+c)^2*b^3+2*cos(d*x+c)*a^2*b+cos(d*x+c)^3*a^2*b-cos(d*x+c)^3*b^3+3*cos(d*x+c)^2*a^3+3*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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-cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*sin(d*x+c)+3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)/(1+cos(d*x+c)))^(1/2)*((a+b*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)-2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)*((a+b*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)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+3*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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-cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^2*(1/cos(d*x+c))^(5/2)/sin(d*x+c)/(a+b*cos(d*x+c))^(1/2)/(a+b)/(a-b)/b^2","B"
763,1,4197,467,0.270000," ","int(sec(d*x+c)^(5/2)/(a+b*cos(d*x+c))^(5/2),x)","\text{output too large to display}"," ",0,"-2/3/d*(16*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^3*sin(d*x+c)*b^7+cos(d*x+c)^4*a^5*b^2-16*cos(d*x+c)^2*a^2*b^5+24*cos(d*x+c)^2*a*b^6+6*cos(d*x+c)*a^6*b-12*cos(d*x+c)*a^4*b^3+6*cos(d*x+c)*a^2*b^5-8*cos(d*x+c)^4*a^4*b^3-13*cos(d*x+c)^4*a^3*b^4+28*cos(d*x+c)^4*a^2*b^5+8*cos(d*x+c)^4*a*b^6+2*cos(d*x+c)^3*a^6*b-16*cos(d*x+c)^3*a^5*b^2-8*cos(d*x+c)^3*a^4*b^3+56*cos(d*x+c)^3*a^3*b^4-18*cos(d*x+c)^3*a^2*b^5-32*cos(d*x+c)^3*a*b^6-8*cos(d*x+c)^2*a^6*b+13*cos(d*x+c)^2*a^5*b^2+28*cos(d*x+c)^2*a^4*b^3-42*cos(d*x+c)^2*a^3*b^4+cos(d*x+c)^2*a^7-16*cos(d*x+c)^4*b^7+16*cos(d*x+c)^3*b^7-a^7+2*a^5*b^2-a^3*b^4+(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^2*sin(d*x+c)*a^7+16*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^2*sin(d*x+c)*b^7+(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)*sin(d*x+c)*a^7+(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^3*sin(d*x+c)*a^6*b-8*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^3*sin(d*x+c)*a^5*b^2+7*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^3*sin(d*x+c)*a^4*b^3+28*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^3*sin(d*x+c)*a^3*b^4-4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^3*sin(d*x+c)*a^2*b^5-16*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^3*sin(d*x+c)*a*b^6+8*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^3*sin(d*x+c)*a^5*b^2+8*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^3*sin(d*x+c)*a^4*b^3-28*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^3*sin(d*x+c)*a^3*b^4-28*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^3*sin(d*x+c)*a^2*b^5+16*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^3*sin(d*x+c)*a*b^6-7*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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-cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+35*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+24*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^4-20*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^5-16*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+8*cos(d*x+c)^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)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^6*b+16*cos(d*x+c)^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)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^5*b^2-20*cos(d*x+c)^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)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^4*b^3-56*cos(d*x+c)^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)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^3*b^4-12*cos(d*x+c)^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)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^2*b^5+32*cos(d*x+c)^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)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a*b^6-8*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)*sin(d*x+c)*a^6*b+7*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)*sin(d*x+c)*a^5*b^2+28*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^3-4*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^4-16*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)*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)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^6*b+8*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^5*b^2-28*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)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^4*b^3-28*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^3*b^4+16*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)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^2*b^5+16*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)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a*b^6)*cos(d*x+c)*(1/cos(d*x+c))^(5/2)/(a+b*cos(d*x+c))^(3/2)/sin(d*x+c)/(a-b)^2/(a+b)^2/a^4","B"
764,1,3701,398,0.291000," ","int(sec(d*x+c)^(3/2)/(a+b*cos(d*x+c))^(5/2),x)","\text{output too large to display}"," ",0,"2/3/d*(15*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^2*sin(d*x+c)-8*cos(d*x+c)^3*b^6+8*cos(d*x+c)^2*b^6-3*cos(d*x+c)*a^6-6*b^2*a^4+3*b^4*a^2+3*a^6-3*cos(d*x+c)^3*a^4*b^2+15*cos(d*x+c)^3*a^2*b^4+4*cos(d*x+c)^3*a*b^5-6*cos(d*x+c)^2*a^5*b+30*cos(d*x+c)^2*a^3*b^3-10*cos(d*x+c)^2*a^2*b^4-16*cos(d*x+c)^2*a*b^5+15*cos(d*x+c)*a^4*b^2-22*cos(d*x+c)*a^3*b^3-8*cos(d*x+c)*a^2*b^4+12*cos(d*x+c)*a*b^5-3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*sin(d*x+c)+3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*sin(d*x+c)-8*cos(d*x+c)^3*a^3*b^3-6*cos(d*x+c)^2*a^4*b^2+6*cos(d*x+c)*a^5*b-2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^3*sin(d*x+c)-8*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^4*sin(d*x+c)+3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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-15*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^2-15*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+8*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)+8*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^2*sin(d*x+c)*b^6-3*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+3*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+8*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^6+6*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*sin(d*x+c)-7*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^4+16*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*b^5+3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)*sin(d*x+c)*a^5*b+21*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)*sin(d*x+c)*a^4*b^2+13*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^3-10*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)*sin(d*x+c)*a^2*b^4-8*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)*sin(d*x+c)*a*b^5+6*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^5*b-12*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^2-30*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^3*b^3-3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^2*sin(d*x+c)*a^5*b+6*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^2*sin(d*x+c)*a^4*b^2+15*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^2*sin(d*x+c)*a^3*b^3-2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^2*sin(d*x+c)*a^2*b^4-8*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^2*sin(d*x+c)*a*b^5+3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^2*sin(d*x+c)*a^5*b+3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^2*sin(d*x+c)*a^4*b^2-15*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^2*sin(d*x+c)*a^3*b^3-15*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^2*sin(d*x+c)*a^2*b^4+8*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^2*sin(d*x+c)*a*b^5)*cos(d*x+c)*(1/cos(d*x+c))^(3/2)/(a+b*cos(d*x+c))^(3/2)/sin(d*x+c)/(a-b)^2/(a+b)^2/a^3","B"
765,1,2745,381,0.306000," ","int(sec(d*x+c)^(1/2)/(a+b*cos(d*x+c))^(5/2),x)","\text{Expression too large to display}"," ",0,"2/3/d*(1/cos(d*x+c))^(1/2)/(a+b*cos(d*x+c))^(3/2)*(6*cos(d*x+c)^2*a^4*b-6*cos(d*x+c)^3*a^2*b^3-2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*sin(d*x+c)+2*cos(d*x+c)^3*b^5-3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)*sin(d*x+c)*a^5-2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)*b^5+4*cos(d*x+c)^2*a^2*b^3+7*cos(d*x+c)*a^3*b^2-12*cos(d*x+c)^2*a^3*b^2-6*cos(d*x+c)*a^4*b-3*cos(d*x+c)*a*b^4-2*cos(d*x+c)^2*b^5+5*cos(d*x+c)^3*a^3*b^2-cos(d*x+c)^3*a*b^4+4*cos(d*x+c)^2*a*b^4+2*cos(d*x+c)*a^2*b^3-3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*sin(d*x+c)-6*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*sin(d*x+c)-(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)+2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^3*sin(d*x+c)+6*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*sin(d*x+c)+6*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^2*sin(d*x+c)-2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)+2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)*a*b^4+12*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)*a^3*b^2-4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)*a*b^4+6*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)*a^4*b+4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)*a^2*b^3-9*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)*a^4*b-7*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)*a^3*b^2-2*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^5-3*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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-6*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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-cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^3+2*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^4+6*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^2+6*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^3-2*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)/(1+cos(d*x+c)))^(1/2)*((a+b*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)*a^2*b^3)/sin(d*x+c)/a^2/(a+b)^2/(a-b)^2","B"
766,1,2419,359,0.274000," ","int(1/(a+b*cos(d*x+c))^(5/2)/sec(d*x+c)^(1/2),x)","\text{Expression too large to display}"," ",0,"-2/3/d*(cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^4-3*cos(d*x+c)^3*a^2*b^2-6*cos(d*x+c)^2*a^3*b-2*cos(d*x+c)^2*a*b^3-cos(d*x+c)*a^2*b^2-cos(d*x+c)^3*b^4+cos(d*x+c)^2*b^4+2*cos(d*x+c)^3*a^3*b+2*cos(d*x+c)^3*a*b^3+4*cos(d*x+c)^2*a^2*b^2+4*cos(d*x+c)*a^3*b+sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)/(1+cos(d*x+c)))^(1/2)*((a+b*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^3-4*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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-sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+3*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+2*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^3-7*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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-5*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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-cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+3*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^3-3*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)*((a+b*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-cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+6*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+4*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*cos(d*x+c)^2*a^4-3*a^4*cos(d*x+c)+3*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^4-3*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^4-3*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)*(1/cos(d*x+c))^(1/2)/sin(d*x+c)/(a+b*cos(d*x+c))^(3/2)/a/(a+b)^2/(a-b)^2","B"
767,1,1790,342,0.341000," ","int(1/(a+b*cos(d*x+c))^(5/2)/sec(d*x+c)^(3/2),x)","-\frac{2 \left(-a^{3} \cos \left(d x +c \right)-4 \left(\cos^{2}\left(d x +c \right)\right) a^{2} b -3 \cos \left(d x +c \right) a \,b^{2}-4 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 \left(\cos^{2}\left(d x +c \right)\right) a \,b^{2}+4 \cos \left(d x +c \right) a^{2} b +\cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}+4 \left(\cos^{3}\left(d x +c \right)\right) b^{3}-4 \left(\cos^{2}\left(d x +c \right)\right) b^{3}+\left(\cos^{3}\left(d x +c \right)\right) a^{3}+\left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 \left(\cos^{3}\left(d x +c \right)\right) a \,b^{2}+3 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}+3 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) b^{3}-4 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}-4 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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)-4 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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)+4 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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)+3 \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}+\sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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)-4 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 -8 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}+5 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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 \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \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}\right) \cos \left(d x +c \right) \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}}}{3 d \sin \left(d x +c \right) \left(a +b \cos \left(d x +c \right)\right)^{\frac{3}{2}} \left(a +b \right)^{2} \left(a -b \right)^{2}}"," ",0,"-2/3/d*(8*cos(d*x+c)^2*a*b^2+cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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-a^3*cos(d*x+c)-3*cos(d*x+c)*a*b^2-4*cos(d*x+c)^2*a^2*b-4*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*cos(d*x+c)^2*b^3+cos(d*x+c)^3*a^3+4*cos(d*x+c)*a^2*b-5*cos(d*x+c)^3*a*b^2+4*cos(d*x+c)^3*b^3+3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)^2*sin(d*x+c)*b^3+3*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+4*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^2-4*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^3-4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)-4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)+4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)+3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)-4*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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-8*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+5*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)*(1/cos(d*x+c))^(3/2)/sin(d*x+c)/(a+b*cos(d*x+c))^(3/2)/(a+b)^2/(a-b)^2","B"
768,1,3920,505,0.281000," ","int(1/(a+b*cos(d*x+c))^(5/2)/sec(d*x+c)^(5/2),x)","\text{output too large to display}"," ",0,"2/3/d*(-6*cos(d*x+c)^2*a^4*b-8*cos(d*x+c)^3*a^2*b^3+14*cos(d*x+c)^2*a^2*b^3+7*cos(d*x+c)*a^3*b^2+4*cos(d*x+c)^3*a^4*b-4*cos(d*x+c)^2*a^3*b^2+2*cos(d*x+c)*a^4*b+3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^5*sin(d*x+c)-6*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,(-(a-b)/(a+b))^(1/2))*a^5*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)-3*a^5*cos(d*x+c)-3*cos(d*x+c)^3*a^3*b^2+7*cos(d*x+c)^3*a*b^4-7*cos(d*x+c)^2*a*b^4-6*cos(d*x+c)*a^2*b^3+3*cos(d*x+c)^2*a^5-2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*sin(d*x+c)+(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)+6*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^3*sin(d*x+c)+3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*sin(d*x+c)-7*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^2*sin(d*x+c)-7*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)-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)*((a+b*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)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^5+3*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^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)*((a+b*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)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*b^5+3*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^5+12*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,(-(a-b)/(a+b))^(1/2))*a^3*b^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)-6*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,(-(a-b)/(a+b))^(1/2))*a*b^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)+3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^4*sin(d*x+c)+9*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)*a*b^4-4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)*a^3*b^2-7*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)*a*b^4+6*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)*a^4*b-14*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)*a^2*b^3-2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)*a^4*b-(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)*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)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^4*b+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)*((a+b*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)*((a+b*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)*((a+b*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)*((a+b*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)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a*b^4-2*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^3+6*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^4+3*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^2-7*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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^3-7*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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+7*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*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)*a^2*b^3)*cos(d*x+c)^2*(1/cos(d*x+c))^(5/2)/sin(d*x+c)/(a+b*cos(d*x+c))^(3/2)/b^2/(a+b)^2/(a-b)^2","B"
769,0,0,318,1.542000," ","int(cos(d*x+c)^m*(a+b*cos(d*x+c))^4,x)","\int \left(\cos^{m}\left(d x +c \right)\right) \left(a +b \cos \left(d x +c \right)\right)^{4}\, dx"," ",0,"int(cos(d*x+c)^m*(a+b*cos(d*x+c))^4,x)","F"
770,0,0,238,1.296000," ","int(cos(d*x+c)^m*(a+b*cos(d*x+c))^3,x)","\int \left(\cos^{m}\left(d x +c \right)\right) \left(a +b \cos \left(d x +c \right)\right)^{3}\, dx"," ",0,"int(cos(d*x+c)^m*(a+b*cos(d*x+c))^3,x)","F"
771,0,0,167,1.120000," ","int(cos(d*x+c)^m*(a+b*cos(d*x+c))^2,x)","\int \left(\cos^{m}\left(d x +c \right)\right) \left(a +b \cos \left(d x +c \right)\right)^{2}\, dx"," ",0,"int(cos(d*x+c)^m*(a+b*cos(d*x+c))^2,x)","F"
772,0,0,119,1.063000," ","int(cos(d*x+c)^m*(a+b*cos(d*x+c)),x)","\int \left(\cos^{m}\left(d x +c \right)\right) \left(a +b \cos \left(d x +c \right)\right)\, dx"," ",0,"int(cos(d*x+c)^m*(a+b*cos(d*x+c)),x)","F"
773,0,0,172,0.770000," ","int(cos(d*x+c)^m/(a+b*cos(d*x+c)),x)","\int \frac{\cos^{m}\left(d x +c \right)}{a +b \cos \left(d x +c \right)}\, dx"," ",0,"int(cos(d*x+c)^m/(a+b*cos(d*x+c)),x)","F"
774,0,0,264,0.426000," ","int(cos(d*x+c)^m/(a+b*cos(d*x+c))^2,x)","\int \frac{\cos^{m}\left(d x +c \right)}{\left(a +b \cos \left(d x +c \right)\right)^{2}}\, dx"," ",0,"int(cos(d*x+c)^m/(a+b*cos(d*x+c))^2,x)","F"
775,0,0,250,1.509000," ","int((a+b*cos(d*x+c))^3*sec(d*x+c)^m,x)","\int \left(a +b \cos \left(d x +c \right)\right)^{3} \left(\sec^{m}\left(d x +c \right)\right)\, dx"," ",0,"int((a+b*cos(d*x+c))^3*sec(d*x+c)^m,x)","F"
776,0,0,176,1.296000," ","int((a+b*cos(d*x+c))^2*sec(d*x+c)^m,x)","\int \left(a +b \cos \left(d x +c \right)\right)^{2} \left(\sec^{m}\left(d x +c \right)\right)\, dx"," ",0,"int((a+b*cos(d*x+c))^2*sec(d*x+c)^m,x)","F"
777,0,0,123,1.096000," ","int((a+b*cos(d*x+c))*sec(d*x+c)^m,x)","\int \left(a +b \cos \left(d x +c \right)\right) \left(\sec^{m}\left(d x +c \right)\right)\, dx"," ",0,"int((a+b*cos(d*x+c))*sec(d*x+c)^m,x)","F"
778,1,67,22,0.193000," ","int((1-cos(x))^(1/2)/(a-cos(x))^(1/2),x)","-\frac{\left(2-2 \cos \left(x \right)\right)^{\frac{3}{2}} \sqrt{a -\cos \left(x \right)}\, \arctan \left(\frac{\sqrt{-\frac{2 \left(-a +\cos \left(x \right)\right)}{\cos \left(x \right)+1}}\, \sqrt{2}}{2}\right)}{\sin \left(x \right) \left(-1+\cos \left(x \right)\right) \sqrt{-\frac{2 \left(-a +\cos \left(x \right)\right)}{\cos \left(x \right)+1}}}"," ",0,"-(2-2*cos(x))^(3/2)*(a-cos(x))^(1/2)*arctan(1/2*(-2*(-a+cos(x))/(cos(x)+1))^(1/2)*2^(1/2))/sin(x)/(-1+cos(x))/(-2*(-a+cos(x))/(cos(x)+1))^(1/2)","B"
779,1,67,55,0.141000," ","int(((1-cos(x))/(a-cos(x)))^(1/2),x)","-\frac{\sqrt{2}\, \sqrt{\frac{-1+\cos \left(x \right)}{-a +\cos \left(x \right)}}\, \sin \left(x \right) \sqrt{-\frac{2 \left(-a +\cos \left(x \right)\right)}{\cos \left(x \right)+1}}\, \arctan \left(\frac{\sqrt{-\frac{2 \left(-a +\cos \left(x \right)\right)}{\cos \left(x \right)+1}}\, \sqrt{2}}{2}\right)}{-1+\cos \left(x \right)}"," ",0,"-2^(1/2)*((-1+cos(x))/(-a+cos(x)))^(1/2)*sin(x)*(-2*(-a+cos(x))/(cos(x)+1))^(1/2)*arctan(1/2*(-2*(-a+cos(x))/(cos(x)+1))^(1/2)*2^(1/2))/(-1+cos(x))","A"
780,1,51,33,0.053000," ","int((a+a*cos(d*x+c))*(-1/2*B+B*cos(d*x+c)),x)","\frac{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)+a B \sin \left(d x +c \right)-a B \left(d x +c \right)}{2 d}"," ",0,"1/2/d*(2*a*B*(1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c)+a*B*sin(d*x+c)-a*B*(d*x+c))","A"
781,1,150,24,0.056000," ","int((a+a*cos(d*x+c))^4*(-4/5*B+B*cos(d*x+c)),x)","\frac{a^{4} 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)+16 a^{4} 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{14 a^{4} B \left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3}-4 a^{4} B \left(\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{2}+\frac{d x}{2}+\frac{c}{2}\right)-11 a^{4} B \sin \left(d x +c \right)-4 a^{4} B \left(d x +c \right)}{5 d}"," ",0,"1/5/d*(a^4*B*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c)+16*a^4*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)+14/3*a^4*B*(2+cos(d*x+c)^2)*sin(d*x+c)-4*a^4*B*(1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c)-11*a^4*B*sin(d*x+c)-4*a^4*B*(d*x+c))","B"
782,1,74,28,0.374000," ","int((a+a*cos(d*x+c))^n*(-B*n/(1+n)+B*cos(d*x+c)),x)","\frac{2 B \tan \left(\frac{d x}{2}+\frac{c}{2}\right) {\mathrm e}^{n \ln \left(a +\frac{a \left(1-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}{1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\right)}}{d \left(1+n \right) \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}"," ",0,"2*B/d/(1+n)*tan(1/2*d*x+1/2*c)*exp(n*ln(a+a*(1-tan(1/2*d*x+1/2*c)^2)/(1+tan(1/2*d*x+1/2*c)^2)))/(1+tan(1/2*d*x+1/2*c)^2)","B"
783,1,48,24,0.072000," ","int((-3/2*B+B*cos(d*x+c))/(a+a*cos(d*x+c))^3,x)","\frac{B \left(-\left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-2 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{8 d \,a^{3}}"," ",0,"1/8/d*B/a^3*(-tan(1/2*d*x+1/2*c)^5-2*tan(1/2*d*x+1/2*c)^3-tan(1/2*d*x+1/2*c))","A"
784,1,48,24,0.301000," ","int((a+a*cos(d*x+c))^(3/2)*(-3/5*B+B*cos(d*x+c)),x)","\frac{8 \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{2} \sin \left(\frac{d x}{2}+\frac{c}{2}\right) B \sqrt{2}}{5 \sqrt{a \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, d}"," ",0,"8/5*cos(1/2*d*x+1/2*c)^5*a^2*sin(1/2*d*x+1/2*c)*B*2^(1/2)/(a*cos(1/2*d*x+1/2*c)^2)^(1/2)/d","A"
785,1,43,24,0.227000," ","int((B+B*cos(d*x+c))/(a+a*cos(d*x+c))^(1/2),x)","\frac{2 B \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2}}{\sqrt{a \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, d}"," ",0,"2*B*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)*2^(1/2)/(a*cos(1/2*d*x+1/2*c)^2)^(1/2)/d","A"
786,1,48,24,0.202000," ","int((-5/3*B+B*cos(d*x+c))/(a+a*cos(d*x+c))^(5/2),x)","-\frac{\sin \left(\frac{d x}{2}+\frac{c}{2}\right) B \sqrt{2}}{6 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)^{3} a^{2} \sqrt{a \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, d}"," ",0,"-1/6/cos(1/2*d*x+1/2*c)^3/a^2*sin(1/2*d*x+1/2*c)*B*2^(1/2)/(a*cos(1/2*d*x+1/2*c)^2)^(1/2)/d","A"
787,0,0,84,0.226000," ","int((a+a*cos(d*x+c))^(2/3)*(A+B*cos(d*x+c)),x)","\int \left(a +a \cos \left(d x +c \right)\right)^{\frac{2}{3}} \left(A +B \cos \left(d x +c \right)\right)\, dx"," ",0,"int((a+a*cos(d*x+c))^(2/3)*(A+B*cos(d*x+c)),x)","F"
788,0,0,82,0.200000," ","int((a+a*cos(d*x+c))^(1/3)*(A+B*cos(d*x+c)),x)","\int \left(a +a \cos \left(d x +c \right)\right)^{\frac{1}{3}} \left(A +B \cos \left(d x +c \right)\right)\, dx"," ",0,"int((a+a*cos(d*x+c))^(1/3)*(A+B*cos(d*x+c)),x)","F"
789,0,0,84,0.245000," ","int((A+B*cos(d*x+c))/(a+a*cos(d*x+c))^(1/3),x)","\int \frac{A +B \cos \left(d x +c \right)}{\left(a +a \cos \left(d x +c \right)\right)^{\frac{1}{3}}}\, dx"," ",0,"int((A+B*cos(d*x+c))/(a+a*cos(d*x+c))^(1/3),x)","F"
790,0,0,89,0.171000," ","int((A+B*cos(d*x+c))/(a+a*cos(d*x+c))^(2/3),x)","\int \frac{A +B \cos \left(d x +c \right)}{\left(a +a \cos \left(d x +c \right)\right)^{\frac{2}{3}}}\, dx"," ",0,"int((A+B*cos(d*x+c))/(a+a*cos(d*x+c))^(2/3),x)","F"
791,1,117,54,0.090000," ","int((b*B/a+B*cos(d*x+c))/(a+b*cos(d*x+c)),x)","-\frac{2 B a \arctan \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{2 B b \arctan \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 B \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d b}"," ",0,"-2/d*B*a/b/((a-b)*(a+b))^(1/2)*arctan(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))+2/d*B/a*b/((a-b)*(a+b))^(1/2)*arctan(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))+2/d*B/b*arctan(tan(1/2*d*x+1/2*c))","B"
792,1,51,22,0.062000," ","int((a+b*cos(d*x+c))/(b+a*cos(d*x+c))^2,x)","-\frac{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)}"," ",0,"-2/d*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)","B"
793,1,39,41,0.096000," ","int((3+cos(d*x+c))/(2-cos(d*x+c)),x)","\frac{10 \sqrt{3}\, \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{3}\right)}{3 d}-\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d}"," ",0,"10/3/d*3^(1/2)*arctan(tan(1/2*d*x+1/2*c)*3^(1/2))-2/d*arctan(tan(1/2*d*x+1/2*c))","A"
794,1,171,83,0.983000," ","int((a*B+b*B*cos(d*x+c))/(a+b*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) b +a -b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) \left(a -b \right)}{\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(a +b \right) \left(\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(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a +b}\, d}"," ",0,"-2*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)*sin(1/2*d*x+1/2*c)^2)^(1/2)*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)/(a-b))^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*(a-b)/(-2*sin(1/2*d*x+1/2*c)^4*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*b+a+b)^(1/2)/d","B"
795,0,0,189,0.186000," ","int((a+b*cos(d*x+c))^(2/3)*(A+B*cos(d*x+c)),x)","\int \left(a +b \cos \left(d x +c \right)\right)^{\frac{2}{3}} \left(A +B \cos \left(d x +c \right)\right)\, dx"," ",0,"int((a+b*cos(d*x+c))^(2/3)*(A+B*cos(d*x+c)),x)","F"
796,0,0,189,0.176000," ","int((a+b*cos(d*x+c))^(1/3)*(A+B*cos(d*x+c)),x)","\int \left(a +b \cos \left(d x +c \right)\right)^{\frac{1}{3}} \left(A +B \cos \left(d x +c \right)\right)\, dx"," ",0,"int((a+b*cos(d*x+c))^(1/3)*(A+B*cos(d*x+c)),x)","F"
797,0,0,186,0.249000," ","int((A+B*cos(d*x+c))/(a+b*cos(d*x+c))^(1/3),x)","\int \frac{A +B \cos \left(d x +c \right)}{\left(a +b \cos \left(d x +c \right)\right)^{\frac{1}{3}}}\, dx"," ",0,"int((A+B*cos(d*x+c))/(a+b*cos(d*x+c))^(1/3),x)","F"
798,0,0,186,0.204000," ","int((A+B*cos(d*x+c))/(a+b*cos(d*x+c))^(2/3),x)","\int \frac{A +B \cos \left(d x +c \right)}{\left(a +b \cos \left(d x +c \right)\right)^{\frac{2}{3}}}\, dx"," ",0,"int((A+B*cos(d*x+c))/(a+b*cos(d*x+c))^(2/3),x)","F"
799,1,299,196,0.875000," ","int(cos(d*x+c)^2*(b*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c)),x)","-\frac{2 \sqrt{b \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)}\, b \left(240 B \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(-168 A -360 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(168 A +280 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(-42 A -80 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)-63 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}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+25 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)\right)}{105 \sqrt{-b \left(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)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}\, d}"," ",0,"-2/105*(b*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*b*(240*B*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^8+(-168*A-360*B)*sin(1/2*d*x+1/2*c)^6*cos(1/2*d*x+1/2*c)+(168*A+280*B)*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+(-42*A-80*B)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)-63*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)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+25*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*(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)/(b*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/d","A"
800,1,271,171,0.894000," ","int(cos(d*x+c)*(b*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c)),x)","-\frac{2 \sqrt{b \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)}\, b \left(-24 B \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(20 A +24 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(-10 A -6 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 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 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)\right)}{15 \sqrt{-b \left(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)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}\, d}"," ",0,"-2/15*(b*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*b*(-24*B*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6+(20*A+24*B)*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+(-10*A-6*B)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+5*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*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)))/(-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)/(b*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/d","A"
801,1,238,146,0.984000," ","int((b*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c)),x)","\frac{2 \sqrt{b \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)}\, b \left(-4 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 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}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\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)+2 B \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{-b \left(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)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}\, d}"," ",0,"2/3*(b*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*b*(-4*B*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4+3*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)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-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))+2*B*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^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)/(b*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/d","A"
802,1,161,124,0.936000," ","int((b*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c))*sec(d*x+c),x)","-\frac{2 \sqrt{b \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)}\, 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}\, \left(A \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-B \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)\right)}{\sqrt{-b \left(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)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}\, d}"," ",0,"-2*(b*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*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)*(A*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-B*EllipticE(cos(1/2*d*x+1/2*c),2^(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)/(b*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/d","A"
803,1,213,147,0.986000," ","int((b*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c))*sec(d*x+c)^2,x)","-\frac{2 b \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b}\, \left(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}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-2 A \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\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)\right)}{\sqrt{-b \left(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)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}\, d}"," ",0,"-2*b*(-2*sin(1/2*d*x+1/2*c)^4*b+sin(1/2*d*x+1/2*c)^2*b)^(1/2)*(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)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-2*A*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^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*(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)/(b*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/d","A"
804,1,453,172,1.091000," ","int((b*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c))*sec(d*x+c)^3,x)","-\frac{2 \left(12 B \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{4}\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) b +\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b}\, \left(A +3 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)-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) b +\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b}\, \left(A \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+3 B \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)+A \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(\sin^{2}\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 B \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(\sin^{2}\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}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)\right) b}{3 \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \sqrt{-b \left(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)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}\, d}"," ",0,"-2/3*(12*B*(-2*sin(1/2*d*x+1/2*c)^4*b+sin(1/2*d*x+1/2*c)^2*b)^(1/2)*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4-2*(-2*sin(1/2*d*x+1/2*c)^4*b+sin(1/2*d*x+1/2*c)^2*b)^(1/2)*(A+3*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)^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*b+sin(1/2*d*x+1/2*c)^2*b)^(1/2)*(A*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+3*B*EllipticE(cos(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*b+sin(1/2*d*x+1/2*c)^2*b)^(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))+3*B*(-2*sin(1/2*d*x+1/2*c)^4*b+sin(1/2*d*x+1/2*c)^2*b)^(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/(2*cos(1/2*d*x+1/2*c)^2-1)/(-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)/(b*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/d","B"
805,1,575,197,2.368000," ","int((b*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c))*sec(d*x+c)^4,x)","\frac{2 \sqrt{b \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 A \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)-72 A \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+20 B \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}}\, \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-36 A \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)+72 A \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-20 B \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}}\, \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+20 B \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+9 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}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-24 A \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\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)-10 B \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) b +\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b}}{15 \sin \left(\frac{d x}{2}+\frac{c}{2}\right)^{3} \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) \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}\, d}"," ",0,"2/15*(b*(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)^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)*(36*A*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)^4-72*A*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6+20*B*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)*sin(1/2*d*x+1/2*c)^4-36*A*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+72*A*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4-20*B*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)*sin(1/2*d*x+1/2*c)^2+20*B*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4+9*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)*EllipticE(cos(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)^2+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))-10*B*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*b+sin(1/2*d*x+1/2*c)^2*b)^(1/2)/(b*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/d","B"
806,1,301,197,0.794000," ","int(cos(d*x+c)*(b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)),x)","-\frac{2 \sqrt{b \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)}\, b^{2} \left(240 B \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(-168 A -360 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(168 A +280 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(-42 A -80 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)-63 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}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+25 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)\right)}{105 \sqrt{-b \left(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)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}\, d}"," ",0,"-2/105*(b*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*b^2*(240*B*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^8+(-168*A-360*B)*sin(1/2*d*x+1/2*c)^6*cos(1/2*d*x+1/2*c)+(168*A+280*B)*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+(-42*A-80*B)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)-63*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)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+25*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*(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)/(b*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/d","A"
807,1,273,172,0.874000," ","int((b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)),x)","-\frac{2 \sqrt{b \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)}\, b^{2} \left(-24 B \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(20 A +24 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(-10 A -6 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 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 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)\right)}{15 \sqrt{-b \left(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)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}\, d}"," ",0,"-2/15*(b*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*b^2*(-24*B*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6+(20*A+24*B)*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+(-10*A-6*B)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+5*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*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)))/(-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)/(b*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/d","A"
808,1,240,150,0.902000," ","int((b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))*sec(d*x+c),x)","\frac{2 \sqrt{b \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)}\, b^{2} \left(-4 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 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}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\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)+2 B \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{-b \left(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)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}\, d}"," ",0,"2/3*(b*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*b^2*(-4*B*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4+3*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)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-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))+2*B*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^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)/(b*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/d","A"
809,1,163,127,0.849000," ","int((b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))*sec(d*x+c)^2,x)","-\frac{2 \sqrt{b \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)}\, 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}\, \left(A \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-B \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)\right)}{\sqrt{-b \left(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)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}\, d}"," ",0,"-2*(b*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*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)*(A*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-B*EllipticE(cos(1/2*d*x+1/2*c),2^(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)/(b*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/d","A"
810,1,215,152,1.017000," ","int((b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))*sec(d*x+c)^3,x)","-\frac{2 b^{2} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b}\, \left(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}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-2 A \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\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)\right)}{\sqrt{-b \left(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)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}\, d}"," ",0,"-2*b^2*(-2*sin(1/2*d*x+1/2*c)^4*b+sin(1/2*d*x+1/2*c)^2*b)^(1/2)*(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)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-2*A*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^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*(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)/(b*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/d","A"
811,1,455,177,0.968000," ","int((b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))*sec(d*x+c)^4,x)","-\frac{2 \left(12 B \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{4}\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) b +\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b}\, \left(A +3 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)-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) b +\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b}\, \left(A \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+3 B \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)+A \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(\sin^{2}\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 B \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(\sin^{2}\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}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)\right) b^{2}}{3 \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \sqrt{-b \left(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)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}\, d}"," ",0,"-2/3*(12*B*(-2*sin(1/2*d*x+1/2*c)^4*b+sin(1/2*d*x+1/2*c)^2*b)^(1/2)*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4-2*(-2*sin(1/2*d*x+1/2*c)^4*b+sin(1/2*d*x+1/2*c)^2*b)^(1/2)*(A+3*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)^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*b+sin(1/2*d*x+1/2*c)^2*b)^(1/2)*(A*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+3*B*EllipticE(cos(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*b+sin(1/2*d*x+1/2*c)^2*b)^(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))+3*B*(-2*sin(1/2*d*x+1/2*c)^4*b+sin(1/2*d*x+1/2*c)^2*b)^(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^2/(2*cos(1/2*d*x+1/2*c)^2-1)/(-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)/(b*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/d","B"
812,1,576,202,2.370000," ","int((b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))*sec(d*x+c)^5,x)","\frac{2 \sqrt{b \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)}\, b \left(36 A \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)-72 A \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+20 B \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}}\, \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-36 A \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)+72 A \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-20 B \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}}\, \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+20 B \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+9 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}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-24 A \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\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)-10 B \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) b +\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b}}{15 \sin \left(\frac{d x}{2}+\frac{c}{2}\right)^{3} \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) \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}\, d}"," ",0,"2/15*(b*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*b/sin(1/2*d*x+1/2*c)^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)*(36*A*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)^4-72*A*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6+20*B*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)*sin(1/2*d*x+1/2*c)^4-36*A*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+72*A*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4-20*B*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)*sin(1/2*d*x+1/2*c)^2+20*B*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4+9*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)*EllipticE(cos(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)^2+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))-10*B*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*b+sin(1/2*d*x+1/2*c)^2*b)^(1/2)/(b*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/d","B"
813,1,301,199,0.898000," ","int((b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)),x)","-\frac{2 \sqrt{b \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)}\, b^{3} \left(240 B \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(-168 A -360 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(168 A +280 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(-42 A -80 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)-63 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}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+25 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)\right)}{105 \sqrt{-b \left(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)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}\, d}"," ",0,"-2/105*(b*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*b^3*(240*B*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^8+(-168*A-360*B)*sin(1/2*d*x+1/2*c)^6*cos(1/2*d*x+1/2*c)+(168*A+280*B)*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+(-42*A-80*B)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)-63*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)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+25*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*(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)/(b*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/d","A"
814,1,273,177,0.960000," ","int((b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))*sec(d*x+c),x)","-\frac{2 \sqrt{b \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)}\, b^{3} \left(-24 B \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(20 A +24 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(-10 A -6 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 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 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)\right)}{15 \sqrt{-b \left(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)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}\, d}"," ",0,"-2/15*(b*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*b^3*(-24*B*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6+(20*A+24*B)*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+(-10*A-6*B)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+5*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*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)))/(-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)/(b*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/d","A"
815,1,240,154,0.879000," ","int((b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))*sec(d*x+c)^2,x)","\frac{2 \sqrt{b \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)}\, b^{3} \left(-4 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 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}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\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)+2 B \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{-b \left(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)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}\, d}"," ",0,"2/3*(b*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*b^3*(-4*B*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4+3*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)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-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))+2*B*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^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)/(b*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/d","A"
816,1,163,129,0.808000," ","int((b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))*sec(d*x+c)^3,x)","-\frac{2 \sqrt{b \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)}\, 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}\, \left(A \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-B \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)\right)}{\sqrt{-b \left(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)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}\, d}"," ",0,"-2*(b*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*b^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)*(A*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-B*EllipticE(cos(1/2*d*x+1/2*c),2^(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)/(b*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/d","A"
817,1,215,154,0.987000," ","int((b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))*sec(d*x+c)^4,x)","-\frac{2 b^{3} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b}\, \left(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}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-2 A \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\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)\right)}{\sqrt{-b \left(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)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}\, d}"," ",0,"-2*b^3*(-2*sin(1/2*d*x+1/2*c)^4*b+sin(1/2*d*x+1/2*c)^2*b)^(1/2)*(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)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-2*A*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^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*(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)/(b*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/d","A"
818,1,455,179,1.135000," ","int((b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))*sec(d*x+c)^5,x)","-\frac{2 \left(12 B \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{4}\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) b +\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b}\, \left(A +3 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)-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) b +\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b}\, \left(A \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+3 B \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)+A \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(\sin^{2}\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 B \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(\sin^{2}\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}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)\right) b^{3}}{3 \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \sqrt{-b \left(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)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}\, d}"," ",0,"-2/3*(12*B*(-2*sin(1/2*d*x+1/2*c)^4*b+sin(1/2*d*x+1/2*c)^2*b)^(1/2)*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4-2*(-2*sin(1/2*d*x+1/2*c)^4*b+sin(1/2*d*x+1/2*c)^2*b)^(1/2)*(A+3*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)^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*b+sin(1/2*d*x+1/2*c)^2*b)^(1/2)*(A*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+3*B*EllipticE(cos(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*b+sin(1/2*d*x+1/2*c)^2*b)^(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))+3*B*(-2*sin(1/2*d*x+1/2*c)^4*b+sin(1/2*d*x+1/2*c)^2*b)^(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^3/(2*cos(1/2*d*x+1/2*c)^2-1)/(-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)/(b*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/d","B"
819,1,578,204,2.435000," ","int((b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))*sec(d*x+c)^6,x)","\frac{2 \sqrt{b \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)}\, b^{2} \left(36 A \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)-72 A \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+20 B \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}}\, \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-36 A \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)+72 A \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-20 B \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}}\, \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+20 B \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+9 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}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-24 A \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\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)-10 B \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) b +\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b}}{15 \sin \left(\frac{d x}{2}+\frac{c}{2}\right)^{3} \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) \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}\, d}"," ",0,"2/15*(b*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*b^2/sin(1/2*d*x+1/2*c)^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)*(36*A*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)^4-72*A*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6+20*B*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)*sin(1/2*d*x+1/2*c)^4-36*A*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+72*A*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4-20*B*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)*sin(1/2*d*x+1/2*c)^2+20*B*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4+9*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)*EllipticE(cos(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)^2+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))-10*B*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*b+sin(1/2*d*x+1/2*c)^2*b)^(1/2)/(b*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/d","B"
820,1,298,201,0.956000," ","int(cos(d*x+c)^3*(A+B*cos(d*x+c))/(b*cos(d*x+c))^(1/2),x)","-\frac{2 \sqrt{b \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 B \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(-168 A -360 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(168 A +280 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(-42 A -80 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)-63 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}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+25 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)\right)}{105 \sqrt{-b \left(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)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}\, d}"," ",0,"-2/105*(b*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(240*B*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^8+(-168*A-360*B)*sin(1/2*d*x+1/2*c)^6*cos(1/2*d*x+1/2*c)+(168*A+280*B)*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+(-42*A-80*B)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)-63*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)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+25*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*(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)/(b*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/d","A"
821,1,270,176,0.958000," ","int(cos(d*x+c)^2*(A+B*cos(d*x+c))/(b*cos(d*x+c))^(1/2),x)","-\frac{2 \sqrt{b \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 B \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(20 A +24 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(-10 A -6 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 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 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)\right)}{15 \sqrt{-b \left(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)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}\, d}"," ",0,"-2/15*(b*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(-24*B*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6+(20*A+24*B)*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+(-10*A-6*B)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+5*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*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)))/(-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)/(b*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/d","A"
822,1,237,151,1.010000," ","int(cos(d*x+c)*(A+B*cos(d*x+c))/(b*cos(d*x+c))^(1/2),x)","\frac{2 \sqrt{b \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 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 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}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\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)+2 B \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{-b \left(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)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}\, d}"," ",0,"2/3*(b*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(-4*B*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4+3*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)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-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))+2*B*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^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)/(b*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/d","A"
823,1,160,126,0.901000," ","int((A+B*cos(d*x+c))/(b*cos(d*x+c))^(1/2),x)","-\frac{2 \sqrt{b \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(A \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-B \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)\right)}{\sqrt{-b \left(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)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}\, d}"," ",0,"-2*(b*(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)*(A*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-B*EllipticE(cos(1/2*d*x+1/2*c),2^(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)/(b*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/d","A"
824,1,212,148,1.158000," ","int((A+B*cos(d*x+c))*sec(d*x+c)/(b*cos(d*x+c))^(1/2),x)","-\frac{2 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b}\, \left(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}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-2 A \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\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)\right)}{\sqrt{-b \left(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)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}\, d}"," ",0,"-2*(-2*sin(1/2*d*x+1/2*c)^4*b+sin(1/2*d*x+1/2*c)^2*b)^(1/2)*(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)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-2*A*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^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*(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)/(b*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/d","A"
825,1,405,171,2.308000," ","int((A+B*cos(d*x+c))*sec(d*x+c)^2/(b*cos(d*x+c))^(1/2),x)","\frac{2 \sqrt{b \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 \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)+6 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) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-12 B \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{4}\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}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+2 A \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-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}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+6 B \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) b +\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b}}{3 b \sin \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) \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}\, d}"," ",0,"2/3*(b*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)/b/sin(1/2*d*x+1/2*c)^3/(4*sin(1/2*d*x+1/2*c)^4-4*sin(1/2*d*x+1/2*c)^2+1)*(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+6*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))*sin(1/2*d*x+1/2*c)^2-12*B*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4-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))+2*A*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2-3*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)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+6*B*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*b+sin(1/2*d*x+1/2*c)^2*b)^(1/2)/(b*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/d","B"
826,1,578,196,2.598000," ","int((A+B*cos(d*x+c))*sec(d*x+c)^3/(b*cos(d*x+c))^(1/2),x)","\frac{2 \sqrt{b \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 A \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)-72 A \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+20 B \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}}\, \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-36 A \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)+72 A \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-20 B \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}}\, \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+20 B \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+9 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}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-24 A \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\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)-10 B \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) b +\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b}}{15 b \sin \left(\frac{d x}{2}+\frac{c}{2}\right)^{3} \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) \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}\, d}"," ",0,"2/15*(b*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)/b/sin(1/2*d*x+1/2*c)^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)*(36*A*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)^4-72*A*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6+20*B*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)*sin(1/2*d*x+1/2*c)^4-36*A*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+72*A*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4-20*B*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)*sin(1/2*d*x+1/2*c)^2+20*B*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4+9*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)*EllipticE(cos(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)^2+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))-10*B*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*b+sin(1/2*d*x+1/2*c)^2*b)^(1/2)/(b*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/d","B"
827,1,301,204,1.083000," ","int(cos(d*x+c)^4*(A+B*cos(d*x+c))/(b*cos(d*x+c))^(3/2),x)","-\frac{2 \sqrt{b \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 B \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(-168 A -360 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(168 A +280 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(-42 A -80 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)-63 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}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+25 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)\right)}{105 b \sqrt{-b \left(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)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}\, d}"," ",0,"-2/105*(b*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)/b*(240*B*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^8+(-168*A-360*B)*sin(1/2*d*x+1/2*c)^6*cos(1/2*d*x+1/2*c)+(168*A+280*B)*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+(-42*A-80*B)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)-63*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)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+25*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*(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)/(b*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/d","A"
828,1,273,179,0.990000," ","int(cos(d*x+c)^3*(A+B*cos(d*x+c))/(b*cos(d*x+c))^(3/2),x)","-\frac{2 \sqrt{b \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 B \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(20 A +24 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(-10 A -6 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 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 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)\right)}{15 b \sqrt{-b \left(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)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}\, d}"," ",0,"-2/15*(b*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)/b*(-24*B*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6+(20*A+24*B)*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+(-10*A-6*B)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+5*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*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)))/(-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)/(b*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/d","A"
829,1,240,154,0.940000," ","int(cos(d*x+c)^2*(A+B*cos(d*x+c))/(b*cos(d*x+c))^(3/2),x)","\frac{2 \sqrt{b \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 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 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}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\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)+2 B \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 b \sqrt{-b \left(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)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}\, d}"," ",0,"2/3*(b*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)/b*(-4*B*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4+3*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)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-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))+2*B*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^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)/(b*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/d","A"
830,1,163,129,0.853000," ","int(cos(d*x+c)*(A+B*cos(d*x+c))/(b*cos(d*x+c))^(3/2),x)","-\frac{2 \sqrt{b \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(A \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-B \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)\right)}{b \sqrt{-b \left(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)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}\, d}"," ",0,"-2*(b*(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)*(A*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-B*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2)))/b/(-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)/(b*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/d","A"
831,1,215,154,1.000000," ","int((A+B*cos(d*x+c))/(b*cos(d*x+c))^(3/2),x)","-\frac{2 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b}\, \left(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}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-2 A \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\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)\right)}{b \sqrt{-b \left(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)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}\, d}"," ",0,"-2/b*(-2*sin(1/2*d*x+1/2*c)^4*b+sin(1/2*d*x+1/2*c)^2*b)^(1/2)*(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)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-2*A*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^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*(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)/(b*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/d","A"
832,1,455,176,1.057000," ","int((A+B*cos(d*x+c))*sec(d*x+c)/(b*cos(d*x+c))^(3/2),x)","-\frac{2 \left(12 B \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{4}\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) b +\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b}\, \left(A +3 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)-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) b +\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b}\, \left(A \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+3 B \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)+A \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(\sin^{2}\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 B \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(\sin^{2}\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}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)\right)}{3 b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \sqrt{-b \left(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)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}\, d}"," ",0,"-2/3*(12*B*(-2*sin(1/2*d*x+1/2*c)^4*b+sin(1/2*d*x+1/2*c)^2*b)^(1/2)*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4-2*(-2*sin(1/2*d*x+1/2*c)^4*b+sin(1/2*d*x+1/2*c)^2*b)^(1/2)*(A+3*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)^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*b+sin(1/2*d*x+1/2*c)^2*b)^(1/2)*(A*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+3*B*EllipticE(cos(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*b+sin(1/2*d*x+1/2*c)^2*b)^(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))+3*B*(-2*sin(1/2*d*x+1/2*c)^4*b+sin(1/2*d*x+1/2*c)^2*b)^(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/(2*cos(1/2*d*x+1/2*c)^2-1)/(-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)/(b*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/d","B"
833,1,578,199,2.731000," ","int((A+B*cos(d*x+c))*sec(d*x+c)^2/(b*cos(d*x+c))^(3/2),x)","\frac{2 \sqrt{b \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 A \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)-72 A \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+20 B \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}}\, \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-36 A \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)+72 A \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-20 B \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}}\, \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+20 B \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+9 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}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-24 A \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\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)-10 B \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) b +\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b}}{15 b^{2} \sin \left(\frac{d x}{2}+\frac{c}{2}\right)^{3} \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) \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}\, d}"," ",0,"2/15*(b*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)/b^2/sin(1/2*d*x+1/2*c)^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)*(36*A*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)^4-72*A*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6+20*B*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)*sin(1/2*d*x+1/2*c)^4-36*A*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+72*A*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4-20*B*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)*sin(1/2*d*x+1/2*c)^2+20*B*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4+9*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)*EllipticE(cos(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)^2+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))-10*B*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*b+sin(1/2*d*x+1/2*c)^2*b)^(1/2)/(b*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/d","B"
834,1,301,204,0.931000," ","int(cos(d*x+c)^5*(A+B*cos(d*x+c))/(b*cos(d*x+c))^(5/2),x)","-\frac{2 \sqrt{b \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 B \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(-168 A -360 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(168 A +280 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(-42 A -80 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)-63 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}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+25 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)\right)}{105 b^{2} \sqrt{-b \left(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)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}\, d}"," ",0,"-2/105*(b*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)/b^2*(240*B*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^8+(-168*A-360*B)*sin(1/2*d*x+1/2*c)^6*cos(1/2*d*x+1/2*c)+(168*A+280*B)*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+(-42*A-80*B)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)-63*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)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+25*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*(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)/(b*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/d","A"
835,1,273,179,0.921000," ","int(cos(d*x+c)^4*(A+B*cos(d*x+c))/(b*cos(d*x+c))^(5/2),x)","-\frac{2 \sqrt{b \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 B \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(20 A +24 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(-10 A -6 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 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 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)\right)}{15 b^{2} \sqrt{-b \left(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)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}\, d}"," ",0,"-2/15*(b*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)/b^2*(-24*B*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6+(20*A+24*B)*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+(-10*A-6*B)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+5*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*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)))/(-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)/(b*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/d","A"
836,1,240,154,1.052000," ","int(cos(d*x+c)^3*(A+B*cos(d*x+c))/(b*cos(d*x+c))^(5/2),x)","\frac{2 \sqrt{b \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 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 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}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\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)+2 B \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 b^{2} \sqrt{-b \left(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)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}\, d}"," ",0,"2/3*(b*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)/b^2*(-4*B*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4+3*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)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-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))+2*B*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^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)/(b*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/d","A"
837,1,163,129,0.995000," ","int(cos(d*x+c)^2*(A+B*cos(d*x+c))/(b*cos(d*x+c))^(5/2),x)","-\frac{2 \sqrt{b \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(A \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-B \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)\right)}{b^{2} \sqrt{-b \left(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)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}\, d}"," ",0,"-2*(b*(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)*(A*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-B*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2)))/b^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)/(b*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/d","A"
838,1,215,154,1.108000," ","int(cos(d*x+c)*(A+B*cos(d*x+c))/(b*cos(d*x+c))^(5/2),x)","-\frac{2 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b}\, \left(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}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-2 A \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\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)\right)}{b^{2} \sqrt{-b \left(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)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}\, d}"," ",0,"-2/b^2*(-2*sin(1/2*d*x+1/2*c)^4*b+sin(1/2*d*x+1/2*c)^2*b)^(1/2)*(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)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-2*A*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^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*(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)/(b*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/d","A"
839,1,455,179,1.056000," ","int((A+B*cos(d*x+c))/(b*cos(d*x+c))^(5/2),x)","-\frac{2 \left(12 B \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{4}\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) b +\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b}\, \left(A +3 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)-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) b +\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b}\, \left(A \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+3 B \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)+A \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(\sin^{2}\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 B \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(\sin^{2}\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}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)\right)}{3 b^{2} \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \sqrt{-b \left(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)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}\, d}"," ",0,"-2/3*(12*B*(-2*sin(1/2*d*x+1/2*c)^4*b+sin(1/2*d*x+1/2*c)^2*b)^(1/2)*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4-2*(-2*sin(1/2*d*x+1/2*c)^4*b+sin(1/2*d*x+1/2*c)^2*b)^(1/2)*(A+3*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)^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*b+sin(1/2*d*x+1/2*c)^2*b)^(1/2)*(A*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+3*B*EllipticE(cos(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*b+sin(1/2*d*x+1/2*c)^2*b)^(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))+3*B*(-2*sin(1/2*d*x+1/2*c)^4*b+sin(1/2*d*x+1/2*c)^2*b)^(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^2/(2*cos(1/2*d*x+1/2*c)^2-1)/(-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)/(b*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/d","B"
840,1,578,201,2.531000," ","int((A+B*cos(d*x+c))*sec(d*x+c)/(b*cos(d*x+c))^(5/2),x)","\frac{2 \sqrt{b \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 A \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)-72 A \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+20 B \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}}\, \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-36 A \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)+72 A \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-20 B \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}}\, \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+20 B \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+9 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}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-24 A \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\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)-10 B \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) b +\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b}}{15 b^{3} \sin \left(\frac{d x}{2}+\frac{c}{2}\right)^{3} \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) \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}\, d}"," ",0,"2/15*(b*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)/b^3/sin(1/2*d*x+1/2*c)^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)*(36*A*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)^4-72*A*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6+20*B*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)*sin(1/2*d*x+1/2*c)^4-36*A*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+72*A*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4-20*B*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)*sin(1/2*d*x+1/2*c)^2+20*B*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4+9*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)*EllipticE(cos(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)^2+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))-10*B*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*b+sin(1/2*d*x+1/2*c)^2*b)^(1/2)/(b*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/d","B"
841,1,578,204,2.507000," ","int((A+B*cos(d*x+c))/(b*cos(d*x+c))^(7/2),x)","\frac{2 \sqrt{b \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 A \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)-72 A \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+20 B \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}}\, \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-36 A \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)+72 A \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-20 B \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}}\, \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+20 B \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+9 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}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-24 A \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\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)-10 B \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) b +\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b}}{15 b^{4} \sin \left(\frac{d x}{2}+\frac{c}{2}\right)^{3} \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) \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}\, d}"," ",0,"2/15*(b*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)/b^4/sin(1/2*d*x+1/2*c)^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)*(36*A*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)^4-72*A*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6+20*B*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)*sin(1/2*d*x+1/2*c)^4-36*A*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+72*A*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4-20*B*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)*sin(1/2*d*x+1/2*c)^2+20*B*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4+9*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)*EllipticE(cos(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)^2+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))-10*B*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*b+sin(1/2*d*x+1/2*c)^2*b)^(1/2)/(b*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/d","B"
842,1,91,144,0.325000," ","int(cos(d*x+c)^(5/2)*(b*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c)),x)","\frac{\sqrt{b \cos \left(d x +c \right)}\, \left(6 B \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)+8 A \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+9 B \cos \left(d x +c \right) \sin \left(d x +c \right)+16 A \sin \left(d x +c \right)+9 B \left(d x +c \right)\right)}{24 d \sqrt{\cos \left(d x +c \right)}}"," ",0,"1/24/d*(b*cos(d*x+c))^(1/2)*(6*B*cos(d*x+c)^3*sin(d*x+c)+8*A*cos(d*x+c)^2*sin(d*x+c)+9*B*cos(d*x+c)*sin(d*x+c)+16*A*sin(d*x+c)+9*B*(d*x+c))/cos(d*x+c)^(1/2)","A"
843,1,74,114,0.261000," ","int(cos(d*x+c)^(3/2)*(b*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c)),x)","\frac{\sqrt{b \cos \left(d x +c \right)}\, \left(2 B \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right)+3 A \cos \left(d x +c \right) \sin \left(d x +c \right)+3 A \left(d x +c \right)+4 B \sin \left(d x +c \right)\right)}{6 d \sqrt{\cos \left(d x +c \right)}}"," ",0,"1/6/d*(b*cos(d*x+c))^(1/2)*(2*B*sin(d*x+c)*cos(d*x+c)^2+3*A*cos(d*x+c)*sin(d*x+c)+3*A*(d*x+c)+4*B*sin(d*x+c))/cos(d*x+c)^(1/2)","A"
844,1,55,82,0.211000," ","int(cos(d*x+c)^(1/2)*(b*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c)),x)","\frac{\sqrt{b \cos \left(d x +c \right)}\, \left(B \cos \left(d x +c \right) \sin \left(d x +c \right)+2 A \sin \left(d x +c \right)+B \left(d x +c \right)\right)}{2 d \sqrt{\cos \left(d x +c \right)}}"," ",0,"1/2/d*(b*cos(d*x+c))^(1/2)*(B*cos(d*x+c)*sin(d*x+c)+2*A*sin(d*x+c)+B*(d*x+c))/cos(d*x+c)^(1/2)","A"
845,1,39,51,0.180000," ","int((b*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(1/2),x)","\frac{\sqrt{b \cos \left(d x +c \right)}\, \left(A \left(d x +c \right)+B \sin \left(d x +c \right)\right)}{d \sqrt{\cos \left(d x +c \right)}}"," ",0,"1/d*(b*cos(d*x+c))^(1/2)*(A*(d*x+c)+B*sin(d*x+c))/cos(d*x+c)^(1/2)","A"
846,1,54,52,0.161000," ","int((b*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(3/2),x)","-\frac{\sqrt{b \cos \left(d x +c \right)}\, \left(2 A \arctanh \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)-B \left(d x +c \right)\right)}{d \sqrt{\cos \left(d x +c \right)}}"," ",0,"-1/d*(b*cos(d*x+c))^(1/2)*(2*A*arctanh((-1+cos(d*x+c))/sin(d*x+c))-B*(d*x+c))/cos(d*x+c)^(1/2)","A"
847,1,59,60,0.171000," ","int((b*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(5/2),x)","\frac{\left(-2 B \cos \left(d x +c \right) \arctanh \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)+A \sin \left(d x +c \right)\right) \sqrt{b \cos \left(d x +c \right)}}{d \cos \left(d x +c \right)^{\frac{3}{2}}}"," ",0,"1/d*(-2*B*cos(d*x+c)*arctanh((-1+cos(d*x+c))/sin(d*x+c))+A*sin(d*x+c))*(b*cos(d*x+c))^(1/2)/cos(d*x+c)^(3/2)","A"
848,1,120,91,0.227000," ","int((b*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(7/2),x)","\frac{\left(-A \left(\cos^{2}\left(d x +c \right)\right) \ln \left(-\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}\right)+A \left(\cos^{2}\left(d x +c \right)\right) \ln \left(\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}\right)+2 B \cos \left(d x +c \right) \sin \left(d x +c \right)+A \sin \left(d x +c \right)\right) \sqrt{b \cos \left(d x +c \right)}}{2 d \cos \left(d x +c \right)^{\frac{5}{2}}}"," ",0,"1/2/d*(-A*cos(d*x+c)^2*ln(-(-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))+A*cos(d*x+c)^2*ln((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))+2*B*cos(d*x+c)*sin(d*x+c)+A*sin(d*x+c))*(b*cos(d*x+c))^(1/2)/cos(d*x+c)^(5/2)","A"
849,1,139,123,0.236000," ","int((b*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(9/2),x)","\frac{\left(-3 B \left(\cos^{3}\left(d x +c \right)\right) \ln \left(-\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}\right)+3 B \left(\cos^{3}\left(d x +c \right)\right) \ln \left(\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}\right)+4 A \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+3 B \cos \left(d x +c \right) \sin \left(d x +c \right)+2 A \sin \left(d x +c \right)\right) \sqrt{b \cos \left(d x +c \right)}}{6 d \cos \left(d x +c \right)^{\frac{7}{2}}}"," ",0,"1/6/d*(-3*B*cos(d*x+c)^3*ln(-(-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))+3*B*cos(d*x+c)^3*ln((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))+4*A*cos(d*x+c)^2*sin(d*x+c)+3*B*cos(d*x+c)*sin(d*x+c)+2*A*sin(d*x+c))*(b*cos(d*x+c))^(1/2)/cos(d*x+c)^(7/2)","A"
850,1,91,149,0.263000," ","int(cos(d*x+c)^(3/2)*(b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)),x)","\frac{\left(b \cos \left(d x +c \right)\right)^{\frac{3}{2}} \left(6 B \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)+8 A \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+9 B \cos \left(d x +c \right) \sin \left(d x +c \right)+16 A \sin \left(d x +c \right)+9 B \left(d x +c \right)\right)}{24 d \cos \left(d x +c \right)^{\frac{3}{2}}}"," ",0,"1/24/d*(b*cos(d*x+c))^(3/2)*(6*B*cos(d*x+c)^3*sin(d*x+c)+8*A*cos(d*x+c)^2*sin(d*x+c)+9*B*cos(d*x+c)*sin(d*x+c)+16*A*sin(d*x+c)+9*B*(d*x+c))/cos(d*x+c)^(3/2)","A"
851,1,74,118,0.233000," ","int(cos(d*x+c)^(1/2)*(b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)),x)","\frac{\left(b \cos \left(d x +c \right)\right)^{\frac{3}{2}} \left(2 B \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right)+3 A \cos \left(d x +c \right) \sin \left(d x +c \right)+3 A \left(d x +c \right)+4 B \sin \left(d x +c \right)\right)}{6 d \cos \left(d x +c \right)^{\frac{3}{2}}}"," ",0,"1/6/d*(b*cos(d*x+c))^(3/2)*(2*B*sin(d*x+c)*cos(d*x+c)^2+3*A*cos(d*x+c)*sin(d*x+c)+3*A*(d*x+c)+4*B*sin(d*x+c))/cos(d*x+c)^(3/2)","A"
852,1,55,85,0.190000," ","int((b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(1/2),x)","\frac{\left(b \cos \left(d x +c \right)\right)^{\frac{3}{2}} \left(B \cos \left(d x +c \right) \sin \left(d x +c \right)+2 A \sin \left(d x +c \right)+B \left(d x +c \right)\right)}{2 d \cos \left(d x +c \right)^{\frac{3}{2}}}"," ",0,"1/2/d*(b*cos(d*x+c))^(3/2)*(B*cos(d*x+c)*sin(d*x+c)+2*A*sin(d*x+c)+B*(d*x+c))/cos(d*x+c)^(3/2)","A"
853,1,39,53,0.183000," ","int((b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(3/2),x)","\frac{\left(b \cos \left(d x +c \right)\right)^{\frac{3}{2}} \left(A \left(d x +c \right)+B \sin \left(d x +c \right)\right)}{d \cos \left(d x +c \right)^{\frac{3}{2}}}"," ",0,"1/d*(b*cos(d*x+c))^(3/2)*(A*(d*x+c)+B*sin(d*x+c))/cos(d*x+c)^(3/2)","A"
854,1,54,54,0.150000," ","int((b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(5/2),x)","-\frac{\left(b \cos \left(d x +c \right)\right)^{\frac{3}{2}} \left(2 A \arctanh \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)-B \left(d x +c \right)\right)}{d \cos \left(d x +c \right)^{\frac{3}{2}}}"," ",0,"-1/d*(b*cos(d*x+c))^(3/2)*(2*A*arctanh((-1+cos(d*x+c))/sin(d*x+c))-B*(d*x+c))/cos(d*x+c)^(3/2)","A"
855,1,59,62,0.155000," ","int((b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(7/2),x)","\frac{\left(-2 B \cos \left(d x +c \right) \arctanh \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)+A \sin \left(d x +c \right)\right) \left(b \cos \left(d x +c \right)\right)^{\frac{3}{2}}}{d \cos \left(d x +c \right)^{\frac{5}{2}}}"," ",0,"1/d*(-2*B*cos(d*x+c)*arctanh((-1+cos(d*x+c))/sin(d*x+c))+A*sin(d*x+c))*(b*cos(d*x+c))^(3/2)/cos(d*x+c)^(5/2)","A"
856,1,120,94,0.171000," ","int((b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(9/2),x)","\frac{\left(-A \left(\cos^{2}\left(d x +c \right)\right) \ln \left(-\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}\right)+A \left(\cos^{2}\left(d x +c \right)\right) \ln \left(\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}\right)+2 B \cos \left(d x +c \right) \sin \left(d x +c \right)+A \sin \left(d x +c \right)\right) \left(b \cos \left(d x +c \right)\right)^{\frac{3}{2}}}{2 d \cos \left(d x +c \right)^{\frac{7}{2}}}"," ",0,"1/2/d*(-A*cos(d*x+c)^2*ln(-(-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))+A*cos(d*x+c)^2*ln((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))+2*B*cos(d*x+c)*sin(d*x+c)+A*sin(d*x+c))*(b*cos(d*x+c))^(3/2)/cos(d*x+c)^(7/2)","A"
857,1,139,127,0.203000," ","int((b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(11/2),x)","\frac{\left(-3 B \left(\cos^{3}\left(d x +c \right)\right) \ln \left(-\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}\right)+3 B \left(\cos^{3}\left(d x +c \right)\right) \ln \left(\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}\right)+4 A \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+3 B \cos \left(d x +c \right) \sin \left(d x +c \right)+2 A \sin \left(d x +c \right)\right) \left(b \cos \left(d x +c \right)\right)^{\frac{3}{2}}}{6 d \cos \left(d x +c \right)^{\frac{9}{2}}}"," ",0,"1/6/d*(-3*B*cos(d*x+c)^3*ln(-(-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))+3*B*cos(d*x+c)^3*ln((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))+4*A*cos(d*x+c)^2*sin(d*x+c)+3*B*cos(d*x+c)*sin(d*x+c)+2*A*sin(d*x+c))*(b*cos(d*x+c))^(3/2)/cos(d*x+c)^(9/2)","A"
858,1,91,159,0.255000," ","int(cos(d*x+c)^(1/2)*(b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)),x)","\frac{\left(b \cos \left(d x +c \right)\right)^{\frac{5}{2}} \left(6 B \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)+8 A \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+9 B \cos \left(d x +c \right) \sin \left(d x +c \right)+16 A \sin \left(d x +c \right)+9 B \left(d x +c \right)\right)}{24 d \cos \left(d x +c \right)^{\frac{5}{2}}}"," ",0,"1/24/d*(b*cos(d*x+c))^(5/2)*(6*B*cos(d*x+c)^3*sin(d*x+c)+8*A*cos(d*x+c)^2*sin(d*x+c)+9*B*cos(d*x+c)*sin(d*x+c)+16*A*sin(d*x+c)+9*B*(d*x+c))/cos(d*x+c)^(5/2)","A"
859,1,74,126,0.218000," ","int((b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(1/2),x)","\frac{\left(b \cos \left(d x +c \right)\right)^{\frac{5}{2}} \left(2 B \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right)+3 A \cos \left(d x +c \right) \sin \left(d x +c \right)+3 A \left(d x +c \right)+4 B \sin \left(d x +c \right)\right)}{6 d \cos \left(d x +c \right)^{\frac{5}{2}}}"," ",0,"1/6/d*(b*cos(d*x+c))^(5/2)*(2*B*sin(d*x+c)*cos(d*x+c)^2+3*A*cos(d*x+c)*sin(d*x+c)+3*A*(d*x+c)+4*B*sin(d*x+c))/cos(d*x+c)^(5/2)","A"
860,1,55,91,0.166000," ","int((b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(3/2),x)","\frac{\left(b \cos \left(d x +c \right)\right)^{\frac{5}{2}} \left(B \cos \left(d x +c \right) \sin \left(d x +c \right)+2 A \sin \left(d x +c \right)+B \left(d x +c \right)\right)}{2 d \cos \left(d x +c \right)^{\frac{5}{2}}}"," ",0,"1/2/d*(b*cos(d*x+c))^(5/2)*(B*cos(d*x+c)*sin(d*x+c)+2*A*sin(d*x+c)+B*(d*x+c))/cos(d*x+c)^(5/2)","A"
861,1,39,57,0.141000," ","int((b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(5/2),x)","\frac{\left(b \cos \left(d x +c \right)\right)^{\frac{5}{2}} \left(A \left(d x +c \right)+B \sin \left(d x +c \right)\right)}{d \cos \left(d x +c \right)^{\frac{5}{2}}}"," ",0,"1/d*(b*cos(d*x+c))^(5/2)*(A*(d*x+c)+B*sin(d*x+c))/cos(d*x+c)^(5/2)","A"
862,1,54,58,0.188000," ","int((b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(7/2),x)","-\frac{\left(b \cos \left(d x +c \right)\right)^{\frac{5}{2}} \left(2 A \arctanh \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)-B \left(d x +c \right)\right)}{d \cos \left(d x +c \right)^{\frac{5}{2}}}"," ",0,"-1/d*(b*cos(d*x+c))^(5/2)*(2*A*arctanh((-1+cos(d*x+c))/sin(d*x+c))-B*(d*x+c))/cos(d*x+c)^(5/2)","A"
863,1,59,66,0.160000," ","int((b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(9/2),x)","\frac{\left(-2 B \cos \left(d x +c \right) \arctanh \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)+A \sin \left(d x +c \right)\right) \left(b \cos \left(d x +c \right)\right)^{\frac{5}{2}}}{d \cos \left(d x +c \right)^{\frac{7}{2}}}"," ",0,"1/d*(-2*B*cos(d*x+c)*arctanh((-1+cos(d*x+c))/sin(d*x+c))+A*sin(d*x+c))*(b*cos(d*x+c))^(5/2)/cos(d*x+c)^(7/2)","A"
864,1,121,100,0.181000," ","int((b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(11/2),x)","-\frac{\left(A \left(\cos^{2}\left(d x +c \right)\right) \ln \left(-\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}\right)-A \left(\cos^{2}\left(d x +c \right)\right) \ln \left(\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}\right)-2 B \cos \left(d x +c \right) \sin \left(d x +c \right)-A \sin \left(d x +c \right)\right) \left(b \cos \left(d x +c \right)\right)^{\frac{5}{2}}}{2 d \cos \left(d x +c \right)^{\frac{9}{2}}}"," ",0,"-1/2/d*(A*cos(d*x+c)^2*ln(-(-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))-A*cos(d*x+c)^2*ln((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))-2*B*cos(d*x+c)*sin(d*x+c)-A*sin(d*x+c))*(b*cos(d*x+c))^(5/2)/cos(d*x+c)^(9/2)","A"
865,1,139,135,0.211000," ","int((b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(13/2),x)","\frac{\left(-3 B \left(\cos^{3}\left(d x +c \right)\right) \ln \left(-\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}\right)+3 B \left(\cos^{3}\left(d x +c \right)\right) \ln \left(\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}\right)+4 A \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+3 B \cos \left(d x +c \right) \sin \left(d x +c \right)+2 A \sin \left(d x +c \right)\right) \left(b \cos \left(d x +c \right)\right)^{\frac{5}{2}}}{6 d \cos \left(d x +c \right)^{\frac{11}{2}}}"," ",0,"1/6/d*(-3*B*cos(d*x+c)^3*ln(-(-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))+3*B*cos(d*x+c)^3*ln((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))+4*A*cos(d*x+c)^2*sin(d*x+c)+3*B*cos(d*x+c)*sin(d*x+c)+2*A*sin(d*x+c))*(b*cos(d*x+c))^(5/2)/cos(d*x+c)^(11/2)","A"
866,1,74,114,0.264000," ","int(cos(d*x+c)^(5/2)*(A+B*cos(d*x+c))/(b*cos(d*x+c))^(1/2),x)","\frac{\left(\sqrt{\cos}\left(d x +c \right)\right) \left(2 B \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right)+3 A \cos \left(d x +c \right) \sin \left(d x +c \right)+3 A \left(d x +c \right)+4 B \sin \left(d x +c \right)\right)}{6 d \sqrt{b \cos \left(d x +c \right)}}"," ",0,"1/6/d*cos(d*x+c)^(1/2)*(2*B*sin(d*x+c)*cos(d*x+c)^2+3*A*cos(d*x+c)*sin(d*x+c)+3*A*(d*x+c)+4*B*sin(d*x+c))/(b*cos(d*x+c))^(1/2)","A"
867,1,55,82,0.227000," ","int(cos(d*x+c)^(3/2)*(A+B*cos(d*x+c))/(b*cos(d*x+c))^(1/2),x)","\frac{\left(\sqrt{\cos}\left(d x +c \right)\right) \left(B \cos \left(d x +c \right) \sin \left(d x +c \right)+2 A \sin \left(d x +c \right)+B \left(d x +c \right)\right)}{2 d \sqrt{b \cos \left(d x +c \right)}}"," ",0,"1/2/d*cos(d*x+c)^(1/2)*(B*cos(d*x+c)*sin(d*x+c)+2*A*sin(d*x+c)+B*(d*x+c))/(b*cos(d*x+c))^(1/2)","A"
868,1,39,51,0.184000," ","int(cos(d*x+c)^(1/2)*(A+B*cos(d*x+c))/(b*cos(d*x+c))^(1/2),x)","\frac{\left(\sqrt{\cos}\left(d x +c \right)\right) \left(A \left(d x +c \right)+B \sin \left(d x +c \right)\right)}{d \sqrt{b \cos \left(d x +c \right)}}"," ",0,"1/d*cos(d*x+c)^(1/2)*(A*(d*x+c)+B*sin(d*x+c))/(b*cos(d*x+c))^(1/2)","A"
869,1,54,52,0.183000," ","int((A+B*cos(d*x+c))/cos(d*x+c)^(1/2)/(b*cos(d*x+c))^(1/2),x)","-\frac{\left(2 A \arctanh \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)-B \left(d x +c \right)\right) \left(\sqrt{\cos}\left(d x +c \right)\right)}{d \sqrt{b \cos \left(d x +c \right)}}"," ",0,"-1/d*(2*A*arctanh((-1+cos(d*x+c))/sin(d*x+c))-B*(d*x+c))*cos(d*x+c)^(1/2)/(b*cos(d*x+c))^(1/2)","A"
870,1,59,60,0.173000," ","int((A+B*cos(d*x+c))/cos(d*x+c)^(3/2)/(b*cos(d*x+c))^(1/2),x)","\frac{-2 B \cos \left(d x +c \right) \arctanh \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)+A \sin \left(d x +c \right)}{d \sqrt{b \cos \left(d x +c \right)}\, \sqrt{\cos \left(d x +c \right)}}"," ",0,"1/d*(-2*B*cos(d*x+c)*arctanh((-1+cos(d*x+c))/sin(d*x+c))+A*sin(d*x+c))/(b*cos(d*x+c))^(1/2)/cos(d*x+c)^(1/2)","A"
871,1,120,91,0.196000," ","int((A+B*cos(d*x+c))/cos(d*x+c)^(5/2)/(b*cos(d*x+c))^(1/2),x)","\frac{-A \left(\cos^{2}\left(d x +c \right)\right) \ln \left(-\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}\right)+A \left(\cos^{2}\left(d x +c \right)\right) \ln \left(\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}\right)+2 B \cos \left(d x +c \right) \sin \left(d x +c \right)+A \sin \left(d x +c \right)}{2 d \sqrt{b \cos \left(d x +c \right)}\, \cos \left(d x +c \right)^{\frac{3}{2}}}"," ",0,"1/2/d*(-A*cos(d*x+c)^2*ln(-(-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))+A*cos(d*x+c)^2*ln((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))+2*B*cos(d*x+c)*sin(d*x+c)+A*sin(d*x+c))/(b*cos(d*x+c))^(1/2)/cos(d*x+c)^(3/2)","A"
872,1,139,123,0.215000," ","int((A+B*cos(d*x+c))/cos(d*x+c)^(7/2)/(b*cos(d*x+c))^(1/2),x)","\frac{-3 B \left(\cos^{3}\left(d x +c \right)\right) \ln \left(-\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}\right)+3 B \left(\cos^{3}\left(d x +c \right)\right) \ln \left(\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}\right)+4 A \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+3 B \cos \left(d x +c \right) \sin \left(d x +c \right)+2 A \sin \left(d x +c \right)}{6 d \sqrt{b \cos \left(d x +c \right)}\, \cos \left(d x +c \right)^{\frac{5}{2}}}"," ",0,"1/6/d*(-3*B*cos(d*x+c)^3*ln(-(-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))+3*B*cos(d*x+c)^3*ln((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))+4*A*cos(d*x+c)^2*sin(d*x+c)+3*B*cos(d*x+c)*sin(d*x+c)+2*A*sin(d*x+c))/(b*cos(d*x+c))^(1/2)/cos(d*x+c)^(5/2)","A"
873,1,74,126,0.216000," ","int(cos(d*x+c)^(7/2)*(A+B*cos(d*x+c))/(b*cos(d*x+c))^(3/2),x)","\frac{\left(\cos^{\frac{3}{2}}\left(d x +c \right)\right) \left(2 B \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right)+3 A \cos \left(d x +c \right) \sin \left(d x +c \right)+3 A \left(d x +c \right)+4 B \sin \left(d x +c \right)\right)}{6 d \left(b \cos \left(d x +c \right)\right)^{\frac{3}{2}}}"," ",0,"1/6/d*cos(d*x+c)^(3/2)*(2*B*sin(d*x+c)*cos(d*x+c)^2+3*A*cos(d*x+c)*sin(d*x+c)+3*A*(d*x+c)+4*B*sin(d*x+c))/(b*cos(d*x+c))^(3/2)","A"
874,1,55,91,0.174000," ","int(cos(d*x+c)^(5/2)*(A+B*cos(d*x+c))/(b*cos(d*x+c))^(3/2),x)","\frac{\left(\cos^{\frac{3}{2}}\left(d x +c \right)\right) \left(B \cos \left(d x +c \right) \sin \left(d x +c \right)+2 A \sin \left(d x +c \right)+B \left(d x +c \right)\right)}{2 d \left(b \cos \left(d x +c \right)\right)^{\frac{3}{2}}}"," ",0,"1/2/d*cos(d*x+c)^(3/2)*(B*cos(d*x+c)*sin(d*x+c)+2*A*sin(d*x+c)+B*(d*x+c))/(b*cos(d*x+c))^(3/2)","A"
875,1,39,57,0.166000," ","int(cos(d*x+c)^(3/2)*(A+B*cos(d*x+c))/(b*cos(d*x+c))^(3/2),x)","\frac{\left(\cos^{\frac{3}{2}}\left(d x +c \right)\right) \left(A \left(d x +c \right)+B \sin \left(d x +c \right)\right)}{d \left(b \cos \left(d x +c \right)\right)^{\frac{3}{2}}}"," ",0,"1/d*cos(d*x+c)^(3/2)*(A*(d*x+c)+B*sin(d*x+c))/(b*cos(d*x+c))^(3/2)","A"
876,1,54,58,0.158000," ","int(cos(d*x+c)^(1/2)*(A+B*cos(d*x+c))/(b*cos(d*x+c))^(3/2),x)","-\frac{\left(\cos^{\frac{3}{2}}\left(d x +c \right)\right) \left(2 A \arctanh \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)-B \left(d x +c \right)\right)}{d \left(b \cos \left(d x +c \right)\right)^{\frac{3}{2}}}"," ",0,"-1/d*cos(d*x+c)^(3/2)*(2*A*arctanh((-1+cos(d*x+c))/sin(d*x+c))-B*(d*x+c))/(b*cos(d*x+c))^(3/2)","A"
877,1,59,66,0.190000," ","int((A+B*cos(d*x+c))/cos(d*x+c)^(1/2)/(b*cos(d*x+c))^(3/2),x)","\frac{\left(-2 B \cos \left(d x +c \right) \arctanh \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)+A \sin \left(d x +c \right)\right) \left(\sqrt{\cos}\left(d x +c \right)\right)}{d \left(b \cos \left(d x +c \right)\right)^{\frac{3}{2}}}"," ",0,"1/d*(-2*B*cos(d*x+c)*arctanh((-1+cos(d*x+c))/sin(d*x+c))+A*sin(d*x+c))*cos(d*x+c)^(1/2)/(b*cos(d*x+c))^(3/2)","A"
878,1,121,100,0.175000," ","int((A+B*cos(d*x+c))/cos(d*x+c)^(3/2)/(b*cos(d*x+c))^(3/2),x)","-\frac{A \left(\cos^{2}\left(d x +c \right)\right) \ln \left(-\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}\right)-A \left(\cos^{2}\left(d x +c \right)\right) \ln \left(\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}\right)-2 B \cos \left(d x +c \right) \sin \left(d x +c \right)-A \sin \left(d x +c \right)}{2 d \left(b \cos \left(d x +c \right)\right)^{\frac{3}{2}} \sqrt{\cos \left(d x +c \right)}}"," ",0,"-1/2/d*(A*cos(d*x+c)^2*ln(-(-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))-A*cos(d*x+c)^2*ln((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))-2*B*cos(d*x+c)*sin(d*x+c)-A*sin(d*x+c))/(b*cos(d*x+c))^(3/2)/cos(d*x+c)^(1/2)","A"
879,1,139,135,0.199000," ","int((A+B*cos(d*x+c))/cos(d*x+c)^(5/2)/(b*cos(d*x+c))^(3/2),x)","\frac{-3 B \left(\cos^{3}\left(d x +c \right)\right) \ln \left(-\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}\right)+3 B \left(\cos^{3}\left(d x +c \right)\right) \ln \left(\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}\right)+4 A \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+3 B \cos \left(d x +c \right) \sin \left(d x +c \right)+2 A \sin \left(d x +c \right)}{6 d \left(b \cos \left(d x +c \right)\right)^{\frac{3}{2}} \cos \left(d x +c \right)^{\frac{3}{2}}}"," ",0,"1/6/d*(-3*B*cos(d*x+c)^3*ln(-(-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))+3*B*cos(d*x+c)^3*ln((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))+4*A*cos(d*x+c)^2*sin(d*x+c)+3*B*cos(d*x+c)*sin(d*x+c)+2*A*sin(d*x+c))/(b*cos(d*x+c))^(3/2)/cos(d*x+c)^(3/2)","A"
880,1,74,126,0.214000," ","int(cos(d*x+c)^(9/2)*(A+B*cos(d*x+c))/(b*cos(d*x+c))^(5/2),x)","\frac{\left(\cos^{\frac{5}{2}}\left(d x +c \right)\right) \left(2 B \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right)+3 A \cos \left(d x +c \right) \sin \left(d x +c \right)+3 A \left(d x +c \right)+4 B \sin \left(d x +c \right)\right)}{6 d \left(b \cos \left(d x +c \right)\right)^{\frac{5}{2}}}"," ",0,"1/6/d*cos(d*x+c)^(5/2)*(2*B*sin(d*x+c)*cos(d*x+c)^2+3*A*cos(d*x+c)*sin(d*x+c)+3*A*(d*x+c)+4*B*sin(d*x+c))/(b*cos(d*x+c))^(5/2)","A"
881,1,55,91,0.176000," ","int(cos(d*x+c)^(7/2)*(A+B*cos(d*x+c))/(b*cos(d*x+c))^(5/2),x)","\frac{\left(\cos^{\frac{5}{2}}\left(d x +c \right)\right) \left(B \cos \left(d x +c \right) \sin \left(d x +c \right)+2 A \sin \left(d x +c \right)+B \left(d x +c \right)\right)}{2 d \left(b \cos \left(d x +c \right)\right)^{\frac{5}{2}}}"," ",0,"1/2/d*cos(d*x+c)^(5/2)*(B*cos(d*x+c)*sin(d*x+c)+2*A*sin(d*x+c)+B*(d*x+c))/(b*cos(d*x+c))^(5/2)","A"
882,1,39,57,0.147000," ","int(cos(d*x+c)^(5/2)*(A+B*cos(d*x+c))/(b*cos(d*x+c))^(5/2),x)","\frac{\left(\cos^{\frac{5}{2}}\left(d x +c \right)\right) \left(A \left(d x +c \right)+B \sin \left(d x +c \right)\right)}{d \left(b \cos \left(d x +c \right)\right)^{\frac{5}{2}}}"," ",0,"1/d*cos(d*x+c)^(5/2)*(A*(d*x+c)+B*sin(d*x+c))/(b*cos(d*x+c))^(5/2)","A"
883,1,54,58,0.144000," ","int(cos(d*x+c)^(3/2)*(A+B*cos(d*x+c))/(b*cos(d*x+c))^(5/2),x)","-\frac{\left(\cos^{\frac{5}{2}}\left(d x +c \right)\right) \left(2 A \arctanh \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)-B \left(d x +c \right)\right)}{d \left(b \cos \left(d x +c \right)\right)^{\frac{5}{2}}}"," ",0,"-1/d*cos(d*x+c)^(5/2)*(2*A*arctanh((-1+cos(d*x+c))/sin(d*x+c))-B*(d*x+c))/(b*cos(d*x+c))^(5/2)","A"
884,1,59,66,0.167000," ","int(cos(d*x+c)^(1/2)*(A+B*cos(d*x+c))/(b*cos(d*x+c))^(5/2),x)","\frac{\left(-2 B \cos \left(d x +c \right) \arctanh \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)+A \sin \left(d x +c \right)\right) \left(\cos^{\frac{3}{2}}\left(d x +c \right)\right)}{d \left(b \cos \left(d x +c \right)\right)^{\frac{5}{2}}}"," ",0,"1/d*(-2*B*cos(d*x+c)*arctanh((-1+cos(d*x+c))/sin(d*x+c))+A*sin(d*x+c))*cos(d*x+c)^(3/2)/(b*cos(d*x+c))^(5/2)","A"
885,1,120,100,0.199000," ","int((A+B*cos(d*x+c))/cos(d*x+c)^(1/2)/(b*cos(d*x+c))^(5/2),x)","\frac{\left(-A \left(\cos^{2}\left(d x +c \right)\right) \ln \left(-\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}\right)+A \left(\cos^{2}\left(d x +c \right)\right) \ln \left(\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}\right)+2 B \cos \left(d x +c \right) \sin \left(d x +c \right)+A \sin \left(d x +c \right)\right) \left(\sqrt{\cos}\left(d x +c \right)\right)}{2 d \left(b \cos \left(d x +c \right)\right)^{\frac{5}{2}}}"," ",0,"1/2/d*(-A*cos(d*x+c)^2*ln(-(-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))+A*cos(d*x+c)^2*ln((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))+2*B*cos(d*x+c)*sin(d*x+c)+A*sin(d*x+c))*cos(d*x+c)^(1/2)/(b*cos(d*x+c))^(5/2)","A"
886,1,139,135,0.201000," ","int((A+B*cos(d*x+c))/cos(d*x+c)^(3/2)/(b*cos(d*x+c))^(5/2),x)","\frac{-3 B \left(\cos^{3}\left(d x +c \right)\right) \ln \left(-\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}\right)+3 B \left(\cos^{3}\left(d x +c \right)\right) \ln \left(\frac{1-\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}\right)+4 A \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+3 B \cos \left(d x +c \right) \sin \left(d x +c \right)+2 A \sin \left(d x +c \right)}{6 d \left(b \cos \left(d x +c \right)\right)^{\frac{5}{2}} \sqrt{\cos \left(d x +c \right)}}"," ",0,"1/6/d*(-3*B*cos(d*x+c)^3*ln(-(-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))+3*B*cos(d*x+c)^3*ln((1-cos(d*x+c)+sin(d*x+c))/sin(d*x+c))+4*A*cos(d*x+c)^2*sin(d*x+c)+3*B*cos(d*x+c)*sin(d*x+c)+2*A*sin(d*x+c))/(b*cos(d*x+c))^(5/2)/cos(d*x+c)^(1/2)","A"
887,0,0,99,0.395000," ","int(cos(d*x+c)^2*(b*cos(d*x+c))^(1/3)*(A+B*cos(d*x+c)),x)","\int \left(\cos^{2}\left(d x +c \right)\right) \left(b \cos \left(d x +c \right)\right)^{\frac{1}{3}} \left(A +B \cos \left(d x +c \right)\right)\, dx"," ",0,"int(cos(d*x+c)^2*(b*cos(d*x+c))^(1/3)*(A+B*cos(d*x+c)),x)","F"
888,0,0,99,0.291000," ","int(cos(d*x+c)*(b*cos(d*x+c))^(1/3)*(A+B*cos(d*x+c)),x)","\int \cos \left(d x +c \right) \left(b \cos \left(d x +c \right)\right)^{\frac{1}{3}} \left(A +B \cos \left(d x +c \right)\right)\, dx"," ",0,"int(cos(d*x+c)*(b*cos(d*x+c))^(1/3)*(A+B*cos(d*x+c)),x)","F"
889,0,0,99,0.158000," ","int((b*cos(d*x+c))^(1/3)*(A+B*cos(d*x+c)),x)","\int \left(b \cos \left(d x +c \right)\right)^{\frac{1}{3}} \left(A +B \cos \left(d x +c \right)\right)\, dx"," ",0,"int((b*cos(d*x+c))^(1/3)*(A+B*cos(d*x+c)),x)","F"
890,0,0,96,0.275000," ","int((b*cos(d*x+c))^(1/3)*(A+B*cos(d*x+c))*sec(d*x+c),x)","\int \left(b \cos \left(d x +c \right)\right)^{\frac{1}{3}} \left(A +B \cos \left(d x +c \right)\right) \sec \left(d x +c \right)\, dx"," ",0,"int((b*cos(d*x+c))^(1/3)*(A+B*cos(d*x+c))*sec(d*x+c),x)","F"
891,0,0,94,0.260000," ","int((b*cos(d*x+c))^(1/3)*(A+B*cos(d*x+c))*sec(d*x+c)^2,x)","\int \left(b \cos \left(d x +c \right)\right)^{\frac{1}{3}} \left(A +B \cos \left(d x +c \right)\right) \left(\sec^{2}\left(d x +c \right)\right)\, dx"," ",0,"int((b*cos(d*x+c))^(1/3)*(A+B*cos(d*x+c))*sec(d*x+c)^2,x)","F"
892,0,0,97,0.255000," ","int((b*cos(d*x+c))^(1/3)*(A+B*cos(d*x+c))*sec(d*x+c)^3,x)","\int \left(b \cos \left(d x +c \right)\right)^{\frac{1}{3}} \left(A +B \cos \left(d x +c \right)\right) \left(\sec^{3}\left(d x +c \right)\right)\, dx"," ",0,"int((b*cos(d*x+c))^(1/3)*(A+B*cos(d*x+c))*sec(d*x+c)^3,x)","F"
893,0,0,99,0.362000," ","int(cos(d*x+c)^2*(b*cos(d*x+c))^(4/3)*(A+B*cos(d*x+c)),x)","\int \left(\cos^{2}\left(d x +c \right)\right) \left(b \cos \left(d x +c \right)\right)^{\frac{4}{3}} \left(A +B \cos \left(d x +c \right)\right)\, dx"," ",0,"int(cos(d*x+c)^2*(b*cos(d*x+c))^(4/3)*(A+B*cos(d*x+c)),x)","F"
894,0,0,99,0.299000," ","int(cos(d*x+c)*(b*cos(d*x+c))^(4/3)*(A+B*cos(d*x+c)),x)","\int \cos \left(d x +c \right) \left(b \cos \left(d x +c \right)\right)^{\frac{4}{3}} \left(A +B \cos \left(d x +c \right)\right)\, dx"," ",0,"int(cos(d*x+c)*(b*cos(d*x+c))^(4/3)*(A+B*cos(d*x+c)),x)","F"
895,0,0,99,0.143000," ","int((b*cos(d*x+c))^(4/3)*(A+B*cos(d*x+c)),x)","\int \left(b \cos \left(d x +c \right)\right)^{\frac{4}{3}} \left(A +B \cos \left(d x +c \right)\right)\, dx"," ",0,"int((b*cos(d*x+c))^(4/3)*(A+B*cos(d*x+c)),x)","F"
896,0,0,96,0.229000," ","int((b*cos(d*x+c))^(4/3)*(A+B*cos(d*x+c))*sec(d*x+c),x)","\int \left(b \cos \left(d x +c \right)\right)^{\frac{4}{3}} \left(A +B \cos \left(d x +c \right)\right) \sec \left(d x +c \right)\, dx"," ",0,"int((b*cos(d*x+c))^(4/3)*(A+B*cos(d*x+c))*sec(d*x+c),x)","F"
897,0,0,94,0.243000," ","int((b*cos(d*x+c))^(4/3)*(A+B*cos(d*x+c))*sec(d*x+c)^2,x)","\int \left(b \cos \left(d x +c \right)\right)^{\frac{4}{3}} \left(A +B \cos \left(d x +c \right)\right) \left(\sec^{2}\left(d x +c \right)\right)\, dx"," ",0,"int((b*cos(d*x+c))^(4/3)*(A+B*cos(d*x+c))*sec(d*x+c)^2,x)","F"
898,0,0,97,0.271000," ","int((b*cos(d*x+c))^(4/3)*(A+B*cos(d*x+c))*sec(d*x+c)^3,x)","\int \left(b \cos \left(d x +c \right)\right)^{\frac{4}{3}} \left(A +B \cos \left(d x +c \right)\right) \left(\sec^{3}\left(d x +c \right)\right)\, dx"," ",0,"int((b*cos(d*x+c))^(4/3)*(A+B*cos(d*x+c))*sec(d*x+c)^3,x)","F"
899,0,0,99,0.330000," ","int(cos(d*x+c)^2*(A+B*cos(d*x+c))/(b*cos(d*x+c))^(2/3),x)","\int \frac{\left(\cos^{2}\left(d x +c \right)\right) \left(A +B \cos \left(d x +c \right)\right)}{\left(b \cos \left(d x +c \right)\right)^{\frac{2}{3}}}\, dx"," ",0,"int(cos(d*x+c)^2*(A+B*cos(d*x+c))/(b*cos(d*x+c))^(2/3),x)","F"
900,0,0,99,0.252000," ","int(cos(d*x+c)*(A+B*cos(d*x+c))/(b*cos(d*x+c))^(2/3),x)","\int \frac{\cos \left(d x +c \right) \left(A +B \cos \left(d x +c \right)\right)}{\left(b \cos \left(d x +c \right)\right)^{\frac{2}{3}}}\, dx"," ",0,"int(cos(d*x+c)*(A+B*cos(d*x+c))/(b*cos(d*x+c))^(2/3),x)","F"
901,0,0,99,0.121000," ","int((A+B*cos(d*x+c))/(b*cos(d*x+c))^(2/3),x)","\int \frac{A +B \cos \left(d x +c \right)}{\left(b \cos \left(d x +c \right)\right)^{\frac{2}{3}}}\, dx"," ",0,"int((A+B*cos(d*x+c))/(b*cos(d*x+c))^(2/3),x)","F"
902,0,0,96,0.200000," ","int((A+B*cos(d*x+c))*sec(d*x+c)/(b*cos(d*x+c))^(2/3),x)","\int \frac{\left(A +B \cos \left(d x +c \right)\right) \sec \left(d x +c \right)}{\left(b \cos \left(d x +c \right)\right)^{\frac{2}{3}}}\, dx"," ",0,"int((A+B*cos(d*x+c))*sec(d*x+c)/(b*cos(d*x+c))^(2/3),x)","F"
903,0,0,94,0.234000," ","int((A+B*cos(d*x+c))*sec(d*x+c)^2/(b*cos(d*x+c))^(2/3),x)","\int \frac{\left(A +B \cos \left(d x +c \right)\right) \left(\sec^{2}\left(d x +c \right)\right)}{\left(b \cos \left(d x +c \right)\right)^{\frac{2}{3}}}\, dx"," ",0,"int((A+B*cos(d*x+c))*sec(d*x+c)^2/(b*cos(d*x+c))^(2/3),x)","F"
904,0,0,97,0.282000," ","int((A+B*cos(d*x+c))*sec(d*x+c)^3/(b*cos(d*x+c))^(2/3),x)","\int \frac{\left(A +B \cos \left(d x +c \right)\right) \left(\sec^{3}\left(d x +c \right)\right)}{\left(b \cos \left(d x +c \right)\right)^{\frac{2}{3}}}\, dx"," ",0,"int((A+B*cos(d*x+c))*sec(d*x+c)^3/(b*cos(d*x+c))^(2/3),x)","F"
905,0,0,99,0.326000," ","int(cos(d*x+c)^2*(A+B*cos(d*x+c))/(b*cos(d*x+c))^(4/3),x)","\int \frac{\left(\cos^{2}\left(d x +c \right)\right) \left(A +B \cos \left(d x +c \right)\right)}{\left(b \cos \left(d x +c \right)\right)^{\frac{4}{3}}}\, dx"," ",0,"int(cos(d*x+c)^2*(A+B*cos(d*x+c))/(b*cos(d*x+c))^(4/3),x)","F"
906,0,0,99,0.321000," ","int(cos(d*x+c)*(A+B*cos(d*x+c))/(b*cos(d*x+c))^(4/3),x)","\int \frac{\cos \left(d x +c \right) \left(A +B \cos \left(d x +c \right)\right)}{\left(b \cos \left(d x +c \right)\right)^{\frac{4}{3}}}\, dx"," ",0,"int(cos(d*x+c)*(A+B*cos(d*x+c))/(b*cos(d*x+c))^(4/3),x)","F"
907,0,0,99,0.107000," ","int((A+B*cos(d*x+c))/(b*cos(d*x+c))^(4/3),x)","\int \frac{A +B \cos \left(d x +c \right)}{\left(b \cos \left(d x +c \right)\right)^{\frac{4}{3}}}\, dx"," ",0,"int((A+B*cos(d*x+c))/(b*cos(d*x+c))^(4/3),x)","F"
908,0,0,96,0.190000," ","int((A+B*cos(d*x+c))*sec(d*x+c)/(b*cos(d*x+c))^(4/3),x)","\int \frac{\left(A +B \cos \left(d x +c \right)\right) \sec \left(d x +c \right)}{\left(b \cos \left(d x +c \right)\right)^{\frac{4}{3}}}\, dx"," ",0,"int((A+B*cos(d*x+c))*sec(d*x+c)/(b*cos(d*x+c))^(4/3),x)","F"
909,0,0,94,0.224000," ","int((A+B*cos(d*x+c))*sec(d*x+c)^2/(b*cos(d*x+c))^(4/3),x)","\int \frac{\left(A +B \cos \left(d x +c \right)\right) \left(\sec^{2}\left(d x +c \right)\right)}{\left(b \cos \left(d x +c \right)\right)^{\frac{4}{3}}}\, dx"," ",0,"int((A+B*cos(d*x+c))*sec(d*x+c)^2/(b*cos(d*x+c))^(4/3),x)","F"
910,0,0,97,0.251000," ","int((A+B*cos(d*x+c))*sec(d*x+c)^3/(b*cos(d*x+c))^(4/3),x)","\int \frac{\left(A +B \cos \left(d x +c \right)\right) \left(\sec^{3}\left(d x +c \right)\right)}{\left(b \cos \left(d x +c \right)\right)^{\frac{4}{3}}}\, dx"," ",0,"int((A+B*cos(d*x+c))*sec(d*x+c)^3/(b*cos(d*x+c))^(4/3),x)","F"
911,0,0,153,1.685000," ","int(cos(d*x+c)^m*(b*cos(d*x+c))^n*(A+B*cos(d*x+c)),x)","\int \left(\cos^{m}\left(d x +c \right)\right) \left(b \cos \left(d x +c \right)\right)^{n} \left(A +B \cos \left(d x +c \right)\right)\, dx"," ",0,"int(cos(d*x+c)^m*(b*cos(d*x+c))^n*(A+B*cos(d*x+c)),x)","F"
912,0,0,129,1.636000," ","int(cos(d*x+c)^2*(b*cos(d*x+c))^n*(A+B*cos(d*x+c)),x)","\int \left(\cos^{2}\left(d x +c \right)\right) \left(b \cos \left(d x +c \right)\right)^{n} \left(A +B \cos \left(d x +c \right)\right)\, dx"," ",0,"int(cos(d*x+c)^2*(b*cos(d*x+c))^n*(A+B*cos(d*x+c)),x)","F"
913,0,0,129,1.178000," ","int(cos(d*x+c)*(b*cos(d*x+c))^n*(A+B*cos(d*x+c)),x)","\int \cos \left(d x +c \right) \left(b \cos \left(d x +c \right)\right)^{n} \left(A +B \cos \left(d x +c \right)\right)\, dx"," ",0,"int(cos(d*x+c)*(b*cos(d*x+c))^n*(A+B*cos(d*x+c)),x)","F"
914,0,0,129,1.163000," ","int((b*cos(d*x+c))^n*(A+B*cos(d*x+c)),x)","\int \left(b \cos \left(d x +c \right)\right)^{n} \left(A +B \cos \left(d x +c \right)\right)\, dx"," ",0,"int((b*cos(d*x+c))^n*(A+B*cos(d*x+c)),x)","F"
915,0,0,120,0.894000," ","int((b*cos(d*x+c))^n*(A+B*cos(d*x+c))*sec(d*x+c),x)","\int \left(b \cos \left(d x +c \right)\right)^{n} \left(A +B \cos \left(d x +c \right)\right) \sec \left(d x +c \right)\, dx"," ",0,"int((b*cos(d*x+c))^n*(A+B*cos(d*x+c))*sec(d*x+c),x)","F"
916,0,0,119,1.085000," ","int((b*cos(d*x+c))^n*(A+B*cos(d*x+c))*sec(d*x+c)^2,x)","\int \left(b \cos \left(d x +c \right)\right)^{n} \left(A +B \cos \left(d x +c \right)\right) \left(\sec^{2}\left(d x +c \right)\right)\, dx"," ",0,"int((b*cos(d*x+c))^n*(A+B*cos(d*x+c))*sec(d*x+c)^2,x)","F"
917,0,0,127,1.370000," ","int((b*cos(d*x+c))^n*(A+B*cos(d*x+c))*sec(d*x+c)^3,x)","\int \left(b \cos \left(d x +c \right)\right)^{n} \left(A +B \cos \left(d x +c \right)\right) \left(\sec^{3}\left(d x +c \right)\right)\, dx"," ",0,"int((b*cos(d*x+c))^n*(A+B*cos(d*x+c))*sec(d*x+c)^3,x)","F"
918,0,0,129,0.817000," ","int((b*cos(d*x+c))^n*(A+B*cos(d*x+c))*sec(d*x+c)^4,x)","\int \left(b \cos \left(d x +c \right)\right)^{n} \left(A +B \cos \left(d x +c \right)\right) \left(\sec^{4}\left(d x +c \right)\right)\, dx"," ",0,"int((b*cos(d*x+c))^n*(A+B*cos(d*x+c))*sec(d*x+c)^4,x)","F"
919,0,0,139,0.335000," ","int(cos(d*x+c)^(5/2)*(b*cos(d*x+c))^n*(A+B*cos(d*x+c)),x)","\int \left(\cos^{\frac{5}{2}}\left(d x +c \right)\right) \left(b \cos \left(d x +c \right)\right)^{n} \left(A +B \cos \left(d x +c \right)\right)\, dx"," ",0,"int(cos(d*x+c)^(5/2)*(b*cos(d*x+c))^n*(A+B*cos(d*x+c)),x)","F"
920,0,0,139,0.279000," ","int(cos(d*x+c)^(3/2)*(b*cos(d*x+c))^n*(A+B*cos(d*x+c)),x)","\int \left(\cos^{\frac{3}{2}}\left(d x +c \right)\right) \left(b \cos \left(d x +c \right)\right)^{n} \left(A +B \cos \left(d x +c \right)\right)\, dx"," ",0,"int(cos(d*x+c)^(3/2)*(b*cos(d*x+c))^n*(A+B*cos(d*x+c)),x)","F"
921,0,0,139,0.257000," ","int((b*cos(d*x+c))^n*(A+B*cos(d*x+c))*cos(d*x+c)^(1/2),x)","\int \left(b \cos \left(d x +c \right)\right)^{n} \left(A +B \cos \left(d x +c \right)\right) \left(\sqrt{\cos}\left(d x +c \right)\right)\, dx"," ",0,"int((b*cos(d*x+c))^n*(A+B*cos(d*x+c))*cos(d*x+c)^(1/2),x)","F"
922,0,0,139,0.211000," ","int((b*cos(d*x+c))^n*(A+B*cos(d*x+c))/cos(d*x+c)^(1/2),x)","\int \frac{\left(b \cos \left(d x +c \right)\right)^{n} \left(A +B \cos \left(d x +c \right)\right)}{\sqrt{\cos \left(d x +c \right)}}\, dx"," ",0,"int((b*cos(d*x+c))^n*(A+B*cos(d*x+c))/cos(d*x+c)^(1/2),x)","F"
923,0,0,139,0.233000," ","int((b*cos(d*x+c))^n*(A+B*cos(d*x+c))/cos(d*x+c)^(3/2),x)","\int \frac{\left(b \cos \left(d x +c \right)\right)^{n} \left(A +B \cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)^{\frac{3}{2}}}\, dx"," ",0,"int((b*cos(d*x+c))^n*(A+B*cos(d*x+c))/cos(d*x+c)^(3/2),x)","F"
924,0,0,139,0.205000," ","int((b*cos(d*x+c))^n*(A+B*cos(d*x+c))/cos(d*x+c)^(5/2),x)","\int \frac{\left(b \cos \left(d x +c \right)\right)^{n} \left(A +B \cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)^{\frac{5}{2}}}\, dx"," ",0,"int((b*cos(d*x+c))^n*(A+B*cos(d*x+c))/cos(d*x+c)^(5/2),x)","F"
925,0,0,139,0.199000," ","int((b*cos(d*x+c))^n*(A+B*cos(d*x+c))/cos(d*x+c)^(7/2),x)","\int \frac{\left(b \cos \left(d x +c \right)\right)^{n} \left(A +B \cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)^{\frac{7}{2}}}\, dx"," ",0,"int((b*cos(d*x+c))^n*(A+B*cos(d*x+c))/cos(d*x+c)^(7/2),x)","F"
926,0,0,139,0.214000," ","int((b*cos(d*x+c))^n*(A+B*cos(d*x+c))/cos(d*x+c)^(9/2),x)","\int \frac{\left(b \cos \left(d x +c \right)\right)^{n} \left(A +B \cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)^{\frac{9}{2}}}\, dx"," ",0,"int((b*cos(d*x+c))^n*(A+B*cos(d*x+c))/cos(d*x+c)^(9/2),x)","F"
927,0,0,145,0.243000," ","int(cos(d*x+c)^m*(b*cos(d*x+c))^(4/3)*(A+B*cos(d*x+c)),x)","\int \left(\cos^{m}\left(d x +c \right)\right) \left(b \cos \left(d x +c \right)\right)^{\frac{4}{3}} \left(A +B \cos \left(d x +c \right)\right)\, dx"," ",0,"int(cos(d*x+c)^m*(b*cos(d*x+c))^(4/3)*(A+B*cos(d*x+c)),x)","F"
928,0,0,143,0.243000," ","int(cos(d*x+c)^m*(b*cos(d*x+c))^(2/3)*(A+B*cos(d*x+c)),x)","\int \left(\cos^{m}\left(d x +c \right)\right) \left(b \cos \left(d x +c \right)\right)^{\frac{2}{3}} \left(A +B \cos \left(d x +c \right)\right)\, dx"," ",0,"int(cos(d*x+c)^m*(b*cos(d*x+c))^(2/3)*(A+B*cos(d*x+c)),x)","F"
929,0,0,143,0.220000," ","int(cos(d*x+c)^m*(b*cos(d*x+c))^(1/3)*(A+B*cos(d*x+c)),x)","\int \left(\cos^{m}\left(d x +c \right)\right) \left(b \cos \left(d x +c \right)\right)^{\frac{1}{3}} \left(A +B \cos \left(d x +c \right)\right)\, dx"," ",0,"int(cos(d*x+c)^m*(b*cos(d*x+c))^(1/3)*(A+B*cos(d*x+c)),x)","F"
930,0,0,143,0.188000," ","int(cos(d*x+c)^m*(A+B*cos(d*x+c))/(b*cos(d*x+c))^(1/3),x)","\int \frac{\left(\cos^{m}\left(d x +c \right)\right) \left(A +B \cos \left(d x +c \right)\right)}{\left(b \cos \left(d x +c \right)\right)^{\frac{1}{3}}}\, dx"," ",0,"int(cos(d*x+c)^m*(A+B*cos(d*x+c))/(b*cos(d*x+c))^(1/3),x)","F"
931,0,0,143,0.186000," ","int(cos(d*x+c)^m*(A+B*cos(d*x+c))/(b*cos(d*x+c))^(2/3),x)","\int \frac{\left(\cos^{m}\left(d x +c \right)\right) \left(A +B \cos \left(d x +c \right)\right)}{\left(b \cos \left(d x +c \right)\right)^{\frac{2}{3}}}\, dx"," ",0,"int(cos(d*x+c)^m*(A+B*cos(d*x+c))/(b*cos(d*x+c))^(2/3),x)","F"
932,0,0,147,0.198000," ","int(cos(d*x+c)^m*(A+B*cos(d*x+c))/(b*cos(d*x+c))^(4/3),x)","\int \frac{\left(\cos^{m}\left(d x +c \right)\right) \left(A +B \cos \left(d x +c \right)\right)}{\left(b \cos \left(d x +c \right)\right)^{\frac{4}{3}}}\, dx"," ",0,"int(cos(d*x+c)^m*(A+B*cos(d*x+c))/(b*cos(d*x+c))^(4/3),x)","F"