1,1,128,113,0.066000," ","int(cos(d*x+c)^3*(a+a*cos(d*x+c))*(A+B*cos(d*x+c)),x)","\frac{\frac{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 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 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 A \left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3}}{d}"," ",0,"1/d*(1/5*a*B*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c)+a*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*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*A*(2+cos(d*x+c)^2)*sin(d*x+c))","A"
2,1,107,89,0.065000," ","int(cos(d*x+c)^2*(a+a*cos(d*x+c))*(A+B*cos(d*x+c)),x)","\frac{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 A \left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3}+\frac{a B \left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3}+a 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*(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*A*(2+cos(d*x+c)^2)*sin(d*x+c)+1/3*a*B*(2+cos(d*x+c)^2)*sin(d*x+c)+a*A*(1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c))","A"
3,1,85,69,0.060000," ","int(cos(d*x+c)*(a+a*cos(d*x+c))*(A+B*cos(d*x+c)),x)","\frac{\frac{a B \left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3}+a A \left(\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{2}+\frac{d x}{2}+\frac{c}{2}\right)+a 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 A \sin \left(d x +c \right)}{d}"," ",0,"1/d*(1/3*a*B*(2+cos(d*x+c)^2)*sin(d*x+c)+a*A*(1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c)+a*B*(1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c)+a*A*sin(d*x+c))","A"
4,1,57,43,0.062000," ","int((a+a*cos(d*x+c))*(A+B*cos(d*x+c)),x)","\frac{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 A \sin \left(d x +c \right)+a B \sin \left(d x +c \right)+a A \left(d x +c \right)}{d}"," ",0,"1/d*(a*B*(1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c)+a*A*sin(d*x+c)+a*B*sin(d*x+c)+a*A*(d*x+c))","A"
5,1,56,32,0.110000," ","int((a+a*cos(d*x+c))*(A+B*cos(d*x+c))*sec(d*x+c),x)","a A x +a B x +\frac{a A \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{A a c}{d}+\frac{a B \sin \left(d x +c \right)}{d}+\frac{B a c}{d}"," ",0,"a*A*x+a*B*x+1/d*a*A*ln(sec(d*x+c)+tan(d*x+c))+1/d*A*a*c+a*B*sin(d*x+c)/d+1/d*B*a*c","A"
6,1,65,32,0.120000," ","int((a+a*cos(d*x+c))*(A+B*cos(d*x+c))*sec(d*x+c)^2,x)","a B x +\frac{a A \tan \left(d x +c \right)}{d}+\frac{a A \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{a B \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{B a c}{d}"," ",0,"a*B*x+a*A*tan(d*x+c)/d+1/d*a*A*ln(sec(d*x+c)+tan(d*x+c))+1/d*a*B*ln(sec(d*x+c)+tan(d*x+c))+1/d*B*a*c","A"
7,1,86,52,0.136000," ","int((a+a*cos(d*x+c))*(A+B*cos(d*x+c))*sec(d*x+c)^3,x)","\frac{a A \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{a A \sec \left(d x +c \right) \tan \left(d x +c \right)}{2 d}+\frac{a A \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}+\frac{a B \tan \left(d x +c \right)}{d}"," ",0,"a*A*tan(d*x+c)/d+1/d*a*B*ln(sec(d*x+c)+tan(d*x+c))+1/2*a*A*sec(d*x+c)*tan(d*x+c)/d+1/2/d*a*A*ln(sec(d*x+c)+tan(d*x+c))+1/d*a*B*tan(d*x+c)","A"
8,1,128,78,0.166000," ","int((a+a*cos(d*x+c))*(A+B*cos(d*x+c))*sec(d*x+c)^4,x)","\frac{a A \sec \left(d x +c \right) \tan \left(d x +c \right)}{2 d}+\frac{a A \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}+\frac{a B \tan \left(d x +c \right)}{d}+\frac{2 a A \tan \left(d x +c \right)}{3 d}+\frac{a A \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)}{2 d}+\frac{a B \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}"," ",0,"1/2*a*A*sec(d*x+c)*tan(d*x+c)/d+1/2/d*a*A*ln(sec(d*x+c)+tan(d*x+c))+1/d*a*B*tan(d*x+c)+2/3*a*A*tan(d*x+c)/d+1/3*a*A*sec(d*x+c)^2*tan(d*x+c)/d+1/2/d*a*B*sec(d*x+c)*tan(d*x+c)+1/2/d*a*B*ln(sec(d*x+c)+tan(d*x+c))","A"
9,1,171,98,0.160000," ","int((a+a*cos(d*x+c))*(A+B*cos(d*x+c))*sec(d*x+c)^5,x)","\frac{2 a A \tan \left(d x +c \right)}{3 d}+\frac{a A \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)}{2 d}+\frac{a B \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}+\frac{a A \left(\sec^{3}\left(d x +c \right)\right) \tan \left(d x +c \right)}{4 d}+\frac{3 a A \sec \left(d x +c \right) \tan \left(d x +c \right)}{8 d}+\frac{3 a A \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}+\frac{2 a B \tan \left(d x +c \right)}{3 d}+\frac{a B \tan \left(d x +c \right) \left(\sec^{2}\left(d x +c \right)\right)}{3 d}"," ",0,"2/3*a*A*tan(d*x+c)/d+1/3*a*A*sec(d*x+c)^2*tan(d*x+c)/d+1/2/d*a*B*sec(d*x+c)*tan(d*x+c)+1/2/d*a*B*ln(sec(d*x+c)+tan(d*x+c))+1/4*a*A*sec(d*x+c)^3*tan(d*x+c)/d+3/8*a*A*sec(d*x+c)*tan(d*x+c)/d+3/8/d*a*A*ln(sec(d*x+c)+tan(d*x+c))+2/3/d*a*B*tan(d*x+c)+1/3/d*a*B*tan(d*x+c)*sec(d*x+c)^2","A"
10,1,217,177,0.078000," ","int(cos(d*x+c)^3*(a+a*cos(d*x+c))^2*(A+B*cos(d*x+c)),x)","\frac{\frac{a^{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}+B \,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)+2 a^{2} A \left(\frac{\left(\cos^{3}\left(d x +c \right)+\frac{3 \cos \left(d x +c \right)}{2}\right) \sin \left(d x +c \right)}{4}+\frac{3 d x}{8}+\frac{3 c}{8}\right)+\frac{2 B \,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}+\frac{a^{2} A \left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3}+B \,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*(1/5*a^2*A*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c)+B*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*a^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)+2/5*B*a^2*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c)+1/3*a^2*A*(2+cos(d*x+c)^2)*sin(d*x+c)+B*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"
11,1,186,148,0.076000," ","int(cos(d*x+c)^2*(a+a*cos(d*x+c))^2*(A+B*cos(d*x+c)),x)","\frac{a^{2} A \left(\frac{\left(\cos^{3}\left(d x +c \right)+\frac{3 \cos \left(d x +c \right)}{2}\right) \sin \left(d x +c \right)}{4}+\frac{3 d x}{8}+\frac{3 c}{8}\right)+\frac{B \,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}+\frac{2 a^{2} A \left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3}+2 B \,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)+a^{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)+\frac{B \,a^{2} \left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3}}{d}"," ",0,"1/d*(a^2*A*(1/4*(cos(d*x+c)^3+3/2*cos(d*x+c))*sin(d*x+c)+3/8*d*x+3/8*c)+1/5*B*a^2*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c)+2/3*a^2*A*(2+cos(d*x+c)^2)*sin(d*x+c)+2*B*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^2*A*(1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c)+1/3*B*a^2*(2+cos(d*x+c)^2)*sin(d*x+c))","A"
12,1,154,119,0.055000," ","int(cos(d*x+c)*(a+a*cos(d*x+c))^2*(A+B*cos(d*x+c)),x)","\frac{\frac{a^{2} A \left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3}+B \,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)+2 a^{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)+\frac{2 B \,a^{2} \left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3}+a^{2} A \sin \left(d x +c \right)+B \,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*(1/3*a^2*A*(2+cos(d*x+c)^2)*sin(d*x+c)+B*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*a^2*A*(1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c)+2/3*B*a^2*(2+cos(d*x+c)^2)*sin(d*x+c)+a^2*A*sin(d*x+c)+B*a^2*(1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c))","A"
13,1,116,86,0.065000," ","int((a+a*cos(d*x+c))^2*(A+B*cos(d*x+c)),x)","\frac{\frac{B \,a^{2} \left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3}+a^{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)+2 B \,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} A \sin \left(d x +c \right)+B \,a^{2} \sin \left(d x +c \right)+a^{2} A \left(d x +c \right)}{d}"," ",0,"1/d*(1/3*B*a^2*(2+cos(d*x+c)^2)*sin(d*x+c)+a^2*A*(1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c)+2*B*a^2*(1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c)+2*a^2*A*sin(d*x+c)+B*a^2*sin(d*x+c)+a^2*A*(d*x+c))","A"
14,1,108,76,0.119000," ","int((a+a*cos(d*x+c))^2*(A+B*cos(d*x+c))*sec(d*x+c),x)","\frac{a^{2} A \sin \left(d x +c \right)}{d}+\frac{B \,a^{2} \cos \left(d x +c \right) \sin \left(d x +c \right)}{2 d}+\frac{3 a^{2} B x}{2}+\frac{3 B \,a^{2} c}{2 d}+2 a^{2} A x +\frac{2 A \,a^{2} c}{d}+\frac{2 B \,a^{2} \sin \left(d x +c \right)}{d}+\frac{a^{2} A \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}"," ",0,"1/d*a^2*A*sin(d*x+c)+1/2/d*B*a^2*cos(d*x+c)*sin(d*x+c)+3/2*a^2*B*x+3/2/d*B*a^2*c+2*a^2*A*x+2/d*A*a^2*c+2/d*B*a^2*sin(d*x+c)+1/d*a^2*A*ln(sec(d*x+c)+tan(d*x+c))","A"
15,1,107,74,0.138000," ","int((a+a*cos(d*x+c))^2*(A+B*cos(d*x+c))*sec(d*x+c)^2,x)","a^{2} A x +2 a^{2} B x +\frac{a^{2} A \tan \left(d x +c \right)}{d}+\frac{2 a^{2} A \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{A \,a^{2} c}{d}+\frac{B \,a^{2} \sin \left(d x +c \right)}{d}+\frac{B \,a^{2} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{2 B \,a^{2} c}{d}"," ",0,"a^2*A*x+2*a^2*B*x+a^2*A*tan(d*x+c)/d+2/d*a^2*A*ln(sec(d*x+c)+tan(d*x+c))+1/d*A*a^2*c+1/d*B*a^2*sin(d*x+c)+1/d*B*a^2*ln(sec(d*x+c)+tan(d*x+c))+2/d*B*a^2*c","A"
16,1,113,82,0.146000," ","int((a+a*cos(d*x+c))^2*(A+B*cos(d*x+c))*sec(d*x+c)^3,x)","\frac{3 a^{2} A \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}+a^{2} B x +\frac{B \,a^{2} c}{d}+\frac{2 a^{2} A \tan \left(d x +c \right)}{d}+\frac{2 B \,a^{2} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{a^{2} A \sec \left(d x +c \right) \tan \left(d x +c \right)}{2 d}+\frac{B \,a^{2} \tan \left(d x +c \right)}{d}"," ",0,"3/2/d*a^2*A*ln(sec(d*x+c)+tan(d*x+c))+a^2*B*x+1/d*B*a^2*c+2*a^2*A*tan(d*x+c)/d+2/d*B*a^2*ln(sec(d*x+c)+tan(d*x+c))+1/2*a^2*A*sec(d*x+c)*tan(d*x+c)/d+1/d*B*a^2*tan(d*x+c)","A"
17,1,141,105,0.147000," ","int((a+a*cos(d*x+c))^2*(A+B*cos(d*x+c))*sec(d*x+c)^4,x)","\frac{5 a^{2} A \tan \left(d x +c \right)}{3 d}+\frac{3 B \,a^{2} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}+\frac{a^{2} A \sec \left(d x +c \right) \tan \left(d x +c \right)}{d}+\frac{a^{2} A \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{2 B \,a^{2} \tan \left(d x +c \right)}{d}+\frac{a^{2} A \left(\sec^{2}\left(d x +c \right)\right) \tan \left(d x +c \right)}{3 d}+\frac{B \,a^{2} \sec \left(d x +c \right) \tan \left(d x +c \right)}{2 d}"," ",0,"5/3*a^2*A*tan(d*x+c)/d+3/2/d*B*a^2*ln(sec(d*x+c)+tan(d*x+c))+a^2*A*sec(d*x+c)*tan(d*x+c)/d+1/d*a^2*A*ln(sec(d*x+c)+tan(d*x+c))+2/d*B*a^2*tan(d*x+c)+1/3*a^2*A*sec(d*x+c)^2*tan(d*x+c)/d+1/2/d*B*a^2*sec(d*x+c)*tan(d*x+c)","A"
18,1,187,134,0.165000," ","int((a+a*cos(d*x+c))^2*(A+B*cos(d*x+c))*sec(d*x+c)^5,x)","\frac{7 a^{2} A \sec \left(d x +c \right) \tan \left(d x +c \right)}{8 d}+\frac{7 a^{2} A \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}+\frac{5 B \,a^{2} \tan \left(d x +c \right)}{3 d}+\frac{4 a^{2} A \tan \left(d x +c \right)}{3 d}+\frac{2 a^{2} A \left(\sec^{2}\left(d x +c \right)\right) \tan \left(d x +c \right)}{3 d}+\frac{B \,a^{2} \sec \left(d x +c \right) \tan \left(d x +c \right)}{d}+\frac{B \,a^{2} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{a^{2} A \left(\sec^{3}\left(d x +c \right)\right) \tan \left(d x +c \right)}{4 d}+\frac{B \,a^{2} \tan \left(d x +c \right) \left(\sec^{2}\left(d x +c \right)\right)}{3 d}"," ",0,"7/8*a^2*A*sec(d*x+c)*tan(d*x+c)/d+7/8/d*a^2*A*ln(sec(d*x+c)+tan(d*x+c))+5/3/d*B*a^2*tan(d*x+c)+4/3*a^2*A*tan(d*x+c)/d+2/3*a^2*A*sec(d*x+c)^2*tan(d*x+c)/d+1/d*B*a^2*sec(d*x+c)*tan(d*x+c)+1/d*B*a^2*ln(sec(d*x+c)+tan(d*x+c))+1/4*a^2*A*sec(d*x+c)^3*tan(d*x+c)/d+1/3/d*B*a^2*tan(d*x+c)*sec(d*x+c)^2","A"
19,1,266,187,0.072000," ","int(cos(d*x+c)^2*(a+a*cos(d*x+c))^3*(A+B*cos(d*x+c)),x)","\frac{\frac{A \,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}+a^{3} 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)+3 A \,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{3 a^{3} B \left(\frac{8}{3}+\cos^{4}\left(d x +c \right)+\frac{4 \left(\cos^{2}\left(d x +c \right)\right)}{3}\right) \sin \left(d x +c \right)}{5}+A \,a^{3} \left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+3 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)+A \,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)+\frac{a^{3} B \left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3}}{d}"," ",0,"1/d*(1/5*A*a^3*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c)+a^3*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)+3*A*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)+3/5*a^3*B*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c)+A*a^3*(2+cos(d*x+c)^2)*sin(d*x+c)+3*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)+A*a^3*(1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c)+1/3*a^3*B*(2+cos(d*x+c)^2)*sin(d*x+c))","A"
20,1,223,142,0.062000," ","int(cos(d*x+c)*(a+a*cos(d*x+c))^3*(A+B*cos(d*x+c)),x)","\frac{A \,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} 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 \,a^{3} \left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+3 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)+3 A \,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} B \left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+A \,a^{3} \sin \left(d x +c \right)+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)}{d}"," ",0,"1/d*(A*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)+1/5*a^3*B*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c)+A*a^3*(2+cos(d*x+c)^2)*sin(d*x+c)+3*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)+3*A*a^3*(1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c)+a^3*B*(2+cos(d*x+c)^2)*sin(d*x+c)+A*a^3*sin(d*x+c)+a^3*B*(1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c))","A"
21,1,176,108,0.060000," ","int((a+a*cos(d*x+c))^3*(A+B*cos(d*x+c)),x)","\frac{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 \,a^{3} \left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3}+a^{3} B \left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+3 A \,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} B \left(\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{2}+\frac{d x}{2}+\frac{c}{2}\right)+3 A \,a^{3} \sin \left(d x +c \right)+a^{3} B \sin \left(d x +c \right)+A \,a^{3} \left(d x +c \right)}{d}"," ",0,"1/d*(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*a^3*(2+cos(d*x+c)^2)*sin(d*x+c)+a^3*B*(2+cos(d*x+c)^2)*sin(d*x+c)+3*A*a^3*(1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c)+3*a^3*B*(1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c)+3*A*a^3*sin(d*x+c)+a^3*B*sin(d*x+c)+A*a^3*(d*x+c))","A"
22,1,153,103,0.136000," ","int((a+a*cos(d*x+c))^3*(A+B*cos(d*x+c))*sec(d*x+c),x)","\frac{A \,a^{3} \cos \left(d x +c \right) \sin \left(d x +c \right)}{2 d}+\frac{7 A \,a^{3} x}{2}+\frac{7 A \,a^{3} c}{2 d}+\frac{B \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) a^{3}}{3 d}+\frac{11 a^{3} B \sin \left(d x +c \right)}{3 d}+\frac{3 a^{3} A \sin \left(d x +c \right)}{d}+\frac{3 a^{3} B \cos \left(d x +c \right) \sin \left(d x +c \right)}{2 d}+\frac{5 a^{3} B x}{2}+\frac{5 a^{3} B c}{2 d}+\frac{A \,a^{3} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}"," ",0,"1/2/d*A*a^3*cos(d*x+c)*sin(d*x+c)+7/2*A*a^3*x+7/2/d*A*a^3*c+1/3/d*B*sin(d*x+c)*cos(d*x+c)^2*a^3+11/3*a^3*B*sin(d*x+c)/d+3*a^3*A*sin(d*x+c)/d+3/2/d*a^3*B*cos(d*x+c)*sin(d*x+c)+5/2*a^3*B*x+5/2/d*a^3*B*c+1/d*A*a^3*ln(sec(d*x+c)+tan(d*x+c))","A"
23,1,145,104,0.146000," ","int((a+a*cos(d*x+c))^3*(A+B*cos(d*x+c))*sec(d*x+c)^2,x)","\frac{a^{3} A \sin \left(d x +c \right)}{d}+\frac{a^{3} B \cos \left(d x +c \right) \sin \left(d x +c \right)}{2 d}+\frac{7 a^{3} B x}{2}+\frac{7 a^{3} B c}{2 d}+3 A \,a^{3} x +\frac{3 A \,a^{3} c}{d}+\frac{3 a^{3} B \sin \left(d x +c \right)}{d}+\frac{3 A \,a^{3} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{A \,a^{3} \tan \left(d x +c \right)}{d}+\frac{a^{3} B \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}"," ",0,"a^3*A*sin(d*x+c)/d+1/2/d*a^3*B*cos(d*x+c)*sin(d*x+c)+7/2*a^3*B*x+7/2/d*a^3*B*c+3*A*a^3*x+3/d*A*a^3*c+3*a^3*B*sin(d*x+c)/d+3/d*A*a^3*ln(sec(d*x+c)+tan(d*x+c))+1/d*A*a^3*tan(d*x+c)+1/d*a^3*B*ln(sec(d*x+c)+tan(d*x+c))","A"
24,1,144,108,0.161000," ","int((a+a*cos(d*x+c))^3*(A+B*cos(d*x+c))*sec(d*x+c)^3,x)","A \,a^{3} x +\frac{A \,a^{3} c}{d}+\frac{a^{3} B \sin \left(d x +c \right)}{d}+\frac{7 A \,a^{3} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}+3 a^{3} B x +\frac{3 a^{3} B c}{d}+\frac{3 A \,a^{3} \tan \left(d x +c \right)}{d}+\frac{3 a^{3} B \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{A \,a^{3} \sec \left(d x +c \right) \tan \left(d x +c \right)}{2 d}+\frac{a^{3} B \tan \left(d x +c \right)}{d}"," ",0,"A*a^3*x+1/d*A*a^3*c+a^3*B*sin(d*x+c)/d+7/2/d*A*a^3*ln(sec(d*x+c)+tan(d*x+c))+3*a^3*B*x+3/d*a^3*B*c+3/d*A*a^3*tan(d*x+c)+3/d*a^3*B*ln(sec(d*x+c)+tan(d*x+c))+1/2/d*A*a^3*sec(d*x+c)*tan(d*x+c)+1/d*a^3*B*tan(d*x+c)","A"
25,1,158,117,0.160000," ","int((a+a*cos(d*x+c))^3*(A+B*cos(d*x+c))*sec(d*x+c)^4,x)","\frac{5 A \,a^{3} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}+a^{3} B x +\frac{a^{3} B c}{d}+\frac{11 A \,a^{3} \tan \left(d x +c \right)}{3 d}+\frac{7 a^{3} B \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}+\frac{3 A \,a^{3} \sec \left(d x +c \right) \tan \left(d x +c \right)}{2 d}+\frac{3 a^{3} B \tan \left(d x +c \right)}{d}+\frac{A \,a^{3} \tan \left(d x +c \right) \left(\sec^{2}\left(d x +c \right)\right)}{3 d}+\frac{a^{3} B \sec \left(d x +c \right) \tan \left(d x +c \right)}{2 d}"," ",0,"5/2/d*A*a^3*ln(sec(d*x+c)+tan(d*x+c))+a^3*B*x+1/d*a^3*B*c+11/3/d*A*a^3*tan(d*x+c)+7/2/d*a^3*B*ln(sec(d*x+c)+tan(d*x+c))+3/2/d*A*a^3*sec(d*x+c)*tan(d*x+c)+3/d*a^3*B*tan(d*x+c)+1/3/d*A*a^3*tan(d*x+c)*sec(d*x+c)^2+1/2/d*a^3*B*sec(d*x+c)*tan(d*x+c)","A"
26,1,188,144,0.177000," ","int((a+a*cos(d*x+c))^3*(A+B*cos(d*x+c))*sec(d*x+c)^5,x)","\frac{3 A \,a^{3} \tan \left(d x +c \right)}{d}+\frac{5 a^{3} B \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}+\frac{15 A \,a^{3} \sec \left(d x +c \right) \tan \left(d x +c \right)}{8 d}+\frac{15 A \,a^{3} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}+\frac{11 a^{3} B \tan \left(d x +c \right)}{3 d}+\frac{A \,a^{3} \tan \left(d x +c \right) \left(\sec^{2}\left(d x +c \right)\right)}{d}+\frac{3 a^{3} B \sec \left(d x +c \right) \tan \left(d x +c \right)}{2 d}+\frac{A \,a^{3} \tan \left(d x +c \right) \left(\sec^{3}\left(d x +c \right)\right)}{4 d}+\frac{a^{3} B \tan \left(d x +c \right) \left(\sec^{2}\left(d x +c \right)\right)}{3 d}"," ",0,"3/d*A*a^3*tan(d*x+c)+5/2/d*a^3*B*ln(sec(d*x+c)+tan(d*x+c))+15/8/d*A*a^3*sec(d*x+c)*tan(d*x+c)+15/8/d*A*a^3*ln(sec(d*x+c)+tan(d*x+c))+11/3/d*a^3*B*tan(d*x+c)+1/d*A*a^3*tan(d*x+c)*sec(d*x+c)^2+3/2/d*a^3*B*sec(d*x+c)*tan(d*x+c)+1/4/d*A*a^3*tan(d*x+c)*sec(d*x+c)^3+1/3/d*a^3*B*tan(d*x+c)*sec(d*x+c)^2","A"
27,1,234,173,0.172000," ","int((a+a*cos(d*x+c))^3*(A+B*cos(d*x+c))*sec(d*x+c)^6,x)","\frac{13 A \,a^{3} \sec \left(d x +c \right) \tan \left(d x +c \right)}{8 d}+\frac{13 A \,a^{3} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}+\frac{3 a^{3} B \tan \left(d x +c \right)}{d}+\frac{38 A \,a^{3} \tan \left(d x +c \right)}{15 d}+\frac{19 A \,a^{3} \tan \left(d x +c \right) \left(\sec^{2}\left(d x +c \right)\right)}{15 d}+\frac{15 a^{3} B \sec \left(d x +c \right) \tan \left(d x +c \right)}{8 d}+\frac{15 a^{3} B \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}+\frac{3 A \,a^{3} \tan \left(d x +c \right) \left(\sec^{3}\left(d x +c \right)\right)}{4 d}+\frac{a^{3} B \tan \left(d x +c \right) \left(\sec^{2}\left(d x +c \right)\right)}{d}+\frac{A \,a^{3} \tan \left(d x +c \right) \left(\sec^{4}\left(d x +c \right)\right)}{5 d}+\frac{a^{3} B \tan \left(d x +c \right) \left(\sec^{3}\left(d x +c \right)\right)}{4 d}"," ",0,"13/8/d*A*a^3*sec(d*x+c)*tan(d*x+c)+13/8/d*A*a^3*ln(sec(d*x+c)+tan(d*x+c))+3/d*a^3*B*tan(d*x+c)+38/15/d*A*a^3*tan(d*x+c)+19/15/d*A*a^3*tan(d*x+c)*sec(d*x+c)^2+15/8/d*a^3*B*sec(d*x+c)*tan(d*x+c)+15/8/d*a^3*B*ln(sec(d*x+c)+tan(d*x+c))+3/4/d*A*a^3*tan(d*x+c)*sec(d*x+c)^3+1/d*a^3*B*tan(d*x+c)*sec(d*x+c)^2+1/5/d*A*a^3*tan(d*x+c)*sec(d*x+c)^4+1/4/d*a^3*B*tan(d*x+c)*sec(d*x+c)^3","A"
28,1,358,225,0.069000," ","int(cos(d*x+c)^2*(a+a*cos(d*x+c))^4*(A+B*cos(d*x+c)),x)","\frac{A \,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{a^{4} 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}+\frac{4 A \,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} 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)+6 A \,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{6 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)}{5}+\frac{4 A \,a^{4} \left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3}+4 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)+A \,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)+\frac{a^{4} B \left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3}}{d}"," ",0,"1/d*(A*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)+1/7*a^4*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)+4/5*A*a^4*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c)+4*a^4*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)+6*A*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)+6/5*a^4*B*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c)+4/3*A*a^4*(2+cos(d*x+c)^2)*sin(d*x+c)+4*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)+A*a^4*(1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c)+1/3*a^4*B*(2+cos(d*x+c)^2)*sin(d*x+c))","A"
29,1,306,171,0.071000," ","int(cos(d*x+c)*(a+a*cos(d*x+c))^4*(A+B*cos(d*x+c)),x)","\frac{\frac{A \,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}+a^{4} 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)+4 A \,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} 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}+2 A \,a^{4} \left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+6 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)+4 A \,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)+\frac{4 a^{4} B \left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3}+A \,a^{4} \sin \left(d x +c \right)+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)}{d}"," ",0,"1/d*(1/5*A*a^4*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c)+a^4*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)+4*A*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)+4/5*a^4*B*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c)+2*A*a^4*(2+cos(d*x+c)^2)*sin(d*x+c)+6*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)+4*A*a^4*(1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c)+4/3*a^4*B*(2+cos(d*x+c)^2)*sin(d*x+c)+A*a^4*sin(d*x+c)+a^4*B*(1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c))","A"
30,1,248,138,0.059000," ","int((a+a*cos(d*x+c))^4*(A+B*cos(d*x+c)),x)","\frac{\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)}{5}+A \,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)+4 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{4 A \,a^{4} \left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3}+2 a^{4} B \left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+6 A \,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} B \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 \,a^{4} \sin \left(d x +c \right)+a^{4} B \sin \left(d x +c \right)+A \,a^{4} \left(d x +c \right)}{d}"," ",0,"1/d*(1/5*a^4*B*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c)+A*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*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)+4/3*A*a^4*(2+cos(d*x+c)^2)*sin(d*x+c)+2*a^4*B*(2+cos(d*x+c)^2)*sin(d*x+c)+6*A*a^4*(1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c)+4*a^4*B*(1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c)+4*A*a^4*sin(d*x+c)+a^4*B*sin(d*x+c)+A*a^4*(d*x+c))","A"
31,1,199,141,0.145000," ","int((a+a*cos(d*x+c))^4*(A+B*cos(d*x+c))*sec(d*x+c),x)","\frac{A \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) a^{4}}{3 d}+\frac{20 A \,a^{4} \sin \left(d x +c \right)}{3 d}+\frac{a^{4} B \sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right)}{4 d}+\frac{27 a^{4} B \cos \left(d x +c \right) \sin \left(d x +c \right)}{8 d}+\frac{35 a^{4} B x}{8}+\frac{35 a^{4} B c}{8 d}+\frac{2 A \,a^{4} \cos \left(d x +c \right) \sin \left(d x +c \right)}{d}+6 A \,a^{4} x +\frac{6 A \,a^{4} c}{d}+\frac{4 B \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) a^{4}}{3 d}+\frac{20 a^{4} B \sin \left(d x +c \right)}{3 d}+\frac{A \,a^{4} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}"," ",0,"1/3/d*A*sin(d*x+c)*cos(d*x+c)^2*a^4+20/3/d*A*a^4*sin(d*x+c)+1/4/d*a^4*B*sin(d*x+c)*cos(d*x+c)^3+27/8/d*a^4*B*cos(d*x+c)*sin(d*x+c)+35/8*a^4*B*x+35/8/d*a^4*B*c+2/d*A*a^4*cos(d*x+c)*sin(d*x+c)+6*A*a^4*x+6/d*A*a^4*c+4/3/d*B*sin(d*x+c)*cos(d*x+c)^2*a^4+20/3/d*a^4*B*sin(d*x+c)+1/d*A*a^4*ln(sec(d*x+c)+tan(d*x+c))","A"
32,1,190,142,0.157000," ","int((a+a*cos(d*x+c))^4*(A+B*cos(d*x+c))*sec(d*x+c)^2,x)","\frac{A \,a^{4} \cos \left(d x +c \right) \sin \left(d x +c \right)}{2 d}+\frac{13 A \,a^{4} x}{2}+\frac{13 A \,a^{4} c}{2 d}+\frac{B \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) a^{4}}{3 d}+\frac{20 a^{4} B \sin \left(d x +c \right)}{3 d}+\frac{4 A \,a^{4} \sin \left(d x +c \right)}{d}+\frac{2 a^{4} B \cos \left(d x +c \right) \sin \left(d x +c \right)}{d}+6 a^{4} B x +\frac{6 a^{4} B c}{d}+\frac{4 A \,a^{4} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{A \,a^{4} \tan \left(d x +c \right)}{d}+\frac{a^{4} B \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}"," ",0,"1/2/d*A*a^4*cos(d*x+c)*sin(d*x+c)+13/2*A*a^4*x+13/2/d*A*a^4*c+1/3/d*B*sin(d*x+c)*cos(d*x+c)^2*a^4+20/3/d*a^4*B*sin(d*x+c)+4/d*A*a^4*sin(d*x+c)+2/d*a^4*B*cos(d*x+c)*sin(d*x+c)+6*a^4*B*x+6/d*a^4*B*c+4/d*A*a^4*ln(sec(d*x+c)+tan(d*x+c))+1/d*A*a^4*tan(d*x+c)+1/d*a^4*B*ln(sec(d*x+c)+tan(d*x+c))","A"
33,1,182,150,0.172000," ","int((a+a*cos(d*x+c))^4*(A+B*cos(d*x+c))*sec(d*x+c)^3,x)","\frac{A \,a^{4} \sin \left(d x +c \right)}{d}+\frac{a^{4} B \cos \left(d x +c \right) \sin \left(d x +c \right)}{2 d}+\frac{13 a^{4} B x}{2}+\frac{13 a^{4} B c}{2 d}+4 A \,a^{4} x +\frac{4 A \,a^{4} c}{d}+\frac{4 a^{4} B \sin \left(d x +c \right)}{d}+\frac{13 A \,a^{4} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}+\frac{4 A \,a^{4} \tan \left(d x +c \right)}{d}+\frac{4 a^{4} B \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{A \,a^{4} \sec \left(d x +c \right) \tan \left(d x +c \right)}{2 d}+\frac{a^{4} B \tan \left(d x +c \right)}{d}"," ",0,"1/d*A*a^4*sin(d*x+c)+1/2/d*a^4*B*cos(d*x+c)*sin(d*x+c)+13/2*a^4*B*x+13/2/d*a^4*B*c+4*A*a^4*x+4/d*A*a^4*c+4/d*a^4*B*sin(d*x+c)+13/2/d*A*a^4*ln(sec(d*x+c)+tan(d*x+c))+4/d*A*a^4*tan(d*x+c)+4/d*a^4*B*ln(sec(d*x+c)+tan(d*x+c))+1/2/d*A*a^4*sec(d*x+c)*tan(d*x+c)+1/d*a^4*B*tan(d*x+c)","A"
34,1,189,155,0.176000," ","int((a+a*cos(d*x+c))^4*(A+B*cos(d*x+c))*sec(d*x+c)^4,x)","A \,a^{4} x +\frac{A \,a^{4} c}{d}+\frac{a^{4} B \sin \left(d x +c \right)}{d}+\frac{6 A \,a^{4} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+4 a^{4} B x +\frac{4 a^{4} B c}{d}+\frac{20 A \,a^{4} \tan \left(d x +c \right)}{3 d}+\frac{13 a^{4} B \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}+\frac{2 A \,a^{4} \sec \left(d x +c \right) \tan \left(d x +c \right)}{d}+\frac{4 a^{4} B \tan \left(d x +c \right)}{d}+\frac{A \,a^{4} \tan \left(d x +c \right) \left(\sec^{2}\left(d x +c \right)\right)}{3 d}+\frac{a^{4} B \sec \left(d x +c \right) \tan \left(d x +c \right)}{2 d}"," ",0,"A*a^4*x+1/d*A*a^4*c+1/d*a^4*B*sin(d*x+c)+6/d*A*a^4*ln(sec(d*x+c)+tan(d*x+c))+4*a^4*B*x+4/d*a^4*B*c+20/3/d*A*a^4*tan(d*x+c)+13/2/d*a^4*B*ln(sec(d*x+c)+tan(d*x+c))+2/d*A*a^4*sec(d*x+c)*tan(d*x+c)+4/d*a^4*B*tan(d*x+c)+1/3/d*A*a^4*tan(d*x+c)*sec(d*x+c)^2+1/2/d*a^4*B*sec(d*x+c)*tan(d*x+c)","A"
35,1,204,163,0.203000," ","int((a+a*cos(d*x+c))^4*(A+B*cos(d*x+c))*sec(d*x+c)^5,x)","\frac{35 A \,a^{4} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}+a^{4} B x +\frac{a^{4} B c}{d}+\frac{20 A \,a^{4} \tan \left(d x +c \right)}{3 d}+\frac{6 a^{4} B \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{27 A \,a^{4} \sec \left(d x +c \right) \tan \left(d x +c \right)}{8 d}+\frac{20 a^{4} B \tan \left(d x +c \right)}{3 d}+\frac{4 A \,a^{4} \tan \left(d x +c \right) \left(\sec^{2}\left(d x +c \right)\right)}{3 d}+\frac{2 a^{4} B \sec \left(d x +c \right) \tan \left(d x +c \right)}{d}+\frac{A \,a^{4} \tan \left(d x +c \right) \left(\sec^{3}\left(d x +c \right)\right)}{4 d}+\frac{a^{4} B \tan \left(d x +c \right) \left(\sec^{2}\left(d x +c \right)\right)}{3 d}"," ",0,"35/8/d*A*a^4*ln(sec(d*x+c)+tan(d*x+c))+a^4*B*x+1/d*a^4*B*c+20/3/d*A*a^4*tan(d*x+c)+6/d*a^4*B*ln(sec(d*x+c)+tan(d*x+c))+27/8/d*A*a^4*sec(d*x+c)*tan(d*x+c)+20/3/d*a^4*B*tan(d*x+c)+4/3/d*A*a^4*tan(d*x+c)*sec(d*x+c)^2+2/d*a^4*B*sec(d*x+c)*tan(d*x+c)+1/4/d*A*a^4*tan(d*x+c)*sec(d*x+c)^3+1/3/d*a^4*B*tan(d*x+c)*sec(d*x+c)^2","A"
36,1,234,186,0.199000," ","int((a+a*cos(d*x+c))^4*(A+B*cos(d*x+c))*sec(d*x+c)^6,x)","\frac{83 A \,a^{4} \tan \left(d x +c \right)}{15 d}+\frac{35 a^{4} B \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}+\frac{7 A \,a^{4} \sec \left(d x +c \right) \tan \left(d x +c \right)}{2 d}+\frac{7 A \,a^{4} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}+\frac{20 a^{4} B \tan \left(d x +c \right)}{3 d}+\frac{34 A \,a^{4} \tan \left(d x +c \right) \left(\sec^{2}\left(d x +c \right)\right)}{15 d}+\frac{27 a^{4} B \sec \left(d x +c \right) \tan \left(d x +c \right)}{8 d}+\frac{A \,a^{4} \tan \left(d x +c \right) \left(\sec^{3}\left(d x +c \right)\right)}{d}+\frac{4 a^{4} B \tan \left(d x +c \right) \left(\sec^{2}\left(d x +c \right)\right)}{3 d}+\frac{A \,a^{4} \tan \left(d x +c \right) \left(\sec^{4}\left(d x +c \right)\right)}{5 d}+\frac{a^{4} B \tan \left(d x +c \right) \left(\sec^{3}\left(d x +c \right)\right)}{4 d}"," ",0,"83/15/d*A*a^4*tan(d*x+c)+35/8/d*a^4*B*ln(sec(d*x+c)+tan(d*x+c))+7/2/d*A*a^4*sec(d*x+c)*tan(d*x+c)+7/2/d*A*a^4*ln(sec(d*x+c)+tan(d*x+c))+20/3/d*a^4*B*tan(d*x+c)+34/15/d*A*a^4*tan(d*x+c)*sec(d*x+c)^2+27/8/d*a^4*B*sec(d*x+c)*tan(d*x+c)+1/d*A*a^4*tan(d*x+c)*sec(d*x+c)^3+4/3/d*a^4*B*tan(d*x+c)*sec(d*x+c)^2+1/5/d*A*a^4*tan(d*x+c)*sec(d*x+c)^4+1/4/d*a^4*B*tan(d*x+c)*sec(d*x+c)^3","A"
37,1,280,215,0.221000," ","int((a+a*cos(d*x+c))^4*(A+B*cos(d*x+c))*sec(d*x+c)^7,x)","\frac{49 A \,a^{4} \sec \left(d x +c \right) \tan \left(d x +c \right)}{16 d}+\frac{49 A \,a^{4} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{16 d}+\frac{83 a^{4} B \tan \left(d x +c \right)}{15 d}+\frac{24 A \,a^{4} \tan \left(d x +c \right)}{5 d}+\frac{12 A \,a^{4} \tan \left(d x +c \right) \left(\sec^{2}\left(d x +c \right)\right)}{5 d}+\frac{7 a^{4} B \sec \left(d x +c \right) \tan \left(d x +c \right)}{2 d}+\frac{7 a^{4} B \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}+\frac{41 A \,a^{4} \tan \left(d x +c \right) \left(\sec^{3}\left(d x +c \right)\right)}{24 d}+\frac{34 a^{4} B \tan \left(d x +c \right) \left(\sec^{2}\left(d x +c \right)\right)}{15 d}+\frac{4 A \,a^{4} \tan \left(d x +c \right) \left(\sec^{4}\left(d x +c \right)\right)}{5 d}+\frac{a^{4} B \tan \left(d x +c \right) \left(\sec^{3}\left(d x +c \right)\right)}{d}+\frac{A \,a^{4} \tan \left(d x +c \right) \left(\sec^{5}\left(d x +c \right)\right)}{6 d}+\frac{a^{4} B \tan \left(d x +c \right) \left(\sec^{4}\left(d x +c \right)\right)}{5 d}"," ",0,"49/16/d*A*a^4*sec(d*x+c)*tan(d*x+c)+49/16/d*A*a^4*ln(sec(d*x+c)+tan(d*x+c))+83/15/d*a^4*B*tan(d*x+c)+24/5/d*A*a^4*tan(d*x+c)+12/5/d*A*a^4*tan(d*x+c)*sec(d*x+c)^2+7/2/d*a^4*B*sec(d*x+c)*tan(d*x+c)+7/2/d*a^4*B*ln(sec(d*x+c)+tan(d*x+c))+41/24/d*A*a^4*tan(d*x+c)*sec(d*x+c)^3+34/15/d*a^4*B*tan(d*x+c)*sec(d*x+c)^2+4/5/d*A*a^4*tan(d*x+c)*sec(d*x+c)^4+1/d*a^4*B*tan(d*x+c)*sec(d*x+c)^3+1/6/d*A*a^4*tan(d*x+c)*sec(d*x+c)^5+1/5/d*a^4*B*tan(d*x+c)*sec(d*x+c)^4","A"
38,1,351,145,0.089000," ","int(cos(d*x+c)^4*(A+B*cos(d*x+c))/(a+a*cos(d*x+c)),x)","\frac{A \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{a d}-\frac{B \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) B}{4 a d \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) A}{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) B}{12 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{31 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{3 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) B}{12 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{25 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{3 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{7 B \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{3 A \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)^{4}}-\frac{3 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{a d}+\frac{15 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) B}{4 a d}"," ",0,"1/a/d*A*tan(1/2*d*x+1/2*c)-1/a/d*B*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*B+5/a/d/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^7*A-115/12/a/d/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^5*B+31/3/a/d/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^5*A-109/12/a/d/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^3*B+25/3/a/d/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^3*A-7/4/a/d/(1+tan(1/2*d*x+1/2*c)^2)^4*B*tan(1/2*d*x+1/2*c)+3/a/d/(1+tan(1/2*d*x+1/2*c)^2)^4*A*tan(1/2*d*x+1/2*c)-3/a/d*arctan(tan(1/2*d*x+1/2*c))*A+15/4/a/d*arctan(tan(1/2*d*x+1/2*c))*B","B"
39,1,281,116,0.097000," ","int(cos(d*x+c)^3*(A+B*cos(d*x+c))/(a+a*cos(d*x+c)),x)","-\frac{A \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{a d}+\frac{B \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{a d}-\frac{3 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}+\frac{5 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) B}{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) B}{3 a d \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}{a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}-\frac{A \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 B \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}{a d}-\frac{3 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) B}{a d}"," ",0,"-1/a/d*A*tan(1/2*d*x+1/2*c)+1/a/d*B*tan(1/2*d*x+1/2*c)-3/a/d/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)^5*A+5/a/d/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)^5*B+16/3/a/d/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)^3*B-4/a/d/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)^3*A-1/a/d/(1+tan(1/2*d*x+1/2*c)^2)^3*A*tan(1/2*d*x+1/2*c)+3/a/d/(1+tan(1/2*d*x+1/2*c)^2)^3*B*tan(1/2*d*x+1/2*c)+3/a/d*arctan(tan(1/2*d*x+1/2*c))*A-3/a/d*arctan(tan(1/2*d*x+1/2*c))*B","B"
40,1,211,86,0.096000," ","int(cos(d*x+c)^2*(A+B*cos(d*x+c))/(a+a*cos(d*x+c)),x)","\frac{A \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{a d}-\frac{B \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) B}{a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{2 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}-\frac{B \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{2 A \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{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{a d}+\frac{3 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) B}{a d}"," ",0,"1/a/d*A*tan(1/2*d*x+1/2*c)-1/a/d*B*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*B+2/a/d/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)^3*A-1/a/d/(1+tan(1/2*d*x+1/2*c)^2)^2*B*tan(1/2*d*x+1/2*c)+2/a/d/(1+tan(1/2*d*x+1/2*c)^2)^2*A*tan(1/2*d*x+1/2*c)-2/a/d*arctan(tan(1/2*d*x+1/2*c))*A+3/a/d*arctan(tan(1/2*d*x+1/2*c))*B","B"
41,1,108,54,0.096000," ","int(cos(d*x+c)*(A+B*cos(d*x+c))/(a+a*cos(d*x+c)),x)","-\frac{A \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{a d}+\frac{B \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{a d}+\frac{2 B \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}{a d}-\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) B}{a d}"," ",0,"-1/a/d*A*tan(1/2*d*x+1/2*c)+1/a/d*B*tan(1/2*d*x+1/2*c)+2/a/d*B*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-2/a/d*arctan(tan(1/2*d*x+1/2*c))*B","A"
42,1,56,34,0.065000," ","int((A+B*cos(d*x+c))/(a+a*cos(d*x+c)),x)","\frac{A \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) B}{a d}-\frac{B \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{a d}"," ",0,"1/a/d*A*tan(1/2*d*x+1/2*c)+2/a/d*arctan(tan(1/2*d*x+1/2*c))*B-1/a/d*B*tan(1/2*d*x+1/2*c)","A"
43,1,78,44,0.129000," ","int((A+B*cos(d*x+c))*sec(d*x+c)/(a+a*cos(d*x+c)),x)","-\frac{A \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{a d}+\frac{A \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{a d}-\frac{A \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}{a d}+\frac{B \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{a d}"," ",0,"-1/a/d*A*tan(1/2*d*x+1/2*c)+1/a/d*A*ln(tan(1/2*d*x+1/2*c)+1)-1/a/d*A*ln(tan(1/2*d*x+1/2*c)-1)+1/a/d*B*tan(1/2*d*x+1/2*c)","A"
44,1,163,69,0.144000," ","int((A+B*cos(d*x+c))*sec(d*x+c)^2/(a+a*cos(d*x+c)),x)","\frac{A \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{a d}-\frac{B \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{a d}-\frac{A}{a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{A \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}{a d}-\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right) B}{a d}-\frac{A}{a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}-\frac{A \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{a d}+\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right) B}{a d}"," ",0,"1/a/d*A*tan(1/2*d*x+1/2*c)-1/a/d*B*tan(1/2*d*x+1/2*c)-1/a/d*A/(tan(1/2*d*x+1/2*c)-1)+1/a/d*A*ln(tan(1/2*d*x+1/2*c)-1)-1/a/d*ln(tan(1/2*d*x+1/2*c)-1)*B-1/a/d*A/(tan(1/2*d*x+1/2*c)+1)-1/a/d*A*ln(tan(1/2*d*x+1/2*c)+1)+1/a/d*ln(tan(1/2*d*x+1/2*c)+1)*B","B"
45,1,252,103,0.160000," ","int((A+B*cos(d*x+c))*sec(d*x+c)^3/(a+a*cos(d*x+c)),x)","-\frac{A \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{a d}+\frac{B \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{a d}+\frac{A}{2 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}+\frac{3 A}{2 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{B}{a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{3 A \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}{2 a d}+\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right) B}{a d}-\frac{A}{2 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}+\frac{3 A}{2 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}-\frac{B}{a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}+\frac{3 A \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{2 a d}-\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right) B}{a d}"," ",0,"-1/a/d*A*tan(1/2*d*x+1/2*c)+1/a/d*B*tan(1/2*d*x+1/2*c)+1/2/a/d*A/(tan(1/2*d*x+1/2*c)-1)^2+3/2/a/d*A/(tan(1/2*d*x+1/2*c)-1)-1/a/d/(tan(1/2*d*x+1/2*c)-1)*B-3/2/a/d*A*ln(tan(1/2*d*x+1/2*c)-1)+1/a/d*ln(tan(1/2*d*x+1/2*c)-1)*B-1/2/a/d*A/(tan(1/2*d*x+1/2*c)+1)^2+3/2/a/d*A/(tan(1/2*d*x+1/2*c)+1)-1/a/d/(tan(1/2*d*x+1/2*c)+1)*B+3/2/a/d*A*ln(tan(1/2*d*x+1/2*c)+1)-1/a/d*ln(tan(1/2*d*x+1/2*c)+1)*B","B"
46,1,340,125,0.171000," ","int((A+B*cos(d*x+c))*sec(d*x+c)^4/(a+a*cos(d*x+c)),x)","\frac{A \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{a d}-\frac{B \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{a d}-\frac{A}{3 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{3}}+\frac{B}{2 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}-\frac{A}{a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}+\frac{3 A \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}{2 a d}-\frac{3 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right) B}{2 a d}-\frac{5 A}{2 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{3 B}{2 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{A}{3 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}+\frac{A}{a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}-\frac{B}{2 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}-\frac{3 A \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{2 a d}+\frac{3 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right) B}{2 a d}-\frac{5 A}{2 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}+\frac{3 B}{2 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}"," ",0,"1/a/d*A*tan(1/2*d*x+1/2*c)-1/a/d*B*tan(1/2*d*x+1/2*c)-1/3/a/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*B-1/a/d*A/(tan(1/2*d*x+1/2*c)-1)^2+3/2/a/d*A*ln(tan(1/2*d*x+1/2*c)-1)-3/2/a/d*ln(tan(1/2*d*x+1/2*c)-1)*B-5/2/a/d*A/(tan(1/2*d*x+1/2*c)-1)+3/2/a/d/(tan(1/2*d*x+1/2*c)-1)*B-1/3/a/d*A/(tan(1/2*d*x+1/2*c)+1)^3+1/a/d*A/(tan(1/2*d*x+1/2*c)+1)^2-1/2/a/d/(tan(1/2*d*x+1/2*c)+1)^2*B-3/2/a/d*A*ln(tan(1/2*d*x+1/2*c)+1)+3/2/a/d*ln(tan(1/2*d*x+1/2*c)+1)*B-5/2/a/d*A/(tan(1/2*d*x+1/2*c)+1)+3/2/a/d/(tan(1/2*d*x+1/2*c)+1)*B","B"
47,1,322,160,0.101000," ","int(cos(d*x+c)^4*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^2,x)","\frac{\left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{6 d \,a^{2}}-\frac{B \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{6 d \,a^{2}}-\frac{7 A \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 d \,a^{2}}+\frac{9 B \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 d \,a^{2}}-\frac{5 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}+\frac{10 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) B}{d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}-\frac{8 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}+\frac{40 B \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{3 A \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{6 B \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{7 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{d \,a^{2}}-\frac{10 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) B}{d \,a^{2}}"," ",0,"1/6/d/a^2*tan(1/2*d*x+1/2*c)^3*A-1/6/d/a^2*B*tan(1/2*d*x+1/2*c)^3-7/2/d/a^2*A*tan(1/2*d*x+1/2*c)+9/2/d/a^2*B*tan(1/2*d*x+1/2*c)-5/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)^5*A+10/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)^5*B-8/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)^3*A+40/3/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^3*B*tan(1/2*d*x+1/2*c)^3-3/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^3*A*tan(1/2*d*x+1/2*c)+6/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^3*B*tan(1/2*d*x+1/2*c)+7/d/a^2*arctan(tan(1/2*d*x+1/2*c))*A-10/d/a^2*arctan(tan(1/2*d*x+1/2*c))*B","B"
48,1,252,137,0.102000," ","int(cos(d*x+c)^3*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^2,x)","-\frac{\left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{6 d \,a^{2}}+\frac{B \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{6 d \,a^{2}}+\frac{5 A \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 d \,a^{2}}-\frac{7 B \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 d \,a^{2}}-\frac{5 B \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{2 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}-\frac{3 B \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{2 A \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}-\frac{4 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{d \,a^{2}}+\frac{7 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) B}{d \,a^{2}}"," ",0,"-1/6/d/a^2*tan(1/2*d*x+1/2*c)^3*A+1/6/d/a^2*B*tan(1/2*d*x+1/2*c)^3+5/2/d/a^2*A*tan(1/2*d*x+1/2*c)-7/2/d/a^2*B*tan(1/2*d*x+1/2*c)-5/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^2*B*tan(1/2*d*x+1/2*c)^3+2/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)^3*A-3/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^2*B*tan(1/2*d*x+1/2*c)+2/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^2*A*tan(1/2*d*x+1/2*c)-4/d/a^2*arctan(tan(1/2*d*x+1/2*c))*A+7/d/a^2*arctan(tan(1/2*d*x+1/2*c))*B","A"
49,1,149,95,0.095000," ","int(cos(d*x+c)^2*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^2,x)","\frac{\left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{6 d \,a^{2}}-\frac{B \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{6 d \,a^{2}}-\frac{3 A \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 d \,a^{2}}+\frac{5 B \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 d \,a^{2}}+\frac{2 B \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{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{d \,a^{2}}-\frac{4 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) B}{d \,a^{2}}"," ",0,"1/6/d/a^2*tan(1/2*d*x+1/2*c)^3*A-1/6/d/a^2*B*tan(1/2*d*x+1/2*c)^3-3/2/d/a^2*A*tan(1/2*d*x+1/2*c)+5/2/d/a^2*B*tan(1/2*d*x+1/2*c)+2/d/a^2*B*tan(1/2*d*x+1/2*c)/(1+tan(1/2*d*x+1/2*c)^2)+2/d/a^2*arctan(tan(1/2*d*x+1/2*c))*A-4/d/a^2*arctan(tan(1/2*d*x+1/2*c))*B","A"
50,1,97,66,0.084000," ","int(cos(d*x+c)*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^2,x)","-\frac{\left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{6 d \,a^{2}}+\frac{B \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{6 d \,a^{2}}+\frac{A \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 d \,a^{2}}-\frac{3 B \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) B}{d \,a^{2}}"," ",0,"-1/6/d/a^2*tan(1/2*d*x+1/2*c)^3*A+1/6/d/a^2*B*tan(1/2*d*x+1/2*c)^3+1/2/d/a^2*A*tan(1/2*d*x+1/2*c)-3/2/d/a^2*B*tan(1/2*d*x+1/2*c)+2/d/a^2*arctan(tan(1/2*d*x+1/2*c))*B","A"
51,1,60,61,0.067000," ","int((A+B*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) A}{3}-\frac{B \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3}+A \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+B \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*A-1/3*B*tan(1/2*d*x+1/2*c)^3+A*tan(1/2*d*x+1/2*c)+B*tan(1/2*d*x+1/2*c))","A"
52,1,119,75,0.139000," ","int((A+B*cos(d*x+c))*sec(d*x+c)/(a+a*cos(d*x+c))^2,x)","-\frac{\left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{6 d \,a^{2}}+\frac{B \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{6 d \,a^{2}}-\frac{3 A \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 d \,a^{2}}+\frac{B \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 d \,a^{2}}-\frac{A \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}{d \,a^{2}}+\frac{A \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*A+1/6/d/a^2*B*tan(1/2*d*x+1/2*c)^3-3/2/d/a^2*A*tan(1/2*d*x+1/2*c)+1/2/d/a^2*B*tan(1/2*d*x+1/2*c)-1/d/a^2*A*ln(tan(1/2*d*x+1/2*c)-1)+1/d/a^2*A*ln(tan(1/2*d*x+1/2*c)+1)","A"
53,1,205,103,0.148000," ","int((A+B*cos(d*x+c))*sec(d*x+c)^2/(a+a*cos(d*x+c))^2,x)","\frac{\left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{6 d \,a^{2}}-\frac{B \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{6 d \,a^{2}}+\frac{5 A \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 d \,a^{2}}-\frac{3 B \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 d \,a^{2}}+\frac{2 A \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) B}{d \,a^{2}}-\frac{A}{d \,a^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{2 A \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{d \,a^{2}}+\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right) B}{d \,a^{2}}-\frac{A}{d \,a^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}"," ",0,"1/6/d/a^2*tan(1/2*d*x+1/2*c)^3*A-1/6/d/a^2*B*tan(1/2*d*x+1/2*c)^3+5/2/d/a^2*A*tan(1/2*d*x+1/2*c)-3/2/d/a^2*B*tan(1/2*d*x+1/2*c)+2/d/a^2*A*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-1/d/a^2*A/(tan(1/2*d*x+1/2*c)-1)-2/d/a^2*A*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-1/d/a^2*A/(tan(1/2*d*x+1/2*c)+1)","A"
54,1,294,142,0.178000," ","int((A+B*cos(d*x+c))*sec(d*x+c)^3/(a+a*cos(d*x+c))^2,x)","-\frac{\left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{6 d \,a^{2}}+\frac{B \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{6 d \,a^{2}}-\frac{7 A \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 d \,a^{2}}+\frac{5 B \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 d \,a^{2}}-\frac{7 A \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}{2 d \,a^{2}}+\frac{2 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right) B}{d \,a^{2}}+\frac{5 A}{2 d \,a^{2} \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{A}{2 d \,a^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}+\frac{5 A}{2 d \,a^{2} \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{7 A \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{2 d \,a^{2}}-\frac{2 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right) B}{d \,a^{2}}-\frac{A}{2 d \,a^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}"," ",0,"-1/6/d/a^2*tan(1/2*d*x+1/2*c)^3*A+1/6/d/a^2*B*tan(1/2*d*x+1/2*c)^3-7/2/d/a^2*A*tan(1/2*d*x+1/2*c)+5/2/d/a^2*B*tan(1/2*d*x+1/2*c)-7/2/d/a^2*A*ln(tan(1/2*d*x+1/2*c)-1)+2/d/a^2*ln(tan(1/2*d*x+1/2*c)-1)*B+5/2/d/a^2*A/(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/d/a^2*A/(tan(1/2*d*x+1/2*c)-1)^2+5/2/d/a^2*A/(tan(1/2*d*x+1/2*c)+1)-1/d/a^2/(tan(1/2*d*x+1/2*c)+1)*B+7/2/d/a^2*A*ln(tan(1/2*d*x+1/2*c)+1)-2/d/a^2*ln(tan(1/2*d*x+1/2*c)+1)*B-1/2/d/a^2*A/(tan(1/2*d*x+1/2*c)+1)^2","B"
55,1,382,169,0.176000," ","int((A+B*cos(d*x+c))*sec(d*x+c)^4/(a+a*cos(d*x+c))^2,x)","\frac{\left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{6 d \,a^{2}}-\frac{B \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{6 d \,a^{2}}+\frac{9 A \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 d \,a^{2}}-\frac{7 B \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 d \,a^{2}}-\frac{3 A}{2 d \,a^{2} \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{5 A \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}{d \,a^{2}}-\frac{7 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right) B}{2 d \,a^{2}}-\frac{5 A}{d \,a^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{5 B}{2 d \,a^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{A}{3 d \,a^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{3}}-\frac{5 A \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{d \,a^{2}}+\frac{7 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right) B}{2 d \,a^{2}}+\frac{3 A}{2 d \,a^{2} \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{5 A}{d \,a^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}+\frac{5 B}{2 d \,a^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}-\frac{A}{3 d \,a^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}"," ",0,"1/6/d/a^2*tan(1/2*d*x+1/2*c)^3*A-1/6/d/a^2*B*tan(1/2*d*x+1/2*c)^3+9/2/d/a^2*A*tan(1/2*d*x+1/2*c)-7/2/d/a^2*B*tan(1/2*d*x+1/2*c)-3/2/d/a^2*A/(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+5/d/a^2*A*ln(tan(1/2*d*x+1/2*c)-1)-7/2/d/a^2*ln(tan(1/2*d*x+1/2*c)-1)*B-5/d/a^2*A/(tan(1/2*d*x+1/2*c)-1)+5/2/d/a^2/(tan(1/2*d*x+1/2*c)-1)*B-1/3/d/a^2*A/(tan(1/2*d*x+1/2*c)-1)^3-5/d/a^2*A*ln(tan(1/2*d*x+1/2*c)+1)+7/2/d/a^2*ln(tan(1/2*d*x+1/2*c)+1)*B+3/2/d/a^2*A/(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-5/d/a^2*A/(tan(1/2*d*x+1/2*c)+1)+5/2/d/a^2/(tan(1/2*d*x+1/2*c)+1)*B-1/3/d/a^2*A/(tan(1/2*d*x+1/2*c)+1)^3","B"
56,1,362,204,0.094000," ","int(cos(d*x+c)^5*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^3,x)","-\frac{A \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{20 d \,a^{3}}+\frac{B \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{20 d \,a^{3}}+\frac{2 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{3 d \,a^{3}}-\frac{5 B \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{6 d \,a^{3}}-\frac{31 A \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{4 d \,a^{3}}+\frac{49 B \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{4 d \,a^{3}}-\frac{7 A \left(\tan^{5}\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)^{3}}+\frac{17 B \left(\tan^{5}\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)^{3}}-\frac{12 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}+\frac{76 B \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}-\frac{5 A \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)^{3}}+\frac{11 B \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)^{3}}+\frac{13 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{d \,a^{3}}-\frac{23 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) B}{d \,a^{3}}"," ",0,"-1/20/d/a^3*A*tan(1/2*d*x+1/2*c)^5+1/20/d/a^3*B*tan(1/2*d*x+1/2*c)^5+2/3/d/a^3*tan(1/2*d*x+1/2*c)^3*A-5/6/d/a^3*B*tan(1/2*d*x+1/2*c)^3-31/4/d/a^3*A*tan(1/2*d*x+1/2*c)+49/4/d/a^3*B*tan(1/2*d*x+1/2*c)-7/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^3*A*tan(1/2*d*x+1/2*c)^5+17/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^3*B*tan(1/2*d*x+1/2*c)^5-12/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)^3*A+76/3/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^3*B*tan(1/2*d*x+1/2*c)^3-5/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^3*A*tan(1/2*d*x+1/2*c)+11/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^3*B*tan(1/2*d*x+1/2*c)+13/d/a^3*arctan(tan(1/2*d*x+1/2*c))*A-23/d/a^3*arctan(tan(1/2*d*x+1/2*c))*B","A"
57,1,292,181,0.103000," ","int(cos(d*x+c)^4*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^3,x)","\frac{A \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{20 d \,a^{3}}-\frac{B \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{20 d \,a^{3}}-\frac{\left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{2 d \,a^{3}}+\frac{2 B \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 d \,a^{3}}+\frac{17 A \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{4 d \,a^{3}}-\frac{31 B \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{4 d \,a^{3}}+\frac{2 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}-\frac{7 B \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{2 A \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{5 B \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{6 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{d \,a^{3}}+\frac{13 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) B}{d \,a^{3}}"," ",0,"1/20/d/a^3*A*tan(1/2*d*x+1/2*c)^5-1/20/d/a^3*B*tan(1/2*d*x+1/2*c)^5-1/2/d/a^3*tan(1/2*d*x+1/2*c)^3*A+2/3/d/a^3*B*tan(1/2*d*x+1/2*c)^3+17/4/d/a^3*A*tan(1/2*d*x+1/2*c)-31/4/d/a^3*B*tan(1/2*d*x+1/2*c)+2/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)^3*A-7/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^2*B*tan(1/2*d*x+1/2*c)^3+2/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^2*A*tan(1/2*d*x+1/2*c)-5/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^2*B*tan(1/2*d*x+1/2*c)-6/d/a^3*arctan(tan(1/2*d*x+1/2*c))*A+13/d/a^3*arctan(tan(1/2*d*x+1/2*c))*B","A"
58,1,189,141,0.097000," ","int(cos(d*x+c)^3*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^3,x)","-\frac{A \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{20 d \,a^{3}}+\frac{B \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{20 d \,a^{3}}+\frac{\left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{3 d \,a^{3}}-\frac{B \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{2 d \,a^{3}}-\frac{7 A \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{4 d \,a^{3}}+\frac{17 B \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{4 d \,a^{3}}+\frac{2 B \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{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{d \,a^{3}}-\frac{6 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) B}{d \,a^{3}}"," ",0,"-1/20/d/a^3*A*tan(1/2*d*x+1/2*c)^5+1/20/d/a^3*B*tan(1/2*d*x+1/2*c)^5+1/3/d/a^3*tan(1/2*d*x+1/2*c)^3*A-1/2/d/a^3*B*tan(1/2*d*x+1/2*c)^3-7/4/d/a^3*A*tan(1/2*d*x+1/2*c)+17/4/d/a^3*B*tan(1/2*d*x+1/2*c)+2/d/a^3*B*tan(1/2*d*x+1/2*c)/(1+tan(1/2*d*x+1/2*c)^2)+2/d/a^3*arctan(tan(1/2*d*x+1/2*c))*A-6/d/a^3*arctan(tan(1/2*d*x+1/2*c))*B","A"
59,1,137,110,0.083000," ","int(cos(d*x+c)^2*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^3,x)","\frac{A \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{20 d \,a^{3}}-\frac{B \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{20 d \,a^{3}}-\frac{\left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{6 d \,a^{3}}+\frac{B \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 d \,a^{3}}+\frac{A \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{4 d \,a^{3}}-\frac{7 B \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) B}{d \,a^{3}}"," ",0,"1/20/d/a^3*A*tan(1/2*d*x+1/2*c)^5-1/20/d/a^3*B*tan(1/2*d*x+1/2*c)^5-1/6/d/a^3*tan(1/2*d*x+1/2*c)^3*A+1/3/d/a^3*B*tan(1/2*d*x+1/2*c)^3+1/4/d/a^3*A*tan(1/2*d*x+1/2*c)-7/4/d/a^3*B*tan(1/2*d*x+1/2*c)+2/d/a^3*arctan(tan(1/2*d*x+1/2*c))*B","A"
60,1,64,96,0.082000," ","int(cos(d*x+c)*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^3,x)","\frac{\frac{\left(-A +B \right) \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{5}-\frac{2 B \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3}+A \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+B \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{4 d \,a^{3}}"," ",0,"1/4/d/a^3*(1/5*(-A+B)*tan(1/2*d*x+1/2*c)^5-2/3*B*tan(1/2*d*x+1/2*c)^3+A*tan(1/2*d*x+1/2*c)+B*tan(1/2*d*x+1/2*c))","A"
61,1,64,96,0.071000," ","int((A+B*cos(d*x+c))/(a+a*cos(d*x+c))^3,x)","\frac{\frac{\left(A -B \right) \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) A}{3}+A \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+B \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{4 d \,a^{3}}"," ",0,"1/4/d/a^3*(1/5*(A-B)*tan(1/2*d*x+1/2*c)^5+2/3*tan(1/2*d*x+1/2*c)^3*A+A*tan(1/2*d*x+1/2*c)+B*tan(1/2*d*x+1/2*c))","A"
62,1,159,111,0.157000," ","int((A+B*cos(d*x+c))*sec(d*x+c)/(a+a*cos(d*x+c))^3,x)","\frac{A \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{d \,a^{3}}-\frac{\left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{3 d \,a^{3}}+\frac{B \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{6 d \,a^{3}}-\frac{A \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}{d \,a^{3}}-\frac{A \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{20 d \,a^{3}}+\frac{B \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{20 d \,a^{3}}-\frac{7 A \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{4 d \,a^{3}}+\frac{B \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{4 d \,a^{3}}"," ",0,"1/d/a^3*A*ln(tan(1/2*d*x+1/2*c)+1)-1/3/d/a^3*tan(1/2*d*x+1/2*c)^3*A+1/6/d/a^3*B*tan(1/2*d*x+1/2*c)^3-1/d/a^3*A*ln(tan(1/2*d*x+1/2*c)-1)-1/20/d/a^3*A*tan(1/2*d*x+1/2*c)^5+1/20/d/a^3*B*tan(1/2*d*x+1/2*c)^5-7/4/d/a^3*A*tan(1/2*d*x+1/2*c)+1/4/d/a^3*B*tan(1/2*d*x+1/2*c)","A"
63,1,245,139,0.165000," ","int((A+B*cos(d*x+c))*sec(d*x+c)^2/(a+a*cos(d*x+c))^3,x)","\frac{A \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{20 d \,a^{3}}-\frac{B \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{20 d \,a^{3}}+\frac{\left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{2 d \,a^{3}}-\frac{B \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 d \,a^{3}}+\frac{17 A \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{4 d \,a^{3}}-\frac{7 B \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{4 d \,a^{3}}+\frac{3 A \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) B}{d \,a^{3}}-\frac{A}{d \,a^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{3 A \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{d \,a^{3}}+\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right) B}{d \,a^{3}}-\frac{A}{d \,a^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}"," ",0,"1/20/d/a^3*A*tan(1/2*d*x+1/2*c)^5-1/20/d/a^3*B*tan(1/2*d*x+1/2*c)^5+1/2/d/a^3*tan(1/2*d*x+1/2*c)^3*A-1/3/d/a^3*B*tan(1/2*d*x+1/2*c)^3+17/4/d/a^3*A*tan(1/2*d*x+1/2*c)-7/4/d/a^3*B*tan(1/2*d*x+1/2*c)+3/d/a^3*A*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-1/d/a^3*A/(tan(1/2*d*x+1/2*c)-1)-3/d/a^3*A*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-1/d/a^3*A/(tan(1/2*d*x+1/2*c)+1)","A"
64,1,334,184,0.182000," ","int((A+B*cos(d*x+c))*sec(d*x+c)^3/(a+a*cos(d*x+c))^3,x)","-\frac{A \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{20 d \,a^{3}}+\frac{B \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{20 d \,a^{3}}-\frac{2 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{3 d \,a^{3}}+\frac{B \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{2 d \,a^{3}}-\frac{31 A \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{4 d \,a^{3}}+\frac{17 B \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{4 d \,a^{3}}-\frac{13 A \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}{2 d \,a^{3}}+\frac{3 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right) B}{d \,a^{3}}+\frac{7 A}{2 d \,a^{3} \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{A}{2 d \,a^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}+\frac{7 A}{2 d \,a^{3} \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{13 A \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{2 d \,a^{3}}-\frac{3 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right) B}{d \,a^{3}}-\frac{A}{2 d \,a^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}"," ",0,"-1/20/d/a^3*A*tan(1/2*d*x+1/2*c)^5+1/20/d/a^3*B*tan(1/2*d*x+1/2*c)^5-2/3/d/a^3*tan(1/2*d*x+1/2*c)^3*A+1/2/d/a^3*B*tan(1/2*d*x+1/2*c)^3-31/4/d/a^3*A*tan(1/2*d*x+1/2*c)+17/4/d/a^3*B*tan(1/2*d*x+1/2*c)-13/2/d/a^3*A*ln(tan(1/2*d*x+1/2*c)-1)+3/d/a^3*ln(tan(1/2*d*x+1/2*c)-1)*B+7/2/d/a^3*A/(tan(1/2*d*x+1/2*c)-1)-1/d/a^3/(tan(1/2*d*x+1/2*c)-1)*B+1/2/d/a^3*A/(tan(1/2*d*x+1/2*c)-1)^2+7/2/d/a^3*A/(tan(1/2*d*x+1/2*c)+1)-1/d/a^3/(tan(1/2*d*x+1/2*c)+1)*B+13/2/d/a^3*A*ln(tan(1/2*d*x+1/2*c)+1)-3/d/a^3*ln(tan(1/2*d*x+1/2*c)+1)*B-1/2/d/a^3*A/(tan(1/2*d*x+1/2*c)+1)^2","A"
65,1,332,215,0.094000," ","int(cos(d*x+c)^5*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^4,x)","-\frac{\left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{56 d \,a^{4}}+\frac{B \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{56 d \,a^{4}}+\frac{7 A \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{40 d \,a^{4}}-\frac{9 B \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) A}{24 d \,a^{4}}+\frac{13 B \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{8 d \,a^{4}}+\frac{49 A \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{8 d \,a^{4}}-\frac{111 B \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{8 d \,a^{4}}+\frac{2 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{d \,a^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}-\frac{9 B \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{2 A \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{7 B \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}-\frac{8 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{d \,a^{4}}+\frac{21 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) B}{d \,a^{4}}"," ",0,"-1/56/d/a^4*tan(1/2*d*x+1/2*c)^7*A+1/56/d/a^4*B*tan(1/2*d*x+1/2*c)^7+7/40/d/a^4*A*tan(1/2*d*x+1/2*c)^5-9/40/d/a^4*B*tan(1/2*d*x+1/2*c)^5-23/24/d/a^4*tan(1/2*d*x+1/2*c)^3*A+13/8/d/a^4*B*tan(1/2*d*x+1/2*c)^3+49/8/d/a^4*A*tan(1/2*d*x+1/2*c)-111/8/d/a^4*B*tan(1/2*d*x+1/2*c)+2/d/a^4/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)^3*A-9/d/a^4/(1+tan(1/2*d*x+1/2*c)^2)^2*B*tan(1/2*d*x+1/2*c)^3+2/d/a^4/(1+tan(1/2*d*x+1/2*c)^2)^2*A*tan(1/2*d*x+1/2*c)-7/d/a^4/(1+tan(1/2*d*x+1/2*c)^2)^2*B*tan(1/2*d*x+1/2*c)-8/d/a^4*arctan(tan(1/2*d*x+1/2*c))*A+21/d/a^4*arctan(tan(1/2*d*x+1/2*c))*B","A"
66,1,229,177,0.096000," ","int(cos(d*x+c)^4*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^4,x)","\frac{\left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{56 d \,a^{4}}-\frac{B \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{56 d \,a^{4}}-\frac{A \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{8 d \,a^{4}}+\frac{7 B \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{40 d \,a^{4}}+\frac{11 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{24 d \,a^{4}}-\frac{23 B \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{24 d \,a^{4}}-\frac{15 A \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{8 d \,a^{4}}+\frac{49 B \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{8 d \,a^{4}}+\frac{2 B \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{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{d \,a^{4}}-\frac{8 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) B}{d \,a^{4}}"," ",0,"1/56/d/a^4*tan(1/2*d*x+1/2*c)^7*A-1/56/d/a^4*B*tan(1/2*d*x+1/2*c)^7-1/8/d/a^4*A*tan(1/2*d*x+1/2*c)^5+7/40/d/a^4*B*tan(1/2*d*x+1/2*c)^5+11/24/d/a^4*tan(1/2*d*x+1/2*c)^3*A-23/24/d/a^4*B*tan(1/2*d*x+1/2*c)^3-15/8/d/a^4*A*tan(1/2*d*x+1/2*c)+49/8/d/a^4*B*tan(1/2*d*x+1/2*c)+2/d/a^4*B*tan(1/2*d*x+1/2*c)/(1+tan(1/2*d*x+1/2*c)^2)+2/d/a^4*arctan(tan(1/2*d*x+1/2*c))*A-8/d/a^4*arctan(tan(1/2*d*x+1/2*c))*B","A"
67,1,177,146,0.084000," ","int(cos(d*x+c)^3*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^4,x)","-\frac{\left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{56 d \,a^{4}}+\frac{B \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{56 d \,a^{4}}+\frac{3 A \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{40 d \,a^{4}}-\frac{B \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{8 d \,a^{4}}-\frac{\left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{8 d \,a^{4}}+\frac{11 B \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{24 d \,a^{4}}+\frac{A \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{8 d \,a^{4}}-\frac{15 B \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) B}{d \,a^{4}}"," ",0,"-1/56/d/a^4*tan(1/2*d*x+1/2*c)^7*A+1/56/d/a^4*B*tan(1/2*d*x+1/2*c)^7+3/40/d/a^4*A*tan(1/2*d*x+1/2*c)^5-1/8/d/a^4*B*tan(1/2*d*x+1/2*c)^5-1/8/d/a^4*tan(1/2*d*x+1/2*c)^3*A+11/24/d/a^4*B*tan(1/2*d*x+1/2*c)^3+1/8/d/a^4*A*tan(1/2*d*x+1/2*c)-15/8/d/a^4*B*tan(1/2*d*x+1/2*c)+2/d/a^4*arctan(tan(1/2*d*x+1/2*c))*B","A"
68,1,90,128,0.079000," ","int(cos(d*x+c)^2*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^4,x)","\frac{\frac{\left(A -B \right) \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{7}+\frac{\left(-A +3 B \right) \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{5}+\frac{\left(-A -3 B \right) \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3}+A \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+B \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{8 d \,a^{4}}"," ",0,"1/8/d/a^4*(1/7*(A-B)*tan(1/2*d*x+1/2*c)^7+1/5*(-A+3*B)*tan(1/2*d*x+1/2*c)^5+1/3*(-A-3*B)*tan(1/2*d*x+1/2*c)^3+A*tan(1/2*d*x+1/2*c)+B*tan(1/2*d*x+1/2*c))","A"
69,1,88,130,0.087000," ","int(cos(d*x+c)*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^4,x)","\frac{\frac{\left(-A +B \right) \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{7}+\frac{\left(-A -B \right) \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{5}+\frac{\left(A -B \right) \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3}+A \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+B \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{8 d \,a^{4}}"," ",0,"1/8/d/a^4*(1/7*(-A+B)*tan(1/2*d*x+1/2*c)^7+1/5*(-A-B)*tan(1/2*d*x+1/2*c)^5+1/3*(A-B)*tan(1/2*d*x+1/2*c)^3+A*tan(1/2*d*x+1/2*c)+B*tan(1/2*d*x+1/2*c))","A"
70,1,88,130,0.068000," ","int((A+B*cos(d*x+c))/(a+a*cos(d*x+c))^4,x)","\frac{\frac{\left(A -B \right) \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{7}+\frac{\left(3 A -B \right) \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{5}+\frac{\left(3 A +B \right) \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3}+A \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+B \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{8 d \,a^{4}}"," ",0,"1/8/d/a^4*(1/7*(A-B)*tan(1/2*d*x+1/2*c)^7+1/5*(3*A-B)*tan(1/2*d*x+1/2*c)^5+1/3*(3*A+B)*tan(1/2*d*x+1/2*c)^3+A*tan(1/2*d*x+1/2*c)+B*tan(1/2*d*x+1/2*c))","A"
71,1,199,139,0.150000," ","int((A+B*cos(d*x+c))*sec(d*x+c)/(a+a*cos(d*x+c))^4,x)","\frac{A \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{d \,a^{4}}-\frac{11 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{24 d \,a^{4}}+\frac{B \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{8 d \,a^{4}}-\frac{A \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}{d \,a^{4}}-\frac{A \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{8 d \,a^{4}}+\frac{3 B \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{40 d \,a^{4}}-\frac{\left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{56 d \,a^{4}}+\frac{B \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{56 d \,a^{4}}-\frac{15 A \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{8 d \,a^{4}}+\frac{B \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{8 d \,a^{4}}"," ",0,"1/d/a^4*A*ln(tan(1/2*d*x+1/2*c)+1)-11/24/d/a^4*tan(1/2*d*x+1/2*c)^3*A+1/8/d/a^4*B*tan(1/2*d*x+1/2*c)^3-1/d/a^4*A*ln(tan(1/2*d*x+1/2*c)-1)-1/8/d/a^4*A*tan(1/2*d*x+1/2*c)^5+3/40/d/a^4*B*tan(1/2*d*x+1/2*c)^5-1/56/d/a^4*tan(1/2*d*x+1/2*c)^7*A+1/56/d/a^4*B*tan(1/2*d*x+1/2*c)^7-15/8/d/a^4*A*tan(1/2*d*x+1/2*c)+1/8/d/a^4*B*tan(1/2*d*x+1/2*c)","A"
72,1,285,167,0.164000," ","int((A+B*cos(d*x+c))*sec(d*x+c)^2/(a+a*cos(d*x+c))^4,x)","\frac{\left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{56 d \,a^{4}}-\frac{B \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{56 d \,a^{4}}+\frac{7 A \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{40 d \,a^{4}}-\frac{B \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{8 d \,a^{4}}+\frac{23 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{24 d \,a^{4}}-\frac{11 B \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{24 d \,a^{4}}+\frac{49 A \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{8 d \,a^{4}}-\frac{15 B \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{8 d \,a^{4}}+\frac{4 A \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) B}{d \,a^{4}}-\frac{A}{d \,a^{4} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{4 A \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{d \,a^{4}}+\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right) B}{d \,a^{4}}-\frac{A}{d \,a^{4} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}"," ",0,"1/56/d/a^4*tan(1/2*d*x+1/2*c)^7*A-1/56/d/a^4*B*tan(1/2*d*x+1/2*c)^7+7/40/d/a^4*A*tan(1/2*d*x+1/2*c)^5-1/8/d/a^4*B*tan(1/2*d*x+1/2*c)^5+23/24/d/a^4*tan(1/2*d*x+1/2*c)^3*A-11/24/d/a^4*B*tan(1/2*d*x+1/2*c)^3+49/8/d/a^4*A*tan(1/2*d*x+1/2*c)-15/8/d/a^4*B*tan(1/2*d*x+1/2*c)+4/d/a^4*A*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-1/d/a^4*A/(tan(1/2*d*x+1/2*c)-1)-4/d/a^4*A*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-1/d/a^4*A/(tan(1/2*d*x+1/2*c)+1)","A"
73,1,374,218,0.186000," ","int((A+B*cos(d*x+c))*sec(d*x+c)^3/(a+a*cos(d*x+c))^4,x)","-\frac{\left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{56 d \,a^{4}}+\frac{B \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{56 d \,a^{4}}-\frac{9 A \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{40 d \,a^{4}}+\frac{7 B \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) A}{8 d \,a^{4}}+\frac{23 B \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{24 d \,a^{4}}-\frac{111 A \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{8 d \,a^{4}}+\frac{49 B \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{8 d \,a^{4}}-\frac{21 A \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}{2 d \,a^{4}}+\frac{4 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right) B}{d \,a^{4}}+\frac{9 A}{2 d \,a^{4} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{B}{d \,a^{4} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{A}{2 d \,a^{4} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}+\frac{9 A}{2 d \,a^{4} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}-\frac{B}{d \,a^{4} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}+\frac{21 A \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{2 d \,a^{4}}-\frac{4 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right) B}{d \,a^{4}}-\frac{A}{2 d \,a^{4} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}"," ",0,"-1/56/d/a^4*tan(1/2*d*x+1/2*c)^7*A+1/56/d/a^4*B*tan(1/2*d*x+1/2*c)^7-9/40/d/a^4*A*tan(1/2*d*x+1/2*c)^5+7/40/d/a^4*B*tan(1/2*d*x+1/2*c)^5-13/8/d/a^4*tan(1/2*d*x+1/2*c)^3*A+23/24/d/a^4*B*tan(1/2*d*x+1/2*c)^3-111/8/d/a^4*A*tan(1/2*d*x+1/2*c)+49/8/d/a^4*B*tan(1/2*d*x+1/2*c)-21/2/d/a^4*A*ln(tan(1/2*d*x+1/2*c)-1)+4/d/a^4*ln(tan(1/2*d*x+1/2*c)-1)*B+9/2/d/a^4*A/(tan(1/2*d*x+1/2*c)-1)-1/d/a^4/(tan(1/2*d*x+1/2*c)-1)*B+1/2/d/a^4*A/(tan(1/2*d*x+1/2*c)-1)^2+9/2/d/a^4*A/(tan(1/2*d*x+1/2*c)+1)-1/d/a^4/(tan(1/2*d*x+1/2*c)+1)*B+21/2/d/a^4*A*ln(tan(1/2*d*x+1/2*c)+1)-4/d/a^4*ln(tan(1/2*d*x+1/2*c)+1)*B-1/2/d/a^4*A/(tan(1/2*d*x+1/2*c)+1)^2","A"
74,1,121,167,0.402000," ","int(cos(d*x+c)^3*(a+a*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c)),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 B \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(-360 A -1440 B \right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(756 A +1512 B \right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(-630 A -840 B \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+315 A +315 B \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*B*sin(1/2*d*x+1/2*c)^8+(-360*A-1440*B)*sin(1/2*d*x+1/2*c)^6+(756*A+1512*B)*sin(1/2*d*x+1/2*c)^4+(-630*A-840*B)*sin(1/2*d*x+1/2*c)^2+315*A+315*B)*2^(1/2)/(a*cos(1/2*d*x+1/2*c)^2)^(1/2)/d","A"
75,1,102,128,0.439000," ","int(cos(d*x+c)^2*(a+a*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c)),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(-120 B \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(84 A +252 B \right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(-140 A -210 B \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+105 A +105 B \right) \sqrt{2}}{105 \sqrt{a \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, d}"," ",0,"2/105*cos(1/2*d*x+1/2*c)*a*sin(1/2*d*x+1/2*c)*(-120*B*sin(1/2*d*x+1/2*c)^6+(84*A+252*B)*sin(1/2*d*x+1/2*c)^4+(-140*A-210*B)*sin(1/2*d*x+1/2*c)^2+105*A+105*B)*2^(1/2)/(a*cos(1/2*d*x+1/2*c)^2)^(1/2)/d","A"
76,1,83,89,0.335000," ","int(cos(d*x+c)*(a+a*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c)),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 B \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(-10 A -20 B \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+15 A +15 B \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*B*sin(1/2*d*x+1/2*c)^4+(-10*A-20*B)*sin(1/2*d*x+1/2*c)^2+15*A+15*B)*2^(1/2)/(a*cos(1/2*d*x+1/2*c)^2)^(1/2)/d","A"
77,1,62,54,0.379000," ","int((a+a*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c)),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 B \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+3 A +B \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*B*cos(1/2*d*x+1/2*c)^2+3*A+B)*2^(1/2)/(a*cos(1/2*d*x+1/2*c)^2)^(1/2)/d","A"
78,1,210,58,1.158000," ","int((a+a*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c))*sec(d*x+c),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(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 +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 +2 B \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}\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,"1/a^(1/2)*cos(1/2*d*x+1/2*c)*(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))*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*B*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"
79,1,642,60,1.219000," ","int((a+a*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c))*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(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)+2 B \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)+2 B \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 A \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}+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 +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 +2 B \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 B \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)}{\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*(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*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))+2*B*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))+2*B*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*A*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(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))*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*B*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*B*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^(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"
80,1,991,101,1.328000," ","int((a+a*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c))*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(4 a \left(3 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)+3 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)+4 B \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)+4 B \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)-4 \left(3 A \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}+4 B \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}+3 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 +3 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 +4 B \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 B \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^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+10 A \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}+3 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 +3 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 +8 B \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}+4 B \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 +4 B \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)}{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)*(4*a*(3*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))+3*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))+4*B*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))+4*B*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)^4-4*(3*A*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)+4*B*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)+3*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+3*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+4*B*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*B*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+10*A*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)+3*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+3*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+8*B*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)+4*B*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*B*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^(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"
81,1,1311,140,1.475000," ","int((a+a*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c))*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(-24 a \left(5 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)+5 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)+6 B \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)+6 B \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^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+12 \left(10 A \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}+12 B \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}+15 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 +15 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 +18 B \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 +18 B \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)-2 \left(80 A \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}+96 B \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}+45 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 +45 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 +54 B \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 +54 B \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)+15 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 +15 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 +66 A \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}+18 B \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 B \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 +60 B \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)*(-24*a*(5*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))+5*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))+6*B*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))+6*B*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+12*(10*A*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)+12*B*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)+15*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+15*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+18*B*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*B*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)^4-2*(80*A*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)+96*B*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)+45*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+45*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+54*B*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*B*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+15*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+15*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+66*A*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)+18*B*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*B*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+60*B*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"
82,1,142,210,0.401000," ","int(cos(d*x+c)^3*(a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)),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(-5040 B \left(\sin^{10}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(3080 A +18480 B \right) \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(-9900 A -27720 B \right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(12474 A +22176 B \right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(-8085 A -10395 B \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+3465 A +3465 B \right) \sqrt{2}}{3465 \sqrt{a \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, d}"," ",0,"4/3465*cos(1/2*d*x+1/2*c)*a^2*sin(1/2*d*x+1/2*c)*(-5040*B*sin(1/2*d*x+1/2*c)^10+(3080*A+18480*B)*sin(1/2*d*x+1/2*c)^8+(-9900*A-27720*B)*sin(1/2*d*x+1/2*c)^6+(12474*A+22176*B)*sin(1/2*d*x+1/2*c)^4+(-8085*A-10395*B)*sin(1/2*d*x+1/2*c)^2+3465*A+3465*B)*2^(1/2)/(a*cos(1/2*d*x+1/2*c)^2)^(1/2)/d","A"
83,1,123,169,0.415000," ","int(cos(d*x+c)^2*(a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)),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 B \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(-180 A -900 B \right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(504 A +1134 B \right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(-525 A -735 B \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+315 A +315 B \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*B*sin(1/2*d*x+1/2*c)^8+(-180*A-900*B)*sin(1/2*d*x+1/2*c)^6+(504*A+1134*B)*sin(1/2*d*x+1/2*c)^4+(-525*A-735*B)*sin(1/2*d*x+1/2*c)^2+315*A+315*B)*2^(1/2)/(a*cos(1/2*d*x+1/2*c)^2)^(1/2)/d","A"
84,1,104,122,0.452000," ","int(cos(d*x+c)*(a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)),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 B \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(42 A +168 B \right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(-105 A -175 B \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+105 A +105 B \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*B*sin(1/2*d*x+1/2*c)^6+(42*A+168*B)*sin(1/2*d*x+1/2*c)^4+(-105*A-175*B)*sin(1/2*d*x+1/2*c)^2+105*A+105*B)*2^(1/2)/(a*cos(1/2*d*x+1/2*c)^2)^(1/2)/d","A"
85,1,85,89,0.340000," ","int((a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)),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(6 B \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(-5 A -15 B \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+15 A +15 B \right) \sqrt{2}}{15 \sqrt{a \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, d}"," ",0,"4/15*cos(1/2*d*x+1/2*c)*a^2*sin(1/2*d*x+1/2*c)*(6*B*sin(1/2*d*x+1/2*c)^4+(-5*A-15*B)*sin(1/2*d*x+1/2*c)^2+15*A+15*B)*2^(1/2)/(a*cos(1/2*d*x+1/2*c)^2)^(1/2)/d","A"
86,1,272,91,1.125000," ","int((a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))*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(-4 B \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)+6 A \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}+3 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 +3 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 +12 B \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{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^(1/2)*cos(1/2*d*x+1/2*c)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*(-4*B*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+6*A*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)+3*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+3*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+12*B*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"
87,1,696,93,1.171000," ","int((a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))*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(\left(-6 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 -6 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 -4 B \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 B \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 -8 B \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 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 +3 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 +2 A \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}+2 B \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 B \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 +4 B \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))*a-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))*a-4*B*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*B*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-8*B*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*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+3*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*A*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)+2*B*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*B*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*B*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"
88,1,991,103,1.223000," ","int((a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))*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(4 a \left(7 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)+7 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)+12 B \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)+12 B \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^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-4 \left(7 A \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}+4 B \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}+7 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 +7 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 +12 B \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 B \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)+18 A \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}+7 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 +7 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 +8 B \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}+12 B \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 B \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)}{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)*(4*a*(7*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))+7*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))+12*B*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))+12*B*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)^4-4*(7*A*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)+4*B*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)+7*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+7*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+12*B*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*B*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+18*A*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)+7*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+7*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+8*B*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)+12*B*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*B*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/(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"
89,1,1310,144,1.360000," ","int((a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))*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(-24 a \left(11 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)+11 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)+14 B \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)+14 B \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)+12 \left(22 A \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}+28 B \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}+33 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 +33 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 +42 B \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 +42 B \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(-352 A \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}-198 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 -198 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 -384 B \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}-252 B \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 -252 B \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)+126 A \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}+33 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 +33 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 +108 B \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}+42 B \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 +42 B \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)}{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)*(-24*a*(11*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))+11*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))+14*B*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))+14*B*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+12*(22*A*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)+28*B*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)+33*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+33*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+42*B*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+42*B*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+(-352*A*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)-198*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-198*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-384*B*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)-252*B*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-252*B*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+126*A*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)+33*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+33*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+108*B*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)+42*B*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+42*B*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))^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"
90,1,1631,185,1.409000," ","int((a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))*sec(d*x+c)^5,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(48 a \left(75 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)+75 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)+88 B \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)+88 B \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^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-48 \left(75 A \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}+88 B \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}+150 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 +150 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 +176 B \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 +176 B \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)+8 \left(825 A \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}+968 B \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}+675 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 +675 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 +792 B \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 +792 B \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)-4 \left(1095 A \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}+1208 B \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}+450 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 +450 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 +528 B \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 +528 B \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)+1086 A \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}+225 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 +225 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 +1008 B \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}+264 B \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 +264 B \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)}{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^(1/2)*cos(1/2*d*x+1/2*c)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*(48*a*(75*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))+75*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))+88*B*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))+88*B*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)^8-48*(75*A*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)+88*B*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)+150*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+150*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+176*B*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+176*B*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+8*(825*A*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)+968*B*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)+675*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+675*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+792*B*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+792*B*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)^4-4*(1095*A*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)+1208*B*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)+450*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+450*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+528*B*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+528*B*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+1086*A*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)+225*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+225*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+1008*B*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)+264*B*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+264*B*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))^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"
91,1,142,213,0.339000," ","int(cos(d*x+c)^2*(a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)),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(-2520 B \left(\sin^{10}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(1540 A +10780 B \right) \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(-5940 A -18810 B \right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(9009 A +17325 B \right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(-6930 A -9240 B \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+3465 A +3465 B \right) \sqrt{2}}{3465 \sqrt{a \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, d}"," ",0,"8/3465*cos(1/2*d*x+1/2*c)*a^3*sin(1/2*d*x+1/2*c)*(-2520*B*sin(1/2*d*x+1/2*c)^10+(1540*A+10780*B)*sin(1/2*d*x+1/2*c)^8+(-5940*A-18810*B)*sin(1/2*d*x+1/2*c)^6+(9009*A+17325*B)*sin(1/2*d*x+1/2*c)^4+(-6930*A-9240*B)*sin(1/2*d*x+1/2*c)^2+3465*A+3465*B)*2^(1/2)/(a*cos(1/2*d*x+1/2*c)^2)^(1/2)/d","A"
92,1,123,155,0.467000," ","int(cos(d*x+c)*(a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)),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 B \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(-90 A -540 B \right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(315 A +819 B \right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(-420 A -630 B \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+315 A +315 B \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*B*sin(1/2*d*x+1/2*c)^8+(-90*A-540*B)*sin(1/2*d*x+1/2*c)^6+(315*A+819*B)*sin(1/2*d*x+1/2*c)^4+(-420*A-630*B)*sin(1/2*d*x+1/2*c)^2+315*A+315*B)*2^(1/2)/(a*cos(1/2*d*x+1/2*c)^2)^(1/2)/d","A"
93,1,104,122,0.331000," ","int((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)),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(-30 B \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(21 A +105 B \right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(-70 A -140 B \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+105 A +105 B \right) \sqrt{2}}{105 \sqrt{a \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, d}"," ",0,"8/105*cos(1/2*d*x+1/2*c)*a^3*sin(1/2*d*x+1/2*c)*(-30*B*sin(1/2*d*x+1/2*c)^6+(21*A+105*B)*sin(1/2*d*x+1/2*c)^4+(-70*A-140*B)*sin(1/2*d*x+1/2*c)^2+105*A+105*B)*2^(1/2)/(a*cos(1/2*d*x+1/2*c)^2)^(1/2)/d","A"
94,1,311,124,1.278000," ","int((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))*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(24 B \sqrt{a}\, \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-20 \sqrt{a}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{2}\, \left(A +4 B \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+90 A \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}+15 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 +15 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 +120 B \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}\right)}{15 \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*a^(3/2)*cos(1/2*d*x+1/2*c)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*(24*B*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)^4-20*a^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*2^(1/2)*(A+4*B)*sin(1/2*d*x+1/2*c)^2+90*A*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)+15*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+15*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+120*B*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"
95,1,756,128,1.210000," ","int((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))*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(16 B \sqrt{a}\, \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(-24 A \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}-30 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 -30 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 -80 B \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}-12 B \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 B \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)+18 A \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}+15 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 +15 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 +36 B \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}+6 B \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 +6 B \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)}{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,"1/3*a^(3/2)*cos(1/2*d*x+1/2*c)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*(16*B*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)^4+(-24*A*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)-30*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-30*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-80*B*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)-12*B*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*B*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+18*A*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)+15*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+15*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+36*B*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)+6*B*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+6*B*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"
96,1,1016,136,1.192000," ","int((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))*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(\left(76 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 +76 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 +64 B \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}+80 B \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 +80 B \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(-44 A \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}-76 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 -76 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 -80 B \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}-80 B \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 -80 B \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)+26 A \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}+19 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 +19 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 +24 B \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}+20 B \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 +20 B \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)}{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))*a+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))*a+64*B*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)+80*B*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+80*B*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+(-44*A*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(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))*a-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))*a-80*B*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)-80*B*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-80*B*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+26*A*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)+19*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+19*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+24*B*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)+20*B*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+20*B*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/(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"
97,1,1310,144,1.457000," ","int((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))*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(-24 a \left(25 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)+25 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)+38 B \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)+38 B \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)+12 \left(50 A \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}+44 B \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}+75 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 +75 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 +114 B \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 +114 B \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(-736 A \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}-450 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 -450 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 -576 B \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}-684 B \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 -684 B \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)+234 A \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}+75 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 +75 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 +156 B \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}+114 B \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 +114 B \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)}{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)*(-24*a*(25*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))+25*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))+38*B*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))+38*B*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+12*(50*A*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)+44*B*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)+75*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+75*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+114*B*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+114*B*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+(-736*A*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)-450*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-450*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-576*B*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)-684*B*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-684*B*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+234*A*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)+75*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+75*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+156*B*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)+114*B*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+114*B*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))^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"
98,1,1630,185,1.500000," ","int((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))*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(48 a \left(163 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)+163 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)+200 B \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)+200 B \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^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-48 \left(163 A \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}+200 B \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}+326 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 +326 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 +400 B \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 +400 B \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)+8 \left(1793 A \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}+2072 B \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}+1467 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 +1467 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 +1800 B \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 +1800 B \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(-9212 A \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}-3912 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 -3912 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 -9632 B \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}-4800 B \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 -4800 B \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)+2094 A \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}+489 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 +489 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 +1872 B \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}+600 B \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 +600 B \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)}{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)*(48*a*(163*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))+163*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))+200*B*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))+200*B*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)^8-48*(163*A*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)+200*B*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)+326*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+326*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+400*B*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+400*B*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+8*(1793*A*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)+2072*B*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)+1467*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+1467*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+1800*B*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+1800*B*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+(-9212*A*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)-3912*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-3912*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-9632*B*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)-4800*B*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-4800*B*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+2094*A*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)+489*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+489*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+1872*B*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)+600*B*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+600*B*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))^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"
99,1,1951,226,1.620000," ","int((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))*sec(d*x+c)^6,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(-480 a \left(283 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)+283 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)+326 B \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)+326 B \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^{10}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+240 \left(566 A \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}+652 B \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}+1415 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 +1415 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 +1630 B \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 +1630 B \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^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-80 \left(3962 A \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}+4564 B \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}+4245 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 +4245 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 +4890 B \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 +4890 B \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^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+8 \left(36224 A \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}+40960 B \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}+21225 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 +21225 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 +24450 B \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 +24450 B \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)-10 \left(12556 A \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}+13400 B \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}+4245 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 +4245 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 +4890 B \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 +4890 B \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^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+4245 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 +4245 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 +22230 A \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}+4890 B \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 +4890 B \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 +20940 B \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}\right)}{120 \left(2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\sqrt{2}\right)^{5} \left(2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-\sqrt{2}\right)^{5} \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,"1/120*a^(3/2)*cos(1/2*d*x+1/2*c)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*(-480*a*(283*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))+283*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))+326*B*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))+326*B*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)^10+240*(566*A*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)+652*B*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)+1415*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+1415*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+1630*B*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+1630*B*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)^8-80*(3962*A*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)+4564*B*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)+4245*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+4245*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+4890*B*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+4890*B*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+8*(36224*A*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)+40960*B*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)+21225*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+21225*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+24450*B*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+24450*B*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)^4-10*(12556*A*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)+13400*B*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)+4245*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+4245*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+4890*B*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+4890*B*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+4245*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+4245*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+22230*A*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)+4890*B*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+4890*B*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+20940*B*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))^5/(2*cos(1/2*d*x+1/2*c)-2^(1/2))^5/sin(1/2*d*x+1/2*c)/(a*cos(1/2*d*x+1/2*c)^2)^(1/2)/d","B"
100,1,281,177,0.830000," ","int(cos(d*x+c)^3*(A+B*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{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(-240 B \sqrt{2}\, \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)+168 \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}\, \left(A +2 B \right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-140 \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}\, \left(A +2 B \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-105 \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 A +105 \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 B +210 A \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{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)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*(-240*B*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)^6+168*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)*(A+2*B)*sin(1/2*d*x+1/2*c)^4-140*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)*(A+2*B)*sin(1/2*d*x+1/2*c)^2-105*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+105*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*B+210*A*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(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"
101,1,240,138,0.732000," ","int(cos(d*x+c)^2*(A+B*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{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(24 B \sqrt{a}\, \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-20 \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}\, \left(A +B \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+15 \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 A -15 \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 B +30 B \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}\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)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*(24*B*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)^4-20*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)*(A+B)*sin(1/2*d*x+1/2*c)^2+15*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-15*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*B+30*B*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(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"
102,1,194,101,0.673000," ","int(cos(d*x+c)*(A+B*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(-4 B \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)+6 A \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}-3 A \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 +3 B \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)*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*(-4*B*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)*sin(1/2*d*x+1/2*c)^2+6*A*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)-3*A*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+3*B*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"
103,1,160,67,0.676000," ","int((A+B*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(A \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 B \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}-B \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)}{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)*(A*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*B*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)-B*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","B"
104,1,268,76,1.405000," ","int((A+B*cos(d*x+c))*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) A -\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) B -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)\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))*A-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))*B-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*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"
105,1,810,102,1.457000," ","int((A+B*cos(d*x+c))*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) A +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) B +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)-2 B \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)-2 B \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 A -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 B +2 A \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}-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 -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 +2 B \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 B \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)}{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))*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))*B+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*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))-2*B*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))-2*B*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*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))*a*B+2*A*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(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))*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*B*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*B*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"
106,1,1240,140,1.543000," ","int((A+B*cos(d*x+c))*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) A -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) B -7 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)-7 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)+4 B \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)+4 B \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^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-4 \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) a A +A \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}-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 B -4 B \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}-7 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 -7 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 +4 B \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 +4 B \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)+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 A -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 B -2 A \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}-7 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 -7 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 -8 B \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}+4 B \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 B \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)}{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))*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))*B-7*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))-7*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))+4*B*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))+4*B*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)^4-4*(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*A+A*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)-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*B-4*B*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)-7*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-7*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+4*B*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*B*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+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*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))*a*B-2*A*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)-7*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-7*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-8*B*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)+4*B*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*B*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/(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"
107,1,448,230,0.801000," ","int(cos(d*x+c)^4*(A+B*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(960 B \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}\, \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-96 \sqrt{2}\, \sqrt{a}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(7 A +17 B \right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+224 \sqrt{2}\, \sqrt{a}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(3 A +8 B \right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+35 \sqrt{2}\, \left(45 A \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 -48 A \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}-57 B \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 +16 B \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)-1575 \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 A +1995 \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 B +1785 A \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}-1785 B \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}\right)}{420 \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,"1/420/cos(1/2*d*x+1/2*c)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*(960*B*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)^8-96*2^(1/2)*a^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*(7*A+17*B)*sin(1/2*d*x+1/2*c)^6+224*2^(1/2)*a^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*(3*A+8*B)*sin(1/2*d*x+1/2*c)^4+35*2^(1/2)*(45*A*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-48*A*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)-57*B*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+16*B*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2))*sin(1/2*d*x+1/2*c)^2-1575*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+1995*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*B+1785*A*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)-1785*B*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"
108,1,407,189,0.782000," ","int(cos(d*x+c)^3*(A+B*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(-96 B \sqrt{2}\, \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)+16 \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}\, \left(5 A +6 B \right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+5 \sqrt{2}\, \left(8 A \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}-33 A \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 -48 B \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}+45 B \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) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+165 \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 A -225 \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 B -135 A \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}+255 B \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}\right)}{60 \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,"1/60*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*(-96*B*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)^6+16*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)*(5*A+6*B)*sin(1/2*d*x+1/2*c)^4+5*2^(1/2)*(8*A*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)-33*A*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-48*B*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)+45*B*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+165*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-225*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*B-135*A*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)+255*B*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"
109,1,327,148,0.796000," ","int(cos(d*x+c)^2*(A+B*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(16 B \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 A \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) \sqrt{2}\, \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +33 B \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) \sqrt{2}\, \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +24 A \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)-40 B \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)+3 A \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}-3 B \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{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)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*(16*B*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*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))*2^(1/2)*cos(1/2*d*x+1/2*c)^2*a+33*B*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))*2^(1/2)*cos(1/2*d*x+1/2*c)^2*a+24*A*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)^2-40*B*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+3*A*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)-3*B*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","B"
110,1,256,101,0.742000," ","int(cos(d*x+c)*(A+B*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 A \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) \sqrt{2}\, \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a -7 B \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) \sqrt{2}\, \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +8 B \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)-A \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}+B \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*A*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))*2^(1/2)*cos(1/2*d*x+1/2*c)^2*a-7*B*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))*2^(1/2)*cos(1/2*d*x+1/2*c)^2*a+8*B*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-A*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)+B*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"
111,1,220,72,0.720000," ","int((A+B*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(A \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) \sqrt{2}\, \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +3 B \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) \sqrt{2}\, \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +A \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}-B \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)*(A*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))*2^(1/2)*cos(1/2*d*x+1/2*c)^2*a+3*B*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))*2^(1/2)*cos(1/2*d*x+1/2*c)^2*a+A*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)-B*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","B"
112,1,374,106,1.537000," ","int((A+B*cos(d*x+c))*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 A \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) \sqrt{2}\, \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a -B \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) \sqrt{2}\, \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a -4 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) \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a -4 A \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 +A \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}-B \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)*(5*A*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))*2^(1/2)*cos(1/2*d*x+1/2*c)^2*a-B*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))*2^(1/2)*cos(1/2*d*x+1/2*c)^2*a-4*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))*cos(1/2*d*x+1/2*c)^2*a-4*A*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+A*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)-B*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"
113,1,1051,145,1.570000," ","int((A+B*cos(d*x+c))*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 A \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) \sqrt{2}\, \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a -10 B \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) \sqrt{2}\, \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a -12 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) \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a -12 A \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 +8 B \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 +8 B \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 -9 A \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) \sqrt{2}\, \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +5 B \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) \sqrt{2}\, \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +6 A \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 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) \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +6 A \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 -2 B \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)-4 B \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 -4 B \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 -A \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}+B \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*A*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))*2^(1/2)*cos(1/2*d*x+1/2*c)^4*a-10*B*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))*2^(1/2)*cos(1/2*d*x+1/2*c)^4*a-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))*cos(1/2*d*x+1/2*c)^4*a-12*A*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+8*B*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+8*B*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-9*A*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))*2^(1/2)*cos(1/2*d*x+1/2*c)^2*a+5*B*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))*2^(1/2)*cos(1/2*d*x+1/2*c)^2*a+6*A*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*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))*cos(1/2*d*x+1/2*c)^2*a+6*A*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-2*B*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)^2-4*B*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-4*B*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-A*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)+B*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"
114,1,1540,190,1.679000," ","int((A+B*cos(d*x+c))*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 A \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) \sqrt{2}\, \left(\cos^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a -72 B \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) \sqrt{2}\, \left(\cos^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a -76 A \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 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) \left(\cos^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +48 B \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 +48 B \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 A \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) \sqrt{2}\, \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +72 B \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) \sqrt{2}\, \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +28 A \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 A \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 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) \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a -24 B \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)-48 B \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 -48 B \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 A \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) \sqrt{2}\, \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a -18 B \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) \sqrt{2}\, \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a -22 A \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 A \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 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) \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +16 B \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)+12 B \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 +12 B \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 A \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}-2 B \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*A*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))*2^(1/2)*cos(1/2*d*x+1/2*c)^6*a-72*B*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))*2^(1/2)*cos(1/2*d*x+1/2*c)^6*a-76*A*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*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))*cos(1/2*d*x+1/2*c)^6*a+48*B*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+48*B*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*A*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))*2^(1/2)*cos(1/2*d*x+1/2*c)^4*a+72*B*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))*2^(1/2)*cos(1/2*d*x+1/2*c)^4*a+28*A*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*A*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*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))*cos(1/2*d*x+1/2*c)^4*a-24*B*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)^4-48*B*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-48*B*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*A*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))*2^(1/2)*cos(1/2*d*x+1/2*c)^2*a-18*B*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))*2^(1/2)*cos(1/2*d*x+1/2*c)^2*a-22*A*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*A*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*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))*cos(1/2*d*x+1/2*c)^2*a+16*B*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+12*B*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+12*B*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*A*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)-2*B*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"
115,1,467,230,0.820000," ","int(cos(d*x+c)^4*(A+B*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(768 B \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}\, \left(\cos^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+640 A \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)-2176 B \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)+2445 A \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) \sqrt{2}\, \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a -4245 B \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) \sqrt{2}\, \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a -2560 A \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)+5248 B \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)-435 A \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)+555 B \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)+30 A \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}-30 B \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}\right)}{480 \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,"1/480/cos(1/2*d*x+1/2*c)^3*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*(768*B*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)^8+640*A*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)^6-2176*B*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+2445*A*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))*2^(1/2)*cos(1/2*d*x+1/2*c)^4*a-4245*B*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))*2^(1/2)*cos(1/2*d*x+1/2*c)^4*a-2560*A*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+5248*B*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)^4-435*A*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+555*B*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+30*A*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)-30*B*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","B"
116,1,397,189,0.838000," ","int(cos(d*x+c)^3*(A+B*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(128 B \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)-225 A \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) \sqrt{2}\, \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +489 B \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) \sqrt{2}\, \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +192 A \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)-512 B \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)+63 A \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)-87 B \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 A \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}+6 B \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/cos(1/2*d*x+1/2*c)^3*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*(128*B*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)^6-225*A*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))*2^(1/2)*cos(1/2*d*x+1/2*c)^4*a+489*B*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))*2^(1/2)*cos(1/2*d*x+1/2*c)^4*a+192*A*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)^4-512*B*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+63*A*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)^2-87*B*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*A*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)+6*B*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","B"
117,1,327,146,0.862000," ","int(cos(d*x+c)^2*(A+B*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(19 A \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) \sqrt{2}\, \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a -75 B \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) \sqrt{2}\, \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +64 B \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)-13 A \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)+21 B \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 A \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}-2 B \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*A*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))*2^(1/2)*cos(1/2*d*x+1/2*c)^4*a-75*B*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))*2^(1/2)*cos(1/2*d*x+1/2*c)^4*a+64*B*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)^4-13*A*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+21*B*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*A*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)-2*B*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","B"
118,1,292,107,0.678000," ","int(cos(d*x+c)*(A+B*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 A \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) \sqrt{2}\, \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +19 B \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) \sqrt{2}\, \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +5 A \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)-13 B \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 A \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}+2 B \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*A*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))*2^(1/2)*cos(1/2*d*x+1/2*c)^4*a+19*B*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))*2^(1/2)*cos(1/2*d*x+1/2*c)^4*a+5*A*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)^2-13*B*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*A*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)+2*B*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","B"
119,1,292,107,0.751000," ","int((A+B*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(3 A \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) \sqrt{2}\, \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +5 B \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) \sqrt{2}\, \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +3 A \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)+5 B \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 A \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}-2 B \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)*(3*A*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))*2^(1/2)*cos(1/2*d*x+1/2*c)^4*a+5*B*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))*2^(1/2)*cos(1/2*d*x+1/2*c)^4*a+3*A*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+5*B*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*A*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)-2*B*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","B"
120,1,445,139,1.582000," ","int((A+B*cos(d*x+c))*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 A \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) \sqrt{2}\, \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a -3 B \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) \sqrt{2}\, \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a -32 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) \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a -32 A \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 A \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)-3 B \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 A \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}-2 B \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*A*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))*2^(1/2)*cos(1/2*d*x+1/2*c)^4*a-3*B*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))*2^(1/2)*cos(1/2*d*x+1/2*c)^4*a-32*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))*cos(1/2*d*x+1/2*c)^4*a-32*A*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*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)^2-3*B*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*A*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)-2*B*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"
121,1,1122,178,1.713000," ","int((A+B*cos(d*x+c))*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 A \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) \sqrt{2}\, \left(\cos^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a -86 B \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) \sqrt{2}\, \left(\cos^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a -160 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) \left(\cos^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a -160 A \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 +64 B \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 +64 B \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 A \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) \sqrt{2}\, \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +43 B \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) \sqrt{2}\, \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +70 A \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 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) \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +80 A \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 -22 B \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)-32 B \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 B \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 A \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)+7 B \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 A \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}+2 B \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*A*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))*2^(1/2)*cos(1/2*d*x+1/2*c)^6*a-86*B*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))*2^(1/2)*cos(1/2*d*x+1/2*c)^6*a-160*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))*cos(1/2*d*x+1/2*c)^6*a-160*A*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+64*B*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+64*B*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*A*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))*2^(1/2)*cos(1/2*d*x+1/2*c)^4*a+43*B*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))*2^(1/2)*cos(1/2*d*x+1/2*c)^4*a+70*A*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*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))*cos(1/2*d*x+1/2*c)^4*a+80*A*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-22*B*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)^4-32*B*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*B*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*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+7*B*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*A*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)+2*B*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"
122,1,1610,229,1.989000," ","int((A+B*cos(d*x+c))*sec(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(320 B \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^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a -624 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) \left(\cos^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +219 A \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) \sqrt{2}\, \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a -115 B \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) \sqrt{2}\, \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +624 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) \left(\cos^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a -320 B \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 +624 A \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 -320 B \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 +100 B \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)-2 B \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}+320 B \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^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a -624 A \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^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +19 A \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)-11 B \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)-156 A \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 +80 B \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 -156 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) \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +80 B \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 +2 A \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}+460 B \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) \sqrt{2}\, \left(\cos^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a -140 B \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)+252 A \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)+876 A \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) \sqrt{2}\, \left(\cos^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a -460 B \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) \sqrt{2}\, \left(\cos^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a -188 A \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)-876 A \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) \sqrt{2}\, \left(\cos^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a \right)}{8 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)^{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,"-1/8*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*(320*B*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)^8*a-624*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))*cos(1/2*d*x+1/2*c)^8*a+320*B*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)^8*a-624*A*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)^8*a+624*A*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+624*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))*cos(1/2*d*x+1/2*c)^6*a-320*B*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-320*B*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-2*B*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)-876*A*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))*2^(1/2)*cos(1/2*d*x+1/2*c)^6*a+460*B*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))*2^(1/2)*cos(1/2*d*x+1/2*c)^6*a-188*A*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)^4-156*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))*cos(1/2*d*x+1/2*c)^4*a-156*A*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+80*B*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*B*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+19*A*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)^2-11*B*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+100*B*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+2*A*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2)+219*A*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))*2^(1/2)*cos(1/2*d*x+1/2*c)^4*a-115*B*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))*2^(1/2)*cos(1/2*d*x+1/2*c)^4*a+252*A*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)^6-140*B*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+876*A*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))*2^(1/2)*cos(1/2*d*x+1/2*c)^8*a-460*B*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))*2^(1/2)*cos(1/2*d*x+1/2*c)^8*a)/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/(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"
123,1,411,191,1.066000," ","int(cos(d*x+c)^(5/2)*(a+a*cos(d*x+c))*(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)}\, a \left(-1120 B \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{10}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(720 A +2960 B \right) \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\left(-1584 A -3152 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(1344 A +1792 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(-366 A -408 B \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+75 A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-189 A \sqrt{\frac{1}{2}-\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)+75 B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-147 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)}{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)*a*(-1120*B*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^10+(720*A+2960*B)*sin(1/2*d*x+1/2*c)^8*cos(1/2*d*x+1/2*c)+(-1584*A-3152*B)*sin(1/2*d*x+1/2*c)^6*cos(1/2*d*x+1/2*c)+(1344*A+1792*B)*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+(-366*A-408*B)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+75*A*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-189*A*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+75*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-147*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"
124,1,383,168,0.980000," ","int(cos(d*x+c)^(3/2)*(a+a*cos(d*x+c))*(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)}\, a \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 -528 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(308 A +448 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(-112 A -122 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)+35 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)-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)-63 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)}{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*B*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^8+(-168*A-528*B)*sin(1/2*d*x+1/2*c)^6*cos(1/2*d*x+1/2*c)+(308*A+448*B)*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+(-112*A-122*B)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+35*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))-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))-63*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"
125,1,355,141,1.024000," ","int((a+a*cos(d*x+c))*(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)}\, a \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 +44 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 -16 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)-15 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)+5 B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-9 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)*a*(-24*B*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6+(20*A+44*B)*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+(-10*A-16*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))-15*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))+5*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-9*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"
126,1,321,116,1.244000," ","int((a+a*cos(d*x+c))*(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)}\, a \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}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\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)-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)-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)*a*(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)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-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))-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))-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"
127,1,240,116,1.089000," ","int((a+a*cos(d*x+c))*(A+B*cos(d*x+c))/cos(d*x+c)^(3/2),x)","-\frac{2 a \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}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\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}\, \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)-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)}{\sin \left(\frac{d 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*(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))+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*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*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)^2-1)^(1/2)/d","B"
128,1,426,139,2.330000," ","int((a+a*cos(d*x+c))*(A+B*cos(d*x+c))/cos(d*x+c)^(5/2),x)","-\frac{4 \sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, a \left(\frac{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 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{\left(\frac{A}{2}+\frac{B}{2}\right) \left(-\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+2 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right)^{2} \left(2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}+\frac{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}\right)}{\sin \left(\frac{d 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*(1/2*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))+(1/2*A+1/2*B)*(-(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*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)+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"
129,1,661,168,3.029000," ","int((a+a*cos(d*x+c))*(A+B*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{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)}}{10 \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{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)}{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)}+\left(\frac{A}{2}+\frac{B}{2}\right) \left(-\frac{\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{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,"-4*(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*a*(-1/10*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)+1/2*B*(-(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*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)+(1/2*A+1/2*B)*(-1/6*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^2+1/3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))))/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
130,1,413,226,1.103000," ","int(cos(d*x+c)^(3/2)*(a+a*cos(d*x+c))^2*(A+B*cos(d*x+c)),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 B \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{10}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(360 A +1840 B \right) \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\left(-1044 A -2368 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(1134 A +1568 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(-351 A -387 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)-189 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)+90 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)-168 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)+75 B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)\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*B*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^10+(360*A+1840*B)*sin(1/2*d*x+1/2*c)^8*cos(1/2*d*x+1/2*c)+(-1044*A-2368*B)*sin(1/2*d*x+1/2*c)^6*cos(1/2*d*x+1/2*c)+(1134*A+1568*B)*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+(-351*A-387*B)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)-189*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))+90*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))-168*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))+75*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2)))/(-2*sin(1/2*d*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"
131,1,385,197,1.107000," ","int((a+a*cos(d*x+c))^2*(A+B*cos(d*x+c))*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(120 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(-84 A -348 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(224 A +378 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(-91 A -117 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)+35 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)-84 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)+30 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)-63 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)}{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^2*(120*B*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^8+(-84*A-348*B)*sin(1/2*d*x+1/2*c)^6*cos(1/2*d*x+1/2*c)+(224*A+378*B)*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+(-91*A-117*B)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+35*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))-84*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))+30*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))-63*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"
132,1,357,166,0.989000," ","int((a+a*cos(d*x+c))^2*(A+B*cos(d*x+c))/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(-12 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(10 A +32 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(-5 A -13 B \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+10 A \sqrt{\frac{1}{2}-\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 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)+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)-12 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,"-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*B*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6+(10*A+32*B)*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+(-5*A-13*B)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+10*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*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))+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))-12*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"
133,1,388,162,1.008000," ","int((a+a*cos(d*x+c))^2*(A+B*cos(d*x+c))/cos(d*x+c)^(3/2),x)","-\frac{4 a^{2} \left(2 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)}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \left(3 A +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)+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}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}+2 B \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-3 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)}\, \sqrt{\frac{1}{2}-\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 \sqrt{-2 \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*a^2*(2*B*(-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)^4-(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(3*A+B)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+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)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)+2*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)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-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*sin(1/2*d*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"
134,1,513,162,1.232000," ","int((a+a*cos(d*x+c))^2*(A+B*cos(d*x+c))/cos(d*x+c)^(5/2),x)","-\frac{4 \left(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(2 A +B \right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\sqrt{-2 \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(7 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{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}}\, \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \left(2 A \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+3 A \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+3 B \EllipticF \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)+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) \sqrt{-2 \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 A \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}+3 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)}\, \sqrt{\frac{1}{2}-\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) a^{2}}{3 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)^{\frac{3}{2}} \sin \left(\frac{d x}{2}+\frac{c}{2}\right) d}"," ",0,"-4/3*(6*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*A+B)*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4-(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(7*A+3*B)*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)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*A*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+3*A*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+3*B*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2)))*sin(1/2*d*x+1/2*c)^2+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))*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)+3*A*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)+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)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2)))*a^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)^(3/2)/sin(1/2*d*x+1/2*c)/d","B"
135,1,741,195,3.343000," ","int((a+a*cos(d*x+c))^2*(A+B*cos(d*x+c))/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{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 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{A \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)}}{20 \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{\left(\frac{A}{4}+\frac{B}{2}\right) \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)}+\left(\frac{A}{2}+\frac{B}{4}\right) \left(-\frac{\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{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,"-8*(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^2*(1/4*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-1/20*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)+(1/4*A+1/2*B)*(-(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*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)+(1/2*A+1/4*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"
136,1,851,226,4.040000," ","int((a+a*cos(d*x+c))^2*(A+B*cos(d*x+c))/cos(d*x+c)^(9/2),x)","-\frac{8 \sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, a^{2} \left(-\frac{\left(\frac{A}{2}+\frac{B}{4}\right) \left(12 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \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{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)}{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)-1\right)}+\left(\frac{A}{4}+\frac{B}{2}\right) \left(-\frac{\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{6 \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{3 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}\right)+\frac{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)}}{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)}{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,"-8*(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^2*(-1/5*(1/2*A+1/4*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)+1/4*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)+(1/4*A+1/2*B)*(-1/6*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^2+1/3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2)))+1/4*A*(-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"
137,1,441,265,1.113000," ","int(cos(d*x+c)^(3/2)*(a+a*cos(d*x+c))^3*(A+B*cos(d*x+c)),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(10080 B \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{12}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(-6160 A -43680 B \right) \left(\sin^{10}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\left(24200 A +77280 B \right) \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\left(-37532 A -72240 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(29722 A +39270 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(-8118 A -8820 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)+1815 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)-3927 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)+1575 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)-3465 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)}{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,"-4/3465*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^3*(10080*B*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^12+(-6160*A-43680*B)*sin(1/2*d*x+1/2*c)^10*cos(1/2*d*x+1/2*c)+(24200*A+77280*B)*sin(1/2*d*x+1/2*c)^8*cos(1/2*d*x+1/2*c)+(-37532*A-72240*B)*sin(1/2*d*x+1/2*c)^6*cos(1/2*d*x+1/2*c)+(29722*A+39270*B)*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+(-8118*A-8820*B)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+1815*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))-3927*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))+1575*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))-3465*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"
138,1,413,236,1.059000," ","int((a+a*cos(d*x+c))^3*(A+B*cos(d*x+c))*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(-560 B \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{10}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(360 A +2200 B \right) \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\left(-1296 A -3412 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(1806 A +2702 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(-624 A -738 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)+195 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)-441 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)+165 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)-357 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)}{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*B*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^10+(360*A+2200*B)*sin(1/2*d*x+1/2*c)^8*cos(1/2*d*x+1/2*c)+(-1296*A-3412*B)*sin(1/2*d*x+1/2*c)^6*cos(1/2*d*x+1/2*c)+(1806*A+2702*B)*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+(-624*A-738*B)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+195*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))-441*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))+165*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))-357*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"
139,1,385,207,1.018000," ","int((a+a*cos(d*x+c))^3*(A+B*cos(d*x+c))/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(120 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(-84 A -432 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(294 A +602 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(-126 A -208 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)-189 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)+105 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)-147 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)+65 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,"-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*B*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^8+(-84*A-432*B)*sin(1/2*d*x+1/2*c)^6*cos(1/2*d*x+1/2*c)+(294*A+602*B)*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+(-126*A-208*B)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)-189*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))+105*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))-147*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))+65*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"
140,1,519,207,1.185000," ","int((a+a*cos(d*x+c))^3*(A+B*cos(d*x+c))/cos(d*x+c)^(3/2),x)","-\frac{4 a^{3} \left(-12 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)}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+2 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \left(5 A +21 B \right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-2 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \left(10 A +9 B \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+25 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) \sqrt{-2 \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 A \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}+15 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)}\, \sqrt{\frac{1}{2}-\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)-27 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)}\, \sqrt{\frac{1}{2}-\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,"-4/15*a^3*(-12*B*(-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)^6+2*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(5*A+21*B)*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)-2*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(10*A+9*B)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+25*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*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)-15*A*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)+15*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)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-27*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*sin(1/2*d*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"
141,1,654,199,1.271000," ","int((a+a*cos(d*x+c))^3*(A+B*cos(d*x+c))/cos(d*x+c)^(5/2),x)","-\frac{4 \left(-4 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)}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+2 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \left(9 A +5 B \right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-2 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \left(5 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{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \left(5 A \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+3 A \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+5 B \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)+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) \sqrt{-2 \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 A \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}+5 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)}\, \sqrt{\frac{1}{2}-\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)+\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)\right) a^{3}}{3 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)^{\frac{3}{2}} \sin \left(\frac{d x}{2}+\frac{c}{2}\right) d}"," ",0,"-4/3*(-4*B*(-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)^6+2*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(9*A+5*B)*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)-2*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(5*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*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)*(5*A*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+3*A*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+5*B*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+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))*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)+3*A*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)+5*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)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-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)))*a^3/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(2*cos(1/2*d*x+1/2*c)^2-1)^(3/2)/sin(1/2*d*x+1/2*c)/d","B"
142,1,916,207,3.388000," ","int((a+a*cos(d*x+c))^3*(A+B*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^{3} \left(60 A \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)+108 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)-216 A \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+100 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)+60 B \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-180 B \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-60 A \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)-108 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)+246 A \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-100 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)-60 B \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+190 B \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+15 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)+27 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)-72 A \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\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)+15 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)-50 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)}}{15 \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)^{3} \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^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)^3*(60*A*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+108*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)^4-216*A*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6+100*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+60*B*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^4-180*B*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6-60*A*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)^2-108*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+246*A*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4-100*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)^2-60*B*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^2+190*B*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4+15*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))+27*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))-72*A*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^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))+15*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))-50*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"
143,1,929,236,4.328000," ","int((a+a*cos(d*x+c))^3*(A+B*cos(d*x+c))/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{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 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{\left(\frac{3 A}{8}+\frac{B}{8}\right) \left(12 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \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{\left(\frac{A}{8}+\frac{3 B}{8}\right) \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)}+\left(\frac{3 A}{8}+\frac{3 B}{8}\right) \left(-\frac{\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{6 \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{3 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}\right)+\frac{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)}}{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)}{8}\right)}{\sin \left(\frac{d 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*(1/8*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-1/5*(3/8*A+1/8*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)+(1/8*A+3/8*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)+(3/8*A+3/8*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)))+1/8*A*(-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"
144,1,1178,265,4.922000," ","int((a+a*cos(d*x+c))^3*(A+B*cos(d*x+c))/cos(d*x+c)^(11/2),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{\left(\frac{3 A}{8}+\frac{3 B}{8}\right) \left(12 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \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{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)}}{144 \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}-\frac{7 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{180 \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}-\frac{14 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)}{15 \sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}}+\frac{7 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{15 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{7 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \left(\EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-\EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)\right)}{15 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}\right)}{8}+\frac{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)}{8 \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)}+\left(\frac{A}{8}+\frac{3 B}{8}\right) \left(-\frac{\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{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)+\left(\frac{3 A}{8}+\frac{B}{8}\right) \left(-\frac{\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{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,"-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*(-1/5*(3/8*A+3/8*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)+1/8*A*(-1/144*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^5-7/180*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^3-14/15*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)/(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)+7/15*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-7/15*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))))+1/8*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)+(1/8*A+3/8*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)))+(3/8*A+1/8*B)*(-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"
145,1,281,194,1.159000," ","int(cos(d*x+c)^(5/2)*(A+B*cos(d*x+c))/(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 A \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+45 A \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-25 B \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-63 B \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)\right)+48 B \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(-40 A -56 B \right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(90 A -30 B \right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(-35 A +23 B \right) \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*A*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+45*A*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-25*B*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-63*B*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2)))+48*B*sin(1/2*d*x+1/2*c)^8+(-40*A-56*B)*sin(1/2*d*x+1/2*c)^6+(90*A-30*B)*sin(1/2*d*x+1/2*c)^4+(-35*A+23*B)*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"
146,1,262,167,1.072000," ","int(cos(d*x+c)^(3/2)*(A+B*cos(d*x+c))/(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(3 A \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+9 A \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-5 B \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-9 B \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)\right)+8 B \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(6 A -18 B \right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(-3 A +7 B \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}{3 a \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"1/3*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(cos(1/2*d*x+1/2*c)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(3*A*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+9*A*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-5*B*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-9*B*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2)))+8*B*sin(1/2*d*x+1/2*c)^6+(6*A-18*B)*sin(1/2*d*x+1/2*c)^4+(-3*A+7*B)*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"
147,1,244,135,1.033000," ","int((A+B*cos(d*x+c))*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(A \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 \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(2 A -2 B \right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(-A +B \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}{a \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(cos(1/2*d*x+1/2*c)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(A*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*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)))+(2*A-2*B)*sin(1/2*d*x+1/2*c)^4+(-A+B)*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"
148,1,243,133,1.148000," ","int((A+B*cos(d*x+c))/(a+a*cos(d*x+c))/cos(d*x+c)^(1/2),x)","\frac{\sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(-\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(A \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 \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)+\left(2 A -2 B \right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(-A +B \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)*(A*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*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*A-2*B)*sin(1/2*d*x+1/2*c)^4+(-A+B)*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"
149,1,319,167,2.357000," ","int((A+B*cos(d*x+c))/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}}\, \sqrt{-2 \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 \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-3 A \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-B \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)-2 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \left(3 A -B \right) \left(\sin^{4}\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(5 A -B \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}{a \sin \left(\frac{d x}{2}+\frac{c}{2}\right)^{3} \left(2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)/a*(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)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(A*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-3*A*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-B*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*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(3*A-B)*sin(1/2*d*x+1/2*c)^4+(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(5*A-B)*sin(1/2*d*x+1/2*c)^2)/sin(1/2*d*x+1/2*c)^3/(2*sin(1/2*d*x+1/2*c)^2-1)/cos(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
150,1,493,195,3.156000," ","int((A+B*cos(d*x+c))/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(\frac{\left(-2 A +2 B \right) \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)}+2 A \left(-\frac{\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{6 \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{3 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}\right)+\frac{\left(A -B \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)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\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)}}\right)}{a \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)/a*((-2*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)))+(A-B)*(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)/cos(1/2*d*x+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"
151,1,465,237,1.046000," ","int(cos(d*x+c)^(7/2)*(A+B*cos(d*x+c))/(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 B \left(\cos^{10}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+80 A \left(\cos^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-352 B \left(\cos^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+60 A \left(\cos^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+100 A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+210 A \left(\cos^{3}\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}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+120 B \left(\cos^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-150 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) \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-336 B \left(\cos^{3}\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}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-240 A \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+266 B \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+105 A \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-135 B \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-5 A +5 B \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*B*cos(1/2*d*x+1/2*c)^10+80*A*cos(1/2*d*x+1/2*c)^8-352*B*cos(1/2*d*x+1/2*c)^8+60*A*cos(1/2*d*x+1/2*c)^6+100*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)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*cos(1/2*d*x+1/2*c)^3+210*A*cos(1/2*d*x+1/2*c)^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)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+120*B*cos(1/2*d*x+1/2*c)^6-150*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)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*cos(1/2*d*x+1/2*c)^3-336*B*cos(1/2*d*x+1/2*c)^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)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-240*A*cos(1/2*d*x+1/2*c)^4+266*B*cos(1/2*d*x+1/2*c)^4+105*A*cos(1/2*d*x+1/2*c)^2-135*B*cos(1/2*d*x+1/2*c)^2-5*A+5*B)/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"
152,1,435,204,1.142000," ","int(cos(d*x+c)^(5/2)*(A+B*cos(d*x+c))/(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 B \left(\cos^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+24 A \left(\cos^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+10 A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+24 A \left(\cos^{3}\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}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-12 B \left(\cos^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-20 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) \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-42 B \left(\cos^{3}\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}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-38 A \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+48 B \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+15 A \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-21 B \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-A +B \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)*(-16*B*cos(1/2*d*x+1/2*c)^8+24*A*cos(1/2*d*x+1/2*c)^6+10*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)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*cos(1/2*d*x+1/2*c)^3+24*A*cos(1/2*d*x+1/2*c)^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)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-12*B*cos(1/2*d*x+1/2*c)^6-20*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)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*cos(1/2*d*x+1/2*c)^3-42*B*cos(1/2*d*x+1/2*c)^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)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-38*A*cos(1/2*d*x+1/2*c)^4+48*B*cos(1/2*d*x+1/2*c)^4+15*A*cos(1/2*d*x+1/2*c)^2-21*B*cos(1/2*d*x+1/2*c)^2-A+B)/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"
153,1,421,178,1.171000," ","int(cos(d*x+c)^(3/2)*(A+B*cos(d*x+c))/(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 A \left(\cos^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+4 A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+6 A \left(\cos^{3}\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}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-24 B \left(\cos^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-10 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) \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-24 B \left(\cos^{3}\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}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-20 A \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+38 B \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+9 A \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-15 B \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-A +B \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*A*cos(1/2*d*x+1/2*c)^6+4*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)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*cos(1/2*d*x+1/2*c)^3+6*A*cos(1/2*d*x+1/2*c)^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)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-24*B*cos(1/2*d*x+1/2*c)^6-10*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)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*cos(1/2*d*x+1/2*c)^3-24*B*cos(1/2*d*x+1/2*c)^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)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-20*A*cos(1/2*d*x+1/2*c)^4+38*B*cos(1/2*d*x+1/2*c)^4+9*A*cos(1/2*d*x+1/2*c)^2-15*B*cos(1/2*d*x+1/2*c)^2-A+B)/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"
154,1,350,165,1.308000," ","int((A+B*cos(d*x+c))*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 A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+12 B \left(\cos^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+4 B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \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 B \left(\cos^{3}\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}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+2 A \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-20 B \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-3 A \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+9 B \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+A -B \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*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)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*cos(1/2*d*x+1/2*c)^3+12*B*cos(1/2*d*x+1/2*c)^6+4*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)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*cos(1/2*d*x+1/2*c)^3+6*B*cos(1/2*d*x+1/2*c)^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)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+2*A*cos(1/2*d*x+1/2*c)^4-20*B*cos(1/2*d*x+1/2*c)^4-3*A*cos(1/2*d*x+1/2*c)^2+9*B*cos(1/2*d*x+1/2*c)^2+A-B)/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"
155,1,350,165,1.101000," ","int((A+B*cos(d*x+c))/(a+a*cos(d*x+c))^2/cos(d*x+c)^(1/2),x)","\frac{\sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(12 A \left(\cos^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-4 A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+6 A \left(\cos^{3}\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}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-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}\, \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)-16 A \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-2 B \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+3 A \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+3 B \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+A -B \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*A*cos(1/2*d*x+1/2*c)^6-4*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)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*cos(1/2*d*x+1/2*c)^3+6*A*cos(1/2*d*x+1/2*c)^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)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-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)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*cos(1/2*d*x+1/2*c)^3-16*A*cos(1/2*d*x+1/2*c)^4-2*B*cos(1/2*d*x+1/2*c)^4+3*A*cos(1/2*d*x+1/2*c)^2+3*B*cos(1/2*d*x+1/2*c)^2+A-B)/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"
156,1,494,208,1.346000," ","int((A+B*cos(d*x+c))/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{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \left(5 A \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-12 A \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-2 B \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) \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{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \left(5 A \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-12 A \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-2 B \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) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-12 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \left(4 A -B \right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+2 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \left(43 A -10 B \right) \left(\sin^{4}\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(37 A -7 B \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)*(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)*(5*A*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-12*A*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-2*B*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)))*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)*(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)*(5*A*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-12*A*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-2*B*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)))*cos(1/2*d*x+1/2*c)-12*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(4*A-B)*sin(1/2*d*x+1/2*c)^6+2*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(43*A-10*B)*sin(1/2*d*x+1/2*c)^4-(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(37*A-7*B)*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"
157,1,750,237,3.954000," ","int((A+B*cos(d*x+c))/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{\left(A -B \right) \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}\, \left(2 \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) \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-2 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \left(2 \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) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-12 \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+20 \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 \sqrt{-2 \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(-1+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}+\frac{\left(-8 A +4 B \right) \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 \left(-\frac{\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{6 \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{3 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}\right)+\frac{\left(4 A -2 B \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)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\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)}}\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*(A-B)*(2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(2*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)))*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2-2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(2*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)))*cos(1/2*d*x+1/2*c)-12*sin(1/2*d*x+1/2*c)^6+20*sin(1/2*d*x+1/2*c)^4-7*sin(1/2*d*x+1/2*c)^2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/cos(1/2*d*x+1/2*c)/(-1+sin(1/2*d*x+1/2*c)^2)+(-8*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)+4*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)))+(4*A-2*B)*(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)/cos(1/2*d*x+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"
158,1,493,282,1.418000," ","int(cos(d*x+c)^(9/2)*(A+B*cos(d*x+c))/(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(192 B \left(\cos^{12}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+160 A \left(\cos^{10}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-864 B \left(\cos^{10}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+468 A \left(\cos^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+330 A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+714 A \left(\cos^{5}\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}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-228 B \left(\cos^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-630 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) \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1386 B \left(\cos^{5}\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}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-1058 A \left(\cos^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1590 B \left(\cos^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+474 A \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-744 B \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-47 A \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+57 B \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+3 A -3 B \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)*(192*B*cos(1/2*d*x+1/2*c)^12+160*A*cos(1/2*d*x+1/2*c)^10-864*B*cos(1/2*d*x+1/2*c)^10+468*A*cos(1/2*d*x+1/2*c)^8+330*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)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*cos(1/2*d*x+1/2*c)^5+714*A*cos(1/2*d*x+1/2*c)^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)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-228*B*cos(1/2*d*x+1/2*c)^8-630*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)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*cos(1/2*d*x+1/2*c)^5-1386*B*cos(1/2*d*x+1/2*c)^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)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-1058*A*cos(1/2*d*x+1/2*c)^6+1590*B*cos(1/2*d*x+1/2*c)^6+474*A*cos(1/2*d*x+1/2*c)^4-744*B*cos(1/2*d*x+1/2*c)^4-47*A*cos(1/2*d*x+1/2*c)^2+57*B*cos(1/2*d*x+1/2*c)^2+3*A-3*B)/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"
159,1,465,251,1.128000," ","int(cos(d*x+c)^(7/2)*(A+B*cos(d*x+c))/(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 B \left(\cos^{10}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+348 A \left(\cos^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+130 A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+294 A \left(\cos^{5}\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}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-468 B \left(\cos^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-330 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) \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-714 B \left(\cos^{5}\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}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-578 A \left(\cos^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1058 B \left(\cos^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+264 A \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-474 B \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-37 A \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+47 B \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+3 A -3 B \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)*(-160*B*cos(1/2*d*x+1/2*c)^10+348*A*cos(1/2*d*x+1/2*c)^8+130*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)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*cos(1/2*d*x+1/2*c)^5+294*A*cos(1/2*d*x+1/2*c)^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)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-468*B*cos(1/2*d*x+1/2*c)^8-330*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)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*cos(1/2*d*x+1/2*c)^5-714*B*cos(1/2*d*x+1/2*c)^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)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-578*A*cos(1/2*d*x+1/2*c)^6+1058*B*cos(1/2*d*x+1/2*c)^6+264*A*cos(1/2*d*x+1/2*c)^4-474*B*cos(1/2*d*x+1/2*c)^4-37*A*cos(1/2*d*x+1/2*c)^2+47*B*cos(1/2*d*x+1/2*c)^2+3*A-3*B)/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"
160,1,451,224,1.249000," ","int(cos(d*x+c)^(5/2)*(A+B*cos(d*x+c))/(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(108 A \left(\cos^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+30 A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+54 A \left(\cos^{5}\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}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-348 B \left(\cos^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-130 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) \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-294 B \left(\cos^{5}\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}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-198 A \left(\cos^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+578 B \left(\cos^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+114 A \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-264 B \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-27 A \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+37 B \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+3 A -3 B \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)*(108*A*cos(1/2*d*x+1/2*c)^8+30*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)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*cos(1/2*d*x+1/2*c)^5+54*A*cos(1/2*d*x+1/2*c)^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)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-348*B*cos(1/2*d*x+1/2*c)^8-130*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)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*cos(1/2*d*x+1/2*c)^5-294*B*cos(1/2*d*x+1/2*c)^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)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-198*A*cos(1/2*d*x+1/2*c)^6+578*B*cos(1/2*d*x+1/2*c)^6+114*A*cos(1/2*d*x+1/2*c)^4-264*B*cos(1/2*d*x+1/2*c)^4-27*A*cos(1/2*d*x+1/2*c)^2+37*B*cos(1/2*d*x+1/2*c)^2+3*A-3*B)/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"
161,1,451,216,1.158000," ","int(cos(d*x+c)^(3/2)*(A+B*cos(d*x+c))/(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 A \left(\cos^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+10 A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+6 A \left(\cos^{5}\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}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+108 B \left(\cos^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+30 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) \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+54 B \left(\cos^{5}\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}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-2 A \left(\cos^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-198 B \left(\cos^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-24 A \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+114 B \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+17 A \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-27 B \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-3 A +3 B \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*A*cos(1/2*d*x+1/2*c)^8+10*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)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*cos(1/2*d*x+1/2*c)^5+6*A*cos(1/2*d*x+1/2*c)^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)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+108*B*cos(1/2*d*x+1/2*c)^8+30*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)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*cos(1/2*d*x+1/2*c)^5+54*B*cos(1/2*d*x+1/2*c)^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)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-2*A*cos(1/2*d*x+1/2*c)^6-198*B*cos(1/2*d*x+1/2*c)^6-24*A*cos(1/2*d*x+1/2*c)^4+114*B*cos(1/2*d*x+1/2*c)^4+17*A*cos(1/2*d*x+1/2*c)^2-27*B*cos(1/2*d*x+1/2*c)^2-3*A+3*B)/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"
162,1,451,214,1.275000," ","int((A+B*cos(d*x+c))*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 A \left(\cos^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-10 A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+6 A \left(\cos^{5}\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}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-12 B \left(\cos^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-10 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) \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-6 B \left(\cos^{5}\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}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-22 A \left(\cos^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+2 B \left(\cos^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+6 A \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+24 B \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+7 A \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-17 B \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-3 A +3 B \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*A*cos(1/2*d*x+1/2*c)^8-10*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)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*cos(1/2*d*x+1/2*c)^5+6*A*cos(1/2*d*x+1/2*c)^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)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-12*B*cos(1/2*d*x+1/2*c)^8-10*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)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*cos(1/2*d*x+1/2*c)^5-6*B*cos(1/2*d*x+1/2*c)^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)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-22*A*cos(1/2*d*x+1/2*c)^6+2*B*cos(1/2*d*x+1/2*c)^6+6*A*cos(1/2*d*x+1/2*c)^4+24*B*cos(1/2*d*x+1/2*c)^4+7*A*cos(1/2*d*x+1/2*c)^2-17*B*cos(1/2*d*x+1/2*c)^2-3*A+3*B)/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"
163,1,451,218,1.227000," ","int((A+B*cos(d*x+c))/(a+a*cos(d*x+c))^3/cos(d*x+c)^(1/2),x)","\frac{\sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(108 A \left(\cos^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-30 A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+54 A \left(\cos^{5}\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}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+12 B \left(\cos^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-10 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) \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+6 B \left(\cos^{5}\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}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-138 A \left(\cos^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-22 B \left(\cos^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+24 A \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+6 B \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+3 A \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+7 B \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+3 A -3 B \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)*(108*A*cos(1/2*d*x+1/2*c)^8-30*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)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*cos(1/2*d*x+1/2*c)^5+54*A*cos(1/2*d*x+1/2*c)^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)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+12*B*cos(1/2*d*x+1/2*c)^8-10*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)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*cos(1/2*d*x+1/2*c)^5+6*B*cos(1/2*d*x+1/2*c)^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)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-138*A*cos(1/2*d*x+1/2*c)^6-22*B*cos(1/2*d*x+1/2*c)^6+24*A*cos(1/2*d*x+1/2*c)^4+6*B*cos(1/2*d*x+1/2*c)^4+3*A*cos(1/2*d*x+1/2*c)^2+7*B*cos(1/2*d*x+1/2*c)^2+3*A-3*B)/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"
164,1,685,253,1.662000," ","int((A+B*cos(d*x+c))/cos(d*x+c)^(3/2)/(a+a*cos(d*x+c))^3,x)","-\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}}\, \sqrt{-2 \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(65 A \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-147 A \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-15 B \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+27 B \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^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \left(65 A \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-147 A \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-15 B \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+27 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) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-2 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \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(65 A \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-147 A \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-15 B \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+27 B \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)+12 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \left(49 A -9 B \right) \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-2 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \left(817 A -147 B \right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{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(248 A -43 B \right) \left(\sin^{4}\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(439 A -69 B \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)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(65*A*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-147*A*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-15*B*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+27*B*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)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(65*A*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-147*A*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-15*B*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+27*B*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)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(65*A*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-147*A*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-15*B*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+27*B*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2)))*cos(1/2*d*x+1/2*c)+12*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(49*A-9*B)*sin(1/2*d*x+1/2*c)^8-2*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(817*A-147*B)*sin(1/2*d*x+1/2*c)^6+6*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(248*A-43*B)*sin(1/2*d*x+1/2*c)^4-(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(439*A-69*B)*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"
165,1,876,282,1.676000," ","int((A+B*cos(d*x+c))/cos(d*x+c)^(5/2)/(a+a*cos(d*x+c))^3,x)","\frac{4 \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}}\, \sqrt{-2 \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(165 A \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-357 A \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-65 B \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+147 B \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^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-10 \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}}\, \sqrt{-2 \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(165 A \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-357 A \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-65 B \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+147 B \EllipticE \left(\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) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+8 \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}}\, \sqrt{-2 \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(165 A \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-357 A \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-65 B \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+147 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) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-2 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \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(165 A \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-357 A \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-65 B \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+147 B \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)-168 \sqrt{-2 \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(17 A -7 B \right) \left(\sin^{10}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+8 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \left(1167 A -482 B \right) \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{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)}\, \left(1111 A -461 B \right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+14 \sqrt{-2 \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(404 A -169 B \right) \left(\sin^{4}\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(1029 A -439 B \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{60 \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)^{\frac{3}{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)^{5} a^{3} \sin \left(\frac{d x}{2}+\frac{c}{2}\right) d}"," ",0,"1/60*(4*(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*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(165*A*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-357*A*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-65*B*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+147*B*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)^6-10*(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*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(165*A*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-357*A*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-65*B*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+147*B*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2)))*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+8*(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*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(165*A*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-357*A*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-65*B*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+147*B*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)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(165*A*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-357*A*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-65*B*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+147*B*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2)))*cos(1/2*d*x+1/2*c)-168*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(17*A-7*B)*sin(1/2*d*x+1/2*c)^10+8*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(1167*A-482*B)*sin(1/2*d*x+1/2*c)^8-10*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(1111*A-461*B)*sin(1/2*d*x+1/2*c)^6+14*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(404*A-169*B)*sin(1/2*d*x+1/2*c)^4-(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(1029*A-439*B)*sin(1/2*d*x+1/2*c)^2)/(2*cos(1/2*d*x+1/2*c)^2-1)^(3/2)/(-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)^5/a^3/sin(1/2*d*x+1/2*c)/d","B"
166,1,428,189,0.319000," ","int(cos(d*x+c)^(5/2)*(a+a*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c)),x)","\frac{\left(-1+\cos \left(d x +c \right)\right)^{4} \left(64 A \sin \left(d x +c \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{3}{2}}+144 A \sin \left(d x +c \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}}+48 B \sin \left(d x +c \right) \left(\cos^{4}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+200 A \sin \left(d x +c \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}}+56 B \sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+120 A \sin \left(d x +c \right) \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}}+70 B \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+105 B \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+120 A \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)+105 B \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) \left(\cos^{\frac{5}{2}}\left(d x +c \right)\right) \sqrt{a \left(1+\cos \left(d x +c \right)\right)}}{192 d \sin \left(d x +c \right)^{8} \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{7}{2}}}"," ",0,"1/192/d*(-1+cos(d*x+c))^4*(64*A*sin(d*x+c)*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)+144*A*sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)+48*B*sin(d*x+c)*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+200*A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)+56*B*sin(d*x+c)*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+120*A*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)+70*B*sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+105*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+120*A*cos(d*x+c)*arctan(sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)/cos(d*x+c))+105*B*cos(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)^(5/2)*(a*(1+cos(d*x+c)))^(1/2)/sin(d*x+c)^8/(cos(d*x+c)/(1+cos(d*x+c)))^(7/2)","B"
167,1,356,150,0.392000," ","int(cos(d*x+c)^(3/2)*(a+a*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c)),x)","-\frac{\left(-1+\cos \left(d x +c \right)\right)^{3} \left(12 A \sin \left(d x +c \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}}+30 A \sin \left(d x +c \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}}+8 B \sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+18 A \sin \left(d x +c \right) \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}}+10 B \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+15 B \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+18 A \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)+15 B \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) \left(\cos^{\frac{3}{2}}\left(d x +c \right)\right) \sqrt{a \left(1+\cos \left(d x +c \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*(-1+cos(d*x+c))^3*(12*A*sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)+30*A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)+8*B*sin(d*x+c)*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+18*A*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)+10*B*sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+15*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+18*A*cos(d*x+c)*arctan(sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)/cos(d*x+c))+15*B*cos(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)^(3/2)*(a*(1+cos(d*x+c)))^(1/2)/(cos(d*x+c)/(1+cos(d*x+c)))^(5/2)/sin(d*x+c)^6","B"
168,1,284,111,0.281000," ","int(cos(d*x+c)^(1/2)*(a+a*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c)),x)","\frac{\left(-1+\cos \left(d x +c \right)\right)^{2} \left(4 A \sin \left(d x +c \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}}+4 A \sin \left(d x +c \right) \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}}+2 B \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+3 B \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+4 A \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)+3 B \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) \left(\sqrt{\cos}\left(d x +c \right)\right) \sqrt{a \left(1+\cos \left(d x +c \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*(-1+cos(d*x+c))^2*(4*A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)+4*A*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)+2*B*sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+3*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+4*A*cos(d*x+c)*arctan(sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)/cos(d*x+c))+3*B*cos(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)^(1/2)*(a*(1+cos(d*x+c)))^(1/2)/(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)/sin(d*x+c)^4","B"
169,1,164,68,0.253000," ","int((a+a*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(1/2),x)","-\frac{\left(-1+\cos \left(d x +c \right)\right) \left(B \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+2 A \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)+B \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(\sqrt{\cos}\left(d x +c \right)\right) \sqrt{a \left(1+\cos \left(d x +c \right)\right)}}{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/d*(-1+cos(d*x+c))*(B*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+2*A*arctan(sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)/cos(d*x+c))+B*arctan(sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)/cos(d*x+c)))*cos(d*x+c)^(1/2)*(a*(1+cos(d*x+c)))^(1/2)/(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)/sin(d*x+c)^2","B"
170,1,109,66,0.252000," ","int((a+a*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(3/2),x)","-\frac{2 \sqrt{a \left(1+\cos \left(d x +c \right)\right)}\, \left(-B \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)+A \cos \left(d x +c \right)-A \right)}{d \sin \left(d x +c \right) \sqrt{\cos \left(d x +c \right)}}"," ",0,"-2/d*(a*(1+cos(d*x+c)))^(1/2)*(-B*(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)+A*cos(d*x+c)-A)/sin(d*x+c)/cos(d*x+c)^(1/2)","A"
171,1,62,73,0.222000," ","int((a+a*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(5/2),x)","-\frac{2 \left(-1+\cos \left(d x +c \right)\right) \left(2 A \cos \left(d x +c \right)+3 B \cos \left(d x +c \right)+A \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*(-1+cos(d*x+c))*(2*A*cos(d*x+c)+3*B*cos(d*x+c)+A)*(a*(1+cos(d*x+c)))^(1/2)/sin(d*x+c)/cos(d*x+c)^(3/2)","A"
172,1,86,112,0.235000," ","int((a+a*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(7/2),x)","-\frac{2 \left(-1+\cos \left(d x +c \right)\right) \left(8 A \left(\cos^{2}\left(d x +c \right)\right)+10 B \left(\cos^{2}\left(d x +c \right)\right)+4 A \cos \left(d x +c \right)+5 B \cos \left(d x +c \right)+3 A \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*(-1+cos(d*x+c))*(8*A*cos(d*x+c)^2+10*B*cos(d*x+c)^2+4*A*cos(d*x+c)+5*B*cos(d*x+c)+3*A)*(a*(1+cos(d*x+c)))^(1/2)/sin(d*x+c)/cos(d*x+c)^(5/2)","A"
173,1,108,151,0.237000," ","int((a+a*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(9/2),x)","-\frac{2 \left(-1+\cos \left(d x +c \right)\right) \left(48 A \left(\cos^{3}\left(d x +c \right)\right)+56 B \left(\cos^{3}\left(d x +c \right)\right)+24 A \left(\cos^{2}\left(d x +c \right)\right)+28 B \left(\cos^{2}\left(d x +c \right)\right)+18 A \cos \left(d x +c \right)+21 B \cos \left(d x +c \right)+15 A \right) \sqrt{a \left(1+\cos \left(d x +c \right)\right)}}{105 d \sin \left(d x +c \right) \cos \left(d x +c \right)^{\frac{7}{2}}}"," ",0,"-2/105/d*(-1+cos(d*x+c))*(48*A*cos(d*x+c)^3+56*B*cos(d*x+c)^3+24*A*cos(d*x+c)^2+28*B*cos(d*x+c)^2+18*A*cos(d*x+c)+21*B*cos(d*x+c)+15*A)*(a*(1+cos(d*x+c)))^(1/2)/sin(d*x+c)/cos(d*x+c)^(7/2)","A"
174,1,429,195,0.246000," ","int(cos(d*x+c)^(3/2)*(a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)),x)","-\frac{a \left(-1+\cos \left(d x +c \right)\right)^{3} \left(64 A \sin \left(d x +c \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{3}{2}}+240 A \sin \left(d x +c \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}}+48 B \sin \left(d x +c \right) \left(\cos^{4}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+440 A \sin \left(d x +c \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}}+120 B \sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+264 A \sin \left(d x +c \right) \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}}+150 B \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+225 B \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+264 A \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)+225 B \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)}\, \left(\cos^{\frac{3}{2}}\left(d x +c \right)\right)}{192 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,"-1/192/d*a*(-1+cos(d*x+c))^3*(64*A*sin(d*x+c)*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)+240*A*sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)+48*B*sin(d*x+c)*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+440*A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)+120*B*sin(d*x+c)*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+264*A*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)+150*B*sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+225*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+264*A*cos(d*x+c)*arctan(sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)/cos(d*x+c))+225*B*cos(d*x+c)*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)))^(5/2)/sin(d*x+c)^6","B"
175,1,357,154,0.348000," ","int(cos(d*x+c)^(1/2)*(a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)),x)","\frac{a \left(-1+\cos \left(d x +c \right)\right)^{2} \left(12 A \sin \left(d x +c \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}}+54 A \sin \left(d x +c \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}}+8 B \sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+42 A \sin \left(d x +c \right) \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}}+22 B \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+33 B \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+42 A \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)+33 B \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)}\, \left(\sqrt{\cos}\left(d x +c \right)\right)}{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*a*(-1+cos(d*x+c))^2*(12*A*sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)+54*A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)+8*B*sin(d*x+c)*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+42*A*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)+22*B*sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+33*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+42*A*cos(d*x+c)*arctan(sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)/cos(d*x+c))+33*B*cos(d*x+c)*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)))^(3/2)/sin(d*x+c)^4","B"
176,1,283,113,0.307000," ","int((a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(1/2),x)","-\frac{a \left(-1+\cos \left(d x +c \right)\right) \left(4 A \sin \left(d x +c \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}}+4 A \sin \left(d x +c \right) \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}}+2 B \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+7 B \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+12 A \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)+7 B \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)}}{4 d \sqrt{\cos \left(d x +c \right)}\, \sin \left(d x +c \right)^{2} \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}"," ",0,"-1/4/d*a*(-1+cos(d*x+c))*(4*A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)+4*A*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)+2*B*sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+7*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+12*A*cos(d*x+c)*arctan(sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)/cos(d*x+c))+7*B*cos(d*x+c)*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)/sin(d*x+c)^2/(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)","B"
177,1,300,112,0.283000," ","int((a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(3/2),x)","\frac{\sqrt{a \left(1+\cos \left(d x +c \right)\right)}\, \left(2 A \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)+3 B \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)+2 A \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)+B \cos \left(d x +c \right) \sin \left(d x +c \right)+3 B \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 A \sin \left(d x +c \right)\right) a}{d \left(1+\cos \left(d x +c \right)\right) \sqrt{\cos \left(d x +c \right)}}"," ",0,"1/d*(a*(1+cos(d*x+c)))^(1/2)*(2*A*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))+3*B*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))+2*A*(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))+B*cos(d*x+c)*sin(d*x+c)+3*B*(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*A*sin(d*x+c))*a/(1+cos(d*x+c))/cos(d*x+c)^(1/2)","B"
178,1,211,107,0.289000," ","int((a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(5/2),x)","-\frac{2 a \sqrt{a \left(1+\cos \left(d x +c \right)\right)}\, \left(-3 B \cos \left(d x +c \right) \sin \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 B \sin \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 A \left(\cos^{2}\left(d x +c \right)\right)+3 B \left(\cos^{2}\left(d x +c \right)\right)-4 A \cos \left(d x +c \right)-3 B \cos \left(d x +c \right)-A \right)}{3 d \sin \left(d x +c \right) \cos \left(d x +c \right)^{\frac{3}{2}}}"," ",0,"-2/3/d*a*(a*(1+cos(d*x+c)))^(1/2)*(-3*B*cos(d*x+c)*sin(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*B*sin(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*A*cos(d*x+c)^2+3*B*cos(d*x+c)^2-4*A*cos(d*x+c)-3*B*cos(d*x+c)-A)/sin(d*x+c)/cos(d*x+c)^(3/2)","A"
179,1,87,116,0.227000," ","int((a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(7/2),x)","-\frac{2 a \left(-1+\cos \left(d x +c \right)\right) \left(18 A \left(\cos^{2}\left(d x +c \right)\right)+25 B \left(\cos^{2}\left(d x +c \right)\right)+9 A \cos \left(d x +c \right)+5 B \cos \left(d x +c \right)+3 A \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*a*(-1+cos(d*x+c))*(18*A*cos(d*x+c)^2+25*B*cos(d*x+c)^2+9*A*cos(d*x+c)+5*B*cos(d*x+c)+3*A)*(a*(1+cos(d*x+c)))^(1/2)/sin(d*x+c)/cos(d*x+c)^(5/2)","A"
180,1,109,157,0.235000," ","int((a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(9/2),x)","-\frac{2 a \left(-1+\cos \left(d x +c \right)\right) \left(104 A \left(\cos^{3}\left(d x +c \right)\right)+126 B \left(\cos^{3}\left(d x +c \right)\right)+52 A \left(\cos^{2}\left(d x +c \right)\right)+63 B \left(\cos^{2}\left(d x +c \right)\right)+39 A \cos \left(d x +c \right)+21 B \cos \left(d x +c \right)+15 A \right) \sqrt{a \left(1+\cos \left(d x +c \right)\right)}}{105 d \sin \left(d x +c \right) \cos \left(d x +c \right)^{\frac{7}{2}}}"," ",0,"-2/105/d*a*(-1+cos(d*x+c))*(104*A*cos(d*x+c)^3+126*B*cos(d*x+c)^3+52*A*cos(d*x+c)^2+63*B*cos(d*x+c)^2+39*A*cos(d*x+c)+21*B*cos(d*x+c)+15*A)*(a*(1+cos(d*x+c)))^(1/2)/sin(d*x+c)/cos(d*x+c)^(7/2)","A"
181,1,131,198,0.270000," ","int((a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(11/2),x)","-\frac{2 a \left(-1+\cos \left(d x +c \right)\right) \left(272 A \left(\cos^{4}\left(d x +c \right)\right)+312 B \left(\cos^{4}\left(d x +c \right)\right)+136 A \left(\cos^{3}\left(d x +c \right)\right)+156 B \left(\cos^{3}\left(d x +c \right)\right)+102 A \left(\cos^{2}\left(d x +c \right)\right)+117 B \left(\cos^{2}\left(d x +c \right)\right)+85 A \cos \left(d x +c \right)+45 B \cos \left(d x +c \right)+35 A \right) \sqrt{a \left(1+\cos \left(d x +c \right)\right)}}{315 d \sin \left(d x +c \right) \cos \left(d x +c \right)^{\frac{9}{2}}}"," ",0,"-2/315/d*a*(-1+cos(d*x+c))*(272*A*cos(d*x+c)^4+312*B*cos(d*x+c)^4+136*A*cos(d*x+c)^3+156*B*cos(d*x+c)^3+102*A*cos(d*x+c)^2+117*B*cos(d*x+c)^2+85*A*cos(d*x+c)+45*B*cos(d*x+c)+35*A)*(a*(1+cos(d*x+c)))^(1/2)/sin(d*x+c)/cos(d*x+c)^(9/2)","A"
182,1,503,236,0.260000," ","int(cos(d*x+c)^(3/2)*(a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)),x)","-\frac{a^{2} \left(-1+\cos \left(d x +c \right)\right)^{3} \left(480 A \sin \left(d x +c \right) \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{3}{2}}+2320 A \sin \left(d x +c \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{3}{2}}+384 B \sin \left(d x +c \right) \left(\cos^{5}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+5100 A \sin \left(d x +c \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}}+1392 B \sin \left(d x +c \right) \left(\cos^{4}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+8150 A \sin \left(d x +c \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}}+2264 B \sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+4890 A \sin \left(d x +c \right) \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}}+2830 B \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+4245 B \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+4890 A \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)+4245 B \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)}\, \left(\cos^{\frac{3}{2}}\left(d x +c \right)\right)}{1920 d \sin \left(d x +c \right)^{6} \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}}}"," ",0,"-1/1920/d*a^2*(-1+cos(d*x+c))^3*(480*A*sin(d*x+c)*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)+2320*A*sin(d*x+c)*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)+384*B*sin(d*x+c)*cos(d*x+c)^5*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+5100*A*sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)+1392*B*sin(d*x+c)*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+8150*A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)+2264*B*sin(d*x+c)*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+4890*A*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)+2830*B*sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+4245*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+4890*A*cos(d*x+c)*arctan(sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)/cos(d*x+c))+4245*B*cos(d*x+c)*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)/sin(d*x+c)^6/(cos(d*x+c)/(1+cos(d*x+c)))^(5/2)","B"
183,1,431,195,0.204000," ","int(cos(d*x+c)^(1/2)*(a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)),x)","\frac{a^{2} \left(-1+\cos \left(d x +c \right)\right)^{2} \left(64 A \sin \left(d x +c \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{3}{2}}+336 A \sin \left(d x +c \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}}+48 B \sin \left(d x +c \right) \left(\cos^{4}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+872 A \sin \left(d x +c \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}}+184 B \sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+600 A \sin \left(d x +c \right) \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}}+326 B \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+489 B \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+600 A \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)+489 B \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)}\, \left(\sqrt{\cos}\left(d x +c \right)\right)}{192 d \sin \left(d x +c \right)^{4} \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}}}"," ",0,"1/192/d*a^2*(-1+cos(d*x+c))^2*(64*A*sin(d*x+c)*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)+336*A*sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)+48*B*sin(d*x+c)*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+872*A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)+184*B*sin(d*x+c)*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+600*A*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)+326*B*sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+489*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+600*A*cos(d*x+c)*arctan(sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)/cos(d*x+c))+489*B*cos(d*x+c)*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)/sin(d*x+c)^4/(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)","B"
184,1,357,154,0.336000," ","int((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(1/2),x)","-\frac{a^{2} \left(-1+\cos \left(d x +c \right)\right) \left(12 A \sin \left(d x +c \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}}+78 A \sin \left(d x +c \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}}+8 B \sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+66 A \sin \left(d x +c \right) \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}}+34 B \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+75 B \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+114 A \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)+75 B \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)}}{24 d \sin \left(d x +c \right)^{2} \sqrt{\cos \left(d x +c \right)}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}"," ",0,"-1/24/d*a^2*(-1+cos(d*x+c))*(12*A*sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)+78*A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)+8*B*sin(d*x+c)*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+66*A*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)+34*B*sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+75*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+114*A*cos(d*x+c)*arctan(sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)/cos(d*x+c))+75*B*cos(d*x+c)*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)/sin(d*x+c)^2/cos(d*x+c)^(1/2)/(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)","B"
185,1,336,154,0.314000," ","int((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(3/2),x)","\frac{\sqrt{a \left(1+\cos \left(d x +c \right)\right)}\, \left(20 A \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)+2 B \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right)+19 B \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)+4 A \cos \left(d x +c \right) \sin \left(d x +c \right)+20 A \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 B \cos \left(d x +c \right) \sin \left(d x +c \right)+19 B \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)+8 A \sin \left(d x +c \right)\right) a^{2}}{4 d \left(1+\cos \left(d x +c \right)\right) \sqrt{\cos \left(d x +c \right)}}"," ",0,"1/4/d*(a*(1+cos(d*x+c)))^(1/2)*(20*A*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))+2*B*sin(d*x+c)*cos(d*x+c)^2+19*B*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))+4*A*cos(d*x+c)*sin(d*x+c)+20*A*(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*B*cos(d*x+c)*sin(d*x+c)+19*B*(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))+8*A*sin(d*x+c))*a^2/(1+cos(d*x+c))/cos(d*x+c)^(1/2)","B"
186,1,484,151,0.279000," ","int((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(5/2),x)","-\frac{\sqrt{a \left(1+\cos \left(d x +c \right)\right)}\, \left(\sin^{2}\left(d x +c \right)\right) \left(6 A \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)+15 B \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)+12 A \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)+30 B \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)+6 A \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)+15 B \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 B \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right)+16 A \cos \left(d x +c \right) \sin \left(d x +c \right)+6 B \cos \left(d x +c \right) \sin \left(d x +c \right)+2 A \sin \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} \cos \left(d x +c \right)^{\frac{3}{2}}}"," ",0,"-1/3/d*(a*(1+cos(d*x+c)))^(1/2)*sin(d*x+c)^2*(6*A*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))+15*B*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))+12*A*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))+30*B*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))+6*A*(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))+15*B*(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*B*sin(d*x+c)*cos(d*x+c)^2+16*A*cos(d*x+c)*sin(d*x+c)+6*B*cos(d*x+c)*sin(d*x+c)+2*A*sin(d*x+c))*a^2/(-1+cos(d*x+c))/(1+cos(d*x+c))^2/cos(d*x+c)^(3/2)","B"
187,1,306,148,0.388000," ","int((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(7/2),x)","-\frac{2 a^{2} \sqrt{a \left(1+\cos \left(d x +c \right)\right)}\, \left(-15 B \left(\cos^{2}\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}} \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)-30 B \cos \left(d x +c \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}} \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)-15 B \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}} \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 A \left(\cos^{3}\left(d x +c \right)\right)+40 B \left(\cos^{3}\left(d x +c \right)\right)-29 A \left(\cos^{2}\left(d x +c \right)\right)-35 B \left(\cos^{2}\left(d x +c \right)\right)-11 A \cos \left(d x +c \right)-5 B \cos \left(d x +c \right)-3 A \right)}{15 d \sin \left(d x +c \right) \cos \left(d x +c \right)^{\frac{5}{2}}}"," ",0,"-2/15/d*a^2*(a*(1+cos(d*x+c)))^(1/2)*(-15*B*cos(d*x+c)^2*sin(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))-30*B*cos(d*x+c)*sin(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))-15*B*sin(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))+43*A*cos(d*x+c)^3+40*B*cos(d*x+c)^3-29*A*cos(d*x+c)^2-35*B*cos(d*x+c)^2-11*A*cos(d*x+c)-5*B*cos(d*x+c)-3*A)/sin(d*x+c)/cos(d*x+c)^(5/2)","B"
188,1,111,157,0.229000," ","int((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(9/2),x)","-\frac{2 a^{2} \left(-1+\cos \left(d x +c \right)\right) \left(230 A \left(\cos^{3}\left(d x +c \right)\right)+301 B \left(\cos^{3}\left(d x +c \right)\right)+115 A \left(\cos^{2}\left(d x +c \right)\right)+98 B \left(\cos^{2}\left(d x +c \right)\right)+60 A \cos \left(d x +c \right)+21 B \cos \left(d x +c \right)+15 A \right) \sqrt{a \left(1+\cos \left(d x +c \right)\right)}}{105 d \sin \left(d x +c \right) \cos \left(d x +c \right)^{\frac{7}{2}}}"," ",0,"-2/105/d*a^2*(-1+cos(d*x+c))*(230*A*cos(d*x+c)^3+301*B*cos(d*x+c)^3+115*A*cos(d*x+c)^2+98*B*cos(d*x+c)^2+60*A*cos(d*x+c)+21*B*cos(d*x+c)+15*A)*(a*(1+cos(d*x+c)))^(1/2)/sin(d*x+c)/cos(d*x+c)^(7/2)","A"
189,1,133,198,0.278000," ","int((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(11/2),x)","-\frac{2 a^{2} \left(-1+\cos \left(d x +c \right)\right) \left(584 A \left(\cos^{4}\left(d x +c \right)\right)+690 B \left(\cos^{4}\left(d x +c \right)\right)+292 A \left(\cos^{3}\left(d x +c \right)\right)+345 B \left(\cos^{3}\left(d x +c \right)\right)+219 A \left(\cos^{2}\left(d x +c \right)\right)+180 B \left(\cos^{2}\left(d x +c \right)\right)+130 A \cos \left(d x +c \right)+45 B \cos \left(d x +c \right)+35 A \right) \sqrt{a \left(1+\cos \left(d x +c \right)\right)}}{315 d \sin \left(d x +c \right) \cos \left(d x +c \right)^{\frac{9}{2}}}"," ",0,"-2/315/d*a^2*(-1+cos(d*x+c))*(584*A*cos(d*x+c)^4+690*B*cos(d*x+c)^4+292*A*cos(d*x+c)^3+345*B*cos(d*x+c)^3+219*A*cos(d*x+c)^2+180*B*cos(d*x+c)^2+130*A*cos(d*x+c)+45*B*cos(d*x+c)+35*A)*(a*(1+cos(d*x+c)))^(1/2)/sin(d*x+c)/cos(d*x+c)^(9/2)","A"
190,1,155,239,0.310000," ","int((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(13/2),x)","-\frac{2 a^{2} \left(-1+\cos \left(d x +c \right)\right) \left(5680 A \left(\cos^{5}\left(d x +c \right)\right)+6424 B \left(\cos^{5}\left(d x +c \right)\right)+2840 A \left(\cos^{4}\left(d x +c \right)\right)+3212 B \left(\cos^{4}\left(d x +c \right)\right)+2130 A \left(\cos^{3}\left(d x +c \right)\right)+2409 B \left(\cos^{3}\left(d x +c \right)\right)+1775 A \left(\cos^{2}\left(d x +c \right)\right)+1430 B \left(\cos^{2}\left(d x +c \right)\right)+1120 A \cos \left(d x +c \right)+385 B \cos \left(d x +c \right)+315 A \right) \sqrt{a \left(1+\cos \left(d x +c \right)\right)}}{3465 d \sin \left(d x +c \right) \cos \left(d x +c \right)^{\frac{11}{2}}}"," ",0,"-2/3465/d*a^2*(-1+cos(d*x+c))*(5680*A*cos(d*x+c)^5+6424*B*cos(d*x+c)^5+2840*A*cos(d*x+c)^4+3212*B*cos(d*x+c)^4+2130*A*cos(d*x+c)^3+2409*B*cos(d*x+c)^3+1775*A*cos(d*x+c)^2+1430*B*cos(d*x+c)^2+1120*A*cos(d*x+c)+385*B*cos(d*x+c)+315*A)*(a*(1+cos(d*x+c)))^(1/2)/sin(d*x+c)/cos(d*x+c)^(11/2)","A"
191,1,346,159,0.319000," ","int(cos(d*x+c)^(3/2)*(A+B*cos(d*x+c))/(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)^{3} \left(-4 A \sin \left(d x +c \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}}-4 A \sin \left(d x +c \right) \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}}-2 B \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+4 A \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \cos \left(d x +c \right) \sqrt{2}-4 B \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \cos \left(d x +c \right) \sqrt{2}+B \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+4 A \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)-7 B \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)}{4 d \sin \left(d x +c \right)^{6} \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} a}"," ",0,"1/4/d*cos(d*x+c)^(3/2)*(a*(1+cos(d*x+c)))^(1/2)*(-1+cos(d*x+c))^3*(-4*A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)-4*A*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)-2*B*sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+4*A*arcsin((-1+cos(d*x+c))/sin(d*x+c))*cos(d*x+c)*2^(1/2)-4*B*arcsin((-1+cos(d*x+c))/sin(d*x+c))*cos(d*x+c)*2^(1/2)+B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+4*A*cos(d*x+c)*arctan(sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)/cos(d*x+c))-7*B*cos(d*x+c)*arctan(sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)/cos(d*x+c)))/sin(d*x+c)^6/(cos(d*x+c)/(1+cos(d*x+c)))^(5/2)/a","B"
192,1,216,120,0.262000," ","int(cos(d*x+c)^(1/2)*(A+B*cos(d*x+c))/(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(A \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \sqrt{2}+B \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}-B \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \sqrt{2}+2 A \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)-B \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 \sin \left(d x +c \right)^{4} \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} a}"," ",0,"1/d*cos(d*x+c)^(3/2)*(a*(1+cos(d*x+c)))^(1/2)*(-1+cos(d*x+c))^2*(A*arcsin((-1+cos(d*x+c))/sin(d*x+c))*2^(1/2)+B*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)-B*arcsin((-1+cos(d*x+c))/sin(d*x+c))*2^(1/2)+2*A*arctan(sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)/cos(d*x+c))-B*arctan(sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)/cos(d*x+c)))/sin(d*x+c)^4/(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)/a","A"
193,1,149,83,0.230000," ","int((A+B*cos(d*x+c))/cos(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)}\, \left(\sqrt{\cos}\left(d x +c \right)\right) \left(-1+\cos \left(d x +c \right)\right) \left(A \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \sqrt{2}-B \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \sqrt{2}-2 B \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{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, a \sin \left(d x +c \right)^{2}}"," ",0,"1/d*(a*(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^(1/2)*(-1+cos(d*x+c))*(A*arcsin((-1+cos(d*x+c))/sin(d*x+c))*2^(1/2)-B*arcsin((-1+cos(d*x+c))/sin(d*x+c))*2^(1/2)-2*B*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)/a/sin(d*x+c)^2","A"
194,1,230,84,0.260000," ","int((A+B*cos(d*x+c))/cos(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)}\, \left(A \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)}}\, \cos \left(d x +c \right)-B \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)}}\, \cos \left(d x +c \right)+A \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)}}-B \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 A \sin \left(d x +c \right)\right)}{d a \left(1+\cos \left(d x +c \right)\right) \sqrt{\cos \left(d x +c \right)}}"," ",0,"1/d*(a*(1+cos(d*x+c)))^(1/2)*(A*arcsin((-1+cos(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)-B*arcsin((-1+cos(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)+A*arcsin((-1+cos(d*x+c))/sin(d*x+c))*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)-B*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*A*sin(d*x+c))/a/(1+cos(d*x+c))/cos(d*x+c)^(1/2)","B"
195,1,383,119,0.337000," ","int((A+B*cos(d*x+c))/cos(d*x+c)^(5/2)/(a+a*cos(d*x+c))^(1/2),x)","\frac{\left(\sin^{2}\left(d x +c \right)\right) \sqrt{a \left(1+\cos \left(d x +c \right)\right)}\, \left(3 A \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) \sqrt{2}\, \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}}-3 B \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) \sqrt{2}\, \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}}+6 A \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \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}}-6 B \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \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}}+3 A \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{3}{2}}-3 B \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{3}{2}}+2 A \cos \left(d x +c \right) \sin \left(d x +c \right)-6 B \cos \left(d x +c \right) \sin \left(d x +c \right)-2 A \sin \left(d x +c \right)\right)}{3 d a \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,"1/3/d*sin(d*x+c)^2*(a*(1+cos(d*x+c)))^(1/2)*(3*A*arcsin((-1+cos(d*x+c))/sin(d*x+c))*cos(d*x+c)^2*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)-3*B*arcsin((-1+cos(d*x+c))/sin(d*x+c))*cos(d*x+c)^2*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)+6*A*arcsin((-1+cos(d*x+c))/sin(d*x+c))*cos(d*x+c)*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)-6*B*arcsin((-1+cos(d*x+c))/sin(d*x+c))*cos(d*x+c)*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)+3*A*arcsin((-1+cos(d*x+c))/sin(d*x+c))*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)-3*B*arcsin((-1+cos(d*x+c))/sin(d*x+c))*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)+2*A*cos(d*x+c)*sin(d*x+c)-6*B*cos(d*x+c)*sin(d*x+c)-2*A*sin(d*x+c))/a/(-1+cos(d*x+c))/(1+cos(d*x+c))^2/cos(d*x+c)^(3/2)","B"
196,1,519,158,0.357000," ","int((A+B*cos(d*x+c))/cos(d*x+c)^(7/2)/(a+a*cos(d*x+c))^(1/2),x)","\frac{\sqrt{a \left(1+\cos \left(d x +c \right)\right)}\, \left(\sin^{4}\left(d x +c \right)\right) \left(15 A \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}} \sqrt{2}\, \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)-15 B \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}} \sqrt{2}\, \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)+45 A \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}} \sqrt{2}\, \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)-45 B \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}} \sqrt{2}\, \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)+45 A \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}} \sqrt{2}\, \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)-45 B \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}} \sqrt{2}\, \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)+15 A \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \sqrt{2}\, \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)-15 B \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \sqrt{2}\, \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)+26 A \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)-10 B \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right)-2 A \cos \left(d x +c \right) \sin \left(d x +c \right)+10 B \cos \left(d x +c \right) \sin \left(d x +c \right)+6 A \sin \left(d x +c \right)\right)}{15 d a \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,"1/15/d*(a*(1+cos(d*x+c)))^(1/2)*sin(d*x+c)^4*(15*A*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*2^(1/2)*arcsin((-1+cos(d*x+c))/sin(d*x+c))-15*B*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*2^(1/2)*arcsin((-1+cos(d*x+c))/sin(d*x+c))+45*A*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*2^(1/2)*arcsin((-1+cos(d*x+c))/sin(d*x+c))-45*B*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*2^(1/2)*arcsin((-1+cos(d*x+c))/sin(d*x+c))+45*A*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*2^(1/2)*arcsin((-1+cos(d*x+c))/sin(d*x+c))-45*B*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*2^(1/2)*arcsin((-1+cos(d*x+c))/sin(d*x+c))+15*A*(cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*2^(1/2)*arcsin((-1+cos(d*x+c))/sin(d*x+c))-15*B*(cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*2^(1/2)*arcsin((-1+cos(d*x+c))/sin(d*x+c))+26*A*cos(d*x+c)^2*sin(d*x+c)-10*B*sin(d*x+c)*cos(d*x+c)^2-2*A*cos(d*x+c)*sin(d*x+c)+10*B*cos(d*x+c)*sin(d*x+c)+6*A*sin(d*x+c))/a/(-1+cos(d*x+c))^2/(1+cos(d*x+c))^3/cos(d*x+c)^(5/2)","B"
197,1,379,166,0.296000," ","int(cos(d*x+c)^(3/2)*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^(3/2),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)^{3} \left(2 A \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}}+5 A \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}-9 B \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 B \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+8 A \sin \left(d x +c \right) \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 A \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}}-12 B \sin \left(d x +c \right) \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 B \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+6 B \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\right)}{4 d \sin \left(d x +c \right)^{7} \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} a^{2}}"," ",0,"-1/4/d*cos(d*x+c)^(3/2)*(a*(1+cos(d*x+c)))^(1/2)*(-1+cos(d*x+c))^3*(2*A*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)+5*A*arcsin((-1+cos(d*x+c))/sin(d*x+c))*sin(d*x+c)*cos(d*x+c)*2^(1/2)-9*B*arcsin((-1+cos(d*x+c))/sin(d*x+c))*sin(d*x+c)*cos(d*x+c)*2^(1/2)-4*B*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+8*A*sin(d*x+c)*cos(d*x+c)*arctan(sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)/cos(d*x+c))-2*A*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)-12*B*sin(d*x+c)*cos(d*x+c)*arctan(sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)/cos(d*x+c))-2*B*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+6*B*cos(d*x+c)*(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)))^(5/2)/a^2","B"
198,1,298,120,0.277000," ","int(cos(d*x+c)^(1/2)*(A+B*cos(d*x+c))/(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)^{2} \left(2 A \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}}+A \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}-5 B \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}-2 A \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}}-8 B \sin \left(d x +c \right) \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 B \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+2 B \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\right)}{4 d \sin \left(d x +c \right)^{5} \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} 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))^2*(2*A*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)+A*arcsin((-1+cos(d*x+c))/sin(d*x+c))*sin(d*x+c)*cos(d*x+c)*2^(1/2)-5*B*arcsin((-1+cos(d*x+c))/sin(d*x+c))*sin(d*x+c)*cos(d*x+c)*2^(1/2)-2*A*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)-8*B*sin(d*x+c)*cos(d*x+c)*arctan(sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)/cos(d*x+c))-2*B*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+2*B*cos(d*x+c)*(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)))^(3/2)/a^2","B"
199,1,246,88,0.265000," ","int((A+B*cos(d*x+c))/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(-1+\cos \left(d x +c \right)\right) \left(-2 A \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}}+3 A \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}+B \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}+2 A \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}}+2 B \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}-2 B \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\right)}{4 d \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, a^{2} \sqrt{\cos \left(d x +c \right)}\, \sin \left(d x +c \right)^{3}}"," ",0,"1/4/d*(a*(1+cos(d*x+c)))^(1/2)*(-1+cos(d*x+c))*(-2*A*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)+3*A*arcsin((-1+cos(d*x+c))/sin(d*x+c))*sin(d*x+c)*cos(d*x+c)*2^(1/2)+B*arcsin((-1+cos(d*x+c))/sin(d*x+c))*sin(d*x+c)*cos(d*x+c)*2^(1/2)+2*A*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)+2*B*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)-2*B*cos(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^2/cos(d*x+c)^(1/2)/sin(d*x+c)^3","B"
200,1,299,131,0.284000," ","int((A+B*cos(d*x+c))/cos(d*x+c)^(3/2)/(a+a*cos(d*x+c))^(3/2),x)","-\frac{\sqrt{a \left(1+\cos \left(d x +c \right)\right)}\, \left(-7 A \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) \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+3 B \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) \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}-7 A \sin \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)}}+3 B \sin \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)}}+10 A \left(\cos^{2}\left(d x +c \right)\right)-2 B \left(\cos^{2}\left(d x +c \right)\right)-2 A \cos \left(d x +c \right)+2 B \cos \left(d x +c \right)-8 A \right)}{4 d \,a^{2} \sin \left(d x +c \right) \left(1+\cos \left(d x +c \right)\right) \sqrt{\cos \left(d x +c \right)}}"," ",0,"-1/4/d*(a*(1+cos(d*x+c)))^(1/2)*(-7*A*cos(d*x+c)*sin(d*x+c)*arcsin((-1+cos(d*x+c))/sin(d*x+c))*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+3*B*cos(d*x+c)*sin(d*x+c)*arcsin((-1+cos(d*x+c))/sin(d*x+c))*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)-7*A*sin(d*x+c)*arcsin((-1+cos(d*x+c))/sin(d*x+c))*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+3*B*sin(d*x+c)*arcsin((-1+cos(d*x+c))/sin(d*x+c))*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+10*A*cos(d*x+c)^2-2*B*cos(d*x+c)^2-2*A*cos(d*x+c)+2*B*cos(d*x+c)-8*A)/a^2/sin(d*x+c)/(1+cos(d*x+c))/cos(d*x+c)^(1/2)","B"
201,1,443,172,0.343000," ","int((A+B*cos(d*x+c))/cos(d*x+c)^(5/2)/(a+a*cos(d*x+c))^(3/2),x)","\frac{\sqrt{a \left(1+\cos \left(d x +c \right)\right)}\, \sin \left(d x +c \right) \left(33 A \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}\, \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}}-21 B \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}\, \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}}+66 A \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}\, \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}}-42 B \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}\, \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}}+33 A \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}\, \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}}-21 B \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}\, \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}}-38 A \left(\cos^{3}\left(d x +c \right)\right)+30 B \left(\cos^{3}\left(d x +c \right)\right)+14 A \left(\cos^{2}\left(d x +c \right)\right)-6 B \left(\cos^{2}\left(d x +c \right)\right)+32 A \cos \left(d x +c \right)-24 B \cos \left(d x +c \right)-8 A \right)}{12 d \,a^{2} \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,"1/12/d*(a*(1+cos(d*x+c)))^(1/2)*sin(d*x+c)*(33*A*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)/(1+cos(d*x+c)))^(3/2)-21*B*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)/(1+cos(d*x+c)))^(3/2)+66*A*arcsin((-1+cos(d*x+c))/sin(d*x+c))*sin(d*x+c)*cos(d*x+c)*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)-42*B*arcsin((-1+cos(d*x+c))/sin(d*x+c))*sin(d*x+c)*cos(d*x+c)*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)+33*A*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)))^(3/2)-21*B*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)))^(3/2)-38*A*cos(d*x+c)^3+30*B*cos(d*x+c)^3+14*A*cos(d*x+c)^2-6*B*cos(d*x+c)^2+32*A*cos(d*x+c)-24*B*cos(d*x+c)-8*A)/a^2/(-1+cos(d*x+c))/(1+cos(d*x+c))^2/cos(d*x+c)^(3/2)","B"
202,1,647,209,0.335000," ","int(cos(d*x+c)^(5/2)*(A+B*cos(d*x+c))/(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)^{5} \left(\cos^{\frac{5}{2}}\left(d x +c \right)\right) \left(30 A \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \left(\cos^{3}\left(d x +c \right)\right)+43 A \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) \sin \left(d x +c \right)+22 A \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}}-115 B \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) \sin \left(d x +c \right)-32 B \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \left(\cos^{4}\left(d x +c \right)\right)+43 A \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}-30 A \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \cos \left(d x +c \right)+64 A \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)-115 B \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}-78 B \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}-160 B \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)-22 A \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}}+64 A \sin \left(d x +c \right) \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)+40 B \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}-160 B \sin \left(d x +c \right) \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)+70 B \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\right)}{32 d \sin \left(d x +c \right)^{11} \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{7}{2}} a^{3}}"," ",0,"-1/32/d*(a*(1+cos(d*x+c)))^(1/2)*(-1+cos(d*x+c))^5*cos(d*x+c)^(5/2)*(30*A*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*cos(d*x+c)^3+43*A*arcsin((-1+cos(d*x+c))/sin(d*x+c))*2^(1/2)*cos(d*x+c)^2*sin(d*x+c)+22*A*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)-115*B*arcsin((-1+cos(d*x+c))/sin(d*x+c))*2^(1/2)*cos(d*x+c)^2*sin(d*x+c)-32*B*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^4+43*A*arcsin((-1+cos(d*x+c))/sin(d*x+c))*sin(d*x+c)*cos(d*x+c)*2^(1/2)-30*A*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*cos(d*x+c)+64*A*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)-115*B*arcsin((-1+cos(d*x+c))/sin(d*x+c))*sin(d*x+c)*cos(d*x+c)*2^(1/2)-78*B*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)-160*B*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)-22*A*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)+64*A*sin(d*x+c)*cos(d*x+c)*arctan(sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)/cos(d*x+c))+40*B*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)-160*B*sin(d*x+c)*cos(d*x+c)*arctan(sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)/cos(d*x+c))+70*B*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2))/sin(d*x+c)^11/(cos(d*x+c)/(1+cos(d*x+c)))^(7/2)/a^3","B"
203,1,515,163,0.307000," ","int(cos(d*x+c)^(3/2)*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^(5/2),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(14 A \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \left(\cos^{3}\left(d x +c \right)\right)+3 A \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) \sin \left(d x +c \right)+6 A \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}}-43 B \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) \sin \left(d x +c \right)+3 A \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}-14 A \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \cos \left(d x +c \right)-43 B \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}-64 B \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)-30 B \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}-6 A \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}}-64 B \sin \left(d x +c \right) \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)+8 B \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+22 B \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\right)}{32 d \sin \left(d x +c \right)^{9} \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} a^{3}}"," ",0,"-1/32/d*cos(d*x+c)^(3/2)*(a*(1+cos(d*x+c)))^(1/2)*(-1+cos(d*x+c))^4*(14*A*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*cos(d*x+c)^3+3*A*arcsin((-1+cos(d*x+c))/sin(d*x+c))*2^(1/2)*cos(d*x+c)^2*sin(d*x+c)+6*A*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)-43*B*arcsin((-1+cos(d*x+c))/sin(d*x+c))*2^(1/2)*cos(d*x+c)^2*sin(d*x+c)+3*A*arcsin((-1+cos(d*x+c))/sin(d*x+c))*sin(d*x+c)*cos(d*x+c)*2^(1/2)-14*A*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*cos(d*x+c)-43*B*arcsin((-1+cos(d*x+c))/sin(d*x+c))*sin(d*x+c)*cos(d*x+c)*2^(1/2)-64*B*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)-30*B*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)-6*A*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)-64*B*sin(d*x+c)*cos(d*x+c)*arctan(sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)/cos(d*x+c))+8*B*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+22*B*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2))/sin(d*x+c)^9/(cos(d*x+c)/(1+cos(d*x+c)))^(5/2)/a^3","B"
204,1,413,129,0.321000," ","int(cos(d*x+c)^(1/2)*(A+B*cos(d*x+c))/(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)^{3} \left(2 A \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \left(\cos^{3}\left(d x +c \right)\right)+10 A \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}}+5 A \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) \sin \left(d x +c \right)+3 B \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) \sin \left(d x +c \right)-2 A \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \cos \left(d x +c \right)+5 A \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}+14 B \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+3 B \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}-10 A \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}}-8 B \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}-6 B \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\right)}{32 d \sin \left(d x +c \right)^{7} \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} 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))^3*(2*A*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*cos(d*x+c)^3+10*A*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)+5*A*arcsin((-1+cos(d*x+c))/sin(d*x+c))*2^(1/2)*cos(d*x+c)^2*sin(d*x+c)+3*B*arcsin((-1+cos(d*x+c))/sin(d*x+c))*2^(1/2)*cos(d*x+c)^2*sin(d*x+c)-2*A*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*cos(d*x+c)+5*A*arcsin((-1+cos(d*x+c))/sin(d*x+c))*sin(d*x+c)*cos(d*x+c)*2^(1/2)+14*B*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+3*B*arcsin((-1+cos(d*x+c))/sin(d*x+c))*sin(d*x+c)*cos(d*x+c)*2^(1/2)-10*A*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)-8*B*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)-6*B*cos(d*x+c)*(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)))^(3/2)/a^3","B"
205,1,413,131,0.274000," ","int((A+B*cos(d*x+c))/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)^{2} \left(18 A \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \left(\cos^{3}\left(d x +c \right)\right)+26 A \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}}-19 A \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) \sin \left(d x +c \right)-5 B \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) \sin \left(d x +c \right)-18 A \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \cos \left(d x +c \right)-19 A \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}-2 B \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}-5 B \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}-26 A \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}}-8 B \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+10 B \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\right)}{32 d \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, a^{3} \sqrt{\cos \left(d x +c \right)}\, \sin \left(d x +c \right)^{5}}"," ",0,"1/32/d*(a*(1+cos(d*x+c)))^(1/2)*(-1+cos(d*x+c))^2*(18*A*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*cos(d*x+c)^3+26*A*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)-19*A*arcsin((-1+cos(d*x+c))/sin(d*x+c))*2^(1/2)*cos(d*x+c)^2*sin(d*x+c)-5*B*arcsin((-1+cos(d*x+c))/sin(d*x+c))*2^(1/2)*cos(d*x+c)^2*sin(d*x+c)-18*A*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*cos(d*x+c)-19*A*arcsin((-1+cos(d*x+c))/sin(d*x+c))*sin(d*x+c)*cos(d*x+c)*2^(1/2)-2*B*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)-5*B*arcsin((-1+cos(d*x+c))/sin(d*x+c))*sin(d*x+c)*cos(d*x+c)*2^(1/2)-26*A*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)-8*B*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+10*B*cos(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^3/cos(d*x+c)^(1/2)/sin(d*x+c)^5","B"
206,1,443,172,0.296000," ","int((A+B*cos(d*x+c))/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) \left(75 A \sin \left(d x +c \right) \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) \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}-19 B \sin \left(d x +c \right) \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) \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+150 A \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) \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}-38 B \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) \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+75 A \sin \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)}}-19 B \sin \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)}}-98 A \left(\cos^{3}\left(d x +c \right)\right)+18 B \left(\cos^{3}\left(d x +c \right)\right)-72 A \left(\cos^{2}\left(d x +c \right)\right)+8 B \left(\cos^{2}\left(d x +c \right)\right)+106 A \cos \left(d x +c \right)-26 B \cos \left(d x +c \right)+64 A \right)}{32 d \,a^{3} \sin \left(d x +c \right)^{3} \left(1+\cos \left(d x +c \right)\right) \sqrt{\cos \left(d x +c \right)}}"," ",0,"-1/32/d*(a*(1+cos(d*x+c)))^(1/2)*(-1+cos(d*x+c))*(75*A*sin(d*x+c)*cos(d*x+c)^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)-19*B*sin(d*x+c)*cos(d*x+c)^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)+150*A*cos(d*x+c)*sin(d*x+c)*arcsin((-1+cos(d*x+c))/sin(d*x+c))*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)-38*B*cos(d*x+c)*sin(d*x+c)*arcsin((-1+cos(d*x+c))/sin(d*x+c))*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+75*A*sin(d*x+c)*arcsin((-1+cos(d*x+c))/sin(d*x+c))*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)-19*B*sin(d*x+c)*arcsin((-1+cos(d*x+c))/sin(d*x+c))*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)-98*A*cos(d*x+c)^3+18*B*cos(d*x+c)^3-72*A*cos(d*x+c)^2+8*B*cos(d*x+c)^2+106*A*cos(d*x+c)-26*B*cos(d*x+c)+64*A)/a^3/sin(d*x+c)^3/(1+cos(d*x+c))/cos(d*x+c)^(1/2)","B"
207,1,571,213,0.237000," ","int((A+B*cos(d*x+c))/cos(d*x+c)^(5/2)/(a+a*cos(d*x+c))^(5/2),x)","\frac{\sqrt{a \left(1+\cos \left(d x +c \right)\right)}\, \left(-489 A \left(\cos^{3}\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{3}{2}} \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \sqrt{2}+225 B \left(\cos^{3}\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{3}{2}} \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \sqrt{2}-1467 A \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}\, \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}}+675 B \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}\, \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}}-1467 A \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}\, \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}}+675 B \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}\, \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}}-489 A \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}\, \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}}+225 B \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}\, \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}}+598 A \left(\cos^{4}\left(d x +c \right)\right)-294 B \left(\cos^{4}\left(d x +c \right)\right)+408 A \left(\cos^{3}\left(d x +c \right)\right)-216 B \left(\cos^{3}\left(d x +c \right)\right)-686 A \left(\cos^{2}\left(d x +c \right)\right)+318 B \left(\cos^{2}\left(d x +c \right)\right)-384 A \cos \left(d x +c \right)+192 B \cos \left(d x +c \right)+64 A \right)}{96 d \,a^{3} \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}}}"," ",0,"1/96/d*(a*(1+cos(d*x+c)))^(1/2)*(-489*A*cos(d*x+c)^3*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*arcsin((-1+cos(d*x+c))/sin(d*x+c))*2^(1/2)+225*B*cos(d*x+c)^3*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*arcsin((-1+cos(d*x+c))/sin(d*x+c))*2^(1/2)-1467*A*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)/(1+cos(d*x+c)))^(3/2)+675*B*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)/(1+cos(d*x+c)))^(3/2)-1467*A*arcsin((-1+cos(d*x+c))/sin(d*x+c))*sin(d*x+c)*cos(d*x+c)*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)+675*B*arcsin((-1+cos(d*x+c))/sin(d*x+c))*sin(d*x+c)*cos(d*x+c)*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)-489*A*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)))^(3/2)+225*B*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)))^(3/2)+598*A*cos(d*x+c)^4-294*B*cos(d*x+c)^4+408*A*cos(d*x+c)^3-216*B*cos(d*x+c)^3-686*A*cos(d*x+c)^2+318*B*cos(d*x+c)^2-384*A*cos(d*x+c)+192*B*cos(d*x+c)+64*A)/a^3/sin(d*x+c)/(1+cos(d*x+c))^2/cos(d*x+c)^(3/2)","B"
208,1,887,250,0.385000," ","int(cos(d*x+c)^(7/2)*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^(7/2),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)^{7} \left(494 A \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \left(\cos^{4}\left(d x +c \right)\right)+531 A \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) \sin \left(d x +c \right)+724 A \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \left(\cos^{3}\left(d x +c \right)\right)-1911 B \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) \sin \left(d x +c \right)-384 B \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \left(\cos^{5}\left(d x +c \right)\right)+1062 A \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) \sin \left(d x +c \right)+768 A \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^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)-200 A \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}}-3822 B \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) \sin \left(d x +c \right)-1814 B \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \left(\cos^{4}\left(d x +c \right)\right)-2688 B \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^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)+531 A \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}+1536 A \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)-724 A \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \cos \left(d x +c \right)-1911 B \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}-686 B \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}-5376 B \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)+768 A \sin \left(d x +c \right) \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)-294 A \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}}+1750 B \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}-2688 B \sin \left(d x +c \right) \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)+1134 B \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\right)}{384 d \sin \left(d x +c \right)^{15} \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{9}{2}} a^{4}}"," ",0,"-1/384/d*cos(d*x+c)^(7/2)*(a*(1+cos(d*x+c)))^(1/2)*(-1+cos(d*x+c))^7*(494*A*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*cos(d*x+c)^4+531*A*arcsin((-1+cos(d*x+c))/sin(d*x+c))*2^(1/2)*cos(d*x+c)^3*sin(d*x+c)+724*A*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*cos(d*x+c)^3-1911*B*arcsin((-1+cos(d*x+c))/sin(d*x+c))*2^(1/2)*cos(d*x+c)^3*sin(d*x+c)-384*B*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^5+1062*A*arcsin((-1+cos(d*x+c))/sin(d*x+c))*2^(1/2)*cos(d*x+c)^2*sin(d*x+c)+768*A*arctan(sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)/cos(d*x+c))*cos(d*x+c)^3*sin(d*x+c)-200*A*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)-3822*B*arcsin((-1+cos(d*x+c))/sin(d*x+c))*2^(1/2)*cos(d*x+c)^2*sin(d*x+c)-1814*B*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^4-2688*B*arctan(sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)/cos(d*x+c))*cos(d*x+c)^3*sin(d*x+c)+531*A*arcsin((-1+cos(d*x+c))/sin(d*x+c))*sin(d*x+c)*cos(d*x+c)*2^(1/2)+1536*A*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)-724*A*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*cos(d*x+c)-1911*B*arcsin((-1+cos(d*x+c))/sin(d*x+c))*sin(d*x+c)*cos(d*x+c)*2^(1/2)-686*B*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)-5376*B*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)+768*A*sin(d*x+c)*cos(d*x+c)*arctan(sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)/cos(d*x+c))-294*A*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)+1750*B*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)-2688*B*sin(d*x+c)*cos(d*x+c)*arctan(sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)/cos(d*x+c))+1134*B*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2))/sin(d*x+c)^15/(cos(d*x+c)/(1+cos(d*x+c)))^(9/2)/a^4","B"
209,1,703,204,0.372000," ","int(cos(d*x+c)^(5/2)*(A+B*cos(d*x+c))/(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)^{6} \left(\cos^{\frac{5}{2}}\left(d x +c \right)\right) \left(134 A \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \left(\cos^{4}\left(d x +c \right)\right)+15 A \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) \sin \left(d x +c \right)+100 A \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \left(\cos^{3}\left(d x +c \right)\right)-531 B \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) \sin \left(d x +c \right)+30 A \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) \sin \left(d x +c \right)-104 A \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}}-768 B \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^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)-1062 B \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) \sin \left(d x +c \right)-494 B \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \left(\cos^{4}\left(d x +c \right)\right)+15 A \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}-100 A \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \cos \left(d x +c \right)-1536 B \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)-531 B \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}-230 B \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}-30 A \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}}-768 B \sin \left(d x +c \right) \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)+430 B \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+294 B \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\right)}{384 d \sin \left(d x +c \right)^{13} \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{7}{2}} a^{4}}"," ",0,"-1/384/d*(a*(1+cos(d*x+c)))^(1/2)*(-1+cos(d*x+c))^6*cos(d*x+c)^(5/2)*(134*A*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*cos(d*x+c)^4+15*A*arcsin((-1+cos(d*x+c))/sin(d*x+c))*2^(1/2)*cos(d*x+c)^3*sin(d*x+c)+100*A*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*cos(d*x+c)^3-531*B*arcsin((-1+cos(d*x+c))/sin(d*x+c))*2^(1/2)*cos(d*x+c)^3*sin(d*x+c)+30*A*arcsin((-1+cos(d*x+c))/sin(d*x+c))*2^(1/2)*cos(d*x+c)^2*sin(d*x+c)-104*A*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)-768*B*arctan(sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)/cos(d*x+c))*cos(d*x+c)^3*sin(d*x+c)-1062*B*arcsin((-1+cos(d*x+c))/sin(d*x+c))*2^(1/2)*cos(d*x+c)^2*sin(d*x+c)-494*B*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^4+15*A*arcsin((-1+cos(d*x+c))/sin(d*x+c))*sin(d*x+c)*cos(d*x+c)*2^(1/2)-100*A*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*cos(d*x+c)-1536*B*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)-531*B*arcsin((-1+cos(d*x+c))/sin(d*x+c))*sin(d*x+c)*cos(d*x+c)*2^(1/2)-230*B*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)-30*A*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)-768*B*sin(d*x+c)*cos(d*x+c)*arctan(sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)/cos(d*x+c))+430*B*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+294*B*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2))/sin(d*x+c)^13/(cos(d*x+c)/(1+cos(d*x+c)))^(7/2)/a^4","B"
210,1,549,170,0.339000," ","int(cos(d*x+c)^(3/2)*(A+B*cos(d*x+c))/(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)^{5} \left(34 A \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \left(\cos^{4}\left(d x +c \right)\right)+140 A \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \left(\cos^{3}\left(d x +c \right)\right)+21 A \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) \sin \left(d x +c \right)+15 B \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) \sin \left(d x +c \right)+8 A \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}}+42 A \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) \sin \left(d x +c \right)+134 B \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \left(\cos^{4}\left(d x +c \right)\right)+30 B \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) \sin \left(d x +c \right)-140 A \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \cos \left(d x +c \right)+21 A \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}-34 B \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+15 B \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}-42 A \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}}-70 B \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}-30 B \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\right)}{384 d \sin \left(d x +c \right)^{11} \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} 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))^5*(34*A*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*cos(d*x+c)^4+140*A*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*cos(d*x+c)^3+21*A*arcsin((-1+cos(d*x+c))/sin(d*x+c))*2^(1/2)*cos(d*x+c)^3*sin(d*x+c)+15*B*arcsin((-1+cos(d*x+c))/sin(d*x+c))*2^(1/2)*cos(d*x+c)^3*sin(d*x+c)+8*A*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)+42*A*arcsin((-1+cos(d*x+c))/sin(d*x+c))*2^(1/2)*cos(d*x+c)^2*sin(d*x+c)+134*B*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^4+30*B*arcsin((-1+cos(d*x+c))/sin(d*x+c))*2^(1/2)*cos(d*x+c)^2*sin(d*x+c)-140*A*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*cos(d*x+c)+21*A*arcsin((-1+cos(d*x+c))/sin(d*x+c))*sin(d*x+c)*cos(d*x+c)*2^(1/2)-34*B*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+15*B*arcsin((-1+cos(d*x+c))/sin(d*x+c))*sin(d*x+c)*cos(d*x+c)*2^(1/2)-42*A*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)-70*B*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)-30*B*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2))/sin(d*x+c)^11/(cos(d*x+c)/(1+cos(d*x+c)))^(5/2)/a^4","B"
211,1,549,170,0.336000," ","int(cos(d*x+c)^(1/2)*(A+B*cos(d*x+c))/(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)^{4} \left(10 A \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \left(\cos^{4}\left(d x +c \right)\right)-39 A \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) \sin \left(d x +c \right)-4 A \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \left(\cos^{3}\left(d x +c \right)\right)-21 B \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) \sin \left(d x +c \right)-78 A \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) \sin \left(d x +c \right)-88 A \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}}-34 B \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \left(\cos^{4}\left(d x +c \right)\right)-42 B \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) \sin \left(d x +c \right)-39 A \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 A \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \cos \left(d x +c \right)-106 B \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}-21 B \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}+78 A \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}}+98 B \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+42 B \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\right)}{384 d \sin \left(d x +c \right)^{9} \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} 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))^4*(10*A*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*cos(d*x+c)^4-39*A*arcsin((-1+cos(d*x+c))/sin(d*x+c))*2^(1/2)*cos(d*x+c)^3*sin(d*x+c)-4*A*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*cos(d*x+c)^3-21*B*arcsin((-1+cos(d*x+c))/sin(d*x+c))*2^(1/2)*cos(d*x+c)^3*sin(d*x+c)-78*A*arcsin((-1+cos(d*x+c))/sin(d*x+c))*2^(1/2)*cos(d*x+c)^2*sin(d*x+c)-88*A*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)-34*B*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^4-42*B*arcsin((-1+cos(d*x+c))/sin(d*x+c))*2^(1/2)*cos(d*x+c)^2*sin(d*x+c)-39*A*arcsin((-1+cos(d*x+c))/sin(d*x+c))*sin(d*x+c)*cos(d*x+c)*2^(1/2)+4*A*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*cos(d*x+c)-106*B*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)-21*B*arcsin((-1+cos(d*x+c))/sin(d*x+c))*sin(d*x+c)*cos(d*x+c)*2^(1/2)+78*A*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)+98*B*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+42*B*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2))/sin(d*x+c)^9/(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)/a^4","B"
212,1,549,172,0.326000," ","int((A+B*cos(d*x+c))/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)^{3} \left(-206 A \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \left(\cos^{4}\left(d x +c \right)\right)+189 A \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) \sin \left(d x +c \right)-532 A \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \left(\cos^{3}\left(d x +c \right)\right)+39 B \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) \sin \left(d x +c \right)+378 A \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) \sin \left(d x +c \right)-184 A \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}}+78 B \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) \sin \left(d x +c \right)-10 B \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \left(\cos^{4}\left(d x +c \right)\right)+189 A \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}+532 A \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \cos \left(d x +c \right)+39 B \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}+14 B \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+390 A \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}}+74 B \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}-78 B \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\right)}{384 d \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, a^{4} \sqrt{\cos \left(d x +c \right)}\, \sin \left(d x +c \right)^{7}}"," ",0,"1/384/d*(a*(1+cos(d*x+c)))^(1/2)*(-1+cos(d*x+c))^3*(-206*A*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*cos(d*x+c)^4+189*A*arcsin((-1+cos(d*x+c))/sin(d*x+c))*2^(1/2)*cos(d*x+c)^3*sin(d*x+c)-532*A*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*cos(d*x+c)^3+39*B*arcsin((-1+cos(d*x+c))/sin(d*x+c))*2^(1/2)*cos(d*x+c)^3*sin(d*x+c)+378*A*arcsin((-1+cos(d*x+c))/sin(d*x+c))*2^(1/2)*cos(d*x+c)^2*sin(d*x+c)-184*A*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)+78*B*arcsin((-1+cos(d*x+c))/sin(d*x+c))*2^(1/2)*cos(d*x+c)^2*sin(d*x+c)-10*B*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^4+189*A*arcsin((-1+cos(d*x+c))/sin(d*x+c))*sin(d*x+c)*cos(d*x+c)*2^(1/2)+532*A*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*cos(d*x+c)+39*B*arcsin((-1+cos(d*x+c))/sin(d*x+c))*sin(d*x+c)*cos(d*x+c)*2^(1/2)+14*B*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+390*A*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)+74*B*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)-78*B*cos(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^4/cos(d*x+c)^(1/2)/sin(d*x+c)^7","B"
213,1,581,213,0.375000," ","int((A+B*cos(d*x+c))/cos(d*x+c)^(3/2)/(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(-1089 A \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)}}\, \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \sqrt{2}+189 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)}}\, \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \sqrt{2}-3267 A \sin \left(d x +c \right) \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) \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+567 B \sin \left(d x +c \right) \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) \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}-3267 A \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) \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+567 B \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) \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+1382 A \left(\cos^{4}\left(d x +c \right)\right)-1089 A \sin \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)}}-206 B \left(\cos^{4}\left(d x +c \right)\right)+189 B \sin \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)}}+2366 A \left(\cos^{3}\left(d x +c \right)\right)-326 B \left(\cos^{3}\left(d x +c \right)\right)-550 A \left(\cos^{2}\left(d x +c \right)\right)+142 B \left(\cos^{2}\left(d x +c \right)\right)-2430 A \cos \left(d x +c \right)+390 B \cos \left(d x +c \right)-768 A \right)}{384 d \,a^{4} \sin \left(d x +c \right)^{5} \left(1+\cos \left(d x +c \right)\right) \sqrt{\cos \left(d x +c \right)}}"," ",0,"-1/384/d*(a*(1+cos(d*x+c)))^(1/2)*(-1+cos(d*x+c))^2*(-1089*A*cos(d*x+c)^3*sin(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)+189*B*cos(d*x+c)^3*sin(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)-3267*A*sin(d*x+c)*cos(d*x+c)^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)+567*B*sin(d*x+c)*cos(d*x+c)^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)-3267*A*cos(d*x+c)*sin(d*x+c)*arcsin((-1+cos(d*x+c))/sin(d*x+c))*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+567*B*cos(d*x+c)*sin(d*x+c)*arcsin((-1+cos(d*x+c))/sin(d*x+c))*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+1382*A*cos(d*x+c)^4-1089*A*sin(d*x+c)*arcsin((-1+cos(d*x+c))/sin(d*x+c))*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)-206*B*cos(d*x+c)^4+189*B*sin(d*x+c)*arcsin((-1+cos(d*x+c))/sin(d*x+c))*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+2366*A*cos(d*x+c)^3-326*B*cos(d*x+c)^3-550*A*cos(d*x+c)^2+142*B*cos(d*x+c)^2-2430*A*cos(d*x+c)+390*B*cos(d*x+c)-768*A)/a^4/sin(d*x+c)^5/(1+cos(d*x+c))/cos(d*x+c)^(1/2)","B"
214,1,715,254,0.243000," ","int((A+B*cos(d*x+c))/cos(d*x+c)^(5/2)/(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) \left(-3045 A \left(\cos^{4}\left(d x +c \right)\right) \sqrt{2}\, \sin \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)+1089 B \left(\cos^{4}\left(d x +c \right)\right) \sqrt{2}\, \sin \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)-12180 A \left(\cos^{3}\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{3}{2}} \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \sqrt{2}+4356 B \left(\cos^{3}\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{3}{2}} \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \sqrt{2}-18270 A \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}\, \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}}+6534 B \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}\, \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}}-12180 A \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}\, \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}}+4356 B \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}\, \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}}-3045 A \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}\, \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}}+1089 B \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}\, \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}}+3774 A \left(\cos^{5}\left(d x +c \right)\right)-1382 B \left(\cos^{5}\left(d x +c \right)\right)+6390 A \left(\cos^{4}\left(d x +c \right)\right)-2366 B \left(\cos^{4}\left(d x +c \right)\right)-1662 A \left(\cos^{3}\left(d x +c \right)\right)+550 B \left(\cos^{3}\left(d x +c \right)\right)-6710 A \left(\cos^{2}\left(d x +c \right)\right)+2430 B \left(\cos^{2}\left(d x +c \right)\right)-2048 A \cos \left(d x +c \right)+768 B \cos \left(d x +c \right)+256 A \right)}{384 d \,a^{4} \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}}}"," ",0,"-1/384/d*(a*(1+cos(d*x+c)))^(1/2)*(-1+cos(d*x+c))*(-3045*A*cos(d*x+c)^4*2^(1/2)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*arcsin((-1+cos(d*x+c))/sin(d*x+c))+1089*B*cos(d*x+c)^4*2^(1/2)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*arcsin((-1+cos(d*x+c))/sin(d*x+c))-12180*A*cos(d*x+c)^3*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*arcsin((-1+cos(d*x+c))/sin(d*x+c))*2^(1/2)+4356*B*cos(d*x+c)^3*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*arcsin((-1+cos(d*x+c))/sin(d*x+c))*2^(1/2)-18270*A*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)/(1+cos(d*x+c)))^(3/2)+6534*B*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)/(1+cos(d*x+c)))^(3/2)-12180*A*arcsin((-1+cos(d*x+c))/sin(d*x+c))*sin(d*x+c)*cos(d*x+c)*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)+4356*B*arcsin((-1+cos(d*x+c))/sin(d*x+c))*sin(d*x+c)*cos(d*x+c)*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)-3045*A*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)))^(3/2)+1089*B*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)))^(3/2)+3774*A*cos(d*x+c)^5-1382*B*cos(d*x+c)^5+6390*A*cos(d*x+c)^4-2366*B*cos(d*x+c)^4-1662*A*cos(d*x+c)^3+550*B*cos(d*x+c)^3-6710*A*cos(d*x+c)^2+2430*B*cos(d*x+c)^2-2048*A*cos(d*x+c)+768*B*cos(d*x+c)+256*A)/a^4/sin(d*x+c)^3/(1+cos(d*x+c))^2/cos(d*x+c)^(3/2)","B"
215,1,107,97,0.054000," ","int(cos(d*x+c)^2*(a+b*cos(d*x+c))*(A+B*cos(d*x+c)),x)","\frac{B 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 b \left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3}+\frac{a B \left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3}+a 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*(B*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*b*(2+cos(d*x+c)^2)*sin(d*x+c)+1/3*a*B*(2+cos(d*x+c)^2)*sin(d*x+c)+a*A*(1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c))","A"
216,1,85,76,0.051000," ","int(cos(d*x+c)*(a+b*cos(d*x+c))*(A+B*cos(d*x+c)),x)","\frac{\frac{B b \left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3}+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 \left(\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{2}+\frac{d x}{2}+\frac{c}{2}\right)+a A \sin \left(d x +c \right)}{d}"," ",0,"1/d*(1/3*B*b*(2+cos(d*x+c)^2)*sin(d*x+c)+A*b*(1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c)+a*B*(1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c)+a*A*sin(d*x+c))","A"
217,1,57,48,0.046000," ","int((a+b*cos(d*x+c))*(A+B*cos(d*x+c)),x)","\frac{B 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 \sin \left(d x +c \right)+a A \left(d x +c \right)}{d}"," ",0,"1/d*(B*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*sin(d*x+c)+a*A*(d*x+c))","A"
218,1,56,35,0.090000," ","int((a+b*cos(d*x+c))*(A+B*cos(d*x+c))*sec(d*x+c),x)","A b x +a B x +\frac{a A \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{A b c}{d}+\frac{b B \sin \left(d x +c \right)}{d}+\frac{B a c}{d}"," ",0,"A*b*x+a*B*x+1/d*a*A*ln(sec(d*x+c)+tan(d*x+c))+1/d*A*b*c+b*B*sin(d*x+c)/d+1/d*B*a*c","A"
219,1,65,35,0.103000," ","int((a+b*cos(d*x+c))*(A+B*cos(d*x+c))*sec(d*x+c)^2,x)","b B x +\frac{a A \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{a B \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{B b c}{d}"," ",0,"b*B*x+a*A*tan(d*x+c)/d+1/d*A*b*ln(sec(d*x+c)+tan(d*x+c))+1/d*a*B*ln(sec(d*x+c)+tan(d*x+c))+1/d*B*b*c","A"
220,1,86,57,0.113000," ","int((a+b*cos(d*x+c))*(A+B*cos(d*x+c))*sec(d*x+c)^3,x)","\frac{a A \sec \left(d x +c \right) \tan \left(d x +c \right)}{2 d}+\frac{a A \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}+\frac{a B \tan \left(d x +c \right)}{d}+\frac{A b \tan \left(d x +c \right)}{d}+\frac{B b \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}"," ",0,"1/2*a*A*sec(d*x+c)*tan(d*x+c)/d+1/2/d*a*A*ln(sec(d*x+c)+tan(d*x+c))+1/d*a*B*tan(d*x+c)+1/d*A*b*tan(d*x+c)+1/d*B*b*ln(sec(d*x+c)+tan(d*x+c))","A"
221,1,128,85,0.117000," ","int((a+b*cos(d*x+c))*(A+B*cos(d*x+c))*sec(d*x+c)^4,x)","\frac{2 a A \tan \left(d x +c \right)}{3 d}+\frac{a A \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)}{2 d}+\frac{a B \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}+\frac{A b \sec \left(d x +c \right) \tan \left(d x +c \right)}{2 d}+\frac{A b \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}+\frac{B b \tan \left(d x +c \right)}{d}"," ",0,"2/3*a*A*tan(d*x+c)/d+1/3*a*A*sec(d*x+c)^2*tan(d*x+c)/d+1/2/d*a*B*sec(d*x+c)*tan(d*x+c)+1/2/d*a*B*ln(sec(d*x+c)+tan(d*x+c))+1/2/d*A*b*sec(d*x+c)*tan(d*x+c)+1/2/d*A*b*ln(sec(d*x+c)+tan(d*x+c))+1/d*B*b*tan(d*x+c)","A"
222,1,171,106,0.140000," ","int((a+b*cos(d*x+c))*(A+B*cos(d*x+c))*sec(d*x+c)^5,x)","\frac{a A \left(\sec^{3}\left(d x +c \right)\right) \tan \left(d x +c \right)}{4 d}+\frac{3 a A \sec \left(d x +c \right) \tan \left(d x +c \right)}{8 d}+\frac{3 a A \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}+\frac{2 a B \tan \left(d x +c \right)}{3 d}+\frac{a B \tan \left(d x +c \right) \left(\sec^{2}\left(d x +c \right)\right)}{3 d}+\frac{2 A b \tan \left(d x +c \right)}{3 d}+\frac{A b \tan \left(d x +c \right) \left(\sec^{2}\left(d x +c \right)\right)}{3 d}+\frac{B b \tan \left(d x +c \right) \sec \left(d x +c \right)}{2 d}+\frac{B b \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}"," ",0,"1/4*a*A*sec(d*x+c)^3*tan(d*x+c)/d+3/8*a*A*sec(d*x+c)*tan(d*x+c)/d+3/8/d*a*A*ln(sec(d*x+c)+tan(d*x+c))+2/3/d*a*B*tan(d*x+c)+1/3/d*a*B*tan(d*x+c)*sec(d*x+c)^2+2/3/d*A*b*tan(d*x+c)+1/3/d*A*b*tan(d*x+c)*sec(d*x+c)^2+1/2/d*B*b*tan(d*x+c)*sec(d*x+c)+1/2/d*B*b*ln(sec(d*x+c)+tan(d*x+c))","A"
223,1,184,177,0.052000," ","int(cos(d*x+c)^2*(a+b*cos(d*x+c))^2*(A+B*cos(d*x+c)),x)","\frac{a^{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)+\frac{B \,a^{2} \left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3}+\frac{2 A a b \left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3}+2 B 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)+A \,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{b^{2} B \left(\frac{8}{3}+\cos^{4}\left(d x +c \right)+\frac{4 \left(\cos^{2}\left(d x +c \right)\right)}{3}\right) \sin \left(d x +c \right)}{5}}{d}"," ",0,"1/d*(a^2*A*(1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c)+1/3*B*a^2*(2+cos(d*x+c)^2)*sin(d*x+c)+2/3*A*a*b*(2+cos(d*x+c)^2)*sin(d*x+c)+2*B*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)+A*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)+1/5*b^2*B*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c))","A"
224,1,152,160,0.049000," ","int(cos(d*x+c)*(a+b*cos(d*x+c))^2*(A+B*cos(d*x+c)),x)","\frac{a^{2} A \sin \left(d x +c \right)+B \,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 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)+\frac{2 B a b \left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3}+\frac{A \,b^{2} \left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3}+b^{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)}{d}"," ",0,"1/d*(a^2*A*sin(d*x+c)+B*a^2*(1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c)+2*A*a*b*(1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c)+2/3*B*a*b*(2+cos(d*x+c)^2)*sin(d*x+c)+1/3*A*b^2*(2+cos(d*x+c)^2)*sin(d*x+c)+b^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))","A"
225,1,114,99,0.050000," ","int((a+b*cos(d*x+c))^2*(A+B*cos(d*x+c)),x)","\frac{\frac{b^{2} B \left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3}+A \,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 B 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)+2 A a b \sin \left(d x +c \right)+B \,a^{2} \sin \left(d x +c \right)+a^{2} A \left(d x +c \right)}{d}"," ",0,"1/d*(1/3*b^2*B*(2+cos(d*x+c)^2)*sin(d*x+c)+A*b^2*(1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c)+2*B*a*b*(1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c)+2*A*a*b*sin(d*x+c)+B*a^2*sin(d*x+c)+a^2*A*(d*x+c))","A"
226,1,120,80,0.099000," ","int((a+b*cos(d*x+c))^2*(A+B*cos(d*x+c))*sec(d*x+c),x)","\frac{a^{2} A \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+a^{2} B x +\frac{B \,a^{2} c}{d}+2 A a b x +\frac{2 A a b c}{d}+\frac{2 B a b \sin \left(d x +c \right)}{d}+\frac{A \,b^{2} \sin \left(d x +c \right)}{d}+\frac{b^{2} B \cos \left(d x +c \right) \sin \left(d x +c \right)}{2 d}+\frac{b^{2} B x}{2}+\frac{b^{2} B c}{2 d}"," ",0,"1/d*a^2*A*ln(sec(d*x+c)+tan(d*x+c))+a^2*B*x+1/d*B*a^2*c+2*A*a*b*x+2/d*A*a*b*c+2/d*B*a*b*sin(d*x+c)+1/d*A*b^2*sin(d*x+c)+1/2/d*b^2*B*cos(d*x+c)*sin(d*x+c)+1/2*b^2*B*x+1/2/d*b^2*B*c","A"
227,1,104,60,0.116000," ","int((a+b*cos(d*x+c))^2*(A+B*cos(d*x+c))*sec(d*x+c)^2,x)","A \,b^{2} x +2 B a b x +\frac{a^{2} A \tan \left(d x +c \right)}{d}+\frac{2 A a b \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{A \,b^{2} c}{d}+\frac{b^{2} B \sin \left(d x +c \right)}{d}+\frac{B \,a^{2} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{2 B a b c}{d}"," ",0,"A*b^2*x+2*B*a*b*x+a^2*A*tan(d*x+c)/d+2/d*A*a*b*ln(sec(d*x+c)+tan(d*x+c))+1/d*A*b^2*c+b^2*B*sin(d*x+c)/d+1/d*B*a^2*ln(sec(d*x+c)+tan(d*x+c))+2/d*B*a*b*c","A"
228,1,133,76,0.117000," ","int((a+b*cos(d*x+c))^2*(A+B*cos(d*x+c))*sec(d*x+c)^3,x)","\frac{a^{2} A \sec \left(d x +c \right) \tan \left(d x +c \right)}{2 d}+\frac{a^{2} A \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}+\frac{B \,a^{2} \tan \left(d x +c \right)}{d}+\frac{2 A a b \tan \left(d x +c \right)}{d}+\frac{2 B a b \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{A \,b^{2} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+b^{2} B x +\frac{b^{2} B c}{d}"," ",0,"1/2*a^2*A*sec(d*x+c)*tan(d*x+c)/d+1/2/d*a^2*A*ln(sec(d*x+c)+tan(d*x+c))+1/d*B*a^2*tan(d*x+c)+2/d*A*a*b*tan(d*x+c)+2/d*B*a*b*ln(sec(d*x+c)+tan(d*x+c))+1/d*A*b^2*ln(sec(d*x+c)+tan(d*x+c))+b^2*B*x+1/d*b^2*B*c","A"
229,1,174,108,0.132000," ","int((a+b*cos(d*x+c))^2*(A+B*cos(d*x+c))*sec(d*x+c)^4,x)","\frac{2 a^{2} A \tan \left(d x +c \right)}{3 d}+\frac{a^{2} A \left(\sec^{2}\left(d x +c \right)\right) \tan \left(d x +c \right)}{3 d}+\frac{B \,a^{2} \sec \left(d x +c \right) \tan \left(d x +c \right)}{2 d}+\frac{B \,a^{2} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}+\frac{A a b \sec \left(d x +c \right) \tan \left(d x +c \right)}{d}+\frac{A a b \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{2 B a b \tan \left(d x +c \right)}{d}+\frac{A \,b^{2} \tan \left(d x +c \right)}{d}+\frac{b^{2} B \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}"," ",0,"2/3*a^2*A*tan(d*x+c)/d+1/3*a^2*A*sec(d*x+c)^2*tan(d*x+c)/d+1/2/d*B*a^2*sec(d*x+c)*tan(d*x+c)+1/2/d*B*a^2*ln(sec(d*x+c)+tan(d*x+c))+1/d*A*a*b*sec(d*x+c)*tan(d*x+c)+1/d*A*a*b*ln(sec(d*x+c)+tan(d*x+c))+2/d*B*a*b*tan(d*x+c)+1/d*A*b^2*tan(d*x+c)+1/d*b^2*B*ln(sec(d*x+c)+tan(d*x+c))","A"
230,1,241,146,0.134000," ","int((a+b*cos(d*x+c))^2*(A+B*cos(d*x+c))*sec(d*x+c)^5,x)","\frac{a^{2} A \left(\sec^{3}\left(d x +c \right)\right) \tan \left(d x +c \right)}{4 d}+\frac{3 a^{2} A \sec \left(d x +c \right) \tan \left(d x +c \right)}{8 d}+\frac{3 a^{2} A \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}+\frac{2 B \,a^{2} \tan \left(d x +c \right)}{3 d}+\frac{B \,a^{2} \tan \left(d x +c \right) \left(\sec^{2}\left(d x +c \right)\right)}{3 d}+\frac{4 A a b \tan \left(d x +c \right)}{3 d}+\frac{2 A a b \tan \left(d x +c \right) \left(\sec^{2}\left(d x +c \right)\right)}{3 d}+\frac{B a b \tan \left(d x +c \right) \sec \left(d x +c \right)}{d}+\frac{B a b \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{A \,b^{2} \tan \left(d x +c \right) \sec \left(d x +c \right)}{2 d}+\frac{A \,b^{2} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}+\frac{b^{2} B \tan \left(d x +c \right)}{d}"," ",0,"1/4*a^2*A*sec(d*x+c)^3*tan(d*x+c)/d+3/8*a^2*A*sec(d*x+c)*tan(d*x+c)/d+3/8/d*a^2*A*ln(sec(d*x+c)+tan(d*x+c))+2/3/d*B*a^2*tan(d*x+c)+1/3/d*B*a^2*tan(d*x+c)*sec(d*x+c)^2+4/3/d*A*a*b*tan(d*x+c)+2/3/d*A*a*b*tan(d*x+c)*sec(d*x+c)^2+1/d*B*a*b*tan(d*x+c)*sec(d*x+c)+1/d*B*a*b*ln(sec(d*x+c)+tan(d*x+c))+1/2/d*A*b^2*tan(d*x+c)*sec(d*x+c)+1/2/d*A*b^2*ln(sec(d*x+c)+tan(d*x+c))+1/d*b^2*B*tan(d*x+c)","A"
231,1,270,255,0.096000," ","int(cos(d*x+c)^2*(a+b*cos(d*x+c))^3*(A+B*cos(d*x+c)),x)","\frac{A \,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)+\frac{a^{3} B \left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3}+A \,a^{2} b \left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+3 a^{2} b 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)+3 A a \,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{3 B a \,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}+\frac{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}+b^{3} 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)}{d}"," ",0,"1/d*(A*a^3*(1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c)+1/3*a^3*B*(2+cos(d*x+c)^2)*sin(d*x+c)+A*a^2*b*(2+cos(d*x+c)^2)*sin(d*x+c)+3*a^2*b*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)+3*A*a*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)+3/5*B*a*b^2*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c)+1/5*A*b^3*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c)+b^3*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))","A"
232,1,227,231,0.051000," ","int(cos(d*x+c)*(a+b*cos(d*x+c))^3*(A+B*cos(d*x+c)),x)","\frac{A \,a^{3} \sin \left(d x +c \right)+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)+3 A \,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^{2} b B \left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+A \,b^{2} a \left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+3 B a \,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)+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)+\frac{b^{3} B \left(\frac{8}{3}+\cos^{4}\left(d x +c \right)+\frac{4 \left(\cos^{2}\left(d x +c \right)\right)}{3}\right) \sin \left(d x +c \right)}{5}}{d}"," ",0,"1/d*(A*a^3*sin(d*x+c)+a^3*B*(1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c)+3*A*a^2*b*(1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c)+a^2*b*B*(2+cos(d*x+c)^2)*sin(d*x+c)+A*b^2*a*(2+cos(d*x+c)^2)*sin(d*x+c)+3*B*a*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)+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)+1/5*b^3*B*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c))","A"
233,1,180,161,0.055000," ","int((a+b*cos(d*x+c))^3*(A+B*cos(d*x+c)),x)","\frac{b^{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 \,b^{3} \left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3}+B a \,b^{2} \left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+3 A a \,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)+3 a^{2} b B \left(\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{2}+\frac{d x}{2}+\frac{c}{2}\right)+3 A \,a^{2} b \sin \left(d x +c \right)+a^{3} B \sin \left(d x +c \right)+A \,a^{3} \left(d x +c \right)}{d}"," ",0,"1/d*(b^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*b^3*(2+cos(d*x+c)^2)*sin(d*x+c)+B*a*b^2*(2+cos(d*x+c)^2)*sin(d*x+c)+3*A*a*b^2*(1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c)+3*a^2*b*B*(1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c)+3*A*a^2*b*sin(d*x+c)+a^3*B*sin(d*x+c)+A*a^3*(d*x+c))","A"
234,1,207,129,0.109000," ","int((a+b*cos(d*x+c))^3*(A+B*cos(d*x+c))*sec(d*x+c),x)","\frac{A \,a^{3} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+a^{3} B x +\frac{a^{3} B c}{d}+3 A \,a^{2} b x +\frac{3 A \,a^{2} b c}{d}+\frac{3 a^{2} b B \sin \left(d x +c \right)}{d}+\frac{3 A \,b^{2} a \sin \left(d x +c \right)}{d}+\frac{3 B a \,b^{2} \cos \left(d x +c \right) \sin \left(d x +c \right)}{2 d}+\frac{3 B a \,b^{2} x}{2}+\frac{3 B a \,b^{2} c}{2 d}+\frac{A \,b^{3} \cos \left(d x +c \right) \sin \left(d x +c \right)}{2 d}+\frac{A \,b^{3} x}{2}+\frac{A \,b^{3} c}{2 d}+\frac{B \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) b^{3}}{3 d}+\frac{2 b^{3} B \sin \left(d x +c \right)}{3 d}"," ",0,"1/d*A*a^3*ln(sec(d*x+c)+tan(d*x+c))+a^3*B*x+1/d*a^3*B*c+3*A*a^2*b*x+3/d*A*a^2*b*c+3/d*a^2*b*B*sin(d*x+c)+3/d*A*b^2*a*sin(d*x+c)+3/2/d*B*a*b^2*cos(d*x+c)*sin(d*x+c)+3/2*B*a*b^2*x+3/2/d*B*a*b^2*c+1/2/d*A*b^3*cos(d*x+c)*sin(d*x+c)+1/2*A*b^3*x+1/2/d*A*b^3*c+1/3/d*B*sin(d*x+c)*cos(d*x+c)^2*b^3+2/3/d*b^3*B*sin(d*x+c)","A"
235,1,168,127,0.127000," ","int((a+b*cos(d*x+c))^3*(A+B*cos(d*x+c))*sec(d*x+c)^2,x)","\frac{A \,a^{3} \tan \left(d x +c \right)}{d}+\frac{a^{3} B \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{3 A \,a^{2} b \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+3 a^{2} b B x +\frac{3 B \,a^{2} b c}{d}+3 A \,b^{2} a x +\frac{3 A a \,b^{2} c}{d}+\frac{3 B \,b^{2} a \sin \left(d x +c \right)}{d}+\frac{A \,b^{3} \sin \left(d x +c \right)}{d}+\frac{b^{3} B \cos \left(d x +c \right) \sin \left(d x +c \right)}{2 d}+\frac{b^{3} B x}{2}+\frac{b^{3} B c}{2 d}"," ",0,"1/d*A*a^3*tan(d*x+c)+1/d*a^3*B*ln(sec(d*x+c)+tan(d*x+c))+3/d*A*a^2*b*ln(sec(d*x+c)+tan(d*x+c))+3*a^2*b*B*x+3/d*B*a^2*b*c+3*A*b^2*a*x+3/d*A*a*b^2*c+3/d*B*b^2*a*sin(d*x+c)+1/d*A*b^3*sin(d*x+c)+1/2/d*b^3*B*cos(d*x+c)*sin(d*x+c)+1/2*b^3*B*x+1/2/d*b^3*B*c","A"
236,1,172,118,0.130000," ","int((a+b*cos(d*x+c))^3*(A+B*cos(d*x+c))*sec(d*x+c)^3,x)","\frac{A \,a^{3} \sec \left(d x +c \right) \tan \left(d x +c \right)}{2 d}+\frac{A \,a^{3} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}+\frac{a^{3} B \tan \left(d x +c \right)}{d}+\frac{3 A \,a^{2} b \tan \left(d x +c \right)}{d}+\frac{3 a^{2} b B \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{3 A \,b^{2} a \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+3 B a \,b^{2} x +\frac{3 B a \,b^{2} c}{d}+A \,b^{3} x +\frac{A \,b^{3} c}{d}+\frac{b^{3} B \sin \left(d x +c \right)}{d}"," ",0,"1/2/d*A*a^3*sec(d*x+c)*tan(d*x+c)+1/2/d*A*a^3*ln(sec(d*x+c)+tan(d*x+c))+1/d*a^3*B*tan(d*x+c)+3/d*A*a^2*b*tan(d*x+c)+3/d*a^2*b*B*ln(sec(d*x+c)+tan(d*x+c))+3/d*A*b^2*a*ln(sec(d*x+c)+tan(d*x+c))+3*B*a*b^2*x+3/d*B*a*b^2*c+A*b^3*x+1/d*A*b^3*c+1/d*b^3*B*sin(d*x+c)","A"
237,1,223,137,0.141000," ","int((a+b*cos(d*x+c))^3*(A+B*cos(d*x+c))*sec(d*x+c)^4,x)","\frac{2 A \,a^{3} \tan \left(d x +c \right)}{3 d}+\frac{A \,a^{3} \tan \left(d x +c \right) \left(\sec^{2}\left(d x +c \right)\right)}{3 d}+\frac{a^{3} B \sec \left(d x +c \right) \tan \left(d x +c \right)}{2 d}+\frac{a^{3} B \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}+\frac{3 A \,a^{2} b \sec \left(d x +c \right) \tan \left(d x +c \right)}{2 d}+\frac{3 A \,a^{2} b \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}+\frac{3 a^{2} b B \tan \left(d x +c \right)}{d}+\frac{3 A \,b^{2} a \tan \left(d x +c \right)}{d}+\frac{3 B \,b^{2} a \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{A \,b^{3} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+b^{3} B x +\frac{b^{3} B c}{d}"," ",0,"2/3/d*A*a^3*tan(d*x+c)+1/3/d*A*a^3*tan(d*x+c)*sec(d*x+c)^2+1/2/d*a^3*B*sec(d*x+c)*tan(d*x+c)+1/2/d*a^3*B*ln(sec(d*x+c)+tan(d*x+c))+3/2/d*A*a^2*b*sec(d*x+c)*tan(d*x+c)+3/2/d*A*a^2*b*ln(sec(d*x+c)+tan(d*x+c))+3/d*a^2*b*B*tan(d*x+c)+3/d*A*b^2*a*tan(d*x+c)+3/d*B*b^2*a*ln(sec(d*x+c)+tan(d*x+c))+1/d*A*b^3*ln(sec(d*x+c)+tan(d*x+c))+b^3*B*x+1/d*b^3*B*c","A"
238,1,290,178,0.144000," ","int((a+b*cos(d*x+c))^3*(A+B*cos(d*x+c))*sec(d*x+c)^5,x)","\frac{A \,a^{3} \tan \left(d x +c \right) \left(\sec^{3}\left(d x +c \right)\right)}{4 d}+\frac{3 A \,a^{3} \sec \left(d x +c \right) \tan \left(d x +c \right)}{8 d}+\frac{3 A \,a^{3} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}+\frac{2 a^{3} B \tan \left(d x +c \right)}{3 d}+\frac{a^{3} B \tan \left(d x +c \right) \left(\sec^{2}\left(d x +c \right)\right)}{3 d}+\frac{2 A \,a^{2} b \tan \left(d x +c \right)}{d}+\frac{A \,a^{2} b \tan \left(d x +c \right) \left(\sec^{2}\left(d x +c \right)\right)}{d}+\frac{3 a^{2} b B \tan \left(d x +c \right) \sec \left(d x +c \right)}{2 d}+\frac{3 a^{2} b B \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}+\frac{3 A a \,b^{2} \tan \left(d x +c \right) \sec \left(d x +c \right)}{2 d}+\frac{3 A \,b^{2} a \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}+\frac{3 B a \,b^{2} \tan \left(d x +c \right)}{d}+\frac{A \,b^{3} \tan \left(d x +c \right)}{d}+\frac{b^{3} B \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}"," ",0,"1/4/d*A*a^3*tan(d*x+c)*sec(d*x+c)^3+3/8/d*A*a^3*sec(d*x+c)*tan(d*x+c)+3/8/d*A*a^3*ln(sec(d*x+c)+tan(d*x+c))+2/3/d*a^3*B*tan(d*x+c)+1/3/d*a^3*B*tan(d*x+c)*sec(d*x+c)^2+2/d*A*a^2*b*tan(d*x+c)+1/d*A*a^2*b*tan(d*x+c)*sec(d*x+c)^2+3/2/d*a^2*b*B*tan(d*x+c)*sec(d*x+c)+3/2/d*a^2*b*B*ln(sec(d*x+c)+tan(d*x+c))+3/2/d*A*a*b^2*tan(d*x+c)*sec(d*x+c)+3/2/d*A*b^2*a*ln(sec(d*x+c)+tan(d*x+c))+3/d*B*a*b^2*tan(d*x+c)+1/d*A*b^3*tan(d*x+c)+1/d*b^3*B*ln(sec(d*x+c)+tan(d*x+c))","A"
239,1,382,224,0.152000," ","int((a+b*cos(d*x+c))^3*(A+B*cos(d*x+c))*sec(d*x+c)^6,x)","\frac{8 A \,a^{3} \tan \left(d x +c \right)}{15 d}+\frac{A \,a^{3} \tan \left(d x +c \right) \left(\sec^{4}\left(d x +c \right)\right)}{5 d}+\frac{4 A \,a^{3} \tan \left(d x +c \right) \left(\sec^{2}\left(d x +c \right)\right)}{15 d}+\frac{a^{3} B \tan \left(d x +c \right) \left(\sec^{3}\left(d x +c \right)\right)}{4 d}+\frac{3 a^{3} B \sec \left(d x +c \right) \tan \left(d x +c \right)}{8 d}+\frac{3 a^{3} B \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}+\frac{3 A \,a^{2} b \tan \left(d x +c \right) \left(\sec^{3}\left(d x +c \right)\right)}{4 d}+\frac{9 A \,a^{2} b \sec \left(d x +c \right) \tan \left(d x +c \right)}{8 d}+\frac{9 A \,a^{2} b \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}+\frac{2 a^{2} b B \tan \left(d x +c \right)}{d}+\frac{a^{2} b B \tan \left(d x +c \right) \left(\sec^{2}\left(d x +c \right)\right)}{d}+\frac{2 A \,b^{2} a \tan \left(d x +c \right)}{d}+\frac{A a \,b^{2} \tan \left(d x +c \right) \left(\sec^{2}\left(d x +c \right)\right)}{d}+\frac{3 B a \,b^{2} \tan \left(d x +c \right) \sec \left(d x +c \right)}{2 d}+\frac{3 B \,b^{2} a \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}+\frac{A \,b^{3} \tan \left(d x +c \right) \sec \left(d x +c \right)}{2 d}+\frac{A \,b^{3} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}+\frac{b^{3} B \tan \left(d x +c \right)}{d}"," ",0,"8/15/d*A*a^3*tan(d*x+c)+1/5/d*A*a^3*tan(d*x+c)*sec(d*x+c)^4+4/15/d*A*a^3*tan(d*x+c)*sec(d*x+c)^2+1/4/d*a^3*B*tan(d*x+c)*sec(d*x+c)^3+3/8/d*a^3*B*sec(d*x+c)*tan(d*x+c)+3/8/d*a^3*B*ln(sec(d*x+c)+tan(d*x+c))+3/4/d*A*a^2*b*tan(d*x+c)*sec(d*x+c)^3+9/8/d*A*a^2*b*sec(d*x+c)*tan(d*x+c)+9/8/d*A*a^2*b*ln(sec(d*x+c)+tan(d*x+c))+2/d*a^2*b*B*tan(d*x+c)+1/d*a^2*b*B*tan(d*x+c)*sec(d*x+c)^2+2/d*A*b^2*a*tan(d*x+c)+1/d*A*a*b^2*tan(d*x+c)*sec(d*x+c)^2+3/2/d*B*a*b^2*tan(d*x+c)*sec(d*x+c)+3/2/d*B*b^2*a*ln(sec(d*x+c)+tan(d*x+c))+1/2/d*A*b^3*tan(d*x+c)*sec(d*x+c)+1/2/d*A*b^3*ln(sec(d*x+c)+tan(d*x+c))+1/d*b^3*B*tan(d*x+c)","A"
240,1,368,350,0.061000," ","int(cos(d*x+c)^2*(a+b*cos(d*x+c))^4*(A+B*cos(d*x+c)),x)","\frac{A \,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)+\frac{a^{4} B \left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3}+\frac{4 A \,a^{3} b \left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3}+4 B \,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)+6 A \,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{6 B \,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}+\frac{4 A 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}+4 B 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)+A \,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{B \,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}}{d}"," ",0,"1/d*(A*a^4*(1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c)+1/3*a^4*B*(2+cos(d*x+c)^2)*sin(d*x+c)+4/3*A*a^3*b*(2+cos(d*x+c)^2)*sin(d*x+c)+4*B*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)+6*A*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)+6/5*B*a^2*b^2*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c)+4/5*A*a*b^3*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c)+4*B*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)+A*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)+1/7*B*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))","A"
241,1,316,311,0.055000," ","int(cos(d*x+c)*(a+b*cos(d*x+c))^4*(A+B*cos(d*x+c)),x)","\frac{A \,a^{4} \sin \left(d x +c \right)+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)+4 A \,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)+\frac{4 B \,a^{3} b \left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3}+2 A \,a^{2} b^{2} \left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+6 B \,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)+4 A 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)+\frac{4 B 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}+\frac{A \,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}+B \,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)}{d}"," ",0,"1/d*(A*a^4*sin(d*x+c)+a^4*B*(1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c)+4*A*a^3*b*(1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c)+4/3*B*a^3*b*(2+cos(d*x+c)^2)*sin(d*x+c)+2*A*a^2*b^2*(2+cos(d*x+c)^2)*sin(d*x+c)+6*B*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*A*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)+4/5*B*a*b^3*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c)+1/5*A*b^4*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c)+B*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))","A"
242,1,258,229,0.054000," ","int((a+b*cos(d*x+c))^4*(A+B*cos(d*x+c)),x)","\frac{\frac{B \,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}+A \,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)+4 B 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)+\frac{4 A a \,b^{3} \left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3}+2 B \,a^{2} b^{2} \left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+6 A \,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 B \,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)+4 A \,a^{3} b \sin \left(d x +c \right)+a^{4} B \sin \left(d x +c \right)+A \,a^{4} \left(d x +c \right)}{d}"," ",0,"1/d*(1/5*B*b^4*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c)+A*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*B*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)+4/3*A*a*b^3*(2+cos(d*x+c)^2)*sin(d*x+c)+2*B*a^2*b^2*(2+cos(d*x+c)^2)*sin(d*x+c)+6*A*a^2*b^2*(1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c)+4*B*a^3*b*(1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c)+4*A*a^3*b*sin(d*x+c)+a^4*B*sin(d*x+c)+A*a^4*(d*x+c))","A"
243,1,319,190,0.124000," ","int((a+b*cos(d*x+c))^4*(A+B*cos(d*x+c))*sec(d*x+c),x)","\frac{A \,a^{4} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+a^{4} B x +\frac{a^{4} B c}{d}+4 A \,a^{3} b x +\frac{4 A \,a^{3} b c}{d}+\frac{4 B \,a^{3} b \sin \left(d x +c \right)}{d}+\frac{6 A \,a^{2} b^{2} \sin \left(d x +c \right)}{d}+\frac{3 B \,a^{2} b^{2} \cos \left(d x +c \right) \sin \left(d x +c \right)}{d}+3 B \,a^{2} b^{2} x +\frac{3 B \,a^{2} b^{2} c}{d}+\frac{2 A a \,b^{3} \cos \left(d x +c \right) \sin \left(d x +c \right)}{d}+2 A a \,b^{3} x +\frac{2 A a \,b^{3} c}{d}+\frac{4 B \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) a \,b^{3}}{3 d}+\frac{8 B a \,b^{3} \sin \left(d x +c \right)}{3 d}+\frac{A \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) b^{4}}{3 d}+\frac{2 A \,b^{4} \sin \left(d x +c \right)}{3 d}+\frac{B \,b^{4} \sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right)}{4 d}+\frac{3 B \,b^{4} \cos \left(d x +c \right) \sin \left(d x +c \right)}{8 d}+\frac{3 b^{4} B x}{8}+\frac{3 B \,b^{4} c}{8 d}"," ",0,"1/d*A*a^4*ln(sec(d*x+c)+tan(d*x+c))+a^4*B*x+1/d*a^4*B*c+4*A*a^3*b*x+4/d*A*a^3*b*c+4/d*B*a^3*b*sin(d*x+c)+6/d*A*a^2*b^2*sin(d*x+c)+3/d*B*a^2*b^2*cos(d*x+c)*sin(d*x+c)+3*B*a^2*b^2*x+3/d*B*a^2*b^2*c+2/d*A*a*b^3*cos(d*x+c)*sin(d*x+c)+2*A*a*b^3*x+2/d*A*a*b^3*c+4/3/d*B*sin(d*x+c)*cos(d*x+c)^2*a*b^3+8/3/d*B*a*b^3*sin(d*x+c)+1/3/d*A*sin(d*x+c)*cos(d*x+c)^2*b^4+2/3/d*A*b^4*sin(d*x+c)+1/4/d*B*b^4*sin(d*x+c)*cos(d*x+c)^3+3/8/d*B*b^4*cos(d*x+c)*sin(d*x+c)+3/8*b^4*B*x+3/8/d*B*b^4*c","A"
244,1,255,187,0.127000," ","int((a+b*cos(d*x+c))^4*(A+B*cos(d*x+c))*sec(d*x+c)^2,x)","\frac{A \,a^{4} \tan \left(d x +c \right)}{d}+\frac{a^{4} B \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{4 A \,a^{3} b \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+4 B \,a^{3} b x +\frac{4 B \,a^{3} b c}{d}+6 A \,a^{2} b^{2} x +\frac{6 A \,a^{2} b^{2} c}{d}+\frac{6 B \,a^{2} b^{2} \sin \left(d x +c \right)}{d}+\frac{4 A a \,b^{3} \sin \left(d x +c \right)}{d}+\frac{2 B a \,b^{3} \cos \left(d x +c \right) \sin \left(d x +c \right)}{d}+2 B a \,b^{3} x +\frac{2 B a \,b^{3} c}{d}+\frac{A \,b^{4} \cos \left(d x +c \right) \sin \left(d x +c \right)}{2 d}+\frac{A \,b^{4} x}{2}+\frac{A \,b^{4} c}{2 d}+\frac{B \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) b^{4}}{3 d}+\frac{2 B \,b^{4} \sin \left(d x +c \right)}{3 d}"," ",0,"1/d*A*a^4*tan(d*x+c)+1/d*a^4*B*ln(sec(d*x+c)+tan(d*x+c))+4/d*A*a^3*b*ln(sec(d*x+c)+tan(d*x+c))+4*B*a^3*b*x+4/d*B*a^3*b*c+6*A*a^2*b^2*x+6/d*A*a^2*b^2*c+6/d*B*a^2*b^2*sin(d*x+c)+4/d*A*a*b^3*sin(d*x+c)+2/d*B*a*b^3*cos(d*x+c)*sin(d*x+c)+2*B*a*b^3*x+2/d*B*a*b^3*c+1/2/d*A*b^4*cos(d*x+c)*sin(d*x+c)+1/2*A*b^4*x+1/2/d*A*b^4*c+1/3/d*B*sin(d*x+c)*cos(d*x+c)^2*b^4+2/3/d*B*b^4*sin(d*x+c)","A"
245,1,236,197,0.147000," ","int((a+b*cos(d*x+c))^4*(A+B*cos(d*x+c))*sec(d*x+c)^3,x)","\frac{A \,a^{4} \sec \left(d x +c \right) \tan \left(d x +c \right)}{2 d}+\frac{A \,a^{4} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}+\frac{a^{4} B \tan \left(d x +c \right)}{d}+\frac{4 A \,a^{3} b \tan \left(d x +c \right)}{d}+\frac{4 B \,a^{3} b \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{6 A \,a^{2} b^{2} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+6 B \,a^{2} b^{2} x +\frac{6 B \,a^{2} b^{2} c}{d}+4 A a \,b^{3} x +\frac{4 A a \,b^{3} c}{d}+\frac{4 B a \,b^{3} \sin \left(d x +c \right)}{d}+\frac{A \,b^{4} \sin \left(d x +c \right)}{d}+\frac{B \,b^{4} \cos \left(d x +c \right) \sin \left(d x +c \right)}{2 d}+\frac{b^{4} B x}{2}+\frac{B \,b^{4} c}{2 d}"," ",0,"1/2/d*A*a^4*sec(d*x+c)*tan(d*x+c)+1/2/d*A*a^4*ln(sec(d*x+c)+tan(d*x+c))+1/d*a^4*B*tan(d*x+c)+4/d*A*a^3*b*tan(d*x+c)+4/d*B*a^3*b*ln(sec(d*x+c)+tan(d*x+c))+6/d*A*a^2*b^2*ln(sec(d*x+c)+tan(d*x+c))+6*B*a^2*b^2*x+6/d*B*a^2*b^2*c+4*A*a*b^3*x+4/d*A*a*b^3*c+4/d*B*a*b^3*sin(d*x+c)+1/d*A*b^4*sin(d*x+c)+1/2/d*B*b^4*cos(d*x+c)*sin(d*x+c)+1/2*b^4*B*x+1/2/d*B*b^4*c","A"
246,1,262,188,0.162000," ","int((a+b*cos(d*x+c))^4*(A+B*cos(d*x+c))*sec(d*x+c)^4,x)","\frac{2 A \,a^{4} \tan \left(d x +c \right)}{3 d}+\frac{A \,a^{4} \tan \left(d x +c \right) \left(\sec^{2}\left(d x +c \right)\right)}{3 d}+\frac{a^{4} B \sec \left(d x +c \right) \tan \left(d x +c \right)}{2 d}+\frac{a^{4} B \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}+\frac{2 A \,a^{3} b \sec \left(d x +c \right) \tan \left(d x +c \right)}{d}+\frac{2 A \,a^{3} b \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{4 B \,a^{3} b \tan \left(d x +c \right)}{d}+\frac{6 A \,a^{2} b^{2} \tan \left(d x +c \right)}{d}+\frac{6 B \,a^{2} b^{2} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{4 A a \,b^{3} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+4 B a \,b^{3} x +\frac{4 B a \,b^{3} c}{d}+A \,b^{4} x +\frac{A \,b^{4} c}{d}+\frac{B \,b^{4} \sin \left(d x +c \right)}{d}"," ",0,"2/3/d*A*a^4*tan(d*x+c)+1/3/d*A*a^4*tan(d*x+c)*sec(d*x+c)^2+1/2/d*a^4*B*sec(d*x+c)*tan(d*x+c)+1/2/d*a^4*B*ln(sec(d*x+c)+tan(d*x+c))+2/d*A*a^3*b*sec(d*x+c)*tan(d*x+c)+2/d*A*a^3*b*ln(sec(d*x+c)+tan(d*x+c))+4/d*B*a^3*b*tan(d*x+c)+6/d*A*a^2*b^2*tan(d*x+c)+6/d*B*a^2*b^2*ln(sec(d*x+c)+tan(d*x+c))+4/d*A*a*b^3*ln(sec(d*x+c)+tan(d*x+c))+4*B*a*b^3*x+4/d*B*a*b^3*c+A*b^4*x+1/d*A*b^4*c+1/d*B*b^4*sin(d*x+c)","A"
247,1,338,206,0.160000," ","int((a+b*cos(d*x+c))^4*(A+B*cos(d*x+c))*sec(d*x+c)^5,x)","\frac{A \,a^{4} \tan \left(d x +c \right) \left(\sec^{3}\left(d x +c \right)\right)}{4 d}+\frac{3 A \,a^{4} \sec \left(d x +c \right) \tan \left(d x +c \right)}{8 d}+\frac{3 A \,a^{4} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}+\frac{2 a^{4} B \tan \left(d x +c \right)}{3 d}+\frac{a^{4} B \tan \left(d x +c \right) \left(\sec^{2}\left(d x +c \right)\right)}{3 d}+\frac{8 A \,a^{3} b \tan \left(d x +c \right)}{3 d}+\frac{4 A \,a^{3} b \tan \left(d x +c \right) \left(\sec^{2}\left(d x +c \right)\right)}{3 d}+\frac{2 B \,a^{3} b \tan \left(d x +c \right) \sec \left(d x +c \right)}{d}+\frac{2 B \,a^{3} b \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{3 A \,a^{2} b^{2} \tan \left(d x +c \right) \sec \left(d x +c \right)}{d}+\frac{3 A \,a^{2} b^{2} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{6 B \,a^{2} b^{2} \tan \left(d x +c \right)}{d}+\frac{4 A a \,b^{3} \tan \left(d x +c \right)}{d}+\frac{4 B a \,b^{3} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{A \,b^{4} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+b^{4} B x +\frac{B \,b^{4} c}{d}"," ",0,"1/4/d*A*a^4*tan(d*x+c)*sec(d*x+c)^3+3/8/d*A*a^4*sec(d*x+c)*tan(d*x+c)+3/8/d*A*a^4*ln(sec(d*x+c)+tan(d*x+c))+2/3/d*a^4*B*tan(d*x+c)+1/3/d*a^4*B*tan(d*x+c)*sec(d*x+c)^2+8/3/d*A*a^3*b*tan(d*x+c)+4/3/d*A*a^3*b*tan(d*x+c)*sec(d*x+c)^2+2/d*B*a^3*b*tan(d*x+c)*sec(d*x+c)+2/d*B*a^3*b*ln(sec(d*x+c)+tan(d*x+c))+3/d*A*a^2*b^2*tan(d*x+c)*sec(d*x+c)+3/d*A*a^2*b^2*ln(sec(d*x+c)+tan(d*x+c))+6/d*B*a^2*b^2*tan(d*x+c)+4/d*A*a*b^3*tan(d*x+c)+4/d*B*a*b^3*ln(sec(d*x+c)+tan(d*x+c))+1/d*A*b^4*ln(sec(d*x+c)+tan(d*x+c))+b^4*B*x+1/d*B*b^4*c","A"
248,1,431,255,0.150000," ","int((a+b*cos(d*x+c))^4*(A+B*cos(d*x+c))*sec(d*x+c)^6,x)","\frac{8 A \,a^{4} \tan \left(d x +c \right)}{15 d}+\frac{A \,a^{4} \tan \left(d x +c \right) \left(\sec^{4}\left(d x +c \right)\right)}{5 d}+\frac{4 A \,a^{4} \tan \left(d x +c \right) \left(\sec^{2}\left(d x +c \right)\right)}{15 d}+\frac{a^{4} B \tan \left(d x +c \right) \left(\sec^{3}\left(d x +c \right)\right)}{4 d}+\frac{3 a^{4} B \sec \left(d x +c \right) \tan \left(d x +c \right)}{8 d}+\frac{3 a^{4} B \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}+\frac{A \,a^{3} b \tan \left(d x +c \right) \left(\sec^{3}\left(d x +c \right)\right)}{d}+\frac{3 A \,a^{3} b \sec \left(d x +c \right) \tan \left(d x +c \right)}{2 d}+\frac{3 A \,a^{3} b \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}+\frac{8 B \,a^{3} b \tan \left(d x +c \right)}{3 d}+\frac{4 B \,a^{3} b \tan \left(d x +c \right) \left(\sec^{2}\left(d x +c \right)\right)}{3 d}+\frac{4 A \,a^{2} b^{2} \tan \left(d x +c \right)}{d}+\frac{2 A \,a^{2} b^{2} \tan \left(d x +c \right) \left(\sec^{2}\left(d x +c \right)\right)}{d}+\frac{3 B \,a^{2} b^{2} \tan \left(d x +c \right) \sec \left(d x +c \right)}{d}+\frac{3 B \,a^{2} b^{2} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{2 A a \,b^{3} \tan \left(d x +c \right) \sec \left(d x +c \right)}{d}+\frac{2 A a \,b^{3} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{4 B a \,b^{3} \tan \left(d x +c \right)}{d}+\frac{A \,b^{4} \tan \left(d x +c \right)}{d}+\frac{B \,b^{4} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}"," ",0,"8/15/d*A*a^4*tan(d*x+c)+1/5/d*A*a^4*tan(d*x+c)*sec(d*x+c)^4+4/15/d*A*a^4*tan(d*x+c)*sec(d*x+c)^2+1/4/d*a^4*B*tan(d*x+c)*sec(d*x+c)^3+3/8/d*a^4*B*sec(d*x+c)*tan(d*x+c)+3/8/d*a^4*B*ln(sec(d*x+c)+tan(d*x+c))+1/d*A*a^3*b*tan(d*x+c)*sec(d*x+c)^3+3/2/d*A*a^3*b*sec(d*x+c)*tan(d*x+c)+3/2/d*A*a^3*b*ln(sec(d*x+c)+tan(d*x+c))+8/3/d*B*a^3*b*tan(d*x+c)+4/3/d*B*a^3*b*tan(d*x+c)*sec(d*x+c)^2+4/d*A*a^2*b^2*tan(d*x+c)+2/d*A*a^2*b^2*tan(d*x+c)*sec(d*x+c)^2+3/d*B*a^2*b^2*tan(d*x+c)*sec(d*x+c)+3/d*B*a^2*b^2*ln(sec(d*x+c)+tan(d*x+c))+2/d*A*a*b^3*tan(d*x+c)*sec(d*x+c)+2/d*A*a*b^3*ln(sec(d*x+c)+tan(d*x+c))+4/d*B*a*b^3*tan(d*x+c)+1/d*A*b^4*tan(d*x+c)+1/d*B*b^4*ln(sec(d*x+c)+tan(d*x+c))","A"
249,1,550,310,0.161000," ","int((a+b*cos(d*x+c))^4*(A+B*cos(d*x+c))*sec(d*x+c)^7,x)","\frac{A \,b^{4} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}+\frac{4 A \,a^{3} b \tan \left(d x +c \right) \left(\sec^{4}\left(d x +c \right)\right)}{5 d}+\frac{2 B a \,b^{3} \tan \left(d x +c \right) \sec \left(d x +c \right)}{d}+\frac{2 B \,a^{2} b^{2} \tan \left(d x +c \right) \left(\sec^{2}\left(d x +c \right)\right)}{d}+\frac{4 A a \,b^{3} \tan \left(d x +c \right) \left(\sec^{2}\left(d x +c \right)\right)}{3 d}+\frac{B \,a^{3} b \tan \left(d x +c \right) \left(\sec^{3}\left(d x +c \right)\right)}{d}+\frac{B \,b^{4} \tan \left(d x +c \right)}{d}+\frac{3 A \,a^{2} b^{2} \tan \left(d x +c \right) \left(\sec^{3}\left(d x +c \right)\right)}{2 d}+\frac{8 a^{4} B \tan \left(d x +c \right)}{15 d}+\frac{A \,b^{4} \tan \left(d x +c \right) \sec \left(d x +c \right)}{2 d}+\frac{5 A \,a^{4} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{16 d}+\frac{A \,a^{4} \tan \left(d x +c \right) \left(\sec^{5}\left(d x +c \right)\right)}{6 d}+\frac{a^{4} B \tan \left(d x +c \right) \left(\sec^{4}\left(d x +c \right)\right)}{5 d}+\frac{5 A \,a^{4} \tan \left(d x +c \right) \left(\sec^{3}\left(d x +c \right)\right)}{24 d}+\frac{4 a^{4} B \tan \left(d x +c \right) \left(\sec^{2}\left(d x +c \right)\right)}{15 d}+\frac{32 A \,a^{3} b \tan \left(d x +c \right)}{15 d}+\frac{3 B \,a^{3} b \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}+\frac{9 A \,a^{2} b^{2} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{4 d}+\frac{3 B \,a^{3} b \tan \left(d x +c \right) \sec \left(d x +c \right)}{2 d}+\frac{9 A \,a^{2} b^{2} \tan \left(d x +c \right) \sec \left(d x +c \right)}{4 d}+\frac{16 A \,a^{3} b \tan \left(d x +c \right) \left(\sec^{2}\left(d x +c \right)\right)}{15 d}+\frac{5 A \,a^{4} \sec \left(d x +c \right) \tan \left(d x +c \right)}{16 d}+\frac{4 B \,a^{2} b^{2} \tan \left(d x +c \right)}{d}+\frac{8 A a \,b^{3} \tan \left(d x +c \right)}{3 d}+\frac{2 B a \,b^{3} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}"," ",0,"1/2/d*A*b^4*ln(sec(d*x+c)+tan(d*x+c))+3/2/d*A*a^2*b^2*tan(d*x+c)*sec(d*x+c)^3+2/d*B*a*b^3*tan(d*x+c)*sec(d*x+c)+1/d*B*b^4*tan(d*x+c)+8/15/d*a^4*B*tan(d*x+c)+1/2/d*A*b^4*tan(d*x+c)*sec(d*x+c)+1/6/d*A*a^4*tan(d*x+c)*sec(d*x+c)^5+1/5/d*a^4*B*tan(d*x+c)*sec(d*x+c)^4+4/5/d*A*a^3*b*tan(d*x+c)*sec(d*x+c)^4+2/d*B*a^2*b^2*tan(d*x+c)*sec(d*x+c)^2+4/3/d*A*a*b^3*tan(d*x+c)*sec(d*x+c)^2+5/16/d*A*a^4*ln(sec(d*x+c)+tan(d*x+c))+1/d*B*a^3*b*tan(d*x+c)*sec(d*x+c)^3+32/15/d*A*a^3*b*tan(d*x+c)+3/2/d*B*a^3*b*ln(sec(d*x+c)+tan(d*x+c))+9/4/d*A*a^2*b^2*ln(sec(d*x+c)+tan(d*x+c))+5/24/d*A*a^4*tan(d*x+c)*sec(d*x+c)^3+4/15/d*a^4*B*tan(d*x+c)*sec(d*x+c)^2+16/15/d*A*a^3*b*tan(d*x+c)*sec(d*x+c)^2+3/2/d*B*a^3*b*tan(d*x+c)*sec(d*x+c)+9/4/d*A*a^2*b^2*tan(d*x+c)*sec(d*x+c)+5/16/d*A*a^4*sec(d*x+c)*tan(d*x+c)+4/d*B*a^2*b^2*tan(d*x+c)+8/3/d*A*a*b^3*tan(d*x+c)+2/d*B*a*b^3*ln(sec(d*x+c)+tan(d*x+c))","A"
250,1,641,161,0.087000," ","int(cos(d*x+c)^3*(A+B*cos(d*x+c))/(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) A}{d \,b^{3} \sqrt{\left(a -b \right) \left(a +b \right)}}+\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) B}{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 a}{d \,b^{2} \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 \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^{2} B}{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) B 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) B}{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 a}{d \,b^{2} \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} B}{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) B}{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 a}{d \,b^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}+\frac{2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) a^{2} B}{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) B}{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 \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}-\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) B 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 \,a^{2}}{d \,b^{3}}+\frac{\arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{d b}-\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{3} B}{d \,b^{4}}-\frac{\arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) B a}{d \,b^{2}}"," ",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))*A+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))*B-2/d/b^2/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)^5*A*a-1/d/b/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)^5*A+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*B+1/d/b^2/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)^5*B*a+2/d/b/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)^5*B-4/d/b^2/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)^3*A*a+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*B+4/3/d/b/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)^3*B-2/d/b^2/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)*A*a+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*B+2/d/b/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)*B+1/d/b/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)*A-1/d/b^2/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)*B*a+2/d/b^3*arctan(tan(1/2*d*x+1/2*c))*A*a^2+1/d/b*arctan(tan(1/2*d*x+1/2*c))*A-2/d/b^4*arctan(tan(1/2*d*x+1/2*c))*a^3*B-1/d/b^2*arctan(tan(1/2*d*x+1/2*c))*B*a","B"
251,1,367,121,0.077000," ","int(cos(d*x+c)^2*(A+B*cos(d*x+c))/(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) A}{d \,b^{2} \sqrt{\left(a -b \right) \left(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) B}{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 \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}-\frac{2 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) B a}{d \,b^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}-\frac{\left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) B}{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 \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}-\frac{2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) B 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) B}{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 a}{d \,b^{2}}+\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{2} B}{d \,b^{3}}+\frac{\arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) B}{d b}"," ",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))*A-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))*B+2/d/b/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)^3*A-2/d/b^2/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)^3*B*a-1/d/b/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)^3*B+2/d/b/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)*A-2/d/b^2/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)*B*a+1/d/b/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)*B-2/d/b^2*arctan(tan(1/2*d*x+1/2*c))*A*a+2/d/b^3*arctan(tan(1/2*d*x+1/2*c))*a^2*B+1/d/b*arctan(tan(1/2*d*x+1/2*c))*B","B"
252,1,172,80,0.076000," ","int(cos(d*x+c)*(A+B*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) A}{d b \sqrt{\left(a -b \right) \left(a +b \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) B}{d \,b^{2} \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{2 B \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}-\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) B a}{d \,b^{2}}"," ",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))*A+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))*B+2/d/b*B*tan(1/2*d*x+1/2*c)/(1+tan(1/2*d*x+1/2*c)^2)+2/d/b*arctan(tan(1/2*d*x+1/2*c))*A-2/d/b^2*arctan(tan(1/2*d*x+1/2*c))*B*a","B"
253,1,113,58,0.061000," ","int((A+B*cos(d*x+c))/(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) A}{d \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) a B}{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) B}{d b}"," ",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-2/d/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*B+2/d/b*arctan(tan(1/2*d*x+1/2*c))*B","A"
254,1,135,67,0.122000," ","int((A+B*cos(d*x+c))*sec(d*x+c)/(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) A b}{d a \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}{d \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{A \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}{a d}+\frac{A \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{a d}"," ",0,"-2/d/a/((a-b)*(a+b))^(1/2)*arctan(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))*A*b+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))*B-1/a/d*A*ln(tan(1/2*d*x+1/2*c)-1)+1/a/d*A*ln(tan(1/2*d*x+1/2*c)+1)","A"
255,1,228,90,0.148000," ","int((A+B*cos(d*x+c))*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) A}{d \,a^{2} \sqrt{\left(a -b \right) \left(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) B}{d a \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{A}{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 b}{d \,a^{2}}-\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right) B}{a d}-\frac{A}{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 b}{d \,a^{2}}+\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right) B}{a d}"," ",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))*A-2/d*b/a/((a-b)*(a+b))^(1/2)*arctan(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))*B-1/a/d*A/(tan(1/2*d*x+1/2*c)-1)+1/d/a^2*ln(tan(1/2*d*x+1/2*c)-1)*A*b-1/a/d*ln(tan(1/2*d*x+1/2*c)-1)*B-1/a/d*A/(tan(1/2*d*x+1/2*c)+1)-1/d/a^2*ln(tan(1/2*d*x+1/2*c)+1)*A*b+1/a/d*ln(tan(1/2*d*x+1/2*c)+1)*B","B"
256,1,410,130,0.158000," ","int((A+B*cos(d*x+c))*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) A}{d \,a^{3} \sqrt{\left(a -b \right) \left(a +b \right)}}+\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) B}{d \,a^{2} \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{A}{2 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}+\frac{A}{2 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{A b}{d \,a^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{B}{a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{A \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}{2 a d}-\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right) A \,b^{2}}{d \,a^{3}}+\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right) B b}{d \,a^{2}}-\frac{A}{2 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}+\frac{A}{2 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}+\frac{A b}{d \,a^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}-\frac{B}{a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}+\frac{A \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{2 a d}+\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right) A \,b^{2}}{d \,a^{3}}-\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right) B b}{d \,a^{2}}"," ",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))*A+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))*B+1/2/a/d*A/(tan(1/2*d*x+1/2*c)-1)^2+1/2/a/d*A/(tan(1/2*d*x+1/2*c)-1)+1/d/a^2/(tan(1/2*d*x+1/2*c)-1)*A*b-1/a/d/(tan(1/2*d*x+1/2*c)-1)*B-1/2/a/d*A*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*b^2+1/d/a^2*ln(tan(1/2*d*x+1/2*c)-1)*B*b-1/2/a/d*A/(tan(1/2*d*x+1/2*c)+1)^2+1/2/a/d*A/(tan(1/2*d*x+1/2*c)+1)+1/d/a^2/(tan(1/2*d*x+1/2*c)+1)*A*b-1/a/d/(tan(1/2*d*x+1/2*c)+1)*B+1/2/a/d*A*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*b^2-1/d/a^2*ln(tan(1/2*d*x+1/2*c)+1)*B*b","B"
257,1,688,170,0.175000," ","int((A+B*cos(d*x+c))*sec(d*x+c)^4/(a+b*cos(d*x+c)),x)","\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right) A \,b^{3}}{d \,a^{4}}-\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right) B \,b^{2}}{d \,a^{3}}-\frac{A \,b^{2}}{d \,a^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{B b}{d \,a^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{A b}{2 d \,a^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}-\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right) A \,b^{3}}{d \,a^{4}}+\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right) B \,b^{2}}{d \,a^{3}}-\frac{A}{3 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{3}}+\frac{B}{2 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}-\frac{A}{3 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}-\frac{B}{2 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}+\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right) A b}{2 d \,a^{2}}-\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right) B}{2 a d}-\frac{A}{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) B}{2 a d}-\frac{A}{a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{A b}{2 d \,a^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}-\frac{A \,b^{2}}{d \,a^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}+\frac{B b}{d \,a^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}+\frac{B}{2 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{A}{2 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}+\frac{B}{2 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}-\frac{A}{2 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}-\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right) A b}{2 d \,a^{2}}-\frac{A b}{2 d \,a^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}-\frac{A b}{2 d \,a^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\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) A}{d \,a^{4} \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) B}{d \,a^{3} \sqrt{\left(a -b \right) \left(a +b \right)}}"," ",0,"1/d/a^4*ln(tan(1/2*d*x+1/2*c)-1)*A*b^3-1/d/a^3*ln(tan(1/2*d*x+1/2*c)-1)*B*b^2-1/d/a^3/(tan(1/2*d*x+1/2*c)-1)*A*b^2+1/d/a^2/(tan(1/2*d*x+1/2*c)-1)*B*b+1/2/d/a^2/(tan(1/2*d*x+1/2*c)+1)^2*A*b-1/d/a^4*ln(tan(1/2*d*x+1/2*c)+1)*A*b^3+1/d/a^3*ln(tan(1/2*d*x+1/2*c)+1)*B*b^2-1/3/a/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*B-1/3/a/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*B+1/2/d/a^2*ln(tan(1/2*d*x+1/2*c)-1)*A*b-1/2/a/d*ln(tan(1/2*d*x+1/2*c)-1)*B-1/a/d*A/(tan(1/2*d*x+1/2*c)+1)+1/2/a/d*ln(tan(1/2*d*x+1/2*c)+1)*B-1/a/d*A/(tan(1/2*d*x+1/2*c)-1)-1/2/d/a^2/(tan(1/2*d*x+1/2*c)-1)^2*A*b-1/d/a^3/(tan(1/2*d*x+1/2*c)+1)*A*b^2+1/d/a^2/(tan(1/2*d*x+1/2*c)+1)*B*b+1/2/a/d/(tan(1/2*d*x+1/2*c)-1)*B+1/2/a/d*A/(tan(1/2*d*x+1/2*c)+1)^2+1/2/a/d/(tan(1/2*d*x+1/2*c)+1)*B-1/2/a/d*A/(tan(1/2*d*x+1/2*c)-1)^2-1/2/d/a^2*ln(tan(1/2*d*x+1/2*c)+1)*A*b-1/2/d/a^2/(tan(1/2*d*x+1/2*c)+1)*A*b-1/2/d/a^2/(tan(1/2*d*x+1/2*c)-1)*A*b+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))*A-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))*B","B"
258,1,643,250,0.090000," ","int(cos(d*x+c)^3*(A+B*cos(d*x+c))/(a+b*cos(d*x+c))^2,x)","\frac{2 a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right) A}{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{2 a^{4} \tan \left(\frac{d x}{2}+\frac{c}{2}\right) B}{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{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) A}{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) A}{d b \left(a -b \right) \left(a +b \right) \sqrt{\left(a -b \right) \left(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) B}{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) B}{d \,b^{2} \left(a -b \right) \left(a +b \right) \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{4 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) B a}{d \,b^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}-\frac{\left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) B}{d \,b^{2} \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{4 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) B 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) B}{d \,b^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}-\frac{4 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) A a}{d \,b^{3}}+\frac{6 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{2} B}{d \,b^{4}}+\frac{\arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) B}{d \,b^{2}}"," ",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)*A-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)*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))*A-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))*A-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))*B+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))*B+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-4/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)^3*B*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*B+2/d/b^2/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)*A-4/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)*B*a+1/d/b^2/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)*B-4/d/b^3*arctan(tan(1/2*d*x+1/2*c))*A*a+6/d/b^4*arctan(tan(1/2*d*x+1/2*c))*a^2*B+1/d/b^2*arctan(tan(1/2*d*x+1/2*c))*B","B"
259,1,445,146,0.095000," ","int(cos(d*x+c)^2*(A+B*cos(d*x+c))/(a+b*cos(d*x+c))^2,x)","-\frac{2 a^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right) A}{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} \tan \left(\frac{d x}{2}+\frac{c}{2}\right) B}{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{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) A}{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) A}{d \left(a -b \right) \left(a +b \right) \sqrt{\left(a -b \right) \left(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) B}{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) B}{d b \left(a -b \right) \left(a +b \right) \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{2 B \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{2 A \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,b^{2}}-\frac{4 B \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) a}{d \,b^{3}}"," ",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)*A+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)*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))*A+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))*A+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))*B-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))*B+2/d/b^2*B*tan(1/2*d*x+1/2*c)/(1+tan(1/2*d*x+1/2*c)^2)+2/d/b^2*A*arctan(tan(1/2*d*x+1/2*c))-4/d/b^3*B*arctan(tan(1/2*d*x+1/2*c))*a","B"
260,1,320,113,0.081000," ","int(cos(d*x+c)*(A+B*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) A}{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^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right) B}{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 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) A}{d \left(a -b \right) \left(a +b \right) \sqrt{\left(a -b \right) \left(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) B}{d \,b^{2} \left(a -b \right) \left(a +b \right) \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{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) B a}{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) B}{d \,b^{2}}"," ",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)*A-2/d/b*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)*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-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))*B+4/d/(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))*B*a+2/d/b^2*arctan(tan(1/2*d*x+1/2*c))*B","B"
261,1,234,91,0.071000," ","int((A+B*cos(d*x+c))/(a+b*cos(d*x+c))^2,x)","-\frac{2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) A b}{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 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) a B}{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) A}{d \left(a -b \right) \left(a +b \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 b}{d \left(a -b \right) \left(a +b \right) \sqrt{\left(a -b \right) \left(a +b \right)}}"," ",0,"-2/d/(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)*A*b+2/d/(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)*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-2/d/(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))*B*b","B"
262,1,342,124,0.143000," ","int((A+B*cos(d*x+c))*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) A}{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{2 b \tan \left(\frac{d x}{2}+\frac{c}{2}\right) B}{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{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) A}{d \left(a -b \right) \left(a +b \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) A \,b^{3}}{d \,a^{2} \left(a -b \right) \left(a +b \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 a}{d \left(a -b \right) \left(a +b \right) \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{A \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}{d \,a^{2}}+\frac{A \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{d \,a^{2}}"," ",0,"2/d/a*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)*A-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)*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))*A+2/d/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))*A*b^3+2/d/(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))*B*a-1/d/a^2*A*ln(tan(1/2*d*x+1/2*c)-1)+1/d/a^2*A*ln(tan(1/2*d*x+1/2*c)+1)","B"
263,1,502,180,0.177000," ","int((A+B*cos(d*x+c))*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) A}{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{2 b^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right) B}{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{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) A}{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) A}{d \,a^{3} \left(a -b \right) \left(a +b \right) \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{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) B b}{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) B}{d \,a^{2} \left(a -b \right) \left(a +b \right) \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{A}{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) A b}{d \,a^{3}}-\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right) B}{d \,a^{2}}-\frac{A}{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) A b}{d \,a^{3}}+\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right) B}{d \,a^{2}}"," ",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)*A+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)*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))*A-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))*A-4/d/(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))*B*b+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))*B-1/d/a^2*A/(tan(1/2*d*x+1/2*c)-1)+2/d/a^3*ln(tan(1/2*d*x+1/2*c)-1)*A*b-1/d/a^2*ln(tan(1/2*d*x+1/2*c)-1)*B-1/d/a^2*A/(tan(1/2*d*x+1/2*c)+1)-2/d/a^3*ln(tan(1/2*d*x+1/2*c)+1)*A*b+1/d/a^2*ln(tan(1/2*d*x+1/2*c)+1)*B","B"
264,1,690,257,0.192000," ","int((A+B*cos(d*x+c))*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) A}{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{2 b^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right) B}{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{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) A \,b^{3}}{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) A}{d \,a^{4} \left(a -b \right) \left(a +b \right) \sqrt{\left(a -b \right) \left(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) B}{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) B}{d \,a^{3} \left(a -b \right) \left(a +b \right) \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{A}{2 d \,a^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}+\frac{A}{2 d \,a^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{2 A b}{d \,a^{3} \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{A \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) A \,b^{2}}{d \,a^{4}}+\frac{2 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right) B b}{d \,a^{3}}-\frac{A}{2 d \,a^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}+\frac{A}{2 d \,a^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}+\frac{2 A b}{d \,a^{3} \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{A \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) A \,b^{2}}{d \,a^{4}}-\frac{2 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right) B b}{d \,a^{3}}"," ",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)*A-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)*B-8/d/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))*A*b^3+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))*A+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))*B-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))*B+1/2/d/a^2*A/(tan(1/2*d*x+1/2*c)-1)^2+1/2/d/a^2*A/(tan(1/2*d*x+1/2*c)-1)+2/d/a^3/(tan(1/2*d*x+1/2*c)-1)*A*b-1/d/a^2/(tan(1/2*d*x+1/2*c)-1)*B-1/2/d/a^2*A*ln(tan(1/2*d*x+1/2*c)-1)-3/d/a^4*ln(tan(1/2*d*x+1/2*c)-1)*A*b^2+2/d/a^3*ln(tan(1/2*d*x+1/2*c)-1)*B*b-1/2/d/a^2*A/(tan(1/2*d*x+1/2*c)+1)^2+1/2/d/a^2*A/(tan(1/2*d*x+1/2*c)+1)+2/d/a^3/(tan(1/2*d*x+1/2*c)+1)*A*b-1/d/a^2/(tan(1/2*d*x+1/2*c)+1)*B+1/2/d/a^2*A*ln(tan(1/2*d*x+1/2*c)+1)+3/d/a^4*ln(tan(1/2*d*x+1/2*c)+1)*A*b^2-2/d/a^3*ln(tan(1/2*d*x+1/2*c)+1)*B*b","B"
265,1,1504,379,0.097000," ","int(cos(d*x+c)^4*(A+B*cos(d*x+c))/(a+b*cos(d*x+c))^3,x)","-\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) B}{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^{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) A}{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) A}{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^{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) B}{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) B}{d \,b^{3} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right) \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{\arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) B}{d \,b^{3}}+\frac{4 a^{5} \tan \left(\frac{d x}{2}+\frac{c}{2}\right) A}{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 -b \right)^{2}}+\frac{a^{4} \tan \left(\frac{d x}{2}+\frac{c}{2}\right) A}{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 -b \right)^{2}}+\frac{4 a^{5} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{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) A}{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^{5} \tan \left(\frac{d x}{2}+\frac{c}{2}\right) B}{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 -b \right)^{2}}+\frac{10 a^{4} \tan \left(\frac{d x}{2}+\frac{c}{2}\right) B}{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 -b \right)^{2}}-\frac{8 a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right) A}{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 -b \right)^{2}}-\frac{6 a^{6} \tan \left(\frac{d x}{2}+\frac{c}{2}\right) B}{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 -b \right)^{2}}-\frac{8 a^{3} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{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} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) B}{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) B}{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) B}{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{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) B}{d \,b^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}-\frac{6 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) B a}{d \,b^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}-\frac{6 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) B a}{d \,b^{4} \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 a}{d \,b^{4}}+\frac{12 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{2} B}{d \,b^{5}}+\frac{2 \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{\left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) B}{d \,b^{3} \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^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\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) A}{d \left(a^{4}-2 a^{2} b^{2}+b^{4}\right) \sqrt{\left(a -b \right) \left(a +b \right)}}"," ",0,"-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))*B+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))*A-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))*A-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))*B+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))*B+1/d/b^3*arctan(tan(1/2*d*x+1/2*c))*B+2/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)*A+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-b)^2*tan(1/2*d*x+1/2*c)*A+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-b)^2*tan(1/2*d*x+1/2*c)*A+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*A-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*A-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-b)^2*tan(1/2*d*x+1/2*c)*B+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-b)^2*tan(1/2*d*x+1/2*c)*B-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-b)^2*tan(1/2*d*x+1/2*c)*A-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-b)^2*tan(1/2*d*x+1/2*c)*B-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*A-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*B+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*B+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*B-1/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)^3*B+2/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^3/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)*B-6/d/b^4*arctan(tan(1/2*d*x+1/2*c))*A*a+12/d/b^5*arctan(tan(1/2*d*x+1/2*c))*a^2*B+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))*A-6/d/b^4/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)^3*B*a-6/d/b^4/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)*B*a","B"
266,1,1301,265,0.094000," ","int(cos(d*x+c)^3*(A+B*cos(d*x+c))/(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) A}{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) A}{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) A}{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^{5} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) B}{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) B}{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) B}{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{2 a^{4} \tan \left(\frac{d x}{2}+\frac{c}{2}\right) A}{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 -b \right)^{2}}-\frac{a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right) A}{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 -b \right)^{2}}+\frac{6 a^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right) A}{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 -b \right)^{2}}+\frac{4 a^{5} \tan \left(\frac{d x}{2}+\frac{c}{2}\right) B}{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 -b \right)^{2}}+\frac{a^{4} \tan \left(\frac{d x}{2}+\frac{c}{2}\right) B}{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 -b \right)^{2}}-\frac{8 a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right) B}{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 -b \right)^{2}}-\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) A}{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) A}{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) A}{d \left(a^{4}-2 a^{2} b^{2}+b^{4}\right) \sqrt{\left(a -b \right) \left(a +b \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) B}{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) B}{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) B}{d \left(a^{4}-2 a^{2} b^{2}+b^{4}\right) \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{2 B \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{2 A \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,b^{3}}-\frac{6 B \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) a}{d \,b^{4}}"," ",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*A+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*A+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*A+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*B-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*B-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*B-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-b)^2*tan(1/2*d*x+1/2*c)*A-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-b)^2*tan(1/2*d*x+1/2*c)*A+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-b)^2*tan(1/2*d*x+1/2*c)*A+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-b)^2*tan(1/2*d*x+1/2*c)*B+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-b)^2*tan(1/2*d*x+1/2*c)*B-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-b)^2*tan(1/2*d*x+1/2*c)*B-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))*A+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))*A-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))*A+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))*B-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))*B+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))*B+2/d/b^3*B*tan(1/2*d*x+1/2*c)/(1+tan(1/2*d*x+1/2*c)^2)+2/d/b^3*A*arctan(tan(1/2*d*x+1/2*c))-6/d/b^4*B*arctan(tan(1/2*d*x+1/2*c))*a","B"
267,1,1023,198,0.096000," ","int(cos(d*x+c)^2*(A+B*cos(d*x+c))/(a+b*cos(d*x+c))^3,x)","-\frac{a^{2} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{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 b a \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{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} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) B}{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) B}{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) 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) A}{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 -b \right)^{2}}-\frac{4 b a \tan \left(\frac{d x}{2}+\frac{c}{2}\right) A}{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 -b \right)^{2}}-\frac{2 a^{4} \tan \left(\frac{d x}{2}+\frac{c}{2}\right) B}{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 -b \right)^{2}}-\frac{a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right) B}{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 -b \right)^{2}}+\frac{6 a^{2} \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 -b \right)^{2}}+\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) A}{d \left(a^{4}-2 a^{2} b^{2}+b^{4}\right) \sqrt{\left(a -b \right) \left(a +b \right)}}+\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) A}{d \left(a^{4}-2 a^{2} b^{2}+b^{4}\right) \sqrt{\left(a -b \right) \left(a +b \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) B}{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) B}{d b \left(a^{4}-2 a^{2} b^{2}+b^{4}\right) \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{6 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) B a}{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) B}{d \,b^{3}}"," ",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*A-4/d*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/(a-b)/(a^2+2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3*A-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*B+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*B+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^2/(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-b)^2*tan(1/2*d*x+1/2*c)*A-4/d*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/(a+b)/(a-b)^2*tan(1/2*d*x+1/2*c)*A-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-b)^2*tan(1/2*d*x+1/2*c)*B-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-b)^2*tan(1/2*d*x+1/2*c)*B+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^2/(a+b)/(a-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))*A+2/d*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))*A-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))*B+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))*B-6/d*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*a+2/d/b^3*arctan(tan(1/2*d*x+1/2*c))*B","B"
268,1,886,167,0.079000," ","int(cos(d*x+c)*(A+B*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) A}{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 a \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{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) A \,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{a^{2} \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{4 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) B a 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) a^{2} A}{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) A a 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) A \,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{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) a^{2} 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{4 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) B a 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{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) A}{d \left(a^{4}-2 a^{2} b^{2}+b^{4}\right) \sqrt{\left(a -b \right) \left(a +b \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) B}{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} B}{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*A+1/d*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/(a-b)/(a^2+2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3*A+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*A*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)^2*a^2/(a-b)/(a^2+2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3*B-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-b)/(a^2+2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3*B*a*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)*a^2*A-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)*A*a*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)*A*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)^2/(a+b)/(a^2-2*a*b+b^2)*tan(1/2*d*x+1/2*c)*a^2*B-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+b)/(a^2-2*a*b+b^2)*tan(1/2*d*x+1/2*c)*B*a*b-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))*A+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))*B+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","B"
269,1,886,151,0.070000," ","int((A+B*cos(d*x+c))/(a+b*cos(d*x+c))^3,x)","-\frac{4 b a \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{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) A \,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} \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 a 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} 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{4 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) A a 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) A \,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 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) a^{2} 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 a 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} 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 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) A}{d \left(a^{4}-2 a^{2} b^{2}+b^{4}\right) \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{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) A}{d \left(a^{4}-2 a^{2} b^{2}+b^{4}\right) \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{3 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) B a}{d \left(a^{4}-2 a^{2} b^{2}+b^{4}\right) \sqrt{\left(a -b \right) \left(a +b \right)}}"," ",0,"-4/d*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/(a-b)/(a^2+2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3*A-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*A*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)^2*a^2/(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*a*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*B-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+b)/(a^2-2*a*b+b^2)*tan(1/2*d*x+1/2*c)*A*a*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)*A*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)^2/(a+b)/(a^2-2*a*b+b^2)*tan(1/2*d*x+1/2*c)*a^2*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*a*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*B+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))*A+1/d*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))*A-3/d*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*a","B"
270,1,1045,201,0.156000," ","int((A+B*cos(d*x+c))*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) A \,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) A}{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) A}{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 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) B a 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} 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{6 b^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right) A}{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 -b \right)^{2}}-\frac{b^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right) A}{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 -b \right)^{2}}-\frac{2 b^{4} \tan \left(\frac{d x}{2}+\frac{c}{2}\right) A}{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 -b \right)^{2}}-\frac{4 a b \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 -b \right)^{2}}+\frac{b^{2} \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 -b \right)^{2}}-\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) A}{d \left(a^{4}-2 a^{2} b^{2}+b^{4}\right) \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{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) A \,b^{3}}{d a \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) A \,b^{5}}{d \,a^{3} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right) \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{2 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) B}{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} B}{d \left(a^{4}-2 a^{2} b^{2}+b^{4}\right) \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{A \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}{d \,a^{3}}+\frac{A \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*A*b^2+1/d/a/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b+a+b)^2*b^3/(a-b)/(a^2+2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3*A-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*b^4/(a-b)/(a^2+2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3*A-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-b)/(a^2+2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3*B*a*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*B+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*b^2/(a+b)/(a-b)^2*tan(1/2*d*x+1/2*c)*A-1/d/a/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b+a+b)^2*b^3/(a+b)/(a-b)^2*tan(1/2*d*x+1/2*c)*A-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*b^4/(a+b)/(a-b)^2*tan(1/2*d*x+1/2*c)*A-4/d*a/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b+a+b)^2*b/(a+b)/(a-b)^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*b^2/(a+b)/(a-b)^2*tan(1/2*d*x+1/2*c)*B-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))*A+5/d/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))*A*b^3-2/d/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))*A*b^5+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))*B+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-1/d/a^3*A*ln(tan(1/2*d*x+1/2*c)-1)+1/d/a^3*A*ln(tan(1/2*d*x+1/2*c)+1)","B"
271,1,1358,284,0.183000," ","int((A+B*cos(d*x+c))*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) A}{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) A}{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) A}{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 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{2} 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{b^{3} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) B}{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) B}{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{8 b^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right) A}{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 -b \right)^{2}}+\frac{b^{4} \tan \left(\frac{d x}{2}+\frac{c}{2}\right) A}{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 -b \right)^{2}}+\frac{4 b^{5} \tan \left(\frac{d x}{2}+\frac{c}{2}\right) A}{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 -b \right)^{2}}+\frac{6 b^{2} \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 -b \right)^{2}}-\frac{b^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right) B}{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 -b \right)^{2}}-\frac{2 b^{4} \tan \left(\frac{d x}{2}+\frac{c}{2}\right) B}{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 -b \right)^{2}}+\frac{12 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) A}{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) A}{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) A}{d \,a^{4} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right) \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{6 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) B a}{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) B}{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) B}{d \,a^{3} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right) \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{A}{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) A b}{d \,a^{4}}-\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right) B}{d \,a^{3}}-\frac{A}{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) A b}{d \,a^{4}}+\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right) B}{d \,a^{3}}"," ",0,"-8/d/a/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b+a+b)^2*b^3/(a-b)/(a^2+2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3*A-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*b^4/(a-b)/(a^2+2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3*A+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*A+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*B+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*B-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*B-8/d/a/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b+a+b)^2*b^3/(a+b)/(a-b)^2*tan(1/2*d*x+1/2*c)*A+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*b^4/(a+b)/(a-b)^2*tan(1/2*d*x+1/2*c)*A+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-b)^2*tan(1/2*d*x+1/2*c)*A+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*b^2/(a+b)/(a-b)^2*tan(1/2*d*x+1/2*c)*B-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-b)^2*tan(1/2*d*x+1/2*c)*B-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-b)^2*tan(1/2*d*x+1/2*c)*B+12/d*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))*A-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))*A+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))*A-6/d*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*a+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))*B-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))*B-1/d/a^3*A/(tan(1/2*d*x+1/2*c)-1)+3/d/a^4*ln(tan(1/2*d*x+1/2*c)-1)*A*b-1/d/a^3*ln(tan(1/2*d*x+1/2*c)-1)*B-1/d/a^3*A/(tan(1/2*d*x+1/2*c)+1)-3/d/a^4*ln(tan(1/2*d*x+1/2*c)+1)*A*b+1/d/a^3*ln(tan(1/2*d*x+1/2*c)+1)*B","B"
272,1,1551,383,0.198000," ","int((A+B*cos(d*x+c))*sec(d*x+c)^3/(a+b*cos(d*x+c))^3,x)","-\frac{B}{d \,a^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{A}{2 d \,a^{3} \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)}-\frac{A}{2 d \,a^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}-\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) A}{d \,a^{5} \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) B}{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) B}{d \,a^{4} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right) \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{3 A b}{d \,a^{4} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{4 b^{5} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) B}{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) A}{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 -b \right)^{2}}+\frac{4 b^{5} \tan \left(\frac{d x}{2}+\frac{c}{2}\right) B}{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 -b \right)^{2}}-\frac{6 b^{6} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{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 \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) A \,b^{3}}{d a \left(a^{4}-2 a^{2} b^{2}+b^{4}\right) \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{29 \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) A \,b^{5}}{d \,a^{3} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right) \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{10 b^{4} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{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{10 b^{4} \tan \left(\frac{d x}{2}+\frac{c}{2}\right) A}{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 -b \right)^{2}}-\frac{8 b^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right) B}{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 -b \right)^{2}}+\frac{b^{4} \tan \left(\frac{d x}{2}+\frac{c}{2}\right) B}{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 -b \right)^{2}}+\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} B}{d \left(a^{4}-2 a^{2} b^{2}+b^{4}\right) \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{b^{5} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{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} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) B}{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) B}{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) A}{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 -b \right)^{2}}+\frac{A \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{2 d \,a^{3}}-\frac{A \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) A \,b^{2}}{d \,a^{5}}+\frac{3 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right) B b}{d \,a^{4}}+\frac{3 A b}{d \,a^{4} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}+\frac{6 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right) A \,b^{2}}{d \,a^{5}}-\frac{3 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right) B b}{d \,a^{4}}+\frac{A}{2 d \,a^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{A}{2 d \,a^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}"," ",0,"-1/d/a^3/(tan(1/2*d*x+1/2*c)-1)*B+1/2/d/a^3*A/(tan(1/2*d*x+1/2*c)-1)^2-1/d/a^3/(tan(1/2*d*x+1/2*c)+1)*B-1/2/d/a^3*A/(tan(1/2*d*x+1/2*c)+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))*A-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))*B+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))*B+3/d/a^4/(tan(1/2*d*x+1/2*c)-1)*A*b+10/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*b^4/(a-b)/(a^2+2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3*A+10/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*b^4/(a+b)/(a-b)^2*tan(1/2*d*x+1/2*c)*A-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*B-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*B+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*A-20/d/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))*A*b^3+29/d/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))*A*b^5+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*B-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-b)^2*tan(1/2*d*x+1/2*c)*A+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-b)^2*tan(1/2*d*x+1/2*c)*B-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*A-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-b)^2*tan(1/2*d*x+1/2*c)*B+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-b)^2*tan(1/2*d*x+1/2*c)*B-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-b)^2*tan(1/2*d*x+1/2*c)*A+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*B+1/2/d/a^3*A*ln(tan(1/2*d*x+1/2*c)+1)-1/2/d/a^3*A*ln(tan(1/2*d*x+1/2*c)-1)-6/d/a^5*ln(tan(1/2*d*x+1/2*c)-1)*A*b^2+3/d/a^4*ln(tan(1/2*d*x+1/2*c)-1)*B*b+3/d/a^4/(tan(1/2*d*x+1/2*c)+1)*A*b+6/d/a^5*ln(tan(1/2*d*x+1/2*c)+1)*A*b^2-3/d/a^4*ln(tan(1/2*d*x+1/2*c)+1)*B*b+1/2/d/a^3*A/(tan(1/2*d*x+1/2*c)-1)+1/2/d/a^3*A/(tan(1/2*d*x+1/2*c)+1)","B"
273,1,2787,392,0.095000," ","int(cos(d*x+c)^4*(A+B*cos(d*x+c))/(a+b*cos(d*x+c))^4,x)","\text{Expression too large to display}"," ",0,"2/d/b^4*B*tan(1/2*d*x+1/2*c)/(1+tan(1/2*d*x+1/2*c)^2)-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)*A-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*A-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))*A-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*B-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*A+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*A-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)*A+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)*B+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*B+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)*A+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)*B-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)*B-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*B-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)*B+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*B-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*A+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*A-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*A-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)*A+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*A-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*A+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*B-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*B+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))*A+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))*B+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))*A-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))*B+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))*B-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))*B+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)*B+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*B+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)*A+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*B-8/d/b^5*B*arctan(tan(1/2*d*x+1/2*c))*a-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))*A+2/d/b^4*A*arctan(tan(1/2*d*x+1/2*c))","B"
274,1,2158,286,0.096000," ","int(cos(d*x+c)^3*(A+B*cos(d*x+c))/(a+b*cos(d*x+c))^4,x)","\frac{2 B \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,b^{4}}-\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) A}{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 \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 \,a^{3}}{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^{3} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{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 a^{3} \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)^{3} \left(a +b \right) \left(a^{3}-3 a^{2} b +3 b^{2} a -b^{3}\right)}+\frac{2 a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right) A}{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^{5}\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)^{3} \left(a -b \right) \left(a^{3}+3 a^{2} b +3 b^{2} a +b^{3}\right)}+\frac{44 a^{4} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) B}{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{4 a^{6} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) B}{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{6 b^{2} a \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{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{24 b \,a^{2} \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)^{3} \left(a^{2}+2 a b +b^{2}\right) \left(a^{2}-2 a b +b^{2}\right)}-\frac{12 b \,a^{2} \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)^{3} \left(a +b \right) \left(a^{3}-3 a^{2} b +3 b^{2} a -b^{3}\right)}-\frac{12 b \,a^{2} \left(\tan^{5}\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)^{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) B}{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{2 a^{6} \tan \left(\frac{d x}{2}+\frac{c}{2}\right) B}{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) B}{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{a^{5} \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) B}{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) B}{d b \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d 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+b^{3}\right)}+\frac{6 b^{2} a \tan \left(\frac{d x}{2}+\frac{c}{2}\right) A}{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 b^{2} a \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{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} \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{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 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) A \,a^{2}}{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 \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 \,a^{5}}{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 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) B a}{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(\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 \,a^{7}}{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)}}"," ",0,"2/d*B/b^4*arctan(tan(1/2*d*x+1/2*c))-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))*A-8/d/(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*a^3+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*A+6/d*b^2/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b+a+b)^3*a/(a+b)/(a^3-3*a^2*b+3*a*b^2-b^3)*tan(1/2*d*x+1/2*c)*A+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*B-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)*B-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)*B+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*B+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)*B-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)*A+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*A-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*B+12/d*b^2/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b+a+b)^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*A-4/d/b^3/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b+a+b)^3*a^6/(a^2+2*a*b+b^2)/(a^2-2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3*B+6/d*b^2/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b+a+b)^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*A+44/3/d/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^4/(a^2+2*a*b+b^2)/(a^2-2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3*B-24/d*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/(a^2+2*a*b+b^2)/(a^2-2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3*B-12/d*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/(a+b)/(a^3-3*a^2*b+3*a*b^2-b^3)*tan(1/2*d*x+1/2*c)*B-12/d*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/(a-b)/(a^3+3*a^2*b+3*a*b^2+b^3)*tan(1/2*d*x+1/2*c)^5*B+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)*B+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)*A-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*B+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*a^3/(a^2+2*a*b+b^2)/(a^2-2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3*A-3/d*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))*A*a^2+7/d/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*a^5+8/d*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*a-2/d/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))*B*a^7","B"
275,1,1726,259,0.085000," ","int(cos(d*x+c)^2*(A+B*cos(d*x+c))/(a+b*cos(d*x+c))^4,x)","-\frac{a^{3} \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{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) A}{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 b^{2} a \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{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) A \,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} \left(\tan^{5}\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)^{3} \left(a -b \right) \left(a^{3}+3 a^{2} b +3 b^{2} a +b^{3}\right)}+\frac{3 b \,a^{2} \left(\tan^{5}\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)^{3} \left(a -b \right) \left(a^{3}+3 a^{2} b +3 b^{2} a +b^{3}\right)}+\frac{6 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) B a \,b^{2}}{d \left(a \left(\tan^{2}\left(\frac{d 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\left(a^{3}-3 a^{2} b +3 b^{2} a -b^{3}\right)}+\frac{6 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) B a \,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{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) A}{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) A}{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^{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) B}{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(\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^{3} B}{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*A-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*A-2/d*b^2/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b+a+b)^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*A-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*A*b^3+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*B+3/d*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/(a-b)/(a^3+3*a^2*b+3*a*b^2+b^3)*tan(1/2*d*x+1/2*c)^5*B+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-b)/(a^3+3*a^2*b+3*a*b^2+b^3)*tan(1/2*d*x+1/2*c)^5*B*a*b^2-28/3/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*A-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^2-2*a*b+b^2)/(a^2+2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3*A*b^3+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*B+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^2-2*a*b+b^2)/(a^2+2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3*B*a*b^2+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)*A-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)*A+2/d*b^2/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b+a+b)^3*a/(a+b)/(a^3-3*a^2*b+3*a*b^2-b^3)*tan(1/2*d*x+1/2*c)*A-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)*A*b^3+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)*B-3/d*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/(a+b)/(a^3-3*a^2*b+3*a*b^2-b^3)*tan(1/2*d*x+1/2*c)*B+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+b)/(a^3-3*a^2*b+3*a*b^2-b^3)*tan(1/2*d*x+1/2*c)*B*a*b^2+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))*A+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))*A-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))*B-2/d/(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^3*B","B"
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+b^{3}\right)}+\frac{\left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A \,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} \left(\tan^{5}\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)^{3} \left(a -b \right) \left(a^{3}+3 a^{2} b +3 b^{2} a +b^{3}\right)}-\frac{6 b \,a^{2} \left(\tan^{5}\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)^{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 a \,b^{2}}{d \left(a 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\left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) A \,a^{2}}{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) A}{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{\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 \,a^{3}}{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 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) B a}{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*A+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*A+6/d*b^2/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b+a+b)^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*A+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*A*b^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)^5*B-6/d*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/(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/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*a*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*B+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^3/(a^2+2*a*b+b^2)/(a^2-2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3*A+28/3/d*b^2/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b+a+b)^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*A-28/3/d*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/(a^2+2*a*b+b^2)/(a^2-2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3*B-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^2-2*a*b+b^2)/(a^2+2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3*b^3*B+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)*A-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)*A+6/d*b^2/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b+a+b)^3*a/(a+b)/(a^3-3*a^2*b+3*a*b^2-b^3)*tan(1/2*d*x+1/2*c)*A-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)*A*b^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)*B-6/d*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/(a+b)/(a^3-3*a^2*b+3*a*b^2-b^3)*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)^3/(a+b)/(a^3-3*a^2*b+3*a*b^2-b^3)*tan(1/2*d*x+1/2*c)*B*a*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*B-4/d*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))*A*a^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))*A+1/d/(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*a^3+4/d*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*a","B"
277,1,1727,222,0.077000," ","int((A+B*cos(d*x+c))/(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) A}{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 b^{2} a \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{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) A \,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} \left(\tan^{5}\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)^{3} \left(a -b \right) \left(a^{3}+3 a^{2} b +3 b^{2} a +b^{3}\right)}+\frac{2 b \,a^{2} \left(\tan^{5}\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)^{3} \left(a -b \right) \left(a^{3}+3 a^{2} b +3 b^{2} a +b^{3}\right)}+\frac{6 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) B a \,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} 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)^{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) A}{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 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A \,b^{3}}{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 a^{3} \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)^{3} \left(a^{2}+2 a b +b^{2}\right) \left(a^{2}-2 a b +b^{2}\right)}+\frac{28 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) B a \,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{6 a^{2} b \tan \left(\frac{d x}{2}+\frac{c}{2}\right) A}{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 b^{2} a \tan \left(\frac{d x}{2}+\frac{c}{2}\right) A}{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) A \,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} \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)^{3} \left(a +b \right) \left(a^{3}-3 a^{2} b +3 b^{2} a -b^{3}\right)}-\frac{2 b \,a^{2} \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)^{3} \left(a +b \right) \left(a^{3}-3 a^{2} b +3 b^{2} a -b^{3}\right)}+\frac{6 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) B a \,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} 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)^{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) A}{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) A}{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^{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) B}{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{\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^{3} B}{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*A-3/d*b^2/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b+a+b)^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*A-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*A*b^3+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*B+2/d*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/(a-b)/(a^3+3*a^2*b+3*a*b^2+b^3)*tan(1/2*d*x+1/2*c)^5*B+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-b)/(a^3+3*a^2*b+3*a*b^2+b^3)*tan(1/2*d*x+1/2*c)^5*B*a*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*B-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*A-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/(a^2-2*a*b+b^2)/(a^2+2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3*A*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*B+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^2-2*a*b+b^2)/(a^2+2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3*B*a*b^2-6/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)*A+3/d*b^2/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b+a+b)^3*a/(a+b)/(a^3-3*a^2*b+3*a*b^2-b^3)*tan(1/2*d*x+1/2*c)*A-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)*A*b^3+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)*B-2/d*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/(a+b)/(a^3-3*a^2*b+3*a*b^2-b^3)*tan(1/2*d*x+1/2*c)*B+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+b)/(a^3-3*a^2*b+3*a*b^2-b^3)*tan(1/2*d*x+1/2*c)*B*a*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*B+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))*A+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))*A-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))*B-1/d/(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^3*B","B"
278,1,2180,286,0.214000," ","int((A+B*cos(d*x+c))*sec(d*x+c)/(a+b*cos(d*x+c))^4,x)","\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) A}{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(\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 \,a^{3}}{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 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{3} 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^{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) A}{d \,a^{3} \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a +b \right)^{3} \left(a^{2}+2 a b +b^{2}\right) \left(a^{2}-2 a b +b^{2}\right)}+\frac{12 b^{2} a \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{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) A}{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) A}{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) A}{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{44 b^{4} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{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{6 b^{4} \tan \left(\frac{d x}{2}+\frac{c}{2}\right) A}{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) A}{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) A}{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{12 b \,a^{2} \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)^{3} \left(a^{2}+2 a b +b^{2}\right) \left(a^{2}-2 a b +b^{2}\right)}-\frac{6 b \,a^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right) B}{d \left(a \left(\tan^{2}\left(\frac{d 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\,a^{4}}-\frac{A \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}{d \,a^{4}}+\frac{4 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A \,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 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b^{3} 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)^{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) A \,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 \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) A \,b^{7}}{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{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) A \,b^{5}}{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{8 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) A \,a^{2}}{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 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) B a}{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,"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))*A+2/d/(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*a^3-6/d/a/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b+a+b)^3*b^4/(a+b)/(a^3-3*a^2*b+3*a*b^2-b^3)*tan(1/2*d*x+1/2*c)*A+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)^3*b^5/(a+b)/(a^3-3*a^2*b+3*a*b^2-b^3)*tan(1/2*d*x+1/2*c)*A+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*b^6/(a+b)/(a^3-3*a^2*b+3*a*b^2-b^3)*tan(1/2*d*x+1/2*c)*A+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+b)/(a^3-3*a^2*b+3*a*b^2-b^3)*tan(1/2*d*x+1/2*c)*B*a*b^2-3/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-b)/(a^3+3*a^2*b+3*a*b^2+b^3)*tan(1/2*d*x+1/2*c)^5*B*a*b^2+12/d*b^2/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b+a+b)^3*a/(a+b)/(a^3-3*a^2*b+3*a*b^2-b^3)*tan(1/2*d*x+1/2*c)*A-6/d/a/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b+a+b)^3*b^4/(a-b)/(a^3+3*a^2*b+3*a*b^2+b^3)*tan(1/2*d*x+1/2*c)^5*A-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)^3*b^5/(a-b)/(a^3+3*a^2*b+3*a*b^2+b^3)*tan(1/2*d*x+1/2*c)^5*A+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*b^6/(a-b)/(a^3+3*a^2*b+3*a*b^2+b^3)*tan(1/2*d*x+1/2*c)^5*A-44/3/d/a/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b+a+b)^3*b^4/(a^2+2*a*b+b^2)/(a^2-2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3*A+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*b^6/(a^2+2*a*b+b^2)/(a^2-2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3*A+24/d*b^2/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b+a+b)^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*A+12/d*b^2/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b+a+b)^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*A-12/d*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/(a^2+2*a*b+b^2)/(a^2-2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3*B-6/d*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/(a+b)/(a^3-3*a^2*b+3*a*b^2-b^3)*tan(1/2*d*x+1/2*c)*B-6/d*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/(a-b)/(a^3+3*a^2*b+3*a*b^2+b^3)*tan(1/2*d*x+1/2*c)^5*B+1/d/a^4*A*ln(tan(1/2*d*x+1/2*c)+1)-1/d/a^4*A*ln(tan(1/2*d*x+1/2*c)-1)-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*B+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*A*b^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/(a^2-2*a*b+b^2)/(a^2+2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3*b^3*B-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)*A*b^3-2/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*B+2/d/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))*A*b^7-7/d/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))*A*b^5-8/d*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))*A*a^2+3/d*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*a","B"
279,1,2844,403,0.211000," ","int((A+B*cos(d*x+c))*sec(d*x+c)^2/(a+b*cos(d*x+c))^4,x)","\text{output too large to display}"," ",0,"-1/d/a^4*ln(tan(1/2*d*x+1/2*c)-1)*B-1/d/a^4*A/(tan(1/2*d*x+1/2*c)-1)+1/d/a^4*ln(tan(1/2*d*x+1/2*c)+1)*B-1/d/a^4*A/(tan(1/2*d*x+1/2*c)+1)+4/d/a^5*ln(tan(1/2*d*x+1/2*c)-1)*A*b-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)*B-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)*A+5/d/a/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b+a+b)^3*b^4/(a+b)/(a^3-3*a^2*b+3*a*b^2-b^3)*tan(1/2*d*x+1/2*c)*A+18/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)^3*b^5/(a+b)/(a^3-3*a^2*b+3*a*b^2-b^3)*tan(1/2*d*x+1/2*c)*A-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*b^6/(a+b)/(a^3-3*a^2*b+3*a*b^2-b^3)*tan(1/2*d*x+1/2*c)*A-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*A-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*A+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+b)/(a^3-3*a^2*b+3*a*b^2-b^3)*tan(1/2*d*x+1/2*c)*B*a*b^2+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-b)/(a^3+3*a^2*b+3*a*b^2+b^3)*tan(1/2*d*x+1/2*c)^5*B*a*b^2+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^2-2*a*b+b^2)/(a^2+2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3*B*a*b^2-5/d/a/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b+a+b)^3*b^4/(a-b)/(a^3+3*a^2*b+3*a*b^2+b^3)*tan(1/2*d*x+1/2*c)^5*A+18/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)^3*b^5/(a-b)/(a^3+3*a^2*b+3*a*b^2+b^3)*tan(1/2*d*x+1/2*c)^5*A+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*b^6/(a-b)/(a^3+3*a^2*b+3*a*b^2+b^3)*tan(1/2*d*x+1/2*c)^5*A+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)*B-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*B-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*B+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*B+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*A-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*B+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*B+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)*B-4/d/a^5*ln(tan(1/2*d*x+1/2*c)+1)*A*b+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))*A-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))*B+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*B-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*A*b^3-40/d/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b+a+b)^3/(a^2-2*a*b+b^2)/(a^2+2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3*A*b^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)*A*b^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/(a+b)/(a^3-3*a^2*b+3*a*b^2-b^3)*tan(1/2*d*x+1/2*c)*b^3*B+8/d/(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^3*B-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))*A-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))*A+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))*A-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))*B+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))*B","B"
280,1,3042,526,0.255000," ","int((A+B*cos(d*x+c))*sec(d*x+c)^3/(a+b*cos(d*x+c))^4,x)","\text{output too large to display}"," ",0,"1/2/d/a^4*A/(tan(1/2*d*x+1/2*c)-1)+1/2/d/a^4*A/(tan(1/2*d*x+1/2*c)+1)-40/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))*A-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)*B+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)*B+3/d*b^7/a^4/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b+a+b)^3/(a+b)/(a^3-3*a^2*b+3*a*b^2-b^3)*tan(1/2*d*x+1/2*c)*A+30/d/a/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b+a+b)^3*b^4/(a+b)/(a^3-3*a^2*b+3*a*b^2-b^3)*tan(1/2*d*x+1/2*c)*A-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)^3*b^5/(a+b)/(a^3-3*a^2*b+3*a*b^2-b^3)*tan(1/2*d*x+1/2*c)*A-34/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*b^6/(a+b)/(a^3-3*a^2*b+3*a*b^2-b^3)*tan(1/2*d*x+1/2*c)*A-3/d*b^7/a^4/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b+a+b)^3/(a-b)/(a^3+3*a^2*b+3*a*b^2+b^3)*tan(1/2*d*x+1/2*c)^5*A+12/d*b^8/a^5/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b+a+b)^3/(a-b)/(a^3+3*a^2*b+3*a*b^2+b^3)*tan(1/2*d*x+1/2*c)^5*A-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*B+24/d*b^8/a^5/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b+a+b)^3/(a^2+2*a*b+b^2)/(a^2-2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3*A+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*B-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*B+12/d*b^8/a^5/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b+a+b)^3/(a+b)/(a^3-3*a^2*b+3*a*b^2-b^3)*tan(1/2*d*x+1/2*c)*A+30/d/a/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b+a+b)^3*b^4/(a-b)/(a^3+3*a^2*b+3*a*b^2+b^3)*tan(1/2*d*x+1/2*c)^5*A+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)^3*b^5/(a-b)/(a^3+3*a^2*b+3*a*b^2+b^3)*tan(1/2*d*x+1/2*c)^5*A-34/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*b^6/(a-b)/(a^3+3*a^2*b+3*a*b^2+b^3)*tan(1/2*d*x+1/2*c)^5*A+60/d/a/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b+a+b)^3*b^4/(a^2+2*a*b+b^2)/(a^2-2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3*A-212/3/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*b^6/(a^2+2*a*b+b^2)/(a^2-2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3*A-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)*B-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*B+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*B+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*B+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)*B+1/2/d/a^4*A*ln(tan(1/2*d*x+1/2*c)+1)-1/2/d/a^4*A*ln(tan(1/2*d*x+1/2*c)-1)-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*B-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/(a^2-2*a*b+b^2)/(a^2+2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3*b^3*B-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*B-10/d/a^6*ln(tan(1/2*d*x+1/2*c)-1)*A*b^2+4/d/a^5*ln(tan(1/2*d*x+1/2*c)-1)*B*b+4/d/a^5/(tan(1/2*d*x+1/2*c)+1)*A*b+10/d/a^6*ln(tan(1/2*d*x+1/2*c)+1)*A*b^2+4/d/a^5/(tan(1/2*d*x+1/2*c)-1)*A*b-4/d/a^5*ln(tan(1/2*d*x+1/2*c)+1)*B*b-1/d/a^4/(tan(1/2*d*x+1/2*c)+1)*B-1/2/d/a^4*A/(tan(1/2*d*x+1/2*c)+1)^2-1/d/a^4/(tan(1/2*d*x+1/2*c)-1)*B+1/2/d/a^4*A/(tan(1/2*d*x+1/2*c)-1)^2-69/d/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))*A*b^7+84/d/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))*A*b^5+20/d*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*a+20/d*b^9/a^6/(a^6-3*a^4*b^2+3*a^2*b^4-b^6)/((a-b)*(a+b))^(1/2)*arctan(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))*A-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))*B+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))*B-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))*B","B"
281,1,23,26,0.085000," ","int(cos(d*x+c)^3*(a*B+b*B*cos(d*x+c))/(a+b*cos(d*x+c)),x)","\frac{B \left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3 d}"," ",0,"1/3/d*B*(2+cos(d*x+c)^2)*sin(d*x+c)","A"
282,1,28,23,0.084000," ","int(cos(d*x+c)^2*(a*B+b*B*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)}{d}"," ",0,"1/d*B*(1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c)","A"
283,1,12,11,0.063000," ","int(cos(d*x+c)*(a*B+b*B*cos(d*x+c))/(a+b*cos(d*x+c)),x)","\frac{B \sin \left(d x +c \right)}{d}"," ",0,"B*sin(d*x+c)/d","A"
284,1,4,3,0.000000," ","int((a*B+b*B*cos(d*x+c))/(a+b*cos(d*x+c)),x)","B x"," ",0,"B*x","A"
285,1,20,12,0.073000," ","int((a*B+b*B*cos(d*x+c))*sec(d*x+c)/(a+b*cos(d*x+c)),x)","\frac{B \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}"," ",0,"1/d*B*ln(sec(d*x+c)+tan(d*x+c))","A"
286,1,12,11,0.081000," ","int((a*B+b*B*cos(d*x+c))*sec(d*x+c)^2/(a+b*cos(d*x+c)),x)","\frac{B \tan \left(d x +c \right)}{d}"," ",0,"B*tan(d*x+c)/d","A"
287,1,40,32,0.092000," ","int((a*B+b*B*cos(d*x+c))*sec(d*x+c)^3/(a+b*cos(d*x+c)),x)","\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,"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"
288,1,25,26,0.103000," ","int((a*B+b*B*cos(d*x+c))*sec(d*x+c)^4/(a+b*cos(d*x+c)),x)","-\frac{B \left(-\frac{2}{3}-\frac{\left(\sec^{2}\left(d x +c \right)\right)}{3}\right) \tan \left(d x +c \right)}{d}"," ",0,"-1/d*B*(-2/3-1/3*sec(d*x+c)^2)*tan(d*x+c)","A"
289,1,229,101,0.098000," ","int(cos(d*x+c)^3*(a*B+b*B*cos(d*x+c))/(a+b*cos(d*x+c))^2,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) B}{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) B a}{d \,b^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}-\frac{\left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) B}{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) B 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) B}{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} B}{d \,b^{3}}+\frac{\arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) B}{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))*B-2/d/b^2/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)^3*B*a-1/d/b/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)^3*B-2/d/b^2/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)*B*a+1/d/b/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)*B+2/d/b^3*arctan(tan(1/2*d*x+1/2*c))*a^2*B+1/d/b*arctan(tan(1/2*d*x+1/2*c))*B","B"
290,1,105,70,0.089000," ","int(cos(d*x+c)^2*(a*B+b*B*cos(d*x+c))/(a+b*cos(d*x+c))^2,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) B}{d \,b^{2} \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{2 B \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) B 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))*B+2/d/b*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))*B*a","A"
291,1,69,52,0.080000," ","int(cos(d*x+c)*(a*B+b*B*cos(d*x+c))/(a+b*cos(d*x+c))^2,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) a B}{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) B}{d b}"," ",0,"-2/d/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*B+2/d/b*arctan(tan(1/2*d*x+1/2*c))*B","A"
292,1,45,41,0.048000," ","int((a*B+b*B*cos(d*x+c))/(a+b*cos(d*x+c))^2,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) B}{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))*B","A"
293,1,91,61,0.093000," ","int((a*B+b*B*cos(d*x+c))*sec(d*x+c)/(a+b*cos(d*x+c))^2,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) B}{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) B}{a d}+\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right) B}{a d}"," ",0,"-2/d*b/a/((a-b)*(a+b))^(1/2)*arctan(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))*B-1/a/d*ln(tan(1/2*d*x+1/2*c)-1)*B+1/a/d*ln(tan(1/2*d*x+1/2*c)+1)*B","A"
294,1,139,79,0.110000," ","int((a*B+b*B*cos(d*x+c))*sec(d*x+c)^2/(a+b*cos(d*x+c))^2,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) B}{d \,a^{2} \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{B}{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) B b}{d \,a^{2}}-\frac{B}{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) B b}{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))*B-1/a/d/(tan(1/2*d*x+1/2*c)-1)*B+1/d/a^2*ln(tan(1/2*d*x+1/2*c)-1)*B*b-1/a/d/(tan(1/2*d*x+1/2*c)+1)*B-1/d/a^2*ln(tan(1/2*d*x+1/2*c)+1)*B*b","A"
295,1,273,110,0.133000," ","int((a*B+b*B*cos(d*x+c))*sec(d*x+c)^3/(a+b*cos(d*x+c))^2,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) B}{d \,a^{3} \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{B}{2 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}+\frac{B}{2 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{B 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) B}{2 a d}-\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right) B \,b^{2}}{d \,a^{3}}-\frac{B}{2 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}+\frac{B}{2 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}+\frac{B 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) B}{2 a d}+\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right) B \,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))*B+1/2/a/d/(tan(1/2*d*x+1/2*c)-1)^2*B+1/2/a/d/(tan(1/2*d*x+1/2*c)-1)*B+1/d/a^2/(tan(1/2*d*x+1/2*c)-1)*B*b-1/2/a/d*ln(tan(1/2*d*x+1/2*c)-1)*B-1/d/a^3*ln(tan(1/2*d*x+1/2*c)-1)*B*b^2-1/2/a/d/(tan(1/2*d*x+1/2*c)+1)^2*B+1/2/a/d/(tan(1/2*d*x+1/2*c)+1)*B+1/d/a^2/(tan(1/2*d*x+1/2*c)+1)*B*b+1/2/a/d*ln(tan(1/2*d*x+1/2*c)+1)*B+1/d/a^3*ln(tan(1/2*d*x+1/2*c)+1)*B*b^2","B"
296,1,1635,416,1.582000," ","int(cos(d*x+c)^3*(a+b*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) b +a -b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(-1120 B \,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(720 A \,b^{5}+640 B a \,b^{4}+2240 B \,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(-432 A a \,b^{4}-1080 A \,b^{5}+8 B \,a^{2} b^{3}-960 B a \,b^{4}-2072 B \,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(-12 A \,a^{2} b^{3}+432 A a \,b^{4}+840 A \,b^{5}+8 B \,a^{3} b^{2}-8 B \,a^{2} b^{3}+728 B a \,b^{4}+952 B \,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(24 A \,a^{3} b^{2}+6 A \,a^{2} b^{3}-258 A a \,b^{4}-240 A \,b^{5}-16 B \,a^{4} b -4 B \,a^{3} b^{2}-24 B \,a^{2} b^{3}-204 B a \,b^{4}-168 B \,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)-24 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) a^{4} b -51 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) a^{2} b^{3}+75 A \,b^{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}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right)+24 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^{4} b -24 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^{3} b^{2}+57 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^{2} b^{3}-57 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 \,b^{4}+16 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}+20 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^{3} b^{2}-36 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}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) b^{4}-16 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}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{5}+16 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}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{4} b -24 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}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{3} b^{2}+24 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}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{2} b^{3}+147 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}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a \,b^{4}-147 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}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) b^{5}\right)}{315 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)}\, \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*b^5*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^10+(720*A*b^5+640*B*a*b^4+2240*B*b^5)*sin(1/2*d*x+1/2*c)^8*cos(1/2*d*x+1/2*c)+(-432*A*a*b^4-1080*A*b^5+8*B*a^2*b^3-960*B*a*b^4-2072*B*b^5)*sin(1/2*d*x+1/2*c)^6*cos(1/2*d*x+1/2*c)+(-12*A*a^2*b^3+432*A*a*b^4+840*A*b^5+8*B*a^3*b^2-8*B*a^2*b^3+728*B*a*b^4+952*B*b^5)*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+(24*A*a^3*b^2+6*A*a^2*b^3-258*A*a*b^4-240*A*b^5-16*B*a^4*b-4*B*a^3*b^2-24*B*a^2*b^3-204*B*a*b^4-168*B*b^5)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)-24*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))*a^4*b-51*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))*a^2*b^3+75*A*b^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)*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))+24*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^4*b-24*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^3*b^2+57*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^2*b^3-57*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*b^4+16*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+20*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^3*b^2-36*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)*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*b^4-16*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^5+16*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^4*b-24*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^3*b^2+24*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^2*b^3+147*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^4-147*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))*b^5)/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"
297,1,1305,337,1.641000," ","int(cos(d*x+c)^2*(a+b*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) b +a -b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(240 B \,b^{4} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(-168 A \,b^{4}-144 B a \,b^{3}-360 B \,b^{4}\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(112 A a \,b^{3}+168 A \,b^{4}-4 B \,a^{2} b^{2}+144 B a \,b^{3}+280 B \,b^{4}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\left(-14 A \,a^{2} b^{2}-56 A a \,b^{3}-42 A \,b^{4}+8 B \,a^{3} b +2 B \,a^{2} b^{2}-86 B a \,b^{3}-80 B \,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)+14 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) a^{3} b -14 a 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) b^{3}-14 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^{3} b +14 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^{2} b^{2}+63 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 \,b^{3}-63 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) b^{4}-8 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^{4}-17 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^{2} b^{2}+25 B \,b^{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)+8 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}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{4}-8 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}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{3} b +19 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}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{2} b^{2}-19 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}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a \,b^{3}\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*B*b^4*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^8+(-168*A*b^4-144*B*a*b^3-360*B*b^4)*sin(1/2*d*x+1/2*c)^6*cos(1/2*d*x+1/2*c)+(112*A*a*b^3+168*A*b^4-4*B*a^2*b^2+144*B*a*b^3+280*B*b^4)*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+(-14*A*a^2*b^2-56*A*a*b^3-42*A*b^4+8*B*a^3*b+2*B*a^2*b^2-86*B*a*b^3-80*B*b^4)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+14*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))*a^3*b-14*a*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))*b^3-14*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^3*b+14*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^2*b^2+63*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*b^3-63*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))*b^4-8*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^4-17*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^2*b^2+25*B*b^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)*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))+8*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^4-8*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^3*b+19*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^2*b^2-19*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^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"
298,1,993,269,1.644000," ","int(cos(d*x+c)*(a+b*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) b +a -b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(-24 B \,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 A \,b^{3}+16 B a \,b^{2}+24 b^{3} 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 a \,b^{2}-10 A \,b^{3}-2 a^{2} b B -8 B a \,b^{2}-6 b^{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)-5 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) a^{2} b +5 A \,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)+5 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^{2} b -5 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 \,b^{2}+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}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{3}-2 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}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) b^{2}-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}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{3}+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}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{2} b +9 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}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a \,b^{2}-9 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}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\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*B*b^3*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6+(20*A*b^3+16*B*a*b^2+24*B*b^3)*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+(-10*A*a*b^2-10*A*b^3-2*B*a^2*b-8*B*a*b^2-6*B*b^3)*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*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+5*A*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))+5*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^2*b-5*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*b^2+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)*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a^3-2*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)*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*b^2-2*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^3+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^2*b+9*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^2-9*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))*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"
299,1,600,213,1.648000," ","int((a+b*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) b +a -b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(4 B \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{2}+3 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}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a b -3 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}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) b^{2}+2 B \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a b -6 B \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{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) a^{2}+B \,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)+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) 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}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a b -2 B \cos \left(\frac{d x}{2}+\frac{c}{2}\right) a b +2 B \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*B*cos(1/2*d*x+1/2*c)^5*b^2+3*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)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a*b-3*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)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*b^2+2*B*cos(1/2*d*x+1/2*c)^3*a*b-6*B*cos(1/2*d*x+1/2*c)^3*b^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))*a^2+B*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))+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^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*B*cos(1/2*d*x+1/2*c)*a*b+2*B*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"
300,1,247,253,1.212000," ","int((a+b*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c))*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(A b \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right)-a A \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), 2, \sqrt{-\frac{2 b}{a -b}}\right)+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 \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)*(A*b*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))-a*A*EllipticPi(cos(1/2*d*x+1/2*c),2,(-2*b/(a-b))^(1/2))+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*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"
301,1,746,286,2.254000," ","int((a+b*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c))*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(\frac{2 B 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)}{\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(A b +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}}\, \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)}}+2 a 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)}}{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)\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*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))-2*(A*b+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)*EllipticPi(cos(1/2*d*x+1/2*c),2,(-2*b/(a-b))^(1/2))+2*a*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"
302,1,1290,353,3.455000," ","int((a+b*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c))*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(-\frac{2 B 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)}{\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 \left(A b +a 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)}}{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)+2 a 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)}}{2 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)}}{4 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)}{8 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)}{8 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)}{8 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)}{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{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}}{8 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)\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*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*b+B*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)))+2*a*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))/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"
303,1,2213,435,4.468000," ","int((a+b*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c))*sec(d*x+c)^4,x)","\text{Expression too large to display}"," ",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*A*(-1/3/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)^3+5/12*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)^2-1/24*(16*a^2+15*b^2)/a^3*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)+5/48*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)*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))+1/3*(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))-1/3*(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)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))+1/3/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))-5/16*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))+5/16/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)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*b^3+1/4/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))+5/16*b^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)/(-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*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)))+2*(A*b+B*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))/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"
304,1,1635,408,1.979000," ","int(cos(d*x+c)^2*(a+b*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) b +a -b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(-1120 B \,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(720 A \,b^{5}+1360 B a \,b^{4}+2240 B \,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(-936 A a \,b^{4}-1080 A \,b^{5}-424 B \,a^{2} b^{3}-2040 B a \,b^{4}-2072 B \,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(324 A \,a^{2} b^{3}+936 A a \,b^{4}+840 A \,b^{5}-4 B \,a^{3} b^{2}+424 B \,a^{2} b^{3}+1568 B a \,b^{4}+952 B \,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(-18 A \,a^{3} b^{2}-162 A \,a^{2} b^{3}-384 A a \,b^{4}-240 A \,b^{5}+8 B \,a^{4} b +2 B \,a^{3} b^{2}-282 B \,a^{2} b^{3}-444 B a \,b^{4}-168 B \,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)+18 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) a^{4} b -93 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) a^{2} b^{3}+75 A \,b^{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}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right)-18 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^{4} b +18 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^{3} b^{2}+246 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^{2} b^{3}-246 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 \,b^{4}-8 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}-31 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^{3} b^{2}+39 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}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) b^{4}+8 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}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{5}-8 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}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{4} b +33 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}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{3} b^{2}-33 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}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{2} b^{3}+147 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}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a \,b^{4}-147 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}}\, \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*b^5*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^10+(720*A*b^5+1360*B*a*b^4+2240*B*b^5)*sin(1/2*d*x+1/2*c)^8*cos(1/2*d*x+1/2*c)+(-936*A*a*b^4-1080*A*b^5-424*B*a^2*b^3-2040*B*a*b^4-2072*B*b^5)*sin(1/2*d*x+1/2*c)^6*cos(1/2*d*x+1/2*c)+(324*A*a^2*b^3+936*A*a*b^4+840*A*b^5-4*B*a^3*b^2+424*B*a^2*b^3+1568*B*a*b^4+952*B*b^5)*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+(-18*A*a^3*b^2-162*A*a^2*b^3-384*A*a*b^4-240*A*b^5+8*B*a^4*b+2*B*a^3*b^2-282*B*a^2*b^3-444*B*a*b^4-168*B*b^5)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+18*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))*a^4*b-93*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))*a^2*b^3+75*A*b^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)*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))-18*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^4*b+18*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^3*b^2+246*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^2*b^3-246*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*b^4-8*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^5-31*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^3*b^2+39*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)*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*b^4+8*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^5-8*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^4*b+33*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^3*b^2-33*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^2*b^3+147*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^4-147*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))*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"
305,1,1305,331,1.581000," ","int(cos(d*x+c)*(a+b*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) b +a -b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(240 B \,b^{4} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(-168 A \,b^{4}-312 B a \,b^{3}-360 B \,b^{4}\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(252 A a \,b^{3}+168 A \,b^{4}+108 B \,a^{2} b^{2}+312 B a \,b^{3}+280 B \,b^{4}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\left(-84 A \,a^{2} b^{2}-126 A a \,b^{3}-42 A \,b^{4}-6 B \,a^{3} b -54 B \,a^{2} b^{2}-128 B a \,b^{3}-80 B \,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)-21 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) a^{3} b +21 a 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) b^{3}+21 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^{3} b -21 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^{2} b^{2}+63 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 \,b^{3}-63 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) b^{4}+6 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^{4}-31 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^{2} b^{2}+25 B \,b^{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)-6 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}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{4}+6 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}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{3} b +82 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}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{2} b^{2}-82 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}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a \,b^{3}\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*B*b^4*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^8+(-168*A*b^4-312*B*a*b^3-360*B*b^4)*sin(1/2*d*x+1/2*c)^6*cos(1/2*d*x+1/2*c)+(252*A*a*b^3+168*A*b^4+108*B*a^2*b^2+312*B*a*b^3+280*B*b^4)*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+(-84*A*a^2*b^2-126*A*a*b^3-42*A*b^4-6*B*a^3*b-54*B*a^2*b^2-128*B*a*b^3-80*B*b^4)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)-21*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))*a^3*b+21*a*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))*b^3+21*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^3*b-21*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^2*b^2+63*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*b^3-63*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))*b^4+6*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^4-31*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^2*b^2+25*B*b^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)*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))-6*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^4+6*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^3*b+82*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^2*b^2-82*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^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"
306,1,993,263,1.646000," ","int((a+b*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) b +a -b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(-24 B \,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 A \,b^{3}+36 B a \,b^{2}+24 b^{3} 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 a \,b^{2}-10 A \,b^{3}-12 a^{2} b B -18 B a \,b^{2}-6 b^{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)-5 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) a^{2} b +5 A \,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)+20 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^{2} b -20 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 \,b^{2}-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^{3}+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}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) b^{2}+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}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{3}-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}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{2} b +9 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}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a \,b^{2}-9 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}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) b^{3}\right)}{15 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,"-2/15*((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*B*b^3*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6+(20*A*b^3+36*B*a*b^2+24*B*b^3)*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+(-10*A*a*b^2-10*A*b^3-12*B*a^2*b-18*B*a*b^2-6*B*b^3)*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*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+5*A*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))+20*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^2*b-20*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*b^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^3+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)*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*b^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)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a^3-3*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)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a^2*b+9*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^2-9*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))*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"
307,1,738,303,1.517000," ","int((a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))*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 B \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{2}+3 A a 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)+3 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}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a b -3 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}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) b^{2}-3 a^{2} 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}}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), 2, \sqrt{-\frac{2 b}{a -b}}\right)+2 B \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a b -6 B \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{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) a^{2}+B \,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)+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}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{2}-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}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a b -2 B \cos \left(\frac{d x}{2}+\frac{c}{2}\right) a b +2 B \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*B*cos(1/2*d*x+1/2*c)^5*b^2+3*A*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)*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))+3*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)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a*b-3*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)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*b^2-3*a^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)*EllipticPi(cos(1/2*d*x+1/2*c),2,(-2*b/(a-b))^(1/2))+2*B*cos(1/2*d*x+1/2*c)^3*a*b-6*B*cos(1/2*d*x+1/2*c)^3*b^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))*a^2+B*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))+4*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^2-4*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*B*cos(1/2*d*x+1/2*c)*a*b+2*B*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"
308,1,1167,305,1.595000," ","int((a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))*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 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} A -2 A 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{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(A \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{2}+2 A \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) b^{2}-A \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{2}+A \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a b -3 A \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), 2, \sqrt{-\frac{2 b}{a -b}}\right) a b +2 B \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a b +2 B \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a b -2 B \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) b^{2}-2 B \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), 2, \sqrt{-\frac{2 b}{a -b}}\right) a^{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-\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 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}}\, \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^{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}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a b -3 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) a b +2 B 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}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right)+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}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a b -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}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) b^{2}-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) a^{2}\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*a*b*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4+(-2*A*a^2-2*A*a*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)*(A*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a^2+2*A*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*b^2-A*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a^2+A*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a*b-3*A*EllipticPi(cos(1/2*d*x+1/2*c),2,(-2*b/(a-b))^(1/2))*a*b+2*B*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a*b+2*B*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a*b-2*B*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*b^2-2*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)^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))*a^2+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)*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^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*b-3*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))*a*b+2*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)*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))+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*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))*b^2-2*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))*a^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"
309,1,1403,356,3.674000," ","int((a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))*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(\frac{2 b^{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)}{\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(A b +2 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}}\, \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)}}+2 a \left(2 A b +a 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)}}{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)+2 a^{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)}}{2 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)}}{4 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)}{8 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)}{8 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)}{8 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)}{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{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}}{8 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)\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*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))-2*b*(A*b+2*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)*EllipticPi(cos(1/2*d*x+1/2*c),2,(-2*b/(a-b))^(1/2))+2*a*(2*A*b+B*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)))+2*a^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))/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"
310,1,2327,432,4.807000," ","int((a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))*sec(d*x+c)^4,x)","\text{Expression too large to display}"," ",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*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*A*(-1/3/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)^3+5/12*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)^2-1/24*(16*a^2+15*b^2)/a^3*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)+5/48*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)*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))+1/3*(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))-1/3*(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)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))+1/3/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))-5/16*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))+5/16/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)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*b^3+1/4/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))+5/16*b^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)/(-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*(A*b+2*B*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)))+2*a*(2*A*b+B*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))/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"
311,1,1983,488,1.879000," ","int(cos(d*x+c)^2*(a+b*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) b +a -b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(-245 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^{4} b^{2}-3069 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^{2} b^{4}+110 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^{4} b^{2}-110 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^{5} b +110 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) a^{5} b -1364 A \,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}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) b^{3}+1254 A a \,b^{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}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right)+255 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}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{4} b^{2}+3069 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^{3} b^{3}+1617 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 \,b^{5}+20160 B \,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)-40 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}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{5} b -255 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}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{3} b^{3}+3705 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}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{2} b^{4}-3705 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}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a \,b^{5}-390 a^{2} b^{4} 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)+\left(3520 A \,a^{3} b^{3}+14960 A \,a^{2} b^{4}+26488 A a \,b^{5}+10472 A \,b^{6}-20 B \,a^{4} b^{2}+4640 B \,a^{3} b^{3}+25120 B \,a^{2} b^{4}+30320 B a \,b^{5}+13860 B \,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(-110 A \,a^{4} b^{2}-1760 A \,a^{3} b^{3}-7326 A \,a^{2} b^{4}-7524 A a \,b^{5}-1848 A \,b^{6}+40 B \,a^{5} b +10 B \,a^{4} b^{2}-3210 B \,a^{3} b^{3}-7080 B \,a^{2} b^{4}-6690 B a \,b^{5}-2790 B \,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)+\left(22880 A a \,b^{5}+24640 A \,b^{6}+21920 B \,a^{2} b^{4}+71680 B a \,b^{5}+56880 B \,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(-12320 A \,b^{6}-35840 B a \,b^{5}-50400 B \,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(-14960 A \,a^{2} b^{4}-34320 A a \,b^{5}-22792 A \,b^{6}-4640 B \,a^{3} b^{3}-32880 B \,a^{2} b^{4}-66160 B a \,b^{5}-34920 B \,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)-40 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^{6}-1617 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) b^{6}+675 b^{6} 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)+40 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}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{6}\right)}{3465 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,"-2/3465*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(-245*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^4*b^2-3069*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^2*b^4+110*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^4*b^2-110*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^5*b+110*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))*a^5*b-1364*A*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)*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*b^3+1254*A*a*b^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)*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))+255*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^4*b^2+3069*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^3*b^3+1617*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*b^5-40*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^5*b-255*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^3*b^3+3705*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^2*b^4-3705*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^5-390*a^2*b^4*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))+20160*B*b^6*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^12+(-12320*A*b^6-35840*B*a*b^5-50400*B*b^6)*sin(1/2*d*x+1/2*c)^10*cos(1/2*d*x+1/2*c)+(22880*A*a*b^5+24640*A*b^6+21920*B*a^2*b^4+71680*B*a*b^5+56880*B*b^6)*sin(1/2*d*x+1/2*c)^8*cos(1/2*d*x+1/2*c)+(-14960*A*a^2*b^4-34320*A*a*b^5-22792*A*b^6-4640*B*a^3*b^3-32880*B*a^2*b^4-66160*B*a*b^5-34920*B*b^6)*sin(1/2*d*x+1/2*c)^6*cos(1/2*d*x+1/2*c)+(3520*A*a^3*b^3+14960*A*a^2*b^4+26488*A*a*b^5+10472*A*b^6-20*B*a^4*b^2+4640*B*a^3*b^3+25120*B*a^2*b^4+30320*B*a*b^5+13860*B*b^6)*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+(-110*A*a^4*b^2-1760*A*a^3*b^3-7326*A*a^2*b^4-7524*A*a*b^5-1848*A*b^6+40*B*a^5*b+10*B*a^4*b^2-3210*B*a^3*b^3-7080*B*a^2*b^4-6690*B*a*b^5-2790*B*b^6)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)-40*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^6-1617*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))*b^6+675*b^6*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))+40*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^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"
312,1,1635,402,1.807000," ","int(cos(d*x+c)*(a+b*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) b +a -b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(-1120 B \,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(720 A \,b^{5}+2080 B a \,b^{4}+2240 B \,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(-1440 A a \,b^{4}-1080 A \,b^{5}-1360 B \,a^{2} b^{3}-3120 B a \,b^{4}-2072 B \,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(1080 A \,a^{2} b^{3}+1440 A a \,b^{4}+840 A \,b^{5}+320 B \,a^{3} b^{2}+1360 B \,a^{2} b^{3}+2408 B a \,b^{4}+952 B \,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(-270 A \,a^{3} b^{2}-540 A \,a^{2} b^{3}-510 A a \,b^{4}-240 A \,b^{5}-10 B \,a^{4} b -160 B \,a^{3} b^{2}-666 B \,a^{2} b^{3}-684 B a \,b^{4}-168 B \,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)+45 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^{4} b -45 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^{3} b^{2}+435 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^{2} b^{3}-435 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 \,b^{4}-45 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) a^{4} b -30 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) a^{2} b^{3}+75 A \,b^{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}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right)-10 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}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{5}+10 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}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{4} b +279 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}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{3} b^{2}-279 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}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{2} b^{3}+147 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}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a \,b^{4}-147 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}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) b^{5}+10 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}-124 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^{3} b^{2}+114 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}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) b^{4}\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*b^5*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^10+(720*A*b^5+2080*B*a*b^4+2240*B*b^5)*sin(1/2*d*x+1/2*c)^8*cos(1/2*d*x+1/2*c)+(-1440*A*a*b^4-1080*A*b^5-1360*B*a^2*b^3-3120*B*a*b^4-2072*B*b^5)*sin(1/2*d*x+1/2*c)^6*cos(1/2*d*x+1/2*c)+(1080*A*a^2*b^3+1440*A*a*b^4+840*A*b^5+320*B*a^3*b^2+1360*B*a^2*b^3+2408*B*a*b^4+952*B*b^5)*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+(-270*A*a^3*b^2-540*A*a^2*b^3-510*A*a*b^4-240*A*b^5-10*B*a^4*b-160*B*a^3*b^2-666*B*a^2*b^3-684*B*a*b^4-168*B*b^5)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+45*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^4*b-45*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^3*b^2+435*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^2*b^3-435*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*b^4-45*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))*a^4*b-30*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))*a^2*b^3+75*A*b^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)*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))-10*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^5+10*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^4*b+279*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^3*b^2-279*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^2*b^3+147*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^4-147*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))*b^5+10*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^5-124*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^3*b^2+114*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)*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*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"
313,1,1305,322,1.470000," ","int((a+b*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) b +a -b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(240 B \,b^{4} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(-168 A \,b^{4}-480 B a \,b^{3}-360 B \,b^{4}\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(392 A a \,b^{3}+168 A \,b^{4}+360 B \,a^{2} b^{2}+480 B a \,b^{3}+280 B \,b^{4}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\left(-154 A \,a^{2} b^{2}-196 A a \,b^{3}-42 A \,b^{4}-90 B \,a^{3} b -180 B \,a^{2} b^{2}-170 B a \,b^{3}-80 B \,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)-56 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) a^{3} b +56 a 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) b^{3}+161 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^{3} b -161 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^{2} b^{2}+63 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 \,b^{3}-63 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) b^{4}-15 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^{4}-10 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^{2} b^{2}+25 B \,b^{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)+15 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}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{4}-15 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}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{3} b +145 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}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{2} b^{2}-145 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}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a \,b^{3}\right)}{105 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,"-2/105*((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*B*b^4*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^8+(-168*A*b^4-480*B*a*b^3-360*B*b^4)*sin(1/2*d*x+1/2*c)^6*cos(1/2*d*x+1/2*c)+(392*A*a*b^3+168*A*b^4+360*B*a^2*b^2+480*B*a*b^3+280*B*b^4)*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+(-154*A*a^2*b^2-196*A*a*b^3-42*A*b^4-90*B*a^3*b-180*B*a^2*b^2-170*B*a*b^3-80*B*b^4)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)-56*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))*a^3*b+56*a*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))*b^3+161*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^3*b-161*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^2*b^2+63*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*b^3-63*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))*b^4-15*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^4-10*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^2*b^2+25*B*b^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)*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))+15*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^4-15*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^3*b+145*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^2*b^2-145*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^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"
314,1,1067,355,1.467000," ","int((a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))*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(-24 B \,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 A \,b^{3}+56 B a \,b^{2}+24 b^{3} 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 a \,b^{2}-10 A \,b^{3}-22 a^{2} b B -28 B a \,b^{2}-6 b^{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)+10 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) a^{2} b +5 A \,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)+35 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^{2} b -35 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 \,b^{2}-15 A \,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}}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), 2, \sqrt{-\frac{2 b}{a -b}}\right)-8 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^{3}+8 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}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) b^{2}+23 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}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{3}-23 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}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{2} b +9 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}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a \,b^{2}-9 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}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\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*B*b^3*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6+(20*A*b^3+56*B*a*b^2+24*B*b^3)*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+(-10*A*a*b^2-10*A*b^3-22*B*a^2*b-28*B*a*b^2-6*B*b^3)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+10*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))*a^2*b+5*A*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))+35*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^2*b-35*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*b^2-15*A*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)*EllipticPi(cos(1/2*d*x+1/2*c),2,(-2*b/(a-b))^(1/2))-8*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^3+8*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)*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*b^2+23*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^3-23*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^2*b+9*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^2-9*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))*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"
315,1,1563,361,1.793000," ","int((a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))*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(-16 B \,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(12 A \,a^{2} b +8 B a \,b^{2}+16 b^{3} B \right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\left(-6 A \,a^{3}-6 A \,a^{2} b -4 B a \,b^{2}-4 b^{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{-\frac{2 b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a -b}+\frac{a +b}{a -b}}\, \left(3 A \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{3}+12 A \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a \,b^{2}-3 A \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{3}+3 A \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{2} b +6 A \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a \,b^{2}-6 A \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) b^{3}-15 A \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), 2, \sqrt{-\frac{2 b}{a -b}}\right) a^{2} b +4 B \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{2} b +2 B \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) b^{3}+14 B \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{2} b -14 B \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a \,b^{2}-6 B \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), 2, \sqrt{-\frac{2 b}{a -b}}\right) a^{3}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+3 A \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}}\, a^{3}+12 A 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}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right)-3 A \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) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, a^{3}+3 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^{2} b +6 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 \,b^{2}-6 A \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) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, b^{3}-15 A \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) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, a^{2} b +4 a^{2} b 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)+2 b^{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)+14 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}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{2} b -14 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}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a \,b^{2}-6 B \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) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, a^{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)}\, \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\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,"-1/3*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(-16*B*b^3*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6+(12*A*a^2*b+8*B*a*b^2+16*B*b^3)*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+(-6*A*a^3-6*A*a^2*b-4*B*a*b^2-4*B*b^3)*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)*(3*A*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a^3+12*A*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a*b^2-3*A*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a^3+3*A*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a^2*b+6*A*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a*b^2-6*A*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*b^3-15*A*EllipticPi(cos(1/2*d*x+1/2*c),2,(-2*b/(a-b))^(1/2))*a^2*b+4*B*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a^2*b+2*B*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*b^3+14*B*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a^2*b-14*B*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a*b^2-6*B*EllipticPi(cos(1/2*d*x+1/2*c),2,(-2*b/(a-b))^(1/2))*a^3)*sin(1/2*d*x+1/2*c)^2+3*A*(-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)*a^3+12*A*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)*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))-3*A*(-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)*a^3+3*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^2*b+6*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*b^2-6*A*(-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)*b^3-15*A*(-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))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*a^2*b+4*a^2*b*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))+2*b^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))+14*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^2*b-14*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^2-6*B*(-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))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*a^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*cos(1/2*d*x+1/2*c)^2-1)/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"
316,1,1742,376,3.890000," ","int((a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))*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(-\frac{2 b^{2} B \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)}{\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 A \,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)}{\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 B 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}}\, \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{2 b^{3} 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)}{\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 b \left(A b +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}}\, \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)}}+2 a^{2} \left(3 A b +a 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)}}{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)+2 A \,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)}}{2 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)}}{4 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)}{8 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)}{8 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)}{8 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)}{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{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}}{8 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)\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*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*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))+6*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))-2*b^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)*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))-6*a*b*(A*b+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)*EllipticPi(cos(1/2*d*x+1/2*c),2,(-2*b/(a-b))^(1/2))+2*a^2*(3*A*b+B*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)))+2*A*a^3*(-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))/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"
317,1,2438,433,4.607000," ","int((a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))*sec(d*x+c)^4,x)","\text{Expression too large to display}"," ",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*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))-2*b^2*(A*b+3*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)*EllipticPi(cos(1/2*d*x+1/2*c),2,(-2*b/(a-b))^(1/2))+2*a^2*(3*A*b+B*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*a^3*(-1/3/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)^3+5/12*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)^2-1/24*(16*a^2+15*b^2)/a^3*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)+5/48*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)*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))+1/3*(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))-1/3*(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)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))+1/3/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))-5/16*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))+5/16/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)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*b^3+1/4/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))+5/16*b^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)/(-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)))+6*a*b*(A*b+B*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"
318,1,3548,518,6.827000," ","int((a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))*sec(d*x+c)^5,x)","\text{output too large to display}"," ",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*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))+6*a*b*(A*b+B*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^2*(3*A*b+B*a)*(-1/3/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)^3+5/12*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)^2-1/24*(16*a^2+15*b^2)/a^3*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)+5/48*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)*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))+1/3*(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))-1/3*(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)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))+1/3/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))-5/16*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))+5/16/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)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*b^3+1/4/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))+5/16*b^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)/(-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*b+3*B*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)))+2*A*a^3*(-1/4/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)^4+7/24*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)^3-1/96*(36*a^2+35*b^2)/a^3*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+5/192*b*(20*a^2+21*b^2)/a^4*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)-7/96*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))-35/384*b^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)/(-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))+25/96/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))-25/96*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))+35/128/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)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*b^3-35/128*b^4/a^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)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))-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)/(-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))-3/16/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^2-35/128/a^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)*EllipticPi(cos(1/2*d*x+1/2*c),2,(-2*b/(a-b))^(1/2))*b^4))/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"
319,1,1305,354,1.646000," ","int(cos(d*x+c)^3*(A+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)}\, \left(240 B \,b^{4} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(-168 A \,b^{4}+24 B a \,b^{3}-360 B \,b^{4}\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(-28 A a \,b^{3}+168 A \,b^{4}+24 B \,a^{2} b^{2}-24 B a \,b^{3}+280 B \,b^{4}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\left(56 A \,a^{2} b^{2}+14 A a \,b^{3}-42 A \,b^{4}-48 B \,a^{3} b -12 B \,a^{2} b^{2}-44 B a \,b^{3}-80 B \,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)-56 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) a^{3} b -49 a 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) b^{3}+56 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^{3} b -56 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^{2} b^{2}+63 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 \,b^{3}-63 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) b^{4}+48 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^{4}+32 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^{2} b^{2}+25 B \,b^{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)-48 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}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{4}+48 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}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{3} b -44 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}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{2} b^{2}+44 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}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a \,b^{3}\right)}{105 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)}\, \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*B*b^4*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^8+(-168*A*b^4+24*B*a*b^3-360*B*b^4)*sin(1/2*d*x+1/2*c)^6*cos(1/2*d*x+1/2*c)+(-28*A*a*b^3+168*A*b^4+24*B*a^2*b^2-24*B*a*b^3+280*B*b^4)*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+(56*A*a^2*b^2+14*A*a*b^3-42*A*b^4-48*B*a^3*b-12*B*a^2*b^2-44*B*a*b^3-80*B*b^4)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)-56*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))*a^3*b-49*a*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))*b^3+56*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^3*b-56*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^2*b^2+63*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*b^3-63*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))*b^4+48*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^4+32*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^2*b^2+25*B*b^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)*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))-48*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^4+48*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^3*b-44*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^2*b^2+44*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^3)/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"
320,1,993,284,1.732000," ","int(cos(d*x+c)^2*(A+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)}\, \left(-24 B \,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 A \,b^{3}-4 B a \,b^{2}+24 b^{3} 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 a \,b^{2}-10 A \,b^{3}+8 a^{2} b B +2 B a \,b^{2}-6 b^{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)+10 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) a^{2} b +5 A \,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)-10 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^{2} b +10 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 \,b^{2}-8 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^{3}-7 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}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) b^{2}+8 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}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{3}-8 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}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{2} b +9 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}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a \,b^{2}-9 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}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\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*B*b^3*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6+(20*A*b^3-4*B*a*b^2+24*B*b^3)*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+(-10*A*a*b^2-10*A*b^3+8*B*a^2*b+2*B*a*b^2-6*B*b^3)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+10*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))*a^2*b+5*A*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))-10*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^2*b+10*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*b^2-8*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^3-7*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)*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*b^2+8*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^3-8*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^2*b+9*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^2-9*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))*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"
321,1,671,225,1.749000," ","int(cos(d*x+c)*(A+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)}\, \left(-4 B \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{2}+3 A a 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)-3 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}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a b +3 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}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) b^{2}-2 B \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a b +6 B \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{2}-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) a^{2}-B \,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)+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}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{2}-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}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a b +2 B \cos \left(\frac{d x}{2}+\frac{c}{2}\right) a b -2 B \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*B*cos(1/2*d*x+1/2*c)^5*b^2+3*A*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)*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))-3*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)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a*b+3*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)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*b^2-2*B*cos(1/2*d*x+1/2*c)^3*a*b+6*B*cos(1/2*d*x+1/2*c)^3*b^2-2*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))*a^2-B*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))+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^2-2*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*B*cos(1/2*d*x+1/2*c)*a*b-2*B*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"
322,1,249,180,1.221000," ","int((A+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)}\, \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(A b \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right)-B \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 \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)*(A*b*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))-B*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*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"
323,1,194,168,1.186000," ","int((A+B*cos(d*x+c))*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(A \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), 2, \sqrt{-\frac{2 b}{a -b}}\right)-B \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\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)}\, \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)*(A*EllipticPi(cos(1/2*d*x+1/2*c),2,(-2*b/(a-b))^(1/2))-B*EllipticF(cos(1/2*d*x+1/2*c),(-2*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)/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"
324,1,639,289,1.941000," ","int((A+B*cos(d*x+c))*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 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)}{\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 \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)\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)^(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"
325,1,1182,360,3.275000," ","int((A+B*cos(d*x+c))*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(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)}}{2 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)}}{4 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)}{8 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)}{8 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)}{8 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)}{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{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}}{8 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)+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)\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*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"
326,1,1308,423,5.105000," ","int(cos(d*x+c)^3*(A+B*cos(d*x+c))/(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{16 B \left(-\frac{\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)}}{10 b}-\frac{\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)}}{60 b^{2}}+\frac{\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)}{60 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{\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)}{60 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)}}\right)}{b}+\frac{8 \left(A b -a B -3 B 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^{2}}+\frac{2 \left(A a b +2 A \,b^{2}-a^{2} B -2 B a b -3 b^{2} 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(A \,a^{2} b +A a \,b^{2}+A \,b^{3}-a^{3} B -a^{2} b B -B a \,b^{2}-b^{3} 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)}{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 a^{3} \left(A 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)}\, \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}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) b +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)}\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*B*(-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^2*(A*b-B*a-3*B*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^4*(A*a*b+2*A*b^2-B*a^2-2*B*a*b-3*B*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*(A*a^2*b+A*a*b^2+A*b^3-B*a^3-B*a^2*b-B*a*b^2-B*b^3)/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))-2*a^3*(A*b-B*a)/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)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*b+2*b*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*sin(1/2*d*x+1/2*c)^2*b+a+b)^(1/2)/d","B"
327,1,954,302,4.671000," ","int(cos(d*x+c)^2*(A+B*cos(d*x+c))/(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{8 B \,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}+\frac{2 \left(-2 B a b -2 b^{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)}{3}-4 A 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}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right)+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}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a 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}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) b^{2}+\frac{16 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}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right)}{3}+\frac{2 b^{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}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right)}{3}-\frac{10 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}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{2}}{3}+\frac{10 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}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a b}{3}}{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{2 a^{2} \left(A 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)}\, \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}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) b +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)}\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)*(2/3/b^3*(4*B*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4+(-2*B*a*b-2*B*b^2)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)-6*A*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)*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))+3*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*b-3*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))*b^2+8*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)*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))+b^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)*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))-5*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^2+5*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)^4*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)+2*a^2*(A*b-B*a)/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)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*b+2*b*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*sin(1/2*d*x+1/2*c)^2*b+a+b)^(1/2)/d","B"
328,1,515,252,4.191000," ","int(cos(d*x+c)*(A+B*cos(d*x+c))/(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 \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(A b \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right)-2 B \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 \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{2 a \left(A 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)}\, \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}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) b +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)}\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/(-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)*(A*b*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))-2*B*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*a*(A*b-B*a)/b^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)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*b+2*b*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*sin(1/2*d*x+1/2*c)^2*b+a+b)^(1/2)/d","B"
329,1,428,233,3.451000," ","int((A+B*cos(d*x+c))/(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 \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 \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(A 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)}\, \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}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) b +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)}\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/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))+2*(A*b-B*a)/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)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*b+2*b*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*sin(1/2*d*x+1/2*c)^2*b+a+b)^(1/2)/d","A"
330,1,429,238,3.072000," ","int((A+B*cos(d*x+c))*sec(d*x+c)/(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 \left(-A 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)}\, \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}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) b +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 \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 \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*b+B*a)/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)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*b+2*b*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2)-2/a*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)*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"
331,1,908,374,4.302000," ","int((A+B*cos(d*x+c))*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 \left(A b -a B \right) 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}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) b +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 \left(-A b +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}}\, \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 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)}}{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}\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*b-B*a)*b/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)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*b+2*b*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2)-2*(-A*b+B*a)/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/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"
332,1,1564,455,5.079000," ","int((A+B*cos(d*x+c))*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{2 \left(A 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)}\, \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}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) b +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 \left(A b -a B \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}}\, \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 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)}}{2 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)}}{4 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)}{8 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)}{8 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)}{8 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)}{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{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}}{8 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)}{a}+\frac{2 \left(-A b +a 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)}}{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*b-B*a)*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)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*b+2*b*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2)-2*(A*b-B*a)/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/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*b+B*a)/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))))/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"
333,1,1746,580,8.744000," ","int(cos(d*x+c)^4*(A+B*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{16 B \left(-\frac{\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)}}{10 b}-\frac{\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)}}{60 b^{2}}+\frac{\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)}{60 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{\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)}{60 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)}}\right)}{b^{2}}+\frac{8 \left(A b -2 a B -3 B 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(2 A a b +2 A \,b^{2}-3 a^{2} B -4 B a b -3 b^{2} 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^{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(3 A \,a^{2} b +2 A a \,b^{2}+A \,b^{3}-4 a^{3} B -3 a^{2} b B -2 B a \,b^{2}-b^{3} 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)}{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 a^{3} \left(4 A b -5 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)}\, \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}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) b +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^{4} \left(A b -a 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 \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*B*(-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*(A*b-2*B*a-3*B*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*(2*A*a*b+2*A*b^2-3*B*a^2-4*B*a*b-3*B*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*(3*A*a^2*b+2*A*a*b^2+A*b^3-4*B*a^3-3*B*a^2*b-2*B*a*b^2-B*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))-2*a^3/b^5*(4*A*b-5*B*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)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*b+2*b*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2)+2*a^4*(A*b-B*a)/b^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"
334,1,1389,447,7.258000," ","int(cos(d*x+c)^3*(A+B*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{\frac{8 B \,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}+\frac{2 \left(-2 B a b -2 b^{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)}{3}-6 A 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}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right)+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}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a 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}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) b^{2}+\frac{34 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}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right)}{3}+\frac{2 b^{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}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right)}{3}-\frac{16 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}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{2}}{3}+\frac{16 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}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a b}{3}}{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 a^{2} \left(3 A b -4 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)}\, \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}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) b +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^{3} \left(A b -a 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 \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)*(2/3/b^4*(4*B*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4+(-2*B*a*b-2*B*b^2)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)-9*A*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)*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))+3*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*b-3*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))*b^2+17*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)*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))+b^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)*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))-8*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^2+8*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)^4*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)+2*a^2/b^4*(3*A*b-4*B*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)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*b+2*b*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2)-2*a^3*(A*b-B*a)/b^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"
335,1,950,369,5.832000," ","int(cos(d*x+c)^2*(A+B*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{\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(A b \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right)-3 B \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 \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{2 a \left(2 A b -3 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)}\, \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}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) b +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^{2} \left(A b -a 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 \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)*(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)*(A*b*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))-3*B*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*a/b^3*(2*A*b-3*B*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)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*b+2*b*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2)+2*a^2*(A*b-B*a)/b^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"
336,1,860,345,5.282000," ","int(cos(d*x+c)*(A+B*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 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^{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 \left(A b -2 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)}\, \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}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) b +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 \left(A b -a 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 \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/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))+2/b^2*(A*b-2*B*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)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*b+2*b*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2)-2*a*(A*b-B*a)/b^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"
337,1,750,313,5.005000," ","int((A+B*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 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}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) b +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 \left(A b -a 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 \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/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)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*b+2*b*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2)+2*(A*b-B*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"
338,1,854,412,5.595000," ","int((A+B*cos(d*x+c))*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 A 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}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) b +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 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}}\, \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 \left(-A b +a 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 \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*b/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)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*b+2*b*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2)-2*A/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+B*a)/a*(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"
339,1,1341,498,7.934000," ","int((A+B*cos(d*x+c))*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{2 b \left(2 A 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)}\, \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}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) b +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 \left(-2 A b +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}}\, \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 \left(A b -a B \right) 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^{2}}+\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)}}{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*b*(2*A*b-B*a)/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)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*b+2*b*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2)-2*(-2*A*b+B*a)/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*b-B*a)*b/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))))+2/a^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"
340,1,2000,585,9.707000," ","int((A+B*cos(d*x+c))*sec(d*x+c)^3/(a+b*cos(d*x+c))^(5/2),x)","\text{Expression too large to display}"," ",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*(3*A*b-2*B*a)/a^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)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*b+2*b*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2)-2*b*(3*A*b-2*B*a)/a^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)*EllipticPi(cos(1/2*d*x+1/2*c),2,(-2*b/(a-b))^(1/2))-2*(A*b-B*a)*b^2/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))))+2*A/a^2*(-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*(-2*A*b+B*a)/a^3*(-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"
341,1,76,83,0.130000," ","int((a*B+b*B*cos(d*x+c))/(a+b*cos(d*x+c))^(3/2),x)","\frac{2 B \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*B/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"
342,1,167,84,1.132000," ","int((a*B+b*B*cos(d*x+c))*sec(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)}\, 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)}{\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)/(-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"
343,1,218,131,1.711000," ","int((a*B+b*B*cos(d*x+c))/(a+b*cos(d*x+c))^(5/2),x)","-\frac{2 B \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}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) b +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*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-(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+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"
344,1,377,227,1.808000," ","int((a*B+b*B*cos(d*x+c))*sec(d*x+c)/(a+b*cos(d*x+c))^(5/2),x)","\frac{2 B \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}}\, 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)+\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}+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)}{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*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)*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"
345,1,451,202,1.472000," ","int(cos(d*x+c)^(5/2)*(a+b*cos(d*x+c))*(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(-1120 B b \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{10}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(720 A b +720 a B +2240 B b \right) \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\left(-504 a A -1080 A b -1080 a B -2072 B 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(504 a A +840 A b +840 a B +952 B 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(-126 a A -240 A b -240 a B -168 B b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+75 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)-189 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) a +75 a B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-147 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) b \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*b*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^10+(720*A*b+720*B*a+2240*B*b)*sin(1/2*d*x+1/2*c)^8*cos(1/2*d*x+1/2*c)+(-504*A*a-1080*A*b-1080*B*a-2072*B*b)*sin(1/2*d*x+1/2*c)^6*cos(1/2*d*x+1/2*c)+(504*A*a+840*A*b+840*B*a+952*B*b)*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+(-126*A*a-240*A*b-240*B*a-168*B*b)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+75*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))-189*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))*a+75*a*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-147*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)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
346,1,413,176,1.388000," ","int(cos(d*x+c)^(3/2)*(a+b*cos(d*x+c))*(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 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 b -168 a B -360 B 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(140 a A +168 A b +168 a B +280 B 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(-70 a A -42 A b -42 a B -80 B 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)+35 a 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)-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) b +25 B 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)-63 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) a \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*b*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^8+(-168*A*b-168*B*a-360*B*b)*sin(1/2*d*x+1/2*c)^6*cos(1/2*d*x+1/2*c)+(140*A*a+168*A*b+168*B*a+280*B*b)*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+(-70*A*a-42*A*b-42*B*a-80*B*b)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+35*a*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))-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))*b+25*B*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))-63*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))*a)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
347,1,371,148,1.240000," ","int(cos(d*x+c)^(1/2)*(a+b*cos(d*x+c))*(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 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 b +20 a B +24 B 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 b -10 a B -6 B 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 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 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) a +5 a B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-9 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) b \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*b*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6+(20*A*b+20*B*a+24*B*b)*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+(-10*A*b-10*B*a-6*B*b)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+5*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*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))*a+5*a*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-9*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)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
348,1,326,121,1.284000," ","int((a+b*cos(d*x+c))*(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 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 A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-3 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 +B 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{\frac{1}{2}-\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 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*b*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4+3*a*A*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-3*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+B*b*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-3*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*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*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"
349,1,244,121,1.413000," ","int((a+b*cos(d*x+c))*(A+B*cos(d*x+c))/cos(d*x+c)^(3/2),x)","-\frac{2 \left(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)+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) a -2 A a \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+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)-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) 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*(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))+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))*a-2*A*a*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^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))-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)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
350,1,428,147,3.239000," ","int((a+b*cos(d*x+c))*(A+B*cos(d*x+c))/cos(d*x+c)^(5/2),x)","-\frac{\sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(\frac{2 B b \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{2 \left(A b +a B \right) \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)}+2 a 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)\right)}{\sin \left(\frac{d 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*b*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+2*(A*b+B*a)*(-(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+2*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2)/sin(1/2*d*x+1/2*c)^2/(2*sin(1/2*d*x+1/2*c)^2-1)+2*a*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"
351,1,663,176,4.016000," ","int((a+b*cos(d*x+c))*(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 B b \left(-\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+2 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right)^{2} \left(2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}-\frac{2 a 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 \left(A b +a 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)+\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*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)-2/5*a*A/(8*sin(1/2*d*x+1/2*c)^6-12*sin(1/2*d*x+1/2*c)^4+6*sin(1/2*d*x+1/2*c)^2-1)/sin(1/2*d*x+1/2*c)^2*(12*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^4-24*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6-12*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^2+24*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-8*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c))*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)+2*(A*b+B*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"
352,1,666,292,1.289000," ","int(cos(d*x+c)^(5/2)*(a+b*cos(d*x+c))^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(20160 B \,b^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{12}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(-12320 A \,b^{2}-24640 B a b -50400 b^{2} B \right) \left(\sin^{10}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\left(15840 A a b +24640 A \,b^{2}+7920 a^{2} B +49280 B a b +56880 b^{2} B \right) \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\left(-5544 a^{2} A -23760 A a b -22792 A \,b^{2}-11880 a^{2} B -45584 B a b -34920 b^{2} B \right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\left(5544 a^{2} A +18480 A a b +10472 A \,b^{2}+9240 a^{2} B +20944 B a b +13860 b^{2} B \right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\left(-1386 a^{2} A -5280 A a b -1848 A \,b^{2}-2640 a^{2} B -3696 B a b -2790 b^{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)-2079 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) a^{2}-1617 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^{2}+1650 A 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)-3234 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) a b +825 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)+675 b^{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)\right)}{3465 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-2/3465*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(20160*B*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^12+(-12320*A*b^2-24640*B*a*b-50400*B*b^2)*sin(1/2*d*x+1/2*c)^10*cos(1/2*d*x+1/2*c)+(15840*A*a*b+24640*A*b^2+7920*B*a^2+49280*B*a*b+56880*B*b^2)*sin(1/2*d*x+1/2*c)^8*cos(1/2*d*x+1/2*c)+(-5544*A*a^2-23760*A*a*b-22792*A*b^2-11880*B*a^2-45584*B*a*b-34920*B*b^2)*sin(1/2*d*x+1/2*c)^6*cos(1/2*d*x+1/2*c)+(5544*A*a^2+18480*A*a*b+10472*A*b^2+9240*B*a^2+20944*B*a*b+13860*B*b^2)*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+(-1386*A*a^2-5280*A*a*b-1848*A*b^2-2640*B*a^2-3696*B*a*b-2790*B*b^2)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)-2079*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))*a^2-1617*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^2+1650*A*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))-3234*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))*a*b+825*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))+675*b^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*sin(1/2*d*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"
353,1,610,255,1.306000," ","int(cos(d*x+c)^(3/2)*(a+b*cos(d*x+c))^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(-1120 B \,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(720 A \,b^{2}+1440 B a b +2240 b^{2} B \right) \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\left(-1008 A a b -1080 A \,b^{2}-504 a^{2} B -2160 B a b -2072 b^{2} B \right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\left(420 a^{2} A +1008 A a b +840 A \,b^{2}+504 a^{2} B +1680 B a b +952 b^{2} B \right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\left(-210 a^{2} A -252 A a b -240 A \,b^{2}-126 a^{2} B -480 B a b -168 b^{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)+105 a^{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)+75 A \,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)-378 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) a b +150 B 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)-189 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) a^{2}-147 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) b^{2}\right)}{315 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-2/315*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(-1120*B*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^10+(720*A*b^2+1440*B*a*b+2240*B*b^2)*sin(1/2*d*x+1/2*c)^8*cos(1/2*d*x+1/2*c)+(-1008*A*a*b-1080*A*b^2-504*B*a^2-2160*B*a*b-2072*B*b^2)*sin(1/2*d*x+1/2*c)^6*cos(1/2*d*x+1/2*c)+(420*A*a^2+1008*A*a*b+840*A*b^2+504*B*a^2+1680*B*a*b+952*B*b^2)*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+(-210*A*a^2-252*A*a*b-240*A*b^2-126*B*a^2-480*B*a*b-168*B*b^2)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+105*a^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))+75*A*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))-378*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))*a*b+150*B*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))-189*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))*a^2-147*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)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
354,1,548,218,1.441000," ","int(cos(d*x+c)^(1/2)*(a+b*cos(d*x+c))^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 \,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(-168 A \,b^{2}-336 B a b -360 b^{2} B \right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\left(280 A a b +168 A \,b^{2}+140 a^{2} B +336 B a b +280 b^{2} B \right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\left(-140 A a b -42 A \,b^{2}-70 a^{2} B -84 B a b -80 b^{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)+70 A 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)-105 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) a^{2}-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) b^{2}+35 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^{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)-126 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) 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*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^8+(-168*A*b^2-336*B*a*b-360*B*b^2)*sin(1/2*d*x+1/2*c)^6*cos(1/2*d*x+1/2*c)+(280*A*a*b+168*A*b^2+140*B*a^2+336*B*a*b+280*B*b^2)*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+(-140*A*a*b-42*A*b^2-70*B*a^2-84*B*a*b-80*B*b^2)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+70*A*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))-105*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))*a^2-63*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))*b^2+35*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^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))-126*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))*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"
355,1,487,180,1.189000," ","int((a+b*cos(d*x+c))^2*(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(-24 B \,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(20 A \,b^{2}+40 B a b +24 b^{2} B \right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\left(-10 A \,b^{2}-20 B a b -6 b^{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)+15 a^{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)+5 A \,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)-30 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) a b +10 B 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 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) a^{2}-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) 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*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6+(20*A*b^2+40*B*a*b+24*B*b^2)*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+(-10*A*b^2-20*B*a*b-6*B*b^2)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+15*a^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))+5*A*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))-30*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))*a*b+10*B*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*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))*a^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)/(-2*sin(1/2*d*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"
356,1,404,165,1.391000," ","int((a+b*cos(d*x+c))^2*(A+B*cos(d*x+c))/cos(d*x+c)^(3/2),x)","-\frac{2 \left(4 B \,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)+6 A 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)+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) a^{2}-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^{2}-6 A \,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)+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} 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)-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) a b -2 B \,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 \sin \left(\frac{d 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*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4+6*A*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))+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))*a^2-3*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^2-6*A*a^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^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*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))-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))*a*b-2*B*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
357,1,677,170,3.017000," ","int((a+b*cos(d*x+c))^2*(A+B*cos(d*x+c))/cos(d*x+c)^(5/2),x)","-\frac{\sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(\frac{2 b^{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}\, \left(\EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-\EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)\right)}{\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{2 A \,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}\, \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{4 B 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}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{2 b^{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}\, \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 \left(2 A b +a B \right) \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)}+2 a^{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)\right)}{\sin \left(\frac{d 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*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-EllipticE(cos(1/2*d*x+1/2*c),2^(1/2)))+2*A*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))+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)/(-2*sin(1/2*d*x+1/2*c)^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*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+2*a*(2*A*b+B*a)*(-(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+2*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2)/sin(1/2*d*x+1/2*c)^2/(2*sin(1/2*d*x+1/2*c)^2-1)+2*a^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"
358,1,750,208,4.042000," ","int((a+b*cos(d*x+c))^2*(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 b^{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}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{2 b \left(A b +2 a B \right) \left(-\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+2 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right)^{2} \left(2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}-\frac{2 a^{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 a \left(2 A b +a 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)+\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^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))+2*b*(A*b+2*B*a)*(-(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+2*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2)/sin(1/2*d*x+1/2*c)^2/(2*sin(1/2*d*x+1/2*c)^2-1)-2/5*a^2*A/(8*sin(1/2*d*x+1/2*c)^6-12*sin(1/2*d*x+1/2*c)^4+6*sin(1/2*d*x+1/2*c)^2-1)/sin(1/2*d*x+1/2*c)^2*(12*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^4-24*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6-12*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^2+24*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-8*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c))*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)+2*a*(2*A*b+B*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"
359,1,825,333,1.404000," ","int(cos(d*x+c)^(3/2)*(a+b*cos(d*x+c))^3*(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(20160 B \,b^{3} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{12}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(-12320 A \,b^{3}-36960 B a \,b^{2}-50400 b^{3} B \right) \left(\sin^{10}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\left(23760 A a \,b^{2}+24640 A \,b^{3}+23760 a^{2} b B +73920 B a \,b^{2}+56880 b^{3} B \right) \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\left(-16632 A \,a^{2} b -35640 A a \,b^{2}-22792 A \,b^{3}-5544 a^{3} B -35640 a^{2} b B -68376 B a \,b^{2}-34920 b^{3} B \right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\left(4620 A \,a^{3}+16632 A \,a^{2} b +27720 A a \,b^{2}+10472 A \,b^{3}+5544 a^{3} B +27720 a^{2} b B +31416 B a \,b^{2}+13860 b^{3} 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(-2310 A \,a^{3}-4158 A \,a^{2} b -7920 A a \,b^{2}-1848 A \,b^{3}-1386 a^{3} B -7920 a^{2} b B -5544 B a \,b^{2}-2790 b^{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)-6237 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) a^{2} b -1617 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^{3}+1155 A \,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)+2475 A a \,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)-2079 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) a^{3}-4851 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) a \,b^{2}+2475 a^{2} b 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)+675 b^{3} B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)\right)}{3465 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-2/3465*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(20160*B*b^3*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^12+(-12320*A*b^3-36960*B*a*b^2-50400*B*b^3)*sin(1/2*d*x+1/2*c)^10*cos(1/2*d*x+1/2*c)+(23760*A*a*b^2+24640*A*b^3+23760*B*a^2*b+73920*B*a*b^2+56880*B*b^3)*sin(1/2*d*x+1/2*c)^8*cos(1/2*d*x+1/2*c)+(-16632*A*a^2*b-35640*A*a*b^2-22792*A*b^3-5544*B*a^3-35640*B*a^2*b-68376*B*a*b^2-34920*B*b^3)*sin(1/2*d*x+1/2*c)^6*cos(1/2*d*x+1/2*c)+(4620*A*a^3+16632*A*a^2*b+27720*A*a*b^2+10472*A*b^3+5544*B*a^3+27720*B*a^2*b+31416*B*a*b^2+13860*B*b^3)*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+(-2310*A*a^3-4158*A*a^2*b-7920*A*a*b^2-1848*A*b^3-1386*B*a^3-7920*B*a^2*b-5544*B*a*b^2-2790*B*b^3)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)-6237*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))*a^2*b-1617*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^3+1155*A*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))+2475*A*a*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))-2079*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))*a^3-4851*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))*a*b^2+2475*a^2*b*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))+675*b^3*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2)))/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
360,1,745,287,1.575000," ","int(cos(d*x+c)^(1/2)*(a+b*cos(d*x+c))^3*(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(-1120 B \,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(720 A \,b^{3}+2160 B a \,b^{2}+2240 b^{3} B \right) \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\left(-1512 A a \,b^{2}-1080 A \,b^{3}-1512 a^{2} b B -3240 B a \,b^{2}-2072 b^{3} B \right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\left(1260 A \,a^{2} b +1512 A a \,b^{2}+840 A \,b^{3}+420 a^{3} B +1512 a^{2} b B +2520 B a \,b^{2}+952 b^{3} 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(-630 A \,a^{2} b -378 A a \,b^{2}-240 A \,b^{3}-210 a^{3} B -378 a^{2} b B -720 B a \,b^{2}-168 b^{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)-315 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) a^{3}-567 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) a \,b^{2}+315 A \,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)+75 A \,b^{3} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-567 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) a^{2} b -147 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) b^{3}+105 a^{3} B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+225 B a \,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)\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*b^3*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^10+(720*A*b^3+2160*B*a*b^2+2240*B*b^3)*sin(1/2*d*x+1/2*c)^8*cos(1/2*d*x+1/2*c)+(-1512*A*a*b^2-1080*A*b^3-1512*B*a^2*b-3240*B*a*b^2-2072*B*b^3)*sin(1/2*d*x+1/2*c)^6*cos(1/2*d*x+1/2*c)+(1260*A*a^2*b+1512*A*a*b^2+840*A*b^3+420*B*a^3+1512*B*a^2*b+2520*B*a*b^2+952*B*b^3)*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+(-630*A*a^2*b-378*A*a*b^2-240*A*b^3-210*B*a^3-378*B*a^2*b-720*B*a*b^2-168*B*b^3)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)-315*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))*a^3-567*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))*a*b^2+315*A*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))+75*A*b^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-567*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))*a^2*b-147*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^3+105*a^3*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+225*B*a*b^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2)))/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
361,1,664,241,1.500000," ","int((a+b*cos(d*x+c))^3*(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(240 B \,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(-168 A \,b^{3}-504 B a \,b^{2}-360 b^{3} B \right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\left(420 A a \,b^{2}+168 A \,b^{3}+420 a^{2} b B +504 B a \,b^{2}+280 b^{3} 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(-210 A a \,b^{2}-42 A \,b^{3}-210 a^{2} b B -126 B a \,b^{2}-80 b^{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)+105 A \,a^{3} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+105 A a \,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)-315 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) a^{2} b -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) b^{3}+105 a^{2} b 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} 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)-105 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) a^{3}-189 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) 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*b^3*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^8+(-168*A*b^3-504*B*a*b^2-360*B*b^3)*sin(1/2*d*x+1/2*c)^6*cos(1/2*d*x+1/2*c)+(420*A*a*b^2+168*A*b^3+420*B*a^2*b+504*B*a*b^2+280*B*b^3)*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+(-210*A*a*b^2-42*A*b^3-210*B*a^2*b-126*B*a*b^2-80*B*b^3)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+105*A*a^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+105*A*a*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))-315*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))*a^2*b-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))*b^3+105*a^2*b*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*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-105*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*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*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))*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"
362,1,867,240,1.632000," ","int((a+b*cos(d*x+c))^3*(A+B*cos(d*x+c))/cos(d*x+c)^(3/2),x)","-\frac{2 \left(-24 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)}\, 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)+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)}\, b^{2} \left(5 A b +15 a B +6 B b \right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-2 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \left(15 A \,a^{3}+5 A \,b^{3}+15 B a \,b^{2}+3 b^{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)+45 A \,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) \sqrt{-2 \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 A \,b^{3} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}+15 A \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, a^{3}-45 A \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, a \,b^{2}+15 a^{3} B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}+15 B a \,b^{2} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}-45 B \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, a^{2} b -9 B \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, b^{3}\right)}{15 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-2/15*(-24*B*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*b^3*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6+4*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*b^2*(5*A*b+15*B*a+6*B*b)*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)-2*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(15*A*a^3+5*A*b^3+15*B*a*b^2+3*B*b^3)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+45*A*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))*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)+5*A*b^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)+15*A*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*a^3-45*A*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*a*b^2+15*a^3*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)+15*B*a*b^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)-45*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)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*a^2*b-9*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)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(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"
363,1,1212,230,3.795000," ","int((a+b*cos(d*x+c))^3*(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(8 B \,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)+2 A \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, a^{3} \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+18 A \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, a \,b^{2} \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+18 A \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, a^{2} b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-6 A \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, b^{3} \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-36 A \,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)+18 B \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, a^{2} b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+2 B \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, b^{3} \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+6 B \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, a^{3} \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-18 B \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, a \,b^{2} \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-12 B \,a^{3} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-8 B \,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)-A \,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 A a \,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)-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) a^{2} b +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^{3}+2 A \,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 \,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)-9 a^{2} b 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} 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{\frac{1}{2}-\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 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) a \,b^{2}+6 B \,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 \,b^{3} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{3 \left(4 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-4 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \sin \left(\frac{d x}{2}+\frac{c}{2}\right)^{3} \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"2/3*(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)/(4*sin(1/2*d*x+1/2*c)^4-4*sin(1/2*d*x+1/2*c)^2+1)/sin(1/2*d*x+1/2*c)^3*(8*B*b^3*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6+2*A*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*a^3*sin(1/2*d*x+1/2*c)^2+18*A*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*a*b^2*sin(1/2*d*x+1/2*c)^2+18*A*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*a^2*b*sin(1/2*d*x+1/2*c)^2-6*A*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*b^3*sin(1/2*d*x+1/2*c)^2-36*A*a^2*b*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4+18*B*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*a^2*b*sin(1/2*d*x+1/2*c)^2+2*B*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*b^3*sin(1/2*d*x+1/2*c)^2+6*B*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*a^3*sin(1/2*d*x+1/2*c)^2-18*B*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*a*b^2*sin(1/2*d*x+1/2*c)^2-12*B*a^3*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4-8*B*b^3*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4-A*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*A*a*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))-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))*a^2*b+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^3+2*A*a^3*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2+18*A*a^2*b*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2-9*a^2*b*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*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-3*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*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*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))*a*b^2+6*B*a^3*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2+2*B*b^3*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
364,1,997,240,4.332000," ","int((a+b*cos(d*x+c))^3*(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 b^{3} B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \left(\EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-\EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)\right)}{\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{2 A \,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{6 B a \,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}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{2 b^{3} B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{6 a b \left(A b +a B \right) \left(-\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+2 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right)^{2} \left(2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}-\frac{2 A \,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}}+2 a^{2} \left(3 A b +a 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)+\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*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-EllipticE(cos(1/2*d*x+1/2*c),2^(1/2)))+2*A*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))+6*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+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^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*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))+6*a*b*(A*b+B*a)*(-(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+2*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2)/sin(1/2*d*x+1/2*c)^2/(2*sin(1/2*d*x+1/2*c)^2-1)-2/5*A*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)+2*a^2*(3*A*b+B*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"
365,1,1074,248,1.637000," ","int(cos(d*x+c)^(5/2)*(A+B*cos(d*x+c))/(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(-24 B a \,b^{3}+24 B \,b^{4}\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(20 A a \,b^{3}-20 A \,b^{4}-20 B \,a^{2} b^{2}+44 B a \,b^{3}-24 B \,b^{4}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\left(-10 A a \,b^{3}+10 A \,b^{4}+10 B \,a^{2} b^{2}-16 B a \,b^{3}+6 B \,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)+15 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) a^{3} b -15 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) a^{2} b^{2}+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) a \,b^{3}-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) b^{4}+15 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) a^{2} b^{2}-15 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) a \,b^{3}-15 A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), -\frac{2 b}{a -b}, \sqrt{2}\right) a^{3} b -15 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) a^{4}+15 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) a^{3} b -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) a^{2} b^{2}+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) a \,b^{3}-15 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) a^{3} b +15 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) a^{2} b^{2}-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) a \,b^{3}+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) b^{4}+15 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) a^{4}\right)}{15 b^{4} \left(a -b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-2/15*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*((-24*B*a*b^3+24*B*b^4)*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6+(20*A*a*b^3-20*A*b^4-20*B*a^2*b^2+44*B*a*b^3-24*B*b^4)*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+(-10*A*a*b^3+10*A*b^4+10*B*a^2*b^2-16*B*a*b^3+6*B*b^4)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+15*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))*a^3*b-15*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))*a^2*b^2+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))*a*b^3-5*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))*b^4+15*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))*a^2*b^2-15*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))*a*b^3-15*A*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),-2*b/(a-b),2^(1/2))*a^3*b-15*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))*a^4+15*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))*a^3*b-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))*a^2*b^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))*a*b^3-15*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))*a^3*b+15*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))*a^2*b^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))*a*b^3+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^4+15*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))*a^4)/b^4/(a-b)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
366,1,786,209,1.640000," ","int(cos(d*x+c)^(3/2)*(A+B*cos(d*x+c))/(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 a \,b^{2}+4 b^{3} B \right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(2 B a \,b^{2}-2 b^{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)+3 A \,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)-3 A a \,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)+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) a \,b^{2}-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^{3}-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}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), -\frac{2 b}{a -b}, \sqrt{2}\right) a^{2} b -3 a^{3} B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+3 a^{2} b 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 a \,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)+b^{3} B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-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) a^{2} b +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) a \,b^{2}+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}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), -\frac{2 b}{a -b}, \sqrt{2}\right) a^{3}\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*B*a*b^2+4*B*b^3)*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4+(2*B*a*b^2-2*B*b^3)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+3*A*a^2*b*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-3*A*a*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))+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))*a*b^2-3*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^3-3*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)*EllipticPi(cos(1/2*d*x+1/2*c),-2*b/(a-b),2^(1/2))*a^2*b-3*a^3*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+3*a^2*b*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*a*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))+b^3*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-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))*a^2*b+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))*a*b^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)*EllipticPi(cos(1/2*d*x+1/2*c),-2*b/(a-b),2^(1/2))*a^3)/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"
367,1,295,167,1.414000," ","int(cos(d*x+c)^(1/2)*(A+B*cos(d*x+c))/(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(A \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a b -A \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) b^{2}-A \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), -\frac{2 b}{a -b}, \sqrt{2}\right) a b -B \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a^{2}+B \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a b -B \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a b +B \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) b^{2}+B \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), -\frac{2 b}{a -b}, \sqrt{2}\right) a^{2}\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)*(A*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*a*b-A*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*b^2-A*EllipticPi(cos(1/2*d*x+1/2*c),-2*b/(a-b),2^(1/2))*a*b-B*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*a^2+B*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*a*b-B*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a*b+B*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*b^2+B*EllipticPi(cos(1/2*d*x+1/2*c),-2*b/(a-b),2^(1/2))*a^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"
368,1,217,113,1.365000," ","int((A+B*cos(d*x+c))/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(A \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), -\frac{2 b}{a -b}, \sqrt{2}\right) b +B \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a -B \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) b -B \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), -\frac{2 b}{a -b}, \sqrt{2}\right) a \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)*(A*EllipticPi(cos(1/2*d*x+1/2*c),-2*b/(a-b),2^(1/2))*b+B*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*a-B*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*b-B*EllipticPi(cos(1/2*d*x+1/2*c),-2*b/(a-b),2^(1/2))*a)/(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"
369,1,327,136,2.674000," ","int((A+B*cos(d*x+c))/cos(d*x+c)^(3/2)/(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 \left(-A b +a B \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}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), -\frac{2 b}{a -b}, \sqrt{2}\right)}{a \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(-\sqrt{-2 \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 \sin \left(\frac{d x}{2}+\frac{c}{2}\right)^{2} \left(2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(-4*(-A*b+B*a)/a/(-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*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+2*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2)/sin(1/2*d*x+1/2*c)^2/(2*sin(1/2*d*x+1/2*c)^2-1))/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
370,1,468,220,3.722000," ","int((A+B*cos(d*x+c))/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 \left(A b -a B \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}\, \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 \left(-A b +a B \right) \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{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)}{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*b-B*a)*b^2/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*b+B*a)/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/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"
371,1,1066,373,4.849000," ","int(cos(d*x+c)^(5/2)*(A+B*cos(d*x+c))/(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 \left(-4 B \,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)+6 A 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)+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^{2}-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^{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)-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) a b +2 B \,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 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{4 a^{2} \left(3 A b -4 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}\, \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^{3} \left(A b -a B \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)}-\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)*(-2/3/b^4/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(-4*B*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4+6*A*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))+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^2-9*a^2*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-b^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))-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))*a*b+2*B*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2)-4*a^2/b^3*(3*A*b-4*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*a^3*(A*b-B*a)/b^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"
372,1,849,300,3.957000," ","int(cos(d*x+c)^(3/2)*(A+B*cos(d*x+c))/(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(A \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) b -2 B \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) 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{4 a \left(2 A b -3 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}\, \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^{2} \left(A b -a B \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)}-\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)*(A*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*b-2*B*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))*b)+4*a/b^2*(2*A*b-3*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*a^2*(A*b-B*a)/b^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"
373,1,808,274,3.532000," ","int(cos(d*x+c)^(1/2)*(A+B*cos(d*x+c))/(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 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{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{4 \left(A b -2 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}\, \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 \left(A b -a B \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)}-\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/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))-4/b*(A*b-2*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*a*(A*b-B*a)/b^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"
374,1,721,276,3.361000," ","int((A+B*cos(d*x+c))/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 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(-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 \left(A b -a B \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)}-\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*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))+2*(A*b-B*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"
375,1,883,330,4.253000," ","int((A+B*cos(d*x+c))/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 A \,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 \left(-A b +a B \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)}-\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}+\frac{2 A \left(-\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+2 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}{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)}\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(4*A*b^2/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*b+B*a)/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)))+2*A/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))/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
376,1,1031,413,6.823000," ","int((A+B*cos(d*x+c))/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 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)}{a^{2}}-\frac{4 b^{2} \left(2 A b -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}\, \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{2 \left(A b -a B \right) 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^{2}}+\frac{2 \left(-2 A b +a B \right) \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)}\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*A/a^2*(-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*(2*A*b-B*a)/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*b-B*a)*b/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)))+2*(-2*A*b+B*a)/a^3*(-(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+2*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2)/sin(1/2*d*x+1/2*c)^2/(2*sin(1/2*d*x+1/2*c)^2-1))/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
377,1,1977,431,6.777000," ","int(cos(d*x+c)^(5/2)*(A+B*cos(d*x+c))/(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)*(A*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*b-3*B*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))*b)-2*a^3*(A*b-B*a)/b^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)))+12/b^3*a*(A*b-2*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*a^2/b^4*(3*A*b-4*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"
378,1,1937,408,6.060000," ","int(cos(d*x+c)^(3/2)*(A+B*cos(d*x+c))/(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/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*a^2*(A*b-B*a)/b^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)))-4/b^2*(A*b-3*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*a/b^3*(2*A*b-3*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"
379,1,1850,401,5.815000," ","int(cos(d*x+c)^(1/2)*(A+B*cos(d*x+c))/(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(A b -a B \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)}}{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 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)}{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 \left(A b -2 a B \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)}-\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*a*(A*b-B*a)/b^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/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))+2*(A*b-2*B*a)/b^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"
380,1,1744,409,5.772000," ","int((A+B*cos(d*x+c))/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 \left(A b -a B \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)}}{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{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)}{b}\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*(A*b-B*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)))+2*B/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"
381,1,2002,480,7.374000," ","int((A+B*cos(d*x+c))/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+B*a)/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)))+4*A*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*b/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)))+2/a^3*A*(-(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+2*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2)/sin(1/2*d*x+1/2*c)^2/(2*sin(1/2*d*x+1/2*c)^2-1))/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
382,1,2158,579,11.609000," ","int((A+B*cos(d*x+c))/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*(A*b-B*a)*b/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)))+2*A/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*(3*A*b-B*a)/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))+2*b*(2*A*b-B*a)/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)))+2*(-3*A*b+B*a)/a^4*(-(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+2*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2)/sin(1/2*d*x+1/2*c)^2/(2*sin(1/2*d*x+1/2*c)^2-1))/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
383,1,203,64,1.176000," ","int(cos(d*x+c)^(5/2)*(a*B+b*B*cos(d*x+c))/(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)}\, B \left(-8 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+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 \sqrt{\frac{1}{2}-\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)}{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)*B*(-8*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6+8*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)-3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-2*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+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"
384,1,180,64,1.103000," ","int(cos(d*x+c)^(3/2)*(a*B+b*B*cos(d*x+c))/(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)}\, B \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)-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)*B*(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))-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"
385,1,134,43,0.955000," ","int(cos(d*x+c)^(1/2)*(a*B+b*B*cos(d*x+c))/(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)}\, 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)}{\sqrt{-2 \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)*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)*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"
386,1,19,43,0.008000," ","int((a*B+b*B*cos(d*x+c))/cos(d*x+c)^(1/2)/(a+b*cos(d*x+c)),x)","\frac{2 B \,\mathrm{am}^{-1}\left(\frac{d x}{2}+\frac{c}{2}| \sqrt{2}\right)}{d}"," ",0,"2*B/d*InverseJacobiAM(1/2*d*x+1/2*c,2^(1/2))","C"
387,1,102,64,1.174000," ","int((a*B+b*B*cos(d*x+c))/cos(d*x+c)^(3/2)/(a+b*cos(d*x+c)),x)","-\frac{2 B \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}\, \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*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)^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"
388,1,214,64,1.286000," ","int((a*B+b*B*cos(d*x+c))/cos(d*x+c)^(5/2)/(a+b*cos(d*x+c)),x)","-\frac{2 \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)+\sqrt{\frac{1}{2}-\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 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right) B \sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\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)}\, \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)^{\frac{3}{2}} \sin \left(\frac{d x}{2}+\frac{c}{2}\right) d}"," ",0,"-2/3*(-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+(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-2*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c))*B*((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)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(2*cos(1/2*d*x+1/2*c)^2-1)^(3/2)/sin(1/2*d*x+1/2*c)/d","B"
389,1,517,188,1.510000," ","int(cos(d*x+c)^(5/2)*(a*B+b*B*cos(d*x+c))/(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)}\, B \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 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a^{2} b +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)-\sqrt{\frac{1}{2}-\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}+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)*B*((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*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*a^2*b+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))-(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+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"
390,1,228,156,1.350000," ","int(cos(d*x+c)^(3/2)*(a*B+b*B*cos(d*x+c))/(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)}\, 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(\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)*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)*(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"
391,1,189,107,1.354000," ","int(cos(d*x+c)^(1/2)*(a*B+b*B*cos(d*x+c))/(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)}\, 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(\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)*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)*(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"
392,1,151,56,0.994000," ","int((a*B+b*B*cos(d*x+c))/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)}\, 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 -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)*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)*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"
393,1,355,130,1.477000," ","int((a*B+b*B*cos(d*x+c))/cos(d*x+c)^(3/2)/(a+b*cos(d*x+c))^2,x)","-\frac{2 B \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*B*(-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"
394,1,452,203,3.338000," ","int((a*B+b*B*cos(d*x+c))/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)}\, B \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}\, \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{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)}}{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)}}}{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*(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*B*(-2*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))-1/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)+1/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"
395,1,2949,512,0.439000," ","int(cos(d*x+c)^(3/2)*(a+b*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c)),x)","\text{output too large to display}"," ",0,"-1/24/d/(a+b*cos(d*x+c))^(1/2)*(-12*A*sin(d*x+c)*cos(d*x+c)*(cos(d*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+6*A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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+6*A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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-28*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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+24*B*sin(d*x+c)*cos(d*x+c)*(cos(d*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*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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+12*A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a*b^2+16*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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+12*A*cos(d*x+c)^4*b^3-12*A*cos(d*x+c)^2*b^3+8*B*cos(d*x+c)^5*b^3+8*B*cos(d*x+c)^3*b^3-3*B*cos(d*x+c)^2*a^3-16*B*cos(d*x+c)^2*b^3+3*B*cos(d*x+c)*a^3+18*A*cos(d*x+c)^3*a*b^2+6*A*cos(d*x+c)^2*a^2*b-6*A*cos(d*x+c)^2*a*b^2-6*A*cos(d*x+c)*a^2*b-12*A*cos(d*x+c)*a*b^2+10*B*cos(d*x+c)^4*a*b^2-B*cos(d*x+c)^3*a^2*b+3*B*cos(d*x+c)^2*a^2*b+6*B*cos(d*x+c)^2*a*b^2-2*B*cos(d*x+c)*a^2*b-16*B*cos(d*x+c)*a*b^2+48*A*sin(d*x+c)*cos(d*x+c)*(cos(d*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+6*B*sin(d*x+c)*cos(d*x+c)*(cos(d*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^3-3*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+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+12*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))*a*b^2-12*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)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,(-(a-b)/(a+b))^(1/2))*a^2*b+6*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^2*b+6*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*b^2+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)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a^2*b-28*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*b^2+24*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)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,(-(a-b)/(a+b))^(1/2))*a*b^2-3*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+16*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^2-24*A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+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^3-24*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^3+48*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)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,(-(a-b)/(a+b))^(1/2))*b^3+6*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)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,(-(a-b)/(a+b))^(1/2))*a^3-3*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^3+16*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^3)/sin(d*x+c)/b^2/cos(d*x+c)^(1/2)","B"
396,1,2052,431,0.257000," ","int(cos(d*x+c)^(1/2)*(a+b*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c)),x)","-\frac{-4 A \left(\cos^{2}\left(d x +c \right)\right) b^{2}+4 A \left(\cos^{3}\left(d x +c \right)\right) b^{2}-B \cos \left(d x +c \right) a^{2}+4 A \left(\cos^{2}\left(d x +c \right)\right) a b +3 B \left(\cos^{3}\left(d x +c \right)\right) a b -B \left(\cos^{2}\left(d x +c \right)\right) a b +8 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) \cos \left(d x +c \right) a b +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) \cos \left(d x +c \right) a b +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)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{-\frac{a -b}{a +b}}\right) \cos \left(d x +c \right) a b +4 A \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{-\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \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 b -8 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)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{-\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) \cos \left(d x +c \right) a b +B \left(\cos^{2}\left(d x +c \right)\right) a^{2}-2 B \left(\cos^{2}\left(d x +c \right)\right) b^{2}+2 B \left(\cos^{4}\left(d x +c \right)\right) b^{2}-4 A \cos \left(d x +c \right) a b -2 B \cos \left(d x +c \right) a b +4 A \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{-\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \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 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)}}\, \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 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)}}\, \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}+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^{2}-4 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}+4 A \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{-\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \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 b -8 A \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{-\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \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 b +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 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) a b +4 A \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{-\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \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 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)}}\, \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) a^{2}+8 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)}}\, \EllipticPi \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, -1, \sqrt{-\frac{a -b}{a +b}}\right) \cos \left(d x +c \right) b^{2}+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) \cos \left(d x +c \right) a^{2}-4 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) \cos \left(d x +c \right) b^{2}+8 A \EllipticPi \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, -1, \sqrt{-\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \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 b}{4 d \sqrt{a +b \cos \left(d x +c \right)}\, \sin \left(d x +c \right) b \sqrt{\cos \left(d x +c \right)}}"," ",0,"-1/4/d/(a+b*cos(d*x+c))^(1/2)*(B*cos(d*x+c)^2*a^2-B*cos(d*x+c)*a^2+4*A*cos(d*x+c)^3*b^2-4*A*cos(d*x+c)^2*b^2+2*B*cos(d*x+c)^4*b^2-2*B*cos(d*x+c)^2*b^2+8*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)*a*b+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))*cos(d*x+c)*a*b+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)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*cos(d*x+c)*a*b+4*A*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)*(cos(d*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-8*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)*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*A*cos(d*x+c)^2*a*b-4*A*cos(d*x+c)*a*b+3*B*cos(d*x+c)^3*a*b-B*cos(d*x+c)^2*a*b-2*B*cos(d*x+c)*a*b+4*A*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*b^2-2*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)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,(-(a-b)/(a+b))^(1/2))*a^2+8*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)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,(-(a-b)/(a+b))^(1/2))*b^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^2-4*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))*b^2+4*A*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a*b-8*A*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a*b+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*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*b+4*A*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)*(cos(d*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^2-2*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)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,(-(a-b)/(a+b))^(1/2))*cos(d*x+c)*a^2+8*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)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,(-(a-b)/(a+b))^(1/2))*cos(d*x+c)*b^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))*cos(d*x+c)*a^2-4*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))*cos(d*x+c)*b^2+8*A*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)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a*b)/sin(d*x+c)/b/cos(d*x+c)^(1/2)","B"
397,1,1693,357,0.407000," ","int((a+b*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(1/2),x)","-\frac{2 A \sin \left(d x +c \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}} \sqrt{\frac{a +b \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \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 A \sin \left(d x +c \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}} \sqrt{\frac{a +b \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{-\frac{a -b}{a +b}}\right) b +4 A \sin \left(d x +c \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}} \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 +4 A \sin \left(d x +c \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{\frac{a +b \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \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 \sin \left(d x +c \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{\frac{a +b \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \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 +8 A \sin \left(d x +c \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{\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 A \sin \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{\frac{a +b \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \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 A \sin \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{\frac{a +b \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{-\frac{a -b}{a +b}}\right) b +4 A \sin \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{\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 B \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \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)}}\, a +2 B \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticPi \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, -1, \sqrt{-\frac{a -b}{a +b}}\right) \sqrt{\frac{a +b \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, a +B \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \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) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{-\frac{a -b}{a +b}}\right) b -2 B \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \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)}}\, a +2 B \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticPi \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, -1, \sqrt{-\frac{a -b}{a +b}}\right) \sqrt{\frac{a +b \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, a +B \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{-\frac{a -b}{a +b}}\right) a +B \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{-\frac{a -b}{a +b}}\right) b +B \left(\cos^{4}\left(d x +c \right)\right) b +B \left(\cos^{3}\left(d x +c \right)\right) a -B \left(\cos^{3}\left(d x +c \right)\right) b -B \left(\cos^{2}\left(d x +c \right)\right) a}{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,"-1/d*(2*A*sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*((a+b*cos(d*x+c))/(1+cos(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*A*sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*((a+b*cos(d*x+c))/(1+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*A*sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*((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*A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*((a+b*cos(d*x+c))/(1+cos(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*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*((a+b*cos(d*x+c))/(1+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+8*A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*((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*A*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*((a+b*cos(d*x+c))/(1+cos(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*A*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*((a+b*cos(d*x+c))/(1+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*A*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*((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*B*sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+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)*a+2*B*sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*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)*a+B*sin(d*x+c)*cos(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*sin(d*x+c)*cos(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-2*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+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)*a+2*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*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)*a+B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a+B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+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+B*cos(d*x+c)^4*b+B*cos(d*x+c)^3*a-B*cos(d*x+c)^3*b-B*cos(d*x+c)^2*a)/(a+b*cos(d*x+c))^(1/2)/sin(d*x+c)/cos(d*x+c)^(3/2)","B"
398,1,1687,327,0.294000," ","int((a+b*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(3/2),x)","-\frac{2 \left(B \sin \left(d x +c \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}} \sqrt{\frac{a +b \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{-\frac{a -b}{a +b}}\right) a -B \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sqrt{\frac{a +b \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \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 B \sin \left(d x +c \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}} \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 B \sin \left(d x +c \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{\frac{a +b \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{-\frac{a -b}{a +b}}\right) a -2 B \sin \left(d x +c \right) \cos \left(d x +c \right) \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sqrt{\frac{a +b \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{-\frac{a -b}{a +b}}\right) b +4 B \sin \left(d x +c \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{\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 +A \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \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 +A \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \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 -A \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{-\frac{a -b}{a +b}}\right) a -A \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{-\frac{a -b}{a +b}}\right) b +B \sin \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{\frac{a +b \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{-\frac{a -b}{a +b}}\right) a -B \sin \left(d x +c \right) \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sqrt{\frac{a +b \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \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 B \sin \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{\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 +A \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \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 +A \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \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 -A \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{-\frac{a -b}{a +b}}\right) a -A \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{-\frac{a -b}{a +b}}\right) b +A \left(\cos^{3}\left(d x +c \right)\right) b +A \left(\cos^{2}\left(d x +c \right)\right) a -A \left(\cos^{2}\left(d x +c \right)\right) b -A \cos \left(d x +c \right) a \right)}{d \sqrt{a +b \cos \left(d x +c \right)}\, \cos \left(d x +c \right)^{\frac{3}{2}} \sin \left(d x +c \right)}"," ",0,"-2/d/(a+b*cos(d*x+c))^(1/2)*(B*sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a-B*sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*((a+b*cos(d*x+c))/(1+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*B*sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*((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*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a-2*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*((a+b*cos(d*x+c))/(1+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*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*((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+A*sin(d*x+c)*cos(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+A*sin(d*x+c)*cos(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))*b-A*sin(d*x+c)*cos(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-A*sin(d*x+c)*cos(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+B*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*((a+b*cos(d*x+c))/(1+cos(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)))^(3/2)*((a+b*cos(d*x+c))/(1+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*B*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*((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+A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a+A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+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-A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a-A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+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+A*cos(d*x+c)^3*b+A*cos(d*x+c)^2*a-A*cos(d*x+c)^2*b-A*cos(d*x+c)*a)/cos(d*x+c)^(3/2)/sin(d*x+c)","B"
399,1,1727,258,0.227000," ","int((a+b*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(5/2),x)","-\frac{2 \left(-A \left(\cos^{2}\left(d x +c \right)\right) b^{2}+A \left(\cos^{3}\left(d x +c \right)\right) b^{2}-3 B \cos \left(d x +c \right) a^{2}-a^{2} A +A \sin \left(d x +c \right) \cos \left(d x +c \right) \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{-\frac{a -b}{a +b}}\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \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}+3 B \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{-\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \cos \left(d x +c \right) a^{2}+A \left(\cos^{2}\left(d x +c \right)\right) a b +3 B \left(\cos^{3}\left(d x +c \right)\right) a b -3 B \left(\cos^{2}\left(d x +c \right)\right) a b +A \left(\cos^{2}\left(d x +c \right)\right) a^{2}-3 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) \cos \left(d x +c \right) a b +3 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) \cos \left(d x +c \right) a b -A \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{-\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \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 b +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)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{-\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) \cos \left(d x +c \right) a b +A \left(\cos^{3}\left(d x +c \right)\right) a b +3 B \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{-\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \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(\cos^{2}\left(d x +c \right)\right) a b -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) \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) a b -3 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) \left(\cos^{2}\left(d x +c \right)\right) a b +A \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\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{\cos \left(d x +c \right)}{1+\cos \left(d x +c \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 b +3 B \left(\cos^{2}\left(d x +c \right)\right) a^{2}-2 A \cos \left(d x +c \right) a b +A \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{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) a^{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)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{-\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) b^{2}+3 B \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{-\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \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(\cos^{2}\left(d x +c \right)\right) a^{2}-3 B \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{-\frac{a -b}{a +b}}\right) a^{2}-A \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{-\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \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}-3 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) \cos \left(d x +c \right) a^{2}\right)}{3 d \sqrt{a +b \cos \left(d x +c \right)}\, a \sin \left(d x +c \right) \cos \left(d x +c \right)^{\frac{3}{2}}}"," ",0,"-2/3/d*(3*B*cos(d*x+c)^2*a^2+3*B*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*cos(d*x+c)^2*a*b-3*B*cos(d*x+c)*a^2+A*cos(d*x+c)^3*b^2-A*cos(d*x+c)^2*b^2-a^2*A-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))*sin(d*x+c)*cos(d*x+c)^2*a*b+A*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((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-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))*sin(d*x+c)*cos(d*x+c)^2*b^2+3*B*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*cos(d*x+c)^2*a^2-3*B*sin(d*x+c)*cos(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+A*sin(d*x+c)*cos(d*x+c)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^2+3*B*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*cos(d*x+c)*a^2+A*cos(d*x+c)^2*a^2-3*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))*cos(d*x+c)*a*b+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))*cos(d*x+c)*a*b-A*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)*(cos(d*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+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)*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+A*cos(d*x+c)^3*a*b-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))*cos(d*x+c)^2*a*b+A*sin(d*x+c)*cos(d*x+c)^2*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a*b+A*cos(d*x+c)^2*a*b-2*A*cos(d*x+c)*a*b+3*B*cos(d*x+c)^3*a*b-3*B*cos(d*x+c)^2*a*b-A*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)*(cos(d*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^2-3*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))*cos(d*x+c)*a^2)/(a+b*cos(d*x+c))^(1/2)/a/sin(d*x+c)/cos(d*x+c)^(3/2)","B"
400,1,2481,318,0.332000," ","int((a+b*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(7/2),x)","\text{Expression too large to display}"," ",0,"2/15/d*(3*A*a^3-9*A*cos(d*x+c)^3*a^3-2*A*cos(d*x+c)^3*b^3+6*A*cos(d*x+c)^2*a^3-5*B*cos(d*x+c)^3*a^3-5*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)*sin(d*x+c)*cos(d*x+c)^3*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a^2*b+2*A*cos(d*x+c)^4*b^3+5*B*cos(d*x+c)*a^3+2*A*cos(d*x+c)^3*a*b^2-A*cos(d*x+c)^2*a*b^2+4*A*cos(d*x+c)*a^2*b-5*B*cos(d*x+c)^4*a*b^2-5*B*cos(d*x+c)^3*a^2*b+10*B*cos(d*x+c)^2*a^2*b+9*A*sin(d*x+c)*cos(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-2*A*sin(d*x+c)*cos(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^2-7*A*sin(d*x+c)*cos(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+2*A*sin(d*x+c)*cos(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+5*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)*sin(d*x+c)*cos(d*x+c)^2*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a^2*b+5*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)*sin(d*x+c)*cos(d*x+c)^2*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a*b^2-5*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)*sin(d*x+c)*cos(d*x+c)^2*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a^2*b+5*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)*sin(d*x+c)*cos(d*x+c)^3*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a*b^2+9*A*sin(d*x+c)*cos(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-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)*sin(d*x+c)*cos(d*x+c)^3*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a*b^2-7*A*sin(d*x+c)*cos(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^2*b+2*A*sin(d*x+c)*cos(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+5*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)*sin(d*x+c)*cos(d*x+c)^3*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a^2*b+5*B*cos(d*x+c)^3*a*b^2-9*A*cos(d*x+c)^4*a^2*b-A*cos(d*x+c)^4*a*b^2+5*A*cos(d*x+c)^3*a^2*b-5*B*cos(d*x+c)^4*a^2*b-5*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)*sin(d*x+c)*cos(d*x+c)^2*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a^3+9*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)*sin(d*x+c)*cos(d*x+c)^3*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a^3-2*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)*sin(d*x+c)*cos(d*x+c)^3*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*b^3-9*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)*sin(d*x+c)*cos(d*x+c)^3*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a^3-5*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)*sin(d*x+c)*cos(d*x+c)^3*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a^3+9*A*sin(d*x+c)*cos(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^3-2*A*sin(d*x+c)*cos(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^3-9*A*sin(d*x+c)*cos(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)/(a+b*cos(d*x+c))^(1/2)/a^2/sin(d*x+c)/cos(d*x+c)^(5/2)","B"
401,1,3428,395,0.440000," ","int((a+b*cos(d*x+c))^(1/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(9/2),x)","\text{output too large to display}"," ",0,"2/105/d*(-63*B*cos(d*x+c)^4*a^4+42*B*cos(d*x+c)^3*a^4+21*B*cos(d*x+c)*a^4-25*A*cos(d*x+c)^4*a^4+10*A*cos(d*x+c)^2*a^4-8*A*cos(d*x+c)^5*b^4+8*A*cos(d*x+c)^4*b^4+28*B*cos(d*x+c)^2*a^3*b-25*A*cos(d*x+c)^5*a^3*b-19*A*cos(d*x+c)^5*a^2*b^2+4*A*cos(d*x+c)^5*a*b^3-19*A*cos(d*x+c)^4*a^3*b+20*A*cos(d*x+c)^4*a^2*b^2-8*A*cos(d*x+c)^4*a*b^3+26*A*cos(d*x+c)^3*a^3*b+4*A*cos(d*x+c)^3*a*b^3-A*cos(d*x+c)^2*a^2*b^2+18*A*cos(d*x+c)*a^3*b-63*B*cos(d*x+c)^5*a^3*b-7*B*cos(d*x+c)^5*a^2*b^2+14*B*cos(d*x+c)^5*a*b^3+35*B*cos(d*x+c)^4*a^3*b+14*B*cos(d*x+c)^4*a^2*b^2-14*B*cos(d*x+c)^4*a*b^3-7*B*cos(d*x+c)^3*a^2*b^2-8*A*sin(d*x+c)*cos(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^3+8*A*sin(d*x+c)*cos(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))*b^4-25*A*sin(d*x+c)*cos(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^4+63*B*sin(d*x+c)*cos(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^4-63*B*sin(d*x+c)*cos(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^4+8*A*sin(d*x+c)*cos(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))*b^4-25*A*sin(d*x+c)*cos(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^4+63*B*sin(d*x+c)*cos(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^4-63*B*sin(d*x+c)*cos(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^4+15*A*a^4+63*B*sin(d*x+c)*cos(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^3*b-14*B*sin(d*x+c)*cos(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^2*b^2-14*B*sin(d*x+c)*cos(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^3-49*B*sin(d*x+c)*cos(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^3*b+14*B*sin(d*x+c)*cos(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^2+19*A*sin(d*x+c)*cos(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*b+19*A*sin(d*x+c)*cos(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^2+8*A*sin(d*x+c)*cos(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^3-19*A*sin(d*x+c)*cos(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^3*b-2*A*sin(d*x+c)*cos(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^2*b^2-8*A*sin(d*x+c)*cos(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^3+63*B*sin(d*x+c)*cos(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*b-14*B*sin(d*x+c)*cos(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^2-14*B*sin(d*x+c)*cos(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^3-49*B*sin(d*x+c)*cos(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^3*b+14*B*sin(d*x+c)*cos(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^2*b^2+19*A*sin(d*x+c)*cos(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^3*b+19*A*sin(d*x+c)*cos(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^2*b^2+8*A*sin(d*x+c)*cos(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^3-19*A*sin(d*x+c)*cos(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^3*b-2*A*sin(d*x+c)*cos(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^2)/(a+b*cos(d*x+c))^(1/2)/a^3/sin(d*x+c)/cos(d*x+c)^(7/2)","B"
402,1,4048,616,0.631000," ","int(cos(d*x+c)^(3/2)*(a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)),x)","\text{output too large to display}"," ",0,"-1/192/d/(a+b*cos(d*x+c))^(1/2)*(136*A*cos(d*x+c)^3*a^2*b^2-3*B*cos(d*x+c)^3*a^3*b+108*B*cos(d*x+c)^3*a*b^3+78*B*cos(d*x+c)^2*a^2*b^2-156*B*cos(d*x+c)^2*a*b^3-6*B*cos(d*x+c)*a^3*b-156*B*cos(d*x+c)*a^2*b^2-72*B*cos(d*x+c)*a*b^3+24*A*cos(d*x+c)^2*a^3*b-48*A*cos(d*x+c)^2*a*b^3-112*A*cos(d*x+c)*a^2*b^2-128*A*cos(d*x+c)*a*b^3+128*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^4-9*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^4+18*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)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,(-(a-b)/(a+b))^(1/2))*a^4+288*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)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,(-(a-b)/(a+b))^(1/2))*b^4-144*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^4+48*B*cos(d*x+c)^6*b^4+64*A*cos(d*x+c)^3*b^4-128*A*cos(d*x+c)^2*b^4+24*B*cos(d*x+c)^4*b^4-72*B*cos(d*x+c)^2*b^4-9*B*cos(d*x+c)^2*a^4+9*B*cos(d*x+c)*a^4+64*A*cos(d*x+c)^5*b^4+9*B*cos(d*x+c)^2*a^3*b+176*A*cos(d*x+c)^4*a*b^3-24*A*cos(d*x+c)^2*a^2*b^2-24*A*cos(d*x+c)*a^3*b+120*B*cos(d*x+c)^5*a*b^3+78*B*cos(d*x+c)^4*a^2*b^2+24*A*sin(d*x+c)*cos(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-9*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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+18*B*sin(d*x+c)*cos(d*x+c)*(cos(d*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+288*B*sin(d*x+c)*cos(d*x+c)*(cos(d*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*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+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+24*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^3*b+24*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^2*b^2+128*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*b^3-48*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)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,(-(a-b)/(a+b))^(1/2))*a^3*b+576*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)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,(-(a-b)/(a+b))^(1/2))*a*b^3+112*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))*a^2*b^2-416*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))*a*b^3-9*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^3*b+156*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+156*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^3+144*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)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,(-(a-b)/(a+b))^(1/2))*a^2*b^2+6*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-228*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+72*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*b^3+128*A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+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+24*A*sin(d*x+c)*cos(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^2+128*A*sin(d*x+c)*cos(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^3-48*A*sin(d*x+c)*cos(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+576*A*sin(d*x+c)*cos(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^3+112*A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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^2-416*A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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^3-9*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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+156*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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+156*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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+144*B*sin(d*x+c)*cos(d*x+c)*(cos(d*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+6*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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-228*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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)/b^2/cos(d*x+c)^(1/2)","B"
403,1,3139,518,0.394000," ","int(cos(d*x+c)^(1/2)*(a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)),x)","\text{output too large to display}"," ",0,"1/24/d/(a+b*cos(d*x+c))^(1/2)*(-36*A*sin(d*x+c)*cos(d*x+c)*(cos(d*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-30*A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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-30*A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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^2-72*B*sin(d*x+c)*cos(d*x+c)*(cos(d*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*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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-12*A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a*b^2-16*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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+48*A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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-12*A*cos(d*x+c)^4*b^3+12*A*cos(d*x+c)^2*b^3-8*B*cos(d*x+c)^5*b^3-8*B*cos(d*x+c)^3*b^3-3*B*cos(d*x+c)^2*a^3+16*B*cos(d*x+c)^2*b^3+3*B*cos(d*x+c)*a^3-42*A*cos(d*x+c)^3*a*b^2-30*A*cos(d*x+c)^2*a^2*b+30*A*cos(d*x+c)^2*a*b^2+30*A*cos(d*x+c)*a^2*b+12*A*cos(d*x+c)*a*b^2-22*B*cos(d*x+c)^4*a*b^2-17*B*cos(d*x+c)^3*a^2*b+3*B*cos(d*x+c)^2*a^2*b+6*B*cos(d*x+c)^2*a*b^2+14*B*cos(d*x+c)*a^2*b+16*B*cos(d*x+c)*a*b^2-48*A*sin(d*x+c)*cos(d*x+c)*(cos(d*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+6*B*sin(d*x+c)*cos(d*x+c)*(cos(d*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^3-3*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+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^3-12*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))*a*b^2-36*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)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,(-(a-b)/(a+b))^(1/2))*a^2*b-30*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^2*b-30*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*b^2-14*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+52*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*b^2-72*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)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,(-(a-b)/(a+b))^(1/2))*a*b^2-3*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-16*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+24*A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+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+48*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))*a^2*b+24*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^3-48*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)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,(-(a-b)/(a+b))^(1/2))*b^3+6*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)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,(-(a-b)/(a+b))^(1/2))*a^3-3*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^3-16*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^3)/sin(d*x+c)/b/cos(d*x+c)^(1/2)","B"
404,1,2430,430,0.393000," ","int((a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(1/2),x)","\text{Expression too large to display}"," ",0,"-1/4/d*(5*B*cos(d*x+c)^2*a^2-8*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^2-5*B*cos(d*x+c)*a^2+4*A*cos(d*x+c)^3*b^2-4*A*cos(d*x+c)^2*b^2+2*B*cos(d*x+c)^4*b^2-2*B*cos(d*x+c)^2*b^2+8*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))*a^2+24*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)*a*b+8*A*sin(d*x+c)*cos(d*x+c)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^2-8*B*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*cos(d*x+c)*a^2+5*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))*cos(d*x+c)*a*b+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)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*cos(d*x+c)*a*b+4*A*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)*(cos(d*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-16*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)*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*A*cos(d*x+c)^2*a*b-4*A*cos(d*x+c)*a*b+7*B*cos(d*x+c)^3*a*b-5*B*cos(d*x+c)^2*a*b-2*B*cos(d*x+c)*a*b+4*A*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*b^2+6*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)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,(-(a-b)/(a+b))^(1/2))*a^2+8*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)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,(-(a-b)/(a+b))^(1/2))*b^2+5*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^2-4*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))*b^2+4*A*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a*b-16*A*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a*b+5*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*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*b+4*A*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)*(cos(d*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*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)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,(-(a-b)/(a+b))^(1/2))*cos(d*x+c)*a^2+8*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)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,(-(a-b)/(a+b))^(1/2))*cos(d*x+c)*b^2+5*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))*cos(d*x+c)*a^2-4*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))*cos(d*x+c)*b^2+24*A*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)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a*b)/(a+b*cos(d*x+c))^(1/2)/cos(d*x+c)^(1/2)/sin(d*x+c)","B"
405,1,2185,417,0.237000," ","int((a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(3/2),x)","\text{Expression too large to display}"," ",0,"-1/d*(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)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a^2-B*cos(d*x+c)^2*b^2-2*a^2*A+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))*a^2+6*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)*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)*a*b+2*A*sin(d*x+c)*cos(d*x+c)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^2+2*B*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*cos(d*x+c)*a^2+B*cos(d*x+c)^3*b^2+2*A*cos(d*x+c)*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))*cos(d*x+c)*a*b-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))*cos(d*x+c)*a*b-2*A*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)*(cos(d*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*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)*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-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)*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^2-2*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)*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+4*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)*b^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))*sin(d*x+c)*cos(d*x+c)*b^2+6*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)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*a*b+2*A*cos(d*x+c)^2*a*b-2*A*cos(d*x+c)*a*b+B*cos(d*x+c)^2*a*b-B*cos(d*x+c)*a*b-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)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*b^2-2*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)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*a^2+4*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)*b^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))*sin(d*x+c)*b^2-2*A*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a*b+4*A*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a*b+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-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*b)/(a+b*cos(d*x+c))^(1/2)/sin(d*x+c)/cos(d*x+c)^(1/2)","B"
406,1,2318,385,0.396000," ","int((a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(5/2),x)","\text{Expression too large to display}"," ",0,"-2/3/d*(3*B*cos(d*x+c)^2*a^2+3*A*sin(d*x+c)*cos(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))*b^2+6*B*sin(d*x+c)*cos(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^2-3*B*sin(d*x+c)*cos(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))*b^2+6*B*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*cos(d*x+c)^2*a*b-3*B*cos(d*x+c)*a^2+4*A*cos(d*x+c)^3*b^2-4*A*cos(d*x+c)^2*b^2-a^2*A-4*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))*sin(d*x+c)*cos(d*x+c)^2*a*b+A*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((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^2-4*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))*sin(d*x+c)*cos(d*x+c)^2*b^2+3*B*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*cos(d*x+c)^2*a^2-3*B*sin(d*x+c)*cos(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+A*sin(d*x+c)*cos(d*x+c)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^2+3*B*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*cos(d*x+c)*a^2+A*cos(d*x+c)^2*a^2-3*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))*cos(d*x+c)*a*b+6*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))*cos(d*x+c)*a*b-4*A*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)*(cos(d*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*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)*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+A*cos(d*x+c)^3*a*b-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))*cos(d*x+c)^2*a*b+4*A*sin(d*x+c)*cos(d*x+c)^2*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a*b+3*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)*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^2+4*A*cos(d*x+c)^2*a*b-5*A*cos(d*x+c)*a*b+3*B*cos(d*x+c)^3*a*b-3*B*cos(d*x+c)^2*a*b-4*A*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)*(cos(d*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*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)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,(-(a-b)/(a+b))^(1/2))*cos(d*x+c)*b^2-3*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))*cos(d*x+c)*a^2-3*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))*cos(d*x+c)*b^2)/(a+b*cos(d*x+c))^(1/2)/sin(d*x+c)/cos(d*x+c)^(3/2)","B"
407,1,2666,321,0.325000," ","int((a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(7/2),x)","\text{Expression too large to display}"," ",0,"2/15/d*(3*A*a^3-9*A*cos(d*x+c)^3*a^3+3*A*cos(d*x+c)^3*b^3+6*A*cos(d*x+c)^2*a^3-5*B*cos(d*x+c)^3*a^3-20*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)*sin(d*x+c)*cos(d*x+c)^3*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a^2*b-15*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)*sin(d*x+c)*cos(d*x+c)^2*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a*b^2-3*A*cos(d*x+c)^4*b^3+5*B*cos(d*x+c)*a^3-3*A*cos(d*x+c)^3*a*b^2+9*A*cos(d*x+c)^2*a*b^2+9*A*cos(d*x+c)*a^2*b-20*B*cos(d*x+c)^4*a*b^2-20*B*cos(d*x+c)^3*a^2*b+25*B*cos(d*x+c)^2*a^2*b+9*A*sin(d*x+c)*cos(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*A*sin(d*x+c)*cos(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^2-12*A*sin(d*x+c)*cos(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*A*sin(d*x+c)*cos(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+20*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)*sin(d*x+c)*cos(d*x+c)^2*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a^2*b+20*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)*sin(d*x+c)*cos(d*x+c)^2*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a*b^2-20*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)*sin(d*x+c)*cos(d*x+c)^2*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a^2*b+20*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)*sin(d*x+c)*cos(d*x+c)^3*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a*b^2+9*A*sin(d*x+c)*cos(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+3*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)*sin(d*x+c)*cos(d*x+c)^3*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a*b^2-12*A*sin(d*x+c)*cos(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^2*b-3*A*sin(d*x+c)*cos(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+20*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)*sin(d*x+c)*cos(d*x+c)^3*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a^2*b-15*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)*sin(d*x+c)*cos(d*x+c)^3*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a*b^2+20*B*cos(d*x+c)^3*a*b^2-9*A*cos(d*x+c)^4*a^2*b-6*A*cos(d*x+c)^4*a*b^2-5*B*cos(d*x+c)^4*a^2*b-5*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)*sin(d*x+c)*cos(d*x+c)^2*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a^3+9*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)*sin(d*x+c)*cos(d*x+c)^3*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a^3+3*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)*sin(d*x+c)*cos(d*x+c)^3*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*b^3-9*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)*sin(d*x+c)*cos(d*x+c)^3*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a^3-5*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)*sin(d*x+c)*cos(d*x+c)^3*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a^3+9*A*sin(d*x+c)*cos(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^3+3*A*sin(d*x+c)*cos(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^3-9*A*sin(d*x+c)*cos(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)/(a+b*cos(d*x+c))^(1/2)/a/sin(d*x+c)/cos(d*x+c)^(5/2)","B"
408,1,3413,395,0.533000," ","int((a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(9/2),x)","\text{output too large to display}"," ",0,"2/105/d*(-63*B*cos(d*x+c)^4*a^4+42*B*cos(d*x+c)^3*a^4+21*B*cos(d*x+c)*a^4-25*A*cos(d*x+c)^4*a^4+10*A*cos(d*x+c)^2*a^4+6*A*cos(d*x+c)^5*b^4-6*A*cos(d*x+c)^4*b^4+63*B*cos(d*x+c)^2*a^3*b-25*A*cos(d*x+c)^5*a^3*b-82*A*cos(d*x+c)^5*a^2*b^2-3*A*cos(d*x+c)^5*a*b^3-82*A*cos(d*x+c)^4*a^3*b+55*A*cos(d*x+c)^4*a^2*b^2+6*A*cos(d*x+c)^4*a*b^3+68*A*cos(d*x+c)^3*a^3*b-3*A*cos(d*x+c)^3*a*b^3+27*A*cos(d*x+c)^2*a^2*b^2+39*A*cos(d*x+c)*a^3*b-63*B*cos(d*x+c)^5*a^3*b-42*B*cos(d*x+c)^5*a^2*b^2-21*B*cos(d*x+c)^5*a*b^3-21*B*cos(d*x+c)^4*a^2*b^2+21*B*cos(d*x+c)^4*a*b^3+63*B*cos(d*x+c)^3*a^2*b^2+6*A*sin(d*x+c)*cos(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^3-6*A*sin(d*x+c)*cos(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))*b^4-25*A*sin(d*x+c)*cos(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^4+63*B*sin(d*x+c)*cos(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^4-63*B*sin(d*x+c)*cos(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^4-6*A*sin(d*x+c)*cos(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))*b^4-25*A*sin(d*x+c)*cos(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^4+63*B*sin(d*x+c)*cos(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^4-63*B*sin(d*x+c)*cos(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^4+15*A*a^4+63*B*sin(d*x+c)*cos(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^3*b+21*B*sin(d*x+c)*cos(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^2*b^2+21*B*sin(d*x+c)*cos(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^3-84*B*sin(d*x+c)*cos(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^3*b-21*B*sin(d*x+c)*cos(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^2+82*A*sin(d*x+c)*cos(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*b+82*A*sin(d*x+c)*cos(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^2-6*A*sin(d*x+c)*cos(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^3-82*A*sin(d*x+c)*cos(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^3*b-51*A*sin(d*x+c)*cos(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^2*b^2+6*A*sin(d*x+c)*cos(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^3+63*B*sin(d*x+c)*cos(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*b+21*B*sin(d*x+c)*cos(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^2+21*B*sin(d*x+c)*cos(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^3-84*B*sin(d*x+c)*cos(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^3*b-21*B*sin(d*x+c)*cos(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^2*b^2+82*A*sin(d*x+c)*cos(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^3*b+82*A*sin(d*x+c)*cos(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^2*b^2-6*A*sin(d*x+c)*cos(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^3-82*A*sin(d*x+c)*cos(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^3*b-51*A*sin(d*x+c)*cos(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^2)/(a+b*cos(d*x+c))^(1/2)/a^2/sin(d*x+c)/cos(d*x+c)^(7/2)","B"
409,1,4392,478,0.709000," ","int((a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(11/2),x)","\text{output too large to display}"," ",0,"2/315/d*(-33*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)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)^4*a^3*b^2-2*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)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)^4*a^2*b^3-8*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)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)^4*a*b^4+246*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))*sin(d*x+c)*cos(d*x+c)^4*a^4*b+246*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))*sin(d*x+c)*cos(d*x+c)^4*a^3*b^2-18*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))*sin(d*x+c)*cos(d*x+c)^4*a^2*b^3-18*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))*sin(d*x+c)*cos(d*x+c)^4*a*b^4-246*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)^4*a^4*b-153*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)^4*a^3*b^2+18*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)^4*a^2*b^3+147*A*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(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)*a^4*b+33*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))*sin(d*x+c)*cos(d*x+c)^5*a^3*b^2+33*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))*sin(d*x+c)*cos(d*x+c)^5*a^2*b^3+8*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))*sin(d*x+c)*cos(d*x+c)^5*a*b^4-186*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)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)^5*a^4*b-33*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)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)^5*a^3*b^2-2*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)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)^5*a^2*b^3-8*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)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)^5*a*b^4+246*B*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(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)*a^4*b+246*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))*sin(d*x+c)*cos(d*x+c)^5*a^3*b^2-18*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))*sin(d*x+c)*cos(d*x+c)^5*a^2*b^3-18*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))*sin(d*x+c)*cos(d*x+c)^5*a*b^4-246*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)^5*a^4*b-153*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)^5*a^3*b^2+18*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)^5*a^2*b^3+147*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))*sin(d*x+c)*cos(d*x+c)^4*a^4*b-186*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)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)^4*a^4*b+117*B*cos(d*x+c)^2*a^4*b-75*B*cos(d*x+c)^6*a^4*b-246*B*cos(d*x+c)^6*a^3*b^2-9*B*cos(d*x+c)^6*a^2*b^3+18*B*cos(d*x+c)^6*a*b^4-246*B*cos(d*x+c)^5*a^4*b+165*B*cos(d*x+c)^5*a^3*b^2+18*B*cos(d*x+c)^5*a^2*b^3-18*B*cos(d*x+c)^5*a*b^4+204*B*cos(d*x+c)^4*a^4*b+35*A*a^5-147*A*cos(d*x+c)^6*a^4*b-88*A*cos(d*x+c)^6*a^3*b^2-33*A*cos(d*x+c)^6*a^2*b^3+4*A*cos(d*x+c)^6*a*b^4+10*A*cos(d*x+c)^5*a^4*b-33*A*cos(d*x+c)^5*a^3*b^2+34*A*cos(d*x+c)^5*a^2*b^3-8*A*cos(d*x+c)^5*a*b^4+68*A*cos(d*x+c)^4*a^3*b^2+4*A*cos(d*x+c)^4*a*b^4+52*A*cos(d*x+c)^3*a^4*b-A*cos(d*x+c)^3*a^2*b^3+53*A*cos(d*x+c)^2*a^3*b^2+85*A*cos(d*x+c)*a^4*b-9*B*cos(d*x+c)^4*a^2*b^3+81*B*cos(d*x+c)^3*a^3*b^2-8*A*cos(d*x+c)^6*b^5-147*A*cos(d*x+c)^5*a^5+8*A*cos(d*x+c)^5*b^5+98*A*cos(d*x+c)^4*a^5+14*A*cos(d*x+c)^2*a^5-75*B*cos(d*x+c)^5*a^5+30*B*cos(d*x+c)^3*a^5+45*B*cos(d*x+c)*a^5+147*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))*sin(d*x+c)*cos(d*x+c)^5*a^5+8*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))*sin(d*x+c)*cos(d*x+c)^5*b^5-147*A*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(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)*a^5-75*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)^5*a^5+147*A*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(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)*a^5+8*A*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(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)*b^5-147*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)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)^4*a^5-75*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)^4*a^5+33*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))*sin(d*x+c)*cos(d*x+c)^4*a^3*b^2+33*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))*sin(d*x+c)*cos(d*x+c)^4*a^2*b^3+8*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))*sin(d*x+c)*cos(d*x+c)^4*a*b^4)/(a+b*cos(d*x+c))^(1/2)/a^3/sin(d*x+c)/cos(d*x+c)^(9/2)","B"
410,1,5164,719,0.971000," ","int(cos(d*x+c)^(3/2)*(a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)),x)","\text{output too large to display}"," ",0,"result too large to display","B"
411,1,4238,610,0.584000," ","int(cos(d*x+c)^(1/2)*(a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)),x)","\text{output too large to display}"," ",0,"1/192/d/(a+b*cos(d*x+c))^(1/2)*(-472*A*cos(d*x+c)^3*a^2*b^2-133*B*cos(d*x+c)^3*a^3*b-172*B*cos(d*x+c)^3*a*b^3-30*B*cos(d*x+c)^2*a^2*b^2+284*B*cos(d*x+c)^2*a*b^3+118*B*cos(d*x+c)*a^3*b+284*B*cos(d*x+c)*a^2*b^2+72*B*cos(d*x+c)*a*b^3-264*A*cos(d*x+c)^2*a^3*b+144*A*cos(d*x+c)^2*a*b^3+208*A*cos(d*x+c)*a^2*b^2+128*A*cos(d*x+c)*a*b^3-128*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^4-15*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^4+30*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)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,(-(a-b)/(a+b))^(1/2))*a^4-288*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)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,(-(a-b)/(a+b))^(1/2))*b^4+144*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^4-48*B*cos(d*x+c)^6*b^4-64*A*cos(d*x+c)^3*b^4+128*A*cos(d*x+c)^2*b^4-24*B*cos(d*x+c)^4*b^4+72*B*cos(d*x+c)^2*b^4-15*B*cos(d*x+c)^2*a^4+15*B*cos(d*x+c)*a^4-64*A*cos(d*x+c)^5*b^4+15*B*cos(d*x+c)^2*a^3*b-272*A*cos(d*x+c)^4*a*b^3+264*A*cos(d*x+c)^2*a^2*b^2+264*A*cos(d*x+c)*a^3*b-184*B*cos(d*x+c)^5*a*b^3-254*B*cos(d*x+c)^4*a^2*b^2-264*A*sin(d*x+c)*cos(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-15*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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+30*B*sin(d*x+c)*cos(d*x+c)*(cos(d*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^4-288*B*sin(d*x+c)*cos(d*x+c)*(cos(d*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*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+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^4-264*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^3*b-264*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^2*b^2-128*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*b^3-240*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)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,(-(a-b)/(a+b))^(1/2))*a^3*b-960*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)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,(-(a-b)/(a+b))^(1/2))*a*b^3-208*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))*a^2*b^2+608*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))*a*b^3-15*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^3*b-284*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^2-284*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^3-720*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)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,(-(a-b)/(a+b))^(1/2))*a^2*b^2-118*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+644*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^2-72*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*b^3-128*A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+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^4-264*A*sin(d*x+c)*cos(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^2-128*A*sin(d*x+c)*cos(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^3-240*A*sin(d*x+c)*cos(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-960*A*sin(d*x+c)*cos(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^3-208*A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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+608*A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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^3-720*B*sin(d*x+c)*cos(d*x+c)*(cos(d*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^2-118*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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+384*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))*a^3*b+384*A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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)/b/cos(d*x+c)^(1/2)","B"
412,1,3512,516,0.550000," ","int((a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(1/2),x)","\text{output too large to display}"," ",0,"-1/24/d*(-48*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+48*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))*a^3+180*A*sin(d*x+c)*cos(d*x+c)*(cos(d*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+54*A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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+54*A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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+120*B*sin(d*x+c)*cos(d*x+c)*(cos(d*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*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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+12*A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a*b^2+16*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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^2-144*A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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+12*A*cos(d*x+c)^4*b^3-12*A*cos(d*x+c)^2*b^3+8*B*cos(d*x+c)^5*b^3+8*B*cos(d*x+c)^3*b^3+33*B*cos(d*x+c)^2*a^3-16*B*cos(d*x+c)^2*b^3-33*B*cos(d*x+c)*a^3+66*A*cos(d*x+c)^3*a*b^2+54*A*cos(d*x+c)^2*a^2*b-54*A*cos(d*x+c)^2*a*b^2-54*A*cos(d*x+c)*a^2*b-12*A*cos(d*x+c)*a*b^2+34*B*cos(d*x+c)^4*a*b^2+59*B*cos(d*x+c)^3*a^2*b-33*B*cos(d*x+c)^2*a^2*b-18*B*cos(d*x+c)^2*a*b^2-26*B*cos(d*x+c)*a^2*b-16*B*cos(d*x+c)*a*b^2+48*A*sin(d*x+c)*cos(d*x+c)*(cos(d*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+30*B*sin(d*x+c)*cos(d*x+c)*(cos(d*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+33*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+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+12*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))*a*b^2+180*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)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,(-(a-b)/(a+b))^(1/2))*a^2*b+54*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^2*b+54*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*b^2+26*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-76*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*b^2+120*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)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,(-(a-b)/(a+b))^(1/2))*a*b^2+33*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+16*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^2-24*A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+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^3-144*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))*a^2*b-24*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^3+48*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)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,(-(a-b)/(a+b))^(1/2))*b^3+30*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)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,(-(a-b)/(a+b))^(1/2))*a^3+33*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^3+16*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^3+48*A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a^3-48*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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)/cos(d*x+c)^(1/2)/sin(d*x+c)","B"
413,1,3270,501,0.307000," ","int((a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(3/2),x)","\text{output too large to display}"," ",0,"1/4/d*(8*A*a^3-8*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^3-30*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)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*a^2*b+8*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))*sin(d*x+c)*cos(d*x+c)*a^3-4*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))*sin(d*x+c)*cos(d*x+c)*b^3+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)*b^3-8*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)*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)*b^3-40*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)*a*b^2-40*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)*a*b^2-30*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)*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)*a^2*b-4*A*cos(d*x+c)^3*b^3-8*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))*a^3+8*A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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*A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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+24*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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+24*A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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^2-24*A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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*A*cos(d*x+c)^2*b^3+2*B*cos(d*x+c)^2*b^3-8*A*cos(d*x+c)^2*a^2*b-4*A*cos(d*x+c)^2*a*b^2+8*A*cos(d*x+c)*a^2*b+4*A*cos(d*x+c)*a*b^2-9*B*cos(d*x+c)^2*a^2*b+9*B*cos(d*x+c)^2*a*b^2+9*B*cos(d*x+c)*a^2*b+2*B*cos(d*x+c)*a*b^2-8*A*cos(d*x+c)*a^3-2*B*cos(d*x+c)^4*b^3+24*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))*a*b^2+8*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^2*b-4*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*b^2+24*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*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*b^2-9*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-9*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^2-24*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))*a^2*b-11*B*cos(d*x+c)^3*a*b^2-8*A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a^3-8*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a^3+8*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))*sin(d*x+c)*a^3-4*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))*sin(d*x+c)*b^3+4*B*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*b^3-8*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)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*b^3)/(a+b*cos(d*x+c))^(1/2)/sin(d*x+c)/cos(d*x+c)^(1/2)","B"
414,1,3204,492,0.319000," ","int((a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(5/2),x)","\text{output too large to display}"," ",0,"-1/3/d*(-2*A*a^3+2*A*cos(d*x+c)^2*a^3-14*A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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-14*A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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+18*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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-18*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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+30*B*sin(d*x+c)*cos(d*x+c)*(cos(d*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^2-6*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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+18*A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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^2-18*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)*sin(d*x+c)*cos(d*x+c)^2*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a*b^2+14*A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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*B*cos(d*x+c)^3*b^3+6*B*cos(d*x+c)^2*a^3-6*B*cos(d*x+c)*a^3+14*A*cos(d*x+c)^3*a*b^2+14*A*cos(d*x+c)^2*a^2*b-14*A*cos(d*x+c)^2*a*b^2-16*A*cos(d*x+c)*a^2*b+6*B*cos(d*x+c)^3*a^2*b-6*B*cos(d*x+c)^2*a^2*b-3*B*cos(d*x+c)^2*a*b^2+3*B*cos(d*x+c)^4*b^3+12*A*sin(d*x+c)*cos(d*x+c)*(cos(d*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^3-6*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+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*A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+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^3-14*A*sin(d*x+c)*cos(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-14*A*sin(d*x+c)*cos(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+14*A*sin(d*x+c)*cos(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+18*A*sin(d*x+c)*cos(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^2-6*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)*sin(d*x+c)*cos(d*x+c)^2*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a^2*b+3*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)*sin(d*x+c)*cos(d*x+c)^2*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a*b^2+18*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)*sin(d*x+c)*cos(d*x+c)^2*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a^2*b+30*B*sin(d*x+c)*cos(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*b^2+3*B*cos(d*x+c)^3*a*b^2+2*A*cos(d*x+c)^3*a^2*b+2*A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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*B*sin(d*x+c)*cos(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^3+3*B*sin(d*x+c)*cos(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^3-6*A*sin(d*x+c)*cos(d*x+c)^2*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*b^3+12*A*sin(d*x+c)*cos(d*x+c)^2*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,(-(a-b)/(a+b))^(1/2))*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*b^3+6*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)*sin(d*x+c)*cos(d*x+c)^2*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a^3+2*A*sin(d*x+c)*cos(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)/(a+b*cos(d*x+c))^(1/2)/sin(d*x+c)/cos(d*x+c)^(3/2)","B"
415,1,3274,453,0.376000," ","int((a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(7/2),x)","\text{output too large to display}"," ",0,"2/15/d*(3*A*a^3-9*A*cos(d*x+c)^3*a^3+23*A*cos(d*x+c)^3*b^3+6*A*cos(d*x+c)^2*a^3-5*B*cos(d*x+c)^3*a^3-35*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)*sin(d*x+c)*cos(d*x+c)^3*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a^2*b-45*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)*sin(d*x+c)*cos(d*x+c)^2*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a*b^2-23*A*cos(d*x+c)^4*b^3+5*B*cos(d*x+c)*a^3-23*A*cos(d*x+c)^3*a*b^2+34*A*cos(d*x+c)^2*a*b^2+14*A*cos(d*x+c)*a^2*b-35*B*cos(d*x+c)^4*a*b^2-35*B*cos(d*x+c)^3*a^2*b+40*B*cos(d*x+c)^2*a^2*b+9*A*sin(d*x+c)*cos(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+23*A*sin(d*x+c)*cos(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^2-17*A*sin(d*x+c)*cos(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-23*A*sin(d*x+c)*cos(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+35*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)*sin(d*x+c)*cos(d*x+c)^2*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a^2*b+35*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)*sin(d*x+c)*cos(d*x+c)^2*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a*b^2-35*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)*sin(d*x+c)*cos(d*x+c)^2*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a^2*b+35*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)*sin(d*x+c)*cos(d*x+c)^3*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a*b^2+9*A*sin(d*x+c)*cos(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+23*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)*sin(d*x+c)*cos(d*x+c)^3*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a*b^2-17*A*sin(d*x+c)*cos(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^2*b-23*A*sin(d*x+c)*cos(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+35*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)*sin(d*x+c)*cos(d*x+c)^3*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a^2*b-45*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)*sin(d*x+c)*cos(d*x+c)^3*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a*b^2+35*B*cos(d*x+c)^3*a*b^2-9*A*cos(d*x+c)^4*a^2*b-11*A*cos(d*x+c)^4*a*b^2-5*A*cos(d*x+c)^3*a^2*b-5*B*cos(d*x+c)^4*a^2*b-15*A*sin(d*x+c)*cos(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))*b^3+15*B*sin(d*x+c)*cos(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))*b^3-30*B*sin(d*x+c)*cos(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)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,(-(a-b)/(a+b))^(1/2))*b^3+15*B*sin(d*x+c)*cos(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))*b^3-30*B*sin(d*x+c)*cos(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^3-15*A*sin(d*x+c)*cos(d*x+c)^2*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*b^3-5*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)*sin(d*x+c)*cos(d*x+c)^2*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a^3+9*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)*sin(d*x+c)*cos(d*x+c)^3*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a^3+23*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)*sin(d*x+c)*cos(d*x+c)^3*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*b^3-9*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)*sin(d*x+c)*cos(d*x+c)^3*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a^3-5*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)*sin(d*x+c)*cos(d*x+c)^3*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a^3+9*A*sin(d*x+c)*cos(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^3+23*A*sin(d*x+c)*cos(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^3-9*A*sin(d*x+c)*cos(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)/(a+b*cos(d*x+c))^(1/2)/sin(d*x+c)/cos(d*x+c)^(5/2)","B"
416,1,3628,396,0.453000," ","int((a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(9/2),x)","\text{output too large to display}"," ",0,"-2/105/d*(105*B*sin(d*x+c)*cos(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^3+63*B*cos(d*x+c)^4*a^4-42*B*cos(d*x+c)^3*a^4-21*B*cos(d*x+c)*a^4+25*A*cos(d*x+c)^4*a^4-10*A*cos(d*x+c)^2*a^4+15*A*cos(d*x+c)^5*b^4-15*A*cos(d*x+c)^4*b^4-98*B*cos(d*x+c)^2*a^3*b+25*A*cos(d*x+c)^5*a^3*b+145*A*cos(d*x+c)^5*a^2*b^2+45*A*cos(d*x+c)^5*a*b^3+145*A*cos(d*x+c)^4*a^3*b-55*A*cos(d*x+c)^4*a^2*b^2+15*A*cos(d*x+c)^4*a*b^3-110*A*cos(d*x+c)^3*a^3*b-60*A*cos(d*x+c)^3*a*b^3-90*A*cos(d*x+c)^2*a^2*b^2-60*A*cos(d*x+c)*a^3*b+63*B*cos(d*x+c)^5*a^3*b+77*B*cos(d*x+c)^5*a^2*b^2+161*B*cos(d*x+c)^5*a*b^3+35*B*cos(d*x+c)^4*a^3*b+161*B*cos(d*x+c)^4*a^2*b^2-161*B*cos(d*x+c)^4*a*b^3-238*B*cos(d*x+c)^3*a^2*b^2+15*A*sin(d*x+c)*cos(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^3+105*B*sin(d*x+c)*cos(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^3-15*A*sin(d*x+c)*cos(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))*b^4+25*A*sin(d*x+c)*cos(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^4-63*B*sin(d*x+c)*cos(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^4+63*B*sin(d*x+c)*cos(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^4-15*A*sin(d*x+c)*cos(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))*b^4+25*A*sin(d*x+c)*cos(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^4-63*B*sin(d*x+c)*cos(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+63*B*sin(d*x+c)*cos(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^4-15*A*a^4-63*B*sin(d*x+c)*cos(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^3*b-161*B*sin(d*x+c)*cos(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^2*b^2-161*B*sin(d*x+c)*cos(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^3+119*B*sin(d*x+c)*cos(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^3*b+161*B*sin(d*x+c)*cos(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^2-145*A*sin(d*x+c)*cos(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*b-145*A*sin(d*x+c)*cos(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^2-15*A*sin(d*x+c)*cos(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^3+145*A*sin(d*x+c)*cos(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^3*b+135*A*sin(d*x+c)*cos(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^2*b^2+15*A*sin(d*x+c)*cos(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^3-63*B*sin(d*x+c)*cos(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*b-161*B*sin(d*x+c)*cos(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^2-161*B*sin(d*x+c)*cos(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^3+119*B*sin(d*x+c)*cos(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^3*b+161*B*sin(d*x+c)*cos(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^2*b^2-145*A*sin(d*x+c)*cos(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^3*b-145*A*sin(d*x+c)*cos(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^2*b^2-15*A*sin(d*x+c)*cos(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^3+145*A*sin(d*x+c)*cos(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^3*b+135*A*sin(d*x+c)*cos(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^2)/(a+b*cos(d*x+c))^(1/2)/a/sin(d*x+c)/cos(d*x+c)^(7/2)","B"
417,1,4392,478,0.543000," ","int((a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(11/2),x)","\text{output too large to display}"," ",0,"-2/315/d*(279*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)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)^4*a^3*b^2+155*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)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)^4*a^2*b^3-10*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)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)^4*a*b^4-435*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))*sin(d*x+c)*cos(d*x+c)^4*a^4*b-435*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))*sin(d*x+c)*cos(d*x+c)^4*a^3*b^2-45*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))*sin(d*x+c)*cos(d*x+c)^4*a^2*b^3-45*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))*sin(d*x+c)*cos(d*x+c)^4*a*b^4+435*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)^4*a^4*b+405*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)^4*a^3*b^2+45*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)^4*a^2*b^3-147*A*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(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)*a^4*b-279*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))*sin(d*x+c)*cos(d*x+c)^5*a^3*b^2-279*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))*sin(d*x+c)*cos(d*x+c)^5*a^2*b^3+10*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))*sin(d*x+c)*cos(d*x+c)^5*a*b^4+261*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)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)^5*a^4*b+279*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)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)^5*a^3*b^2+155*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)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)^5*a^2*b^3-10*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)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)^5*a*b^4-435*B*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(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)*a^4*b-435*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))*sin(d*x+c)*cos(d*x+c)^5*a^3*b^2-45*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))*sin(d*x+c)*cos(d*x+c)^5*a^2*b^3-45*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))*sin(d*x+c)*cos(d*x+c)^5*a*b^4+435*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)^5*a^4*b+405*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)^5*a^3*b^2+45*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)^5*a^2*b^3-147*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))*sin(d*x+c)*cos(d*x+c)^4*a^4*b+261*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)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)^4*a^4*b-180*B*cos(d*x+c)^2*a^4*b+75*B*cos(d*x+c)^6*a^4*b+435*B*cos(d*x+c)^6*a^3*b^2+135*B*cos(d*x+c)^6*a^2*b^3+45*B*cos(d*x+c)^6*a*b^4+435*B*cos(d*x+c)^5*a^4*b-165*B*cos(d*x+c)^5*a^3*b^2+45*B*cos(d*x+c)^5*a^2*b^3-45*B*cos(d*x+c)^5*a*b^4-330*B*cos(d*x+c)^4*a^4*b-35*A*a^5+147*A*cos(d*x+c)^6*a^4*b+163*A*cos(d*x+c)^6*a^3*b^2+279*A*cos(d*x+c)^6*a^2*b^3+5*A*cos(d*x+c)^6*a*b^4+65*A*cos(d*x+c)^5*a^4*b+279*A*cos(d*x+c)^5*a^3*b^2-199*A*cos(d*x+c)^5*a^2*b^3-10*A*cos(d*x+c)^5*a*b^4-272*A*cos(d*x+c)^4*a^3*b^2+5*A*cos(d*x+c)^4*a*b^4-82*A*cos(d*x+c)^3*a^4*b-80*A*cos(d*x+c)^3*a^2*b^3-170*A*cos(d*x+c)^2*a^3*b^2-130*A*cos(d*x+c)*a^4*b-180*B*cos(d*x+c)^4*a^2*b^3-270*B*cos(d*x+c)^3*a^3*b^2-10*A*cos(d*x+c)^6*b^5+147*A*cos(d*x+c)^5*a^5+10*A*cos(d*x+c)^5*b^5-98*A*cos(d*x+c)^4*a^5-14*A*cos(d*x+c)^2*a^5+75*B*cos(d*x+c)^5*a^5-30*B*cos(d*x+c)^3*a^5-45*B*cos(d*x+c)*a^5-147*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))*sin(d*x+c)*cos(d*x+c)^5*a^5+10*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))*sin(d*x+c)*cos(d*x+c)^5*b^5+147*A*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(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)*a^5+75*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)^5*a^5-147*A*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(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)*a^5+10*A*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(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)*b^5+147*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)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)^4*a^5+75*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)^4*a^5-279*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))*sin(d*x+c)*cos(d*x+c)^4*a^3*b^2-279*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))*sin(d*x+c)*cos(d*x+c)^4*a^2*b^3+10*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))*sin(d*x+c)*cos(d*x+c)^4*a*b^4)/(a+b*cos(d*x+c))^(1/2)/a^2/sin(d*x+c)/cos(d*x+c)^(9/2)","B"
418,1,5373,572,1.428000," ","int((a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(13/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
419,1,2346,390,0.509000," ","int((a+b*cos(d*x+c))^(5/2)*(3/2*b*B/a+B*cos(d*x+c))/cos(d*x+c)^(5/2),x)","\text{Expression too large to display}"," ",0,"-B/a/d*(-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^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)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,(-(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^2*b^2+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^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^3*b-6*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^2-6*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^3+10*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)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,(-(a-b)/(a+b))^(1/2))*a^2*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)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a^3*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^2*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)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a*b^3-2*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^3*b-6*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^2-6*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^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^2*b^2+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-cos(d*x+c)^2*a^3*b-8*cos(d*x+c)*a^2*b^2+2*cos(d*x+c)^3*a^2*b^2-7*cos(d*x+c)^2*a*b^3-b*a^3+cos(d*x+c)^4*a*b^3+2*cos(d*x+c)^3*a^3*b+6*cos(d*x+c)^3*a*b^3+6*cos(d*x+c)^2*a^2*b^2+2*cos(d*x+c)^2*a^4-2*a^4*cos(d*x+c)+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^4-3*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^4-2*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+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^4+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^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))*b^4)/(a+b*cos(d*x+c))^(1/2)/sin(d*x+c)/cos(d*x+c)^(3/2)","B"
420,1,1871,437,0.383000," ","int(cos(d*x+c)^(3/2)*(A+B*cos(d*x+c))/(a+b*cos(d*x+c))^(1/2),x)","-\frac{-4 A \left(\cos^{2}\left(d x +c \right)\right) b^{2}+4 A \left(\cos^{3}\left(d x +c \right)\right) b^{2}+3 B \cos \left(d x +c \right) a^{2}+4 A \left(\cos^{2}\left(d x +c \right)\right) a b -B \left(\cos^{3}\left(d x +c \right)\right) a b +3 B \left(\cos^{2}\left(d x +c \right)\right) a b -8 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) \cos \left(d x +c \right) a b -3 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) \cos \left(d x +c \right) a b +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)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{-\frac{a -b}{a +b}}\right) \cos \left(d x +c \right) a b +4 A \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{-\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \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 b -3 B \left(\cos^{2}\left(d x +c \right)\right) a^{2}-2 B \left(\cos^{2}\left(d x +c \right)\right) b^{2}+2 B \left(\cos^{4}\left(d x +c \right)\right) b^{2}-4 A \cos \left(d x +c \right) a b -2 B \cos \left(d x +c \right) a b +4 A \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{-\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \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 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)}}\, \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 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)}}\, \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}-3 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^{2}-4 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}+4 A \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{-\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \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 b -3 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 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) a b +4 A \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{-\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \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 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)}}\, \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) a^{2}+8 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)}}\, \EllipticPi \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, -1, \sqrt{-\frac{a -b}{a +b}}\right) \cos \left(d x +c \right) b^{2}-3 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) \cos \left(d x +c \right) a^{2}-4 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) \cos \left(d x +c \right) b^{2}-8 A \EllipticPi \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, -1, \sqrt{-\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \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 b}{4 d \sqrt{a +b \cos \left(d x +c \right)}\, \sin \left(d x +c \right) b^{2} \sqrt{\cos \left(d x +c \right)}}"," ",0,"-1/4/d/(a+b*cos(d*x+c))^(1/2)*(-3*B*cos(d*x+c)^2*a^2+3*B*cos(d*x+c)*a^2+4*A*cos(d*x+c)^3*b^2-4*A*cos(d*x+c)^2*b^2+2*B*cos(d*x+c)^4*b^2-2*B*cos(d*x+c)^2*b^2-8*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)*a*b-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))*cos(d*x+c)*a*b+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)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*cos(d*x+c)*a*b+4*A*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)*(cos(d*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*A*cos(d*x+c)^2*a*b-4*A*cos(d*x+c)*a*b-B*cos(d*x+c)^3*a*b+3*B*cos(d*x+c)^2*a*b-2*B*cos(d*x+c)*a*b+4*A*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*b^2+6*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)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,(-(a-b)/(a+b))^(1/2))*a^2+8*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)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,(-(a-b)/(a+b))^(1/2))*b^2-3*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^2-4*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))*b^2+4*A*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a*b-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*b+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)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a*b+4*A*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)*(cos(d*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*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)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,(-(a-b)/(a+b))^(1/2))*cos(d*x+c)*a^2+8*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)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,(-(a-b)/(a+b))^(1/2))*cos(d*x+c)*b^2-3*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))*cos(d*x+c)*a^2-4*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))*cos(d*x+c)*b^2-8*A*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)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a*b)/sin(d*x+c)/b^2/cos(d*x+c)^(1/2)","B"
421,1,1002,395,0.493000," ","int(cos(d*x+c)^(1/2)*(A+B*cos(d*x+c))/(a+b*cos(d*x+c))^(1/2),x)","-\frac{4 A \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{a +b \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \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 A \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \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 +B \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{-\frac{a -b}{a +b}}\right) a +B \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{-\frac{a -b}{a +b}}\right) b -2 B \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticPi \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, -1, \sqrt{-\frac{a -b}{a +b}}\right) \sqrt{\frac{a +b \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, a +4 A \sin \left(d x +c \right) \sqrt{\frac{a +b \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \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 A \sin \left(d x +c \right) \sqrt{\frac{a +b \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{-\frac{a -b}{a +b}}\right) b +B \sin \left(d x +c \right) \sqrt{\frac{a +b \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \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{a +b \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{-\frac{a -b}{a +b}}\right) b -2 B \sin \left(d x +c \right) \EllipticPi \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, -1, \sqrt{-\frac{a -b}{a +b}}\right) \sqrt{\frac{a +b \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, a +B \left(\cos^{3}\left(d x +c \right)\right) b +B \left(\cos^{2}\left(d x +c \right)\right) a -b B \left(\cos^{2}\left(d x +c \right)\right)-B \cos \left(d x +c \right) a}{d \sqrt{a +b \cos \left(d x +c \right)}\, \sin \left(d x +c \right) b \sqrt{\cos \left(d x +c \right)}}"," ",0,"-1/d/(a+b*cos(d*x+c))^(1/2)*(4*A*sin(d*x+c)*cos(d*x+c)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,(-(a-b)/(a+b))^(1/2))*b-2*A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+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+B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a+B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+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*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*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)*a+4*A*sin(d*x+c)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,(-(a-b)/(a+b))^(1/2))*b-2*A*sin(d*x+c)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*b+B*sin(d*x+c)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a+B*sin(d*x+c)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*b-2*B*sin(d*x+c)*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)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*a+B*cos(d*x+c)^3*b+B*cos(d*x+c)^2*a-b*B*cos(d*x+c)^2-B*cos(d*x+c)*a)/sin(d*x+c)/b/cos(d*x+c)^(1/2)","B"
422,1,197,212,0.283000," ","int((A+B*cos(d*x+c))/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)}}\, \left(\sin^{2}\left(d x +c \right)\right) \left(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 \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{-\frac{a -b}{a +b}}\right)+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)}{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*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)/(a+b*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*(A*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))-B*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))+2*B*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,(-(a-b)/(a+b))^(1/2)))/(-1+cos(d*x+c))/cos(d*x+c)^(1/2)","A"
423,1,935,214,0.273000," ","int((A+B*cos(d*x+c))/cos(d*x+c)^(3/2)/(a+b*cos(d*x+c))^(1/2),x)","-\frac{2 \left(B \sin \left(d x +c \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}} \sqrt{\frac{a +b \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{-\frac{a -b}{a +b}}\right) a +2 B \sin \left(d x +c \right) \cos \left(d x +c \right) \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sqrt{\frac{a +b \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \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 +A \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \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 -A \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{-\frac{a -b}{a +b}}\right) a -A \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{-\frac{a -b}{a +b}}\right) b +B \sin \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{\frac{a +b \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \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 +A \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \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 -A \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{-\frac{a -b}{a +b}}\right) a -A \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{-\frac{a -b}{a +b}}\right) b +A \left(\cos^{3}\left(d x +c \right)\right) b +A \left(\cos^{2}\left(d x +c \right)\right) a -A \left(\cos^{2}\left(d x +c \right)\right) b -A \cos \left(d x +c \right) a \right)}{d \sqrt{a +b \cos \left(d x +c \right)}\, a \cos \left(d x +c \right)^{\frac{3}{2}} \sin \left(d x +c \right)}"," ",0,"-2/d/(a+b*cos(d*x+c))^(1/2)*(B*sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a+2*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a+A*sin(d*x+c)*cos(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-A*sin(d*x+c)*cos(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-A*sin(d*x+c)*cos(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+B*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a+A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a-A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a-A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+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+A*cos(d*x+c)^3*b+A*cos(d*x+c)^2*a-A*cos(d*x+c)^2*b-A*cos(d*x+c)*a)/a/cos(d*x+c)^(3/2)/sin(d*x+c)","B"
424,1,1536,264,0.274000," ","int((A+B*cos(d*x+c))/cos(d*x+c)^(5/2)/(a+b*cos(d*x+c))^(1/2),x)","-\frac{2 \left(2 A \left(\cos^{2}\left(d x +c \right)\right) b^{2}-2 A \left(\cos^{3}\left(d x +c \right)\right) b^{2}-3 B \cos \left(d x +c \right) a^{2}-a^{2} A +A \sin \left(d x +c \right) \cos \left(d x +c \right) \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{-\frac{a -b}{a +b}}\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \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}+3 B \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{-\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \cos \left(d x +c \right) a^{2}-2 A \left(\cos^{2}\left(d x +c \right)\right) a b +3 B \left(\cos^{3}\left(d x +c \right)\right) a b -3 B \left(\cos^{2}\left(d x +c \right)\right) a b +A \left(\cos^{2}\left(d x +c \right)\right) a^{2}-3 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) \cos \left(d x +c \right) a b +2 A \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{-\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \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 b -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)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{-\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) \cos \left(d x +c \right) a b +A \left(\cos^{3}\left(d x +c \right)\right) a b +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)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{-\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) a b -3 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) \left(\cos^{2}\left(d x +c \right)\right) a b -2 A \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\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{\cos \left(d x +c \right)}{1+\cos \left(d x +c \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 b +3 B \left(\cos^{2}\left(d x +c \right)\right) a^{2}+A \cos \left(d x +c \right) a b +A \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{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) a^{2}+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)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{-\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) b^{2}+3 B \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{-\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \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(\cos^{2}\left(d x +c \right)\right) a^{2}-3 B \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \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 A \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{-\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \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}-3 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) \cos \left(d x +c \right) a^{2}\right)}{3 d \sqrt{a +b \cos \left(d x +c \right)}\, a^{2} \sin \left(d x +c \right) \cos \left(d x +c \right)^{\frac{3}{2}}}"," ",0,"-2/3/d*(3*B*cos(d*x+c)^2*a^2-3*B*cos(d*x+c)*a^2-2*A*cos(d*x+c)^3*b^2+2*A*cos(d*x+c)^2*b^2-a^2*A+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)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)^2*a*b+A*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((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+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)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)^2*b^2+3*B*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*cos(d*x+c)^2*a^2-3*B*sin(d*x+c)*cos(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+A*sin(d*x+c)*cos(d*x+c)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^2+3*B*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*cos(d*x+c)*a^2+A*cos(d*x+c)^2*a^2-3*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))*cos(d*x+c)*a*b+2*A*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)*(cos(d*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-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)*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+A*cos(d*x+c)^3*a*b-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))*cos(d*x+c)^2*a*b-2*A*sin(d*x+c)*cos(d*x+c)^2*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a*b-2*A*cos(d*x+c)^2*a*b+A*cos(d*x+c)*a*b+3*B*cos(d*x+c)^3*a*b-3*B*cos(d*x+c)^2*a*b+2*A*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)*(cos(d*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^2-3*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))*cos(d*x+c)*a^2)/(a+b*cos(d*x+c))^(1/2)/a^2/sin(d*x+c)/cos(d*x+c)^(3/2)","B"
425,1,2480,331,0.436000," ","int((A+B*cos(d*x+c))/cos(d*x+c)^(7/2)/(a+b*cos(d*x+c))^(1/2),x)","\text{Expression too large to display}"," ",0,"-2/15/d*(-3*A*a^3+9*A*cos(d*x+c)^3*a^3-8*A*cos(d*x+c)^3*b^3-6*A*cos(d*x+c)^2*a^3+5*B*cos(d*x+c)^3*a^3-10*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)*sin(d*x+c)*cos(d*x+c)^3*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a^2*b+8*A*cos(d*x+c)^4*b^3-5*B*cos(d*x+c)*a^3+8*A*cos(d*x+c)^3*a*b^2-4*A*cos(d*x+c)^2*a*b^2+A*cos(d*x+c)*a^2*b-10*B*cos(d*x+c)^4*a*b^2-10*B*cos(d*x+c)^3*a^2*b+5*B*cos(d*x+c)^2*a^2*b-9*A*sin(d*x+c)*cos(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-8*A*sin(d*x+c)*cos(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+2*A*sin(d*x+c)*cos(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+8*A*sin(d*x+c)*cos(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+10*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)*sin(d*x+c)*cos(d*x+c)^2*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a^2*b+10*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)*sin(d*x+c)*cos(d*x+c)^2*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a*b^2-10*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)*sin(d*x+c)*cos(d*x+c)^2*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a^2*b+10*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)*sin(d*x+c)*cos(d*x+c)^3*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a*b^2-9*A*sin(d*x+c)*cos(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-8*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)*sin(d*x+c)*cos(d*x+c)^3*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a*b^2+2*A*sin(d*x+c)*cos(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^2*b+8*A*sin(d*x+c)*cos(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+10*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)*sin(d*x+c)*cos(d*x+c)^3*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a^2*b+10*B*cos(d*x+c)^3*a*b^2+9*A*cos(d*x+c)^4*a^2*b-4*A*cos(d*x+c)^4*a*b^2-10*A*cos(d*x+c)^3*a^2*b+5*B*cos(d*x+c)^4*a^2*b+5*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)*sin(d*x+c)*cos(d*x+c)^2*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a^3-9*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)*sin(d*x+c)*cos(d*x+c)^3*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a^3-8*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)*sin(d*x+c)*cos(d*x+c)^3*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*b^3+9*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)*sin(d*x+c)*cos(d*x+c)^3*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a^3+5*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)*sin(d*x+c)*cos(d*x+c)^3*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a^3-9*A*sin(d*x+c)*cos(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^3-8*A*sin(d*x+c)*cos(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+9*A*sin(d*x+c)*cos(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)/(a+b*cos(d*x+c))^(1/2)/a^3/sin(d*x+c)/cos(d*x+c)^(5/2)","B"
426,1,2885,468,0.352000," ","int(cos(d*x+c)^(3/2)*(A+B*cos(d*x+c))/(a+b*cos(d*x+c))^(3/2),x)","\text{output too large to display}"," ",0,"-1/d*(4*A*sin(d*x+c)*cos(d*x+c)*(cos(d*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*A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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*A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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+6*B*sin(d*x+c)*cos(d*x+c)*(cos(d*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*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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*A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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-B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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-B*cos(d*x+c)^3*b^3+3*B*cos(d*x+c)^2*a^3+B*cos(d*x+c)^2*b^3-3*B*cos(d*x+c)*a^3-2*A*cos(d*x+c)^2*a^2*b+2*A*cos(d*x+c)^2*a*b^2+2*A*cos(d*x+c)*a^2*b-2*A*cos(d*x+c)*a*b^2+B*cos(d*x+c)^3*a^2*b-3*B*cos(d*x+c)^2*a^2*b-B*cos(d*x+c)^2*a*b^2+2*B*cos(d*x+c)*a^2*b+B*cos(d*x+c)*a*b^2-4*A*sin(d*x+c)*cos(d*x+c)*(cos(d*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^3-6*B*sin(d*x+c)*cos(d*x+c)*(cos(d*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+3*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a^3-B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*b^3+2*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))*a*b^2+4*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)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,(-(a-b)/(a+b))^(1/2))*a^2*b-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^2*b-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*b^2-2*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)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a^2*b-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)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a*b^2+6*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)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,(-(a-b)/(a+b))^(1/2))*a*b^2+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-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+2*A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*b^3+2*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^3-4*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)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,(-(a-b)/(a+b))^(1/2))*b^3-6*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)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,(-(a-b)/(a+b))^(1/2))*a^3+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^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))*b^3)/(a+b*cos(d*x+c))^(1/2)/sin(d*x+c)/b^2/(a^2-b^2)/cos(d*x+c)^(1/2)","B"
427,1,2013,388,0.326000," ","int(cos(d*x+c)^(1/2)*(A+B*cos(d*x+c))/(a+b*cos(d*x+c))^(3/2),x)","\frac{2 A \left(\cos^{2}\left(d x +c \right)\right) b^{2}-2 B \cos \left(d x +c \right) a^{2}-2 A \left(\cos^{2}\left(d x +c \right)\right) a b -2 B \left(\cos^{2}\left(d x +c \right)\right) a b -2 A \cos \left(d x +c \right) b^{2}+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) \cos \left(d x +c \right) a b -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)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{-\frac{a -b}{a +b}}\right) \cos \left(d x +c \right) a b -2 A \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{-\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \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 b +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)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{-\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) \cos \left(d x +c \right) a b +2 B \left(\cos^{2}\left(d x +c \right)\right) a^{2}+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)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{-\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) \cos \left(d x +c \right) b^{2}+2 A \cos \left(d x +c \right) a b +2 B \cos \left(d x +c \right) a b -2 A \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{-\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \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}-4 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)}}\, \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 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)}}\, \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 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^{2}-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)}}\, \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 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)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{-\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) b^{2}-2 A \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{-\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \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 b +2 A \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{-\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \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 b +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 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) a b -2 A \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{-\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \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}-4 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)}}\, \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) a^{2}+4 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)}}\, \EllipticPi \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, -1, \sqrt{-\frac{a -b}{a +b}}\right) \cos \left(d x +c \right) b^{2}+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) \cos \left(d x +c \right) a^{2}-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)}}\, \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) b^{2}}{d \sqrt{a +b \cos \left(d x +c \right)}\, \sin \left(d x +c \right) b \left(a^{2}-b^{2}\right) \sqrt{\cos \left(d x +c \right)}}"," ",0,"2/d/(a+b*cos(d*x+c))^(1/2)*(B*cos(d*x+c)^2*a^2-B*cos(d*x+c)*a^2+A*cos(d*x+c)^2*b^2-A*cos(d*x+c)*b^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))*cos(d*x+c)*a*b-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))*cos(d*x+c)*a*b-A*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)*(cos(d*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+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)*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+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)*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^2-A*cos(d*x+c)^2*a*b+A*cos(d*x+c)*a*b-B*cos(d*x+c)^2*a*b+B*cos(d*x+c)*a*b-A*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*b^2-2*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)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,(-(a-b)/(a+b))^(1/2))*a^2+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)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,(-(a-b)/(a+b))^(1/2))*b^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^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)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*b^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)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*b^2-A*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a*b+A*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a*b+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-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*b-A*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)*(cos(d*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^2-2*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)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,(-(a-b)/(a+b))^(1/2))*cos(d*x+c)*a^2+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)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,(-(a-b)/(a+b))^(1/2))*cos(d*x+c)*b^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))*cos(d*x+c)*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)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*cos(d*x+c)*b^2)/sin(d*x+c)/b/(a^2-b^2)/cos(d*x+c)^(1/2)","B"
428,1,1633,264,0.408000," ","int((A+B*cos(d*x+c))/cos(d*x+c)^(1/2)/(a+b*cos(d*x+c))^(3/2),x)","\frac{2 A \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{-\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \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 b +2 A \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{-\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \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 A \sin \left(d x +c \right) \cos \left(d x +c \right) \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{-\frac{a -b}{a +b}}\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \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 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)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{-\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) \cos \left(d x +c \right) a b -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) \cos \left(d x +c \right) a^{2}-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) \cos \left(d x +c \right) a b +2 B \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{-\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \cos \left(d x +c \right) a^{2}+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)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{-\frac{a -b}{a +b}}\right) \cos \left(d x +c \right) a b +2 A \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{-\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \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 b +2 A \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{-\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \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 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) a^{2}-2 A \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{-\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \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 b -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^{2}-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 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) a^{2}+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)}}\, \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 A \left(\cos^{2}\left(d x +c \right)\right) a b -2 A \left(\cos^{2}\left(d x +c \right)\right) b^{2}-2 B \left(\cos^{2}\left(d x +c \right)\right) a^{2}+2 B \left(\cos^{2}\left(d x +c \right)\right) a b -2 A \cos \left(d x +c \right) a b +2 A \cos \left(d x +c \right) b^{2}+2 B \cos \left(d x +c \right) a^{2}-2 B \cos \left(d x +c \right) a b}{d \sqrt{a +b \cos \left(d x +c \right)}\, \left(a^{2}-b^{2}\right) a \sin \left(d x +c \right) \sqrt{\cos \left(d x +c \right)}}"," ",0,"2/d/(a+b*cos(d*x+c))^(1/2)*(A*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)*(cos(d*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+A*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)*(cos(d*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-A*sin(d*x+c)*cos(d*x+c)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^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)*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-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))*cos(d*x+c)*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))*cos(d*x+c)*a*b+B*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*cos(d*x+c)*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)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*cos(d*x+c)*a*b+A*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a*b+A*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*b^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))*a^2-A*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a*b-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*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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+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*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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+A*cos(d*x+c)^2*a*b-A*cos(d*x+c)^2*b^2-B*cos(d*x+c)^2*a^2+B*cos(d*x+c)^2*a*b-A*cos(d*x+c)*a*b+A*cos(d*x+c)*b^2+B*cos(d*x+c)*a^2-B*cos(d*x+c)*a*b)/(a^2-b^2)/a/sin(d*x+c)/cos(d*x+c)^(1/2)","B"
429,1,2280,285,0.346000," ","int((A+B*cos(d*x+c))/cos(d*x+c)^(3/2)/(a+b*cos(d*x+c))^(3/2),x)","\text{Expression too large to display}"," ",0,"2/d/(a+b*cos(d*x+c))^(1/2)*(A*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^3+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))*sin(d*x+c)*cos(d*x+c)*a^3-2*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)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)*b^3-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))*a^3-A*a*b^2+A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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*A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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-B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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+B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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*A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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+B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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+A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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*A*cos(d*x+c)^2*b^3-2*A*cos(d*x+c)*b^3-A*cos(d*x+c)^2*a^2*b-A*cos(d*x+c)^2*a*b^2+A*cos(d*x+c)*a^2*b+2*A*cos(d*x+c)*a*b^2+B*cos(d*x+c)^2*a^2*b-B*cos(d*x+c)^2*a*b^2-B*cos(d*x+c)*a^2*b+B*cos(d*x+c)*a*b^2-A*cos(d*x+c)*a^3+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))*a*b^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^2*b-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*b^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)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a^2*b+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+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+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))*a^2*b-A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+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^3-2*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)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*b^3)/a^2/(a^2-b^2)/sin(d*x+c)/cos(d*x+c)^(1/2)","B"
430,1,3334,363,0.353000," ","int((A+B*cos(d*x+c))/cos(d*x+c)^(5/2)/(a+b*cos(d*x+c))^(3/2),x)","\text{output too large to display}"," ",0,"-2/3/d*(-5*A*cos(d*x+c)^3*a^2*b^2+3*B*cos(d*x+c)^3*a^3*b-6*B*cos(d*x+c)^3*a*b^3-6*B*cos(d*x+c)^2*a^2*b^2+6*B*cos(d*x+c)^2*a*b^3+3*B*cos(d*x+c)*a^2*b^2-5*A*cos(d*x+c)^2*a^3*b+8*A*cos(d*x+c)^2*a*b^3-4*A*cos(d*x+c)*a*b^3+A*a^2*b^2+8*A*cos(d*x+c)^3*b^4-8*A*cos(d*x+c)^2*b^4+3*B*cos(d*x+c)^2*a^4-3*B*cos(d*x+c)*a^4+A*cos(d*x+c)^2*a^4-3*B*cos(d*x+c)^2*a^3*b+A*cos(d*x+c)^3*a^3*b-4*A*cos(d*x+c)^3*a*b^3+4*A*cos(d*x+c)^2*a^2*b^2+4*A*cos(d*x+c)*a^3*b+3*B*cos(d*x+c)^3*a^2*b^2+5*A*sin(d*x+c)*cos(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-3*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a^4-8*A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+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*a^4+5*A*sin(d*x+c)*cos(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^2-8*A*sin(d*x+c)*cos(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^3+2*A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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*A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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+6*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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+6*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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-6*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a^2*b^2+5*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))*sin(d*x+c)*cos(d*x+c)^2*a^3*b+5*A*sin(d*x+c)*cos(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^2-8*A*sin(d*x+c)*cos(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^3-5*A*sin(d*x+c)*cos(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*b+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)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)^2*a^2*b^2+8*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)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)^2*a*b^3-3*B*sin(d*x+c)*cos(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^3*b+6*B*sin(d*x+c)*cos(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^2+6*B*sin(d*x+c)*cos(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^3-3*B*sin(d*x+c)*cos(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*b-6*B*sin(d*x+c)*cos(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^2+3*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^4-8*A*sin(d*x+c)*cos(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^4+A*sin(d*x+c)*cos(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^4-3*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))*sin(d*x+c)*cos(d*x+c)^2*a^4+3*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)^2*a^4+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)*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^4-5*A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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)/(a+b*cos(d*x+c))^(1/2)/a^3/(a^2-b^2)/sin(d*x+c)/cos(d*x+c)^(3/2)","B"
431,1,8611,628,0.705000," ","int(cos(d*x+c)^(5/2)*(A+B*cos(d*x+c))/(a+b*cos(d*x+c))^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
432,1,5749,505,0.512000," ","int(cos(d*x+c)^(3/2)*(A+B*cos(d*x+c))/(a+b*cos(d*x+c))^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
433,1,4237,359,0.394000," ","int(cos(d*x+c)^(1/2)*(A+B*cos(d*x+c))/(a+b*cos(d*x+c))^(5/2),x)","\text{output too large to display}"," ",0,"-2/3/d/(a+b*cos(d*x+c))^(3/2)*(-3*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)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*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^4+3*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))*sin(d*x+c)*a^4+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))*cos(d*x+c)^2*a*b^3-3*A*cos(d*x+c)^3*a^2*b^2+4*B*cos(d*x+c)^3*a*b^3+8*B*cos(d*x+c)^2*a^2*b^2-4*B*cos(d*x+c)^2*a*b^3+4*B*cos(d*x+c)*a^3*b-3*B*cos(d*x+c)*a^2*b^2-6*A*cos(d*x+c)^2*a^3*b-2*A*cos(d*x+c)^2*a*b^3-A*cos(d*x+c)*a^2*b^2-A*cos(d*x+c)^3*b^4+A*cos(d*x+c)^2*b^4+B*cos(d*x+c)^3*a^4-B*cos(d*x+c)*a^4+3*A*cos(d*x+c)^2*a^4-4*B*cos(d*x+c)^2*a^3*b+2*A*cos(d*x+c)^3*a^3*b+2*A*cos(d*x+c)^3*a*b^3+4*A*cos(d*x+c)^2*a^2*b^2+4*A*cos(d*x+c)*a^3*b-5*B*cos(d*x+c)^3*a^2*b^2+6*A*sin(d*x+c)*cos(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+3*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^3*b+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^2*b^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*b^3-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))*a^2*b^2-4*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)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a^3*b-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)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a^2*b^2+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+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+A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+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*A*cos(d*x+c)*a^4+4*A*sin(d*x+c)*cos(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^2+2*A*sin(d*x+c)*cos(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^3-5*A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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-A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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^3-4*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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-8*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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^2-4*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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+7*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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*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))*sin(d*x+c)*cos(d*x+c)^2*a^3*b+3*A*sin(d*x+c)*cos(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^2+A*sin(d*x+c)*cos(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^3-3*A*sin(d*x+c)*cos(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*b-4*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)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)^2*a^2*b^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)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)^2*a*b^3-4*B*sin(d*x+c)*cos(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^2-4*B*sin(d*x+c)*cos(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^3+B*sin(d*x+c)*cos(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*b+4*B*sin(d*x+c)*cos(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^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)*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^4-4*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))*a^3*b+A*sin(d*x+c)*cos(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^4-3*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)*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^4-7*A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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*A*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)*(cos(d*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)/sin(d*x+c)/a/(a-b)^2/(a+b)^2/cos(d*x+c)^(1/2)","B"
434,1,5203,397,0.905000," ","int((A+B*cos(d*x+c))/cos(d*x+c)^(1/2)/(a+b*cos(d*x+c))^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
435,1,6498,424,1.420000," ","int((A+B*cos(d*x+c))/cos(d*x+c)^(3/2)/(a+b*cos(d*x+c))^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
436,1,8093,529,0.495000," ","int((A+B*cos(d*x+c))/cos(d*x+c)^(5/2)/(a+b*cos(d*x+c))^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
437,1,623,387,0.342000," ","int(cos(d*x+c)^(3/2)*(a*B+b*B*cos(d*x+c))/(a+b*cos(d*x+c))^(3/2),x)","-\frac{B \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)}{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,"-B/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"
438,1,160,109,0.333000," ","int(cos(d*x+c)^(1/2)*(a*B+b*B*cos(d*x+c))/(a+b*cos(d*x+c))^(3/2),x)","-\frac{2 B \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{\cos \left(d x +c \right)}{1+\cos \left(d x +c \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^{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) \sqrt{\cos \left(d x +c \right)}}"," ",0,"-2*B/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)))*(cos(d*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/(a+b*cos(d*x+c))^(1/2)/(-1+cos(d*x+c))/cos(d*x+c)^(1/2)","A"
439,1,124,102,0.233000," ","int((a*B+b*B*cos(d*x+c))/cos(d*x+c)^(1/2)/(a+b*cos(d*x+c))^(3/2),x)","-\frac{2 B \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*B/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"
440,1,613,210,0.257000," ","int((a*B+b*B*cos(d*x+c))/cos(d*x+c)^(3/2)/(a+b*cos(d*x+c))^(3/2),x)","-\frac{2 B \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*B/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"
441,1,658,64,0.449000," ","int((1+cos(d*x+c))/cos(d*x+c)^(3/2)/(2+3*cos(d*x+c))^(1/2),x)","-\frac{2 \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{2+3 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \frac{\sqrt{5}}{5}\right)+4 \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{2+3 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \cos \left(d x +c \right) \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \frac{\sqrt{5}}{5}\right)+2 \sqrt{2}\, \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) \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 \sin \left(d x +c \right) \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)}}\, \sqrt{10}\, \sqrt{\frac{2+3 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \frac{\sqrt{5}}{5}\right)+2 \sin \left(d x +c \right) \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)}}\, \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 \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{10}\, \sqrt{\frac{2+3 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \frac{\sqrt{5}}{5}\right)+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{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)+30 \left(\cos^{3}\left(d x +c \right)\right)-10 \left(\cos^{2}\left(d x +c \right)\right)-20 \cos \left(d x +c \right)}{10 d \sqrt{2+3 \cos \left(d x +c \right)}\, \cos \left(d x +c \right)^{\frac{3}{2}} \sin \left(d x +c \right)}"," ",0,"-1/10/d/(2+3*cos(d*x+c))^(1/2)*(2*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*10^(1/2)*((2+3*cos(d*x+c))/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)*cos(d*x+c)^2*EllipticF((-1+cos(d*x+c))/sin(d*x+c),1/5*5^(1/2))+4*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*10^(1/2)*((2+3*cos(d*x+c))/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)*cos(d*x+c)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),1/5*5^(1/2))+2*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*sin(d*x+c)*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))-5*sin(d*x+c)*cos(d*x+c)^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)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),1/5*5^(1/2))+2*sin(d*x+c)*cos(d*x+c)^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)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),1/5*5^(1/2))-5*sin(d*x+c)*cos(d*x+c)*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)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),1/5*5^(1/2))+2*sin(d*x+c)*cos(d*x+c)*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)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),1/5*5^(1/2))+30*cos(d*x+c)^3-10*cos(d*x+c)^2-20*cos(d*x+c))/cos(d*x+c)^(3/2)/sin(d*x+c)","B"
442,1,600,61,0.424000," ","int((1+cos(d*x+c))/cos(d*x+c)^(3/2)/(-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}} \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \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)}}+4 \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) \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) \sqrt{\frac{-2+3 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+2 \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) \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)+2 \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{-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)+\sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{-2+3 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{5}\right)+2 \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{-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)+\sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{-2+3 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{5}\right)-3 \left(\cos^{3}\left(d x +c \right)\right)+5 \left(\cos^{2}\left(d x +c \right)\right)-2 \cos \left(d x +c \right)}{d \sqrt{-2+3 \cos \left(d x +c \right)}\, \cos \left(d x +c \right)^{\frac{3}{2}} \sin \left(d x +c \right)}"," ",0,"-1/d/(-2+3*cos(d*x+c))^(1/2)*(2*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*sin(d*x+c)*cos(d*x+c)^2*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)+4*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*sin(d*x+c)*cos(d*x+c)*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)+2*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*sin(d*x+c)*((-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))+2*sin(d*x+c)*cos(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)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),5^(1/2))+sin(d*x+c)*cos(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)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),5^(1/2))+2*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+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)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((-2+3*cos(d*x+c))/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),5^(1/2))-3*cos(d*x+c)^3+5*cos(d*x+c)^2-2*cos(d*x+c))/cos(d*x+c)^(3/2)/sin(d*x+c)","B"
443,1,614,80,0.415000," ","int((1+cos(d*x+c))/cos(d*x+c)^(3/2)/(2-3*cos(d*x+c))^(1/2),x)","-\frac{\sqrt{2-3 \cos \left(d x +c \right)}\, \left(-2 \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) \left(\cos^{2}\left(d x +c \right)\right) \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)}}-4 \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) \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) \sqrt{\frac{-2+3 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}-2 \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{-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)-\sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{-2+3 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{5}\right)-2 \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) \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)-2 \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{-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)-\sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{-2+3 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{5}\right)+3 \left(\cos^{3}\left(d x +c \right)\right)-5 \left(\cos^{2}\left(d x +c \right)\right)+2 \cos \left(d x +c \right)\right)}{d \left(-2+3 \cos \left(d x +c \right)\right) \cos \left(d x +c \right)^{\frac{3}{2}} \sin \left(d x +c \right)}"," ",0,"-1/d*(2-3*cos(d*x+c))^(1/2)*(-2*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*sin(d*x+c)*cos(d*x+c)^2*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)-4*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*sin(d*x+c)*cos(d*x+c)*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)-2*sin(d*x+c)*cos(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)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),5^(1/2))-sin(d*x+c)*cos(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)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),5^(1/2))-2*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*sin(d*x+c)*((-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))-2*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+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)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((-2+3*cos(d*x+c))/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),5^(1/2))+3*cos(d*x+c)^3-5*cos(d*x+c)^2+2*cos(d*x+c))/(-2+3*cos(d*x+c))/cos(d*x+c)^(3/2)/sin(d*x+c)","B"
444,1,703,83,0.390000," ","int((1+cos(d*x+c))/cos(d*x+c)^(3/2)/(-2-3*cos(d*x+c))^(1/2),x)","-\frac{\sqrt{-2-3 \cos \left(d x +c \right)}\, \left(-2 \sqrt{2}\, \sin \left(d x +c \right) \left(\cos^{2}\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)}}\, \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \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{5}-4 \sqrt{2}\, \sin \left(d x +c \right) \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(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \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{5}+\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)}}\, \EllipticE \left(\frac{\sqrt{5}\, \left(-1+\cos \left(d x +c \right)\right)}{5 \sin \left(d x +c \right)}, \sqrt{5}\right) \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{5}+2 \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)}}\, \EllipticF \left(\frac{\sqrt{5}\, \left(-1+\cos \left(d x +c \right)\right)}{5 \sin \left(d x +c \right)}, \sqrt{5}\right) \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{5}-2 \sqrt{2}\, \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sqrt{5}\, \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) \sin \left(d x +c \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)}}\, \EllipticE \left(\frac{\sqrt{5}\, \left(-1+\cos \left(d x +c \right)\right)}{5 \sin \left(d x +c \right)}, \sqrt{5}\right) \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{5}+2 \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)}}\, \EllipticF \left(\frac{\sqrt{5}\, \left(-1+\cos \left(d x +c \right)\right)}{5 \sin \left(d x +c \right)}, \sqrt{5}\right) \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{5}-30 \left(\cos^{3}\left(d x +c \right)\right)+10 \left(\cos^{2}\left(d x +c \right)\right)+20 \cos \left(d x +c \right)\right)}{10 d \left(2+3 \cos \left(d x +c \right)\right) \cos \left(d x +c \right)^{\frac{3}{2}} \sin \left(d x +c \right)}"," ",0,"-1/10/d*(-2-3*cos(d*x+c))^(1/2)*(-2*2^(1/2)*sin(d*x+c)*cos(d*x+c)^2*10^(1/2)*((2+3*cos(d*x+c))/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*EllipticF(1/5*5^(1/2)*(-1+cos(d*x+c))/sin(d*x+c),5^(1/2))*5^(1/2)-4*2^(1/2)*sin(d*x+c)*cos(d*x+c)*10^(1/2)*((2+3*cos(d*x+c))/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*EllipticF(1/5*5^(1/2)*(-1+cos(d*x+c))/sin(d*x+c),5^(1/2))*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)*EllipticE(1/5*5^(1/2)*(-1+cos(d*x+c))/sin(d*x+c),5^(1/2))*sin(d*x+c)*cos(d*x+c)^2*5^(1/2)+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)*EllipticF(1/5*5^(1/2)*(-1+cos(d*x+c))/sin(d*x+c),5^(1/2))*sin(d*x+c)*cos(d*x+c)^2*5^(1/2)-2*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*5^(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)+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)*EllipticE(1/5*5^(1/2)*(-1+cos(d*x+c))/sin(d*x+c),5^(1/2))*sin(d*x+c)*cos(d*x+c)*5^(1/2)+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)*EllipticF(1/5*5^(1/2)*(-1+cos(d*x+c))/sin(d*x+c),5^(1/2))*sin(d*x+c)*cos(d*x+c)*5^(1/2)-30*cos(d*x+c)^3+10*cos(d*x+c)^2+20*cos(d*x+c))/(2+3*cos(d*x+c))/cos(d*x+c)^(3/2)/sin(d*x+c)","B"
445,1,665,65,0.423000," ","int((1+cos(d*x+c))/cos(d*x+c)^(3/2)/(3+2*cos(d*x+c))^(1/2),x)","\frac{-3 \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \frac{i \sqrt{5}}{5}\right) \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)}}-6 \sin \left(d x +c \right) \cos \left(d x +c \right) \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \frac{i \sqrt{5}}{5}\right) \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)}}+5 \sin \left(d x +c \right) \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)}}\, \sqrt{10}\, \sqrt{\frac{3+2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \frac{i \sqrt{5}}{5}\right)-3 \sin \left(d x +c \right) \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)}}\, \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)-3 \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) \sin \left(d x +c \right)+5 \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{10}\, \sqrt{\frac{3+2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \frac{i \sqrt{5}}{5}\right)-3 \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{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)-20 \left(\cos^{3}\left(d x +c \right)\right)-10 \left(\cos^{2}\left(d x +c \right)\right)+30 \cos \left(d x +c \right)}{15 d \sqrt{3+2 \cos \left(d x +c \right)}\, \cos \left(d x +c \right)^{\frac{3}{2}} \sin \left(d x +c \right)}"," ",0,"1/15/d/(3+2*cos(d*x+c))^(1/2)*(-3*sin(d*x+c)*cos(d*x+c)^2*EllipticF((-1+cos(d*x+c))/sin(d*x+c),1/5*I*5^(1/2))*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*10^(1/2)*((3+2*cos(d*x+c))/(1+cos(d*x+c)))^(1/2)-6*sin(d*x+c)*cos(d*x+c)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),1/5*I*5^(1/2))*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*10^(1/2)*((3+2*cos(d*x+c))/(1+cos(d*x+c)))^(1/2)+5*sin(d*x+c)*cos(d*x+c)^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)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),1/5*I*5^(1/2))-3*sin(d*x+c)*cos(d*x+c)^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)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),1/5*I*5^(1/2))-3*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*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)+5*sin(d*x+c)*cos(d*x+c)*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)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),1/5*I*5^(1/2))-3*sin(d*x+c)*cos(d*x+c)*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)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),1/5*I*5^(1/2))-20*cos(d*x+c)^3-10*cos(d*x+c)^2+30*cos(d*x+c))/cos(d*x+c)^(3/2)/sin(d*x+c)","B"
446,1,663,64,0.420000," ","int((1+cos(d*x+c))/cos(d*x+c)^(3/2)/(3-2*cos(d*x+c))^(1/2),x)","\frac{\sqrt{3-2 \cos \left(d x +c \right)}\, \left(3 \sqrt{2}\, \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sqrt{-\frac{2 \left(-3+2 \cos \left(d x +c \right)\right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, i \sqrt{5}\right)+6 \sqrt{2}\, \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sqrt{-\frac{2 \left(-3+2 \cos \left(d x +c \right)\right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \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)+3 \sqrt{2}\, \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \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) \sin \left(d x +c \right)-\sqrt{2}\, \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)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, i \sqrt{5}\right) \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right)+3 \sqrt{2}\, \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)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, i \sqrt{5}\right) \sin \left(d x +c \right) \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)}}\, \sqrt{-\frac{2 \left(-3+2 \cos \left(d x +c \right)\right)}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, i \sqrt{5}\right) \sin \left(d x +c \right) \cos \left(d x +c \right)+3 \sqrt{2}\, \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)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, i \sqrt{5}\right) \sin \left(d x +c \right) \cos \left(d x +c \right)-4 \left(\cos^{3}\left(d x +c \right)\right)+10 \left(\cos^{2}\left(d x +c \right)\right)-6 \cos \left(d x +c \right)\right)}{3 d \left(-3+2 \cos \left(d x +c \right)\right) \cos \left(d x +c \right)^{\frac{3}{2}} \sin \left(d x +c \right)}"," ",0,"1/3/d*(3-2*cos(d*x+c))^(1/2)*(3*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*(-2*(-3+2*cos(d*x+c))/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)*cos(d*x+c)^2*EllipticF((-1+cos(d*x+c))/sin(d*x+c),I*5^(1/2))+6*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*(-2*(-3+2*cos(d*x+c))/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)*cos(d*x+c)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),I*5^(1/2))+3*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*(-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)-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)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),I*5^(1/2))*sin(d*x+c)*cos(d*x+c)^2+3*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)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),I*5^(1/2))*sin(d*x+c)*cos(d*x+c)^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)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),I*5^(1/2))*sin(d*x+c)*cos(d*x+c)+3*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)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),I*5^(1/2))*sin(d*x+c)*cos(d*x+c)-4*cos(d*x+c)^3+10*cos(d*x+c)^2-6*cos(d*x+c))/(-3+2*cos(d*x+c))/cos(d*x+c)^(3/2)/sin(d*x+c)","B"
447,1,714,84,0.329000," ","int((1+cos(d*x+c))/cos(d*x+c)^(3/2)/(-3+2*cos(d*x+c))^(1/2),x)","\frac{3 i \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{5}\, \sqrt{-\frac{2 \left(-3+2 \cos \left(d x +c \right)\right)}{1+\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}} \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)+6 i \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{5}\, \sqrt{-\frac{2 \left(-3+2 \cos \left(d x +c \right)\right)}{1+\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}} \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)-3 i \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{5}\, \sqrt{-\frac{2 \left(-3+2 \cos \left(d x +c \right)\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)}}\, \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)+5 i \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{5}\, \sqrt{-\frac{2 \left(-3+2 \cos \left(d x +c \right)\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)}}\, \EllipticE \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)+3 i \sqrt{2}\, \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) \sqrt{5}\, \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)-3 i \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{5}\, \sqrt{-\frac{2 \left(-3+2 \cos \left(d x +c \right)\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)}}\, \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)+5 i \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{5}\, \sqrt{-\frac{2 \left(-3+2 \cos \left(d x +c \right)\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)}}\, \EllipticE \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)+20 \left(\cos^{3}\left(d x +c \right)\right)-50 \left(\cos^{2}\left(d x +c \right)\right)+30 \cos \left(d x +c \right)}{15 d \sqrt{-3+2 \cos \left(d x +c \right)}\, \cos \left(d x +c \right)^{\frac{3}{2}} \sin \left(d x +c \right)}"," ",0,"1/15/d/(-3+2*cos(d*x+c))^(1/2)*(3*I*sin(d*x+c)*cos(d*x+c)^2*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)))^(3/2)*EllipticF(I*(-1+cos(d*x+c))*5^(1/2)/sin(d*x+c),1/5*I*5^(1/2))+6*I*sin(d*x+c)*cos(d*x+c)*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)))^(3/2)*EllipticF(I*(-1+cos(d*x+c))*5^(1/2)/sin(d*x+c),1/5*I*5^(1/2))-3*I*sin(d*x+c)*cos(d*x+c)^2*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)*EllipticF(I*(-1+cos(d*x+c))*5^(1/2)/sin(d*x+c),1/5*I*5^(1/2))+5*I*sin(d*x+c)*cos(d*x+c)^2*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)*EllipticE(I*(-1+cos(d*x+c))*5^(1/2)/sin(d*x+c),1/5*I*5^(1/2))+3*I*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*sin(d*x+c)*5^(1/2)*(-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))-3*I*sin(d*x+c)*cos(d*x+c)*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)*EllipticF(I*(-1+cos(d*x+c))*5^(1/2)/sin(d*x+c),1/5*I*5^(1/2))+5*I*sin(d*x+c)*cos(d*x+c)*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)*EllipticE(I*(-1+cos(d*x+c))*5^(1/2)/sin(d*x+c),1/5*I*5^(1/2))+20*cos(d*x+c)^3-50*cos(d*x+c)^2+30*cos(d*x+c))/cos(d*x+c)^(3/2)/sin(d*x+c)","B"
448,1,740,85,0.335000," ","int((1+cos(d*x+c))/cos(d*x+c)^(3/2)/(-3-2*cos(d*x+c))^(1/2),x)","-\frac{\sqrt{-3-2 \cos \left(d x +c \right)}\, \left(3 i \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{5}\, \sqrt{10}\, \sqrt{\frac{3+2 \cos \left(d x +c \right)}{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}} \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}+6 i \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{5}\, \sqrt{10}\, \sqrt{\frac{3+2 \cos \left(d x +c \right)}{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}} \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}+i \sin \left(d x +c \right) \left(\cos^{2}\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)}}\, \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(d x +c \right)\right) \sqrt{5}}{5 \sin \left(d x +c \right)}, i \sqrt{5}\right) \sqrt{5}-3 i \sin \left(d x +c \right) \left(\cos^{2}\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)}}\, \sqrt{2}\, \sqrt{\frac{\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}+3 i \sqrt{2}\, \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) \sqrt{5}\, \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)+i \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{10}\, \sqrt{\frac{3+2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(d x +c \right)\right) \sqrt{5}}{5 \sin \left(d x +c \right)}, i \sqrt{5}\right) \sqrt{5}-3 i \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{10}\, \sqrt{\frac{3+2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}\, \sqrt{\frac{\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}-20 \left(\cos^{3}\left(d x +c \right)\right)-10 \left(\cos^{2}\left(d x +c \right)\right)+30 \cos \left(d x +c \right)\right)}{15 d \left(3+2 \cos \left(d x +c \right)\right) \cos \left(d x +c \right)^{\frac{3}{2}} \sin \left(d x +c \right)}"," ",0,"-1/15/d*(-3-2*cos(d*x+c))^(1/2)*(3*I*sin(d*x+c)*cos(d*x+c)^2*5^(1/2)*10^(1/2)*((3+2*cos(d*x+c))/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*EllipticF(1/5*I*(-1+cos(d*x+c))*5^(1/2)/sin(d*x+c),I*5^(1/2))*2^(1/2)+6*I*sin(d*x+c)*cos(d*x+c)*5^(1/2)*10^(1/2)*((3+2*cos(d*x+c))/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*EllipticF(1/5*I*(-1+cos(d*x+c))*5^(1/2)/sin(d*x+c),I*5^(1/2))*2^(1/2)+I*sin(d*x+c)*cos(d*x+c)^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)*EllipticE(1/5*I*(-1+cos(d*x+c))*5^(1/2)/sin(d*x+c),I*5^(1/2))*5^(1/2)-3*I*sin(d*x+c)*cos(d*x+c)^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)*EllipticF(1/5*I*(-1+cos(d*x+c))*5^(1/2)/sin(d*x+c),I*5^(1/2))*5^(1/2)+3*I*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*sin(d*x+c)*5^(1/2)*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))+I*sin(d*x+c)*cos(d*x+c)*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)*EllipticE(1/5*I*(-1+cos(d*x+c))*5^(1/2)/sin(d*x+c),I*5^(1/2))*5^(1/2)-3*I*sin(d*x+c)*cos(d*x+c)*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)*EllipticF(1/5*I*(-1+cos(d*x+c))*5^(1/2)/sin(d*x+c),I*5^(1/2))*5^(1/2)-20*cos(d*x+c)^3-10*cos(d*x+c)^2+30*cos(d*x+c))/(3+2*cos(d*x+c))/cos(d*x+c)^(3/2)/sin(d*x+c)","B"
449,0,0,35,3.390000," ","int((c*cos(f*x+e))^m*(a+b*cos(f*x+e))^n*(A+B*cos(f*x+e)),x)","\int \left(c \cos \left(f x +e \right)\right)^{m} \left(a +b \cos \left(f x +e \right)\right)^{n} \left(A +B \cos \left(f x +e \right)\right)\, dx"," ",0,"int((c*cos(f*x+e))^m*(a+b*cos(f*x+e))^n*(A+B*cos(f*x+e)),x)","F"
450,0,0,583,2.882000," ","int((c*cos(f*x+e))^m*(a+b*cos(f*x+e))^4*(A+B*cos(f*x+e)),x)","\int \left(c \cos \left(f x +e \right)\right)^{m} \left(a +b \cos \left(f x +e \right)\right)^{4} \left(A +B \cos \left(f x +e \right)\right)\, dx"," ",0,"int((c*cos(f*x+e))^m*(a+b*cos(f*x+e))^4*(A+B*cos(f*x+e)),x)","F"
451,0,0,394,3.002000," ","int((c*cos(f*x+e))^m*(a+b*cos(f*x+e))^3*(A+B*cos(f*x+e)),x)","\int \left(c \cos \left(f x +e \right)\right)^{m} \left(a +b \cos \left(f x +e \right)\right)^{3} \left(A +B \cos \left(f x +e \right)\right)\, dx"," ",0,"int((c*cos(f*x+e))^m*(a+b*cos(f*x+e))^3*(A+B*cos(f*x+e)),x)","F"
452,0,0,275,1.884000," ","int((c*cos(f*x+e))^m*(a+b*cos(f*x+e))^2*(A+B*cos(f*x+e)),x)","\int \left(c \cos \left(f x +e \right)\right)^{m} \left(a +b \cos \left(f x +e \right)\right)^{2} \left(A +B \cos \left(f x +e \right)\right)\, dx"," ",0,"int((c*cos(f*x+e))^m*(a+b*cos(f*x+e))^2*(A+B*cos(f*x+e)),x)","F"
453,0,0,184,1.993000," ","int((c*cos(f*x+e))^m*(a+b*cos(f*x+e))*(A+B*cos(f*x+e)),x)","\int \left(c \cos \left(f x +e \right)\right)^{m} \left(a +b \cos \left(f x +e \right)\right) \left(A +B \cos \left(f x +e \right)\right)\, dx"," ",0,"int((c*cos(f*x+e))^m*(a+b*cos(f*x+e))*(A+B*cos(f*x+e)),x)","F"
454,0,0,262,1.477000," ","int((c*cos(f*x+e))^m*(A+B*cos(f*x+e))/(a+b*cos(f*x+e)),x)","\int \frac{\left(c \cos \left(f x +e \right)\right)^{m} \left(A +B \cos \left(f x +e \right)\right)}{a +b \cos \left(f x +e \right)}\, dx"," ",0,"int((c*cos(f*x+e))^m*(A+B*cos(f*x+e))/(a+b*cos(f*x+e)),x)","F"
455,0,0,168,0.455000," ","int((c*cos(f*x+e))^m*(a+b*cos(f*x+e))^(3/2)*(A+B*cos(f*x+e)),x)","\int \left(c \cos \left(f x +e \right)\right)^{m} \left(a +b \cos \left(f x +e \right)\right)^{\frac{3}{2}} \left(A +B \cos \left(f x +e \right)\right)\, dx"," ",0,"int((c*cos(f*x+e))^m*(a+b*cos(f*x+e))^(3/2)*(A+B*cos(f*x+e)),x)","F"
456,0,0,35,0.344000," ","int((c*cos(f*x+e))^m*(A+B*cos(f*x+e))*(a+b*cos(f*x+e))^(1/2),x)","\int \left(c \cos \left(f x +e \right)\right)^{m} \left(A +B \cos \left(f x +e \right)\right) \sqrt{a +b \cos \left(f x +e \right)}\, dx"," ",0,"int((c*cos(f*x+e))^m*(A+B*cos(f*x+e))*(a+b*cos(f*x+e))^(1/2),x)","F"
457,0,0,35,0.319000," ","int((c*cos(f*x+e))^m*(A+B*cos(f*x+e))/(a+b*cos(f*x+e))^(1/2),x)","\int \frac{\left(c \cos \left(f x +e \right)\right)^{m} \left(A +B \cos \left(f x +e \right)\right)}{\sqrt{a +b \cos \left(f x +e \right)}}\, dx"," ",0,"int((c*cos(f*x+e))^m*(A+B*cos(f*x+e))/(a+b*cos(f*x+e))^(1/2),x)","F"
458,0,0,178,0.371000," ","int((c*cos(f*x+e))^m*(A+B*cos(f*x+e))/(a+b*cos(f*x+e))^(3/2),x)","\int \frac{\left(c \cos \left(f x +e \right)\right)^{m} \left(A +B \cos \left(f x +e \right)\right)}{\left(a +b \cos \left(f x +e \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int((c*cos(f*x+e))^m*(A+B*cos(f*x+e))/(a+b*cos(f*x+e))^(3/2),x)","F"
459,1,661,200,4.275000," ","int((a+a*cos(d*x+c))*(A+B*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{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)}}{10 \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{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)}{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)}+\left(\frac{A}{2}+\frac{B}{2}\right) \left(-\frac{\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{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,"-4*(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*a*(-1/10*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)+1/2*B*(-(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*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)+(1/2*A+1/2*B)*(-1/6*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^2+1/3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))))/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
460,1,426,171,3.571000," ","int((a+a*cos(d*x+c))*(A+B*cos(d*x+c))*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 \left(\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 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{\left(\frac{A}{2}+\frac{B}{2}\right) \left(-\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+2 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right)^{2} \left(2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}+\frac{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}\right)}{\sin \left(\frac{d 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*(1/2*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))+(1/2*A+1/2*B)*(-(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*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)+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"
461,1,240,148,1.664000," ","int((a+a*cos(d*x+c))*(A+B*cos(d*x+c))*sec(d*x+c)^(3/2),x)","-\frac{2 a \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}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\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}\, \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)-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)}{\sin \left(\frac{d 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*(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))+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*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*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)^2-1)^(1/2)/d","A"
462,1,321,148,1.369000," ","int((a+a*cos(d*x+c))*(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)}\, a \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}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\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)-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)-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)*a*(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)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-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))-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))-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"
463,1,355,173,1.313000," ","int((a+a*cos(d*x+c))*(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)}\, a \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 +44 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 -16 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)-15 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)+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)+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)\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*B*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6+(20*A+44*B)*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+(-10*A-16*B)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)-15*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))+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))+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)))/(-2*sin(1/2*d*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"
464,1,383,200,1.551000," ","int((a+a*cos(d*x+c))*(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)}\, a \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 -528 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(308 A +448 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(-112 A -122 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)+35 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)-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)-63 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)}{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*B*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^8+(-168*A-528*B)*sin(1/2*d*x+1/2*c)^6*cos(1/2*d*x+1/2*c)+(308*A+448*B)*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+(-112*A-122*B)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+35*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))-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))-63*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"
465,1,741,227,4.386000," ","int((a+a*cos(d*x+c))^2*(A+B*cos(d*x+c))*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{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 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{A \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)}}{20 \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{\left(\frac{A}{4}+\frac{B}{2}\right) \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)}+\left(\frac{A}{2}+\frac{B}{4}\right) \left(-\frac{\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{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,"-8*(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^2*(1/4*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-1/20*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)+(1/4*A+1/2*B)*(-(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*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)+(1/2*A+1/4*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"
466,1,513,194,1.623000," ","int((a+a*cos(d*x+c))^2*(A+B*cos(d*x+c))*sec(d*x+c)^(5/2),x)","-\frac{4 \left(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(2 A +B \right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\sqrt{-2 \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(7 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{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(2 A \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+3 A \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+3 B \EllipticF \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)+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) \sqrt{-2 \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 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)+3 B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\right) a^{2}}{3 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)^{\frac{3}{2}} \sin \left(\frac{d x}{2}+\frac{c}{2}\right) d}"," ",0,"-4/3*(6*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*A+B)*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4-(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(7*A+3*B)*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)^2-1)^(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)*(2*A*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+3*A*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+3*B*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2)))*sin(1/2*d*x+1/2*c)^2+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))*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)+3*A*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+3*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2))*a^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)^(3/2)/sin(1/2*d*x+1/2*c)/d","B"
467,1,388,194,1.497000," ","int((a+a*cos(d*x+c))^2*(A+B*cos(d*x+c))*sec(d*x+c)^(3/2),x)","-\frac{4 a^{2} \left(2 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)}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \left(3 A +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)+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}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}+2 B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}-3 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)}\, \sqrt{\frac{1}{2}-\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 \sqrt{-2 \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*a^2*(2*B*(-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)^4-(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(3*A+B)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+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)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)+2*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)-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*sin(1/2*d*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"
468,1,357,198,1.235000," ","int((a+a*cos(d*x+c))^2*(A+B*cos(d*x+c))*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 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(10 A +32 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(-5 A -13 B \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+10 A \sqrt{\frac{1}{2}-\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 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)+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)-12 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,"-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*B*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6+(10*A+32*B)*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+(-5*A-13*B)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+10*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*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))+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))-12*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"
469,1,385,229,1.278000," ","int((a+a*cos(d*x+c))^2*(A+B*cos(d*x+c))/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(120 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(-84 A -348 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(224 A +378 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(-91 A -117 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)+35 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)-84 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)+30 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)-63 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)}{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^2*(120*B*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^8+(-84*A-348*B)*sin(1/2*d*x+1/2*c)^6*cos(1/2*d*x+1/2*c)+(224*A+378*B)*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+(-91*A-117*B)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+35*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))-84*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))+30*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))-63*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"
470,1,929,268,5.512000," ","int((a+a*cos(d*x+c))^3*(A+B*cos(d*x+c))*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{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 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{\left(\frac{3 A}{8}+\frac{B}{8}\right) \left(12 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \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{\left(\frac{A}{8}+\frac{3 B}{8}\right) \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)}+\left(\frac{3 A}{8}+\frac{3 B}{8}\right) \left(-\frac{\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{6 \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{3 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}\right)+\frac{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)}}{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)}{8}\right)}{\sin \left(\frac{d 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*(1/8*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-1/5*(3/8*A+1/8*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)+(1/8*A+3/8*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)+(3/8*A+3/8*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)))+1/8*A*(-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"
471,1,916,239,4.267000," ","int((a+a*cos(d*x+c))^3*(A+B*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^{3} \left(60 A \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)+108 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)-216 A \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+100 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)+60 B \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-180 B \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-60 A \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)-108 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)+246 A \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-100 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)-60 B \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+190 B \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+15 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)+27 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)-72 A \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\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)+15 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)-50 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)}}{15 \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)^{3} \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^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)^3*(60*A*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+108*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)^4-216*A*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6+100*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+60*B*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^4-180*B*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6-60*A*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)^2-108*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+246*A*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4-100*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)^2-60*B*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^2+190*B*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4+15*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))+27*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))-72*A*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^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))+15*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))-50*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"
472,1,654,229,1.604000," ","int((a+a*cos(d*x+c))^3*(A+B*cos(d*x+c))*sec(d*x+c)^(5/2),x)","-\frac{4 \left(-4 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)}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+2 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \left(9 A +5 B \right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-2 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \left(5 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{-2 \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(5 A \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+3 A \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+5 B \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)+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) \sqrt{-2 \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 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)+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) \sqrt{-2 \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 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)}\, \sqrt{\frac{1}{2}-\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) a^{3}}{3 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)^{\frac{3}{2}} \sin \left(\frac{d x}{2}+\frac{c}{2}\right) d}"," ",0,"-4/3*(-4*B*(-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)^6+2*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(9*A+5*B)*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)-2*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(5*A+2*B)*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)*(5*A*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+3*A*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+5*B*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+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))*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)+3*A*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+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))*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)-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)))*a^3/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(2*cos(1/2*d*x+1/2*c)^2-1)^(3/2)/sin(1/2*d*x+1/2*c)/d","B"
473,1,519,239,1.699000," ","int((a+a*cos(d*x+c))^3*(A+B*cos(d*x+c))*sec(d*x+c)^(3/2),x)","-\frac{4 a^{3} \left(-12 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)}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+2 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \left(5 A +21 B \right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-2 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \left(10 A +9 B \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+25 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) \sqrt{-2 \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 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)+15 B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}-27 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)}\, \sqrt{\frac{1}{2}-\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,"-4/15*a^3*(-12*B*(-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)^6+2*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(5*A+21*B)*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)-2*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(10*A+9*B)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+25*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*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)-15*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))+15*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)-27*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*sin(1/2*d*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"
474,1,385,239,1.440000," ","int((a+a*cos(d*x+c))^3*(A+B*cos(d*x+c))*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 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(-84 A -432 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(294 A +602 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(-126 A -208 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)+105 A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-189 A \sqrt{\frac{1}{2}-\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)+65 B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-147 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)}{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*B*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^8+(-84*A-432*B)*sin(1/2*d*x+1/2*c)^6*cos(1/2*d*x+1/2*c)+(294*A+602*B)*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+(-126*A-208*B)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+105*A*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-189*A*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+65*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-147*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"
475,1,413,268,1.389000," ","int((a+a*cos(d*x+c))^3*(A+B*cos(d*x+c))/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(-560 B \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{10}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(360 A +2200 B \right) \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\left(-1296 A -3412 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(1806 A +2702 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(-624 A -738 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)+195 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)-441 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)+165 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)-357 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)}{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*B*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^10+(360*A+2200*B)*sin(1/2*d*x+1/2*c)^8*cos(1/2*d*x+1/2*c)+(-1296*A-3412*B)*sin(1/2*d*x+1/2*c)^6*cos(1/2*d*x+1/2*c)+(1806*A+2702*B)*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+(-624*A-738*B)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+195*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))-441*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))+165*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))-357*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"
476,1,493,227,4.056000," ","int((A+B*cos(d*x+c))*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)}\, \left(\frac{\left(-2 A +2 B \right) \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)}+2 A \left(-\frac{\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{6 \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{3 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}\right)+\frac{\left(A -B \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)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\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)}}\right)}{a \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)/a*((-2*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)))+(A-B)*(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)/cos(1/2*d*x+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"
477,1,319,199,3.357000," ","int((A+B*cos(d*x+c))*sec(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{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \left(A \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-3 A \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-B \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)-2 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \left(3 A -B \right) \left(\sin^{4}\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(5 A -B \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}{a \sin \left(\frac{d x}{2}+\frac{c}{2}\right)^{3} \left(2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)/a*(cos(1/2*d*x+1/2*c)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(A*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-3*A*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-B*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*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(3*A-B)*sin(1/2*d*x+1/2*c)^4+(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(5*A-B)*sin(1/2*d*x+1/2*c)^2)/sin(1/2*d*x+1/2*c)^3/(2*sin(1/2*d*x+1/2*c)^2-1)/cos(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
478,1,243,165,1.384000," ","int((A+B*cos(d*x+c))*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{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(A \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 \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)+\left(2 A -2 B \right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(-A +B \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}{a \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(-cos(1/2*d*x+1/2*c)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(A*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*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*A-2*B)*sin(1/2*d*x+1/2*c)^4+(-A+B)*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"
479,1,244,167,1.479000," ","int((A+B*cos(d*x+c))/(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(A \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 \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(2 A -2 B \right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(-A +B \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}{a \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(cos(1/2*d*x+1/2*c)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(A*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*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)))+(2*A-2*B)*sin(1/2*d*x+1/2*c)^4+(-A+B)*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"
480,1,262,199,1.397000," ","int((A+B*cos(d*x+c))/(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{\frac{1}{2}-\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(3 A \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+9 A \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-5 B \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-9 B \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)\right)+8 B \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(6 A -18 B \right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(-3 A +7 B \right) \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)*(3*A*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+9*A*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-5*B*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-9*B*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2)))+8*B*sin(1/2*d*x+1/2*c)^6+(6*A-18*B)*sin(1/2*d*x+1/2*c)^4+(-3*A+7*B)*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"
481,1,281,226,1.575000," ","int((A+B*cos(d*x+c))/(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{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 A \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+45 A \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-25 B \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-63 B \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)\right)+48 B \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(-40 A -56 B \right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(90 A -30 B \right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(-35 A +23 B \right) \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*A*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+45*A*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-25*B*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-63*B*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2)))+48*B*sin(1/2*d*x+1/2*c)^8+(-40*A-56*B)*sin(1/2*d*x+1/2*c)^6+(90*A-30*B)*sin(1/2*d*x+1/2*c)^4+(-35*A+23*B)*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"
482,1,494,240,1.879000," ","int((A+B*cos(d*x+c))*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{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \left(5 A \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-12 A \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-2 B \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) \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{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \left(5 A \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-12 A \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-2 B \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) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-12 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \left(4 A -B \right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+2 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \left(43 A -10 B \right) \left(\sin^{4}\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(37 A -7 B \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)*(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)*(5*A*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-12*A*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-2*B*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)))*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)*(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)*(5*A*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-12*A*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-2*B*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)))*cos(1/2*d*x+1/2*c)-12*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(4*A-B)*sin(1/2*d*x+1/2*c)^6+2*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(43*A-10*B)*sin(1/2*d*x+1/2*c)^4-(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(37*A-7*B)*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"
483,1,350,197,1.622000," ","int((A+B*cos(d*x+c))*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 A \left(\cos^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-4 A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+6 A \left(\cos^{3}\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}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-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}\, \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)-16 A \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-2 B \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+3 A \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+3 B \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+A -B \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*A*cos(1/2*d*x+1/2*c)^6-4*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)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*cos(1/2*d*x+1/2*c)^3+6*A*cos(1/2*d*x+1/2*c)^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)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-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)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*cos(1/2*d*x+1/2*c)^3-16*A*cos(1/2*d*x+1/2*c)^4-2*B*cos(1/2*d*x+1/2*c)^4+3*A*cos(1/2*d*x+1/2*c)^2+3*B*cos(1/2*d*x+1/2*c)^2+A-B)/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"
484,1,350,202,1.624000," ","int((A+B*cos(d*x+c))/(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 A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+12 B \left(\cos^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+4 B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \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 B \left(\cos^{3}\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}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+2 A \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-20 B \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-3 A \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+9 B \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+A -B \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*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)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*cos(1/2*d*x+1/2*c)^3+12*B*cos(1/2*d*x+1/2*c)^6+4*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)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*cos(1/2*d*x+1/2*c)^3+6*B*cos(1/2*d*x+1/2*c)^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)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+2*A*cos(1/2*d*x+1/2*c)^4-20*B*cos(1/2*d*x+1/2*c)^4-3*A*cos(1/2*d*x+1/2*c)^2+9*B*cos(1/2*d*x+1/2*c)^2+A-B)/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"
485,1,421,210,1.687000," ","int((A+B*cos(d*x+c))/(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 A \left(\cos^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+4 A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+6 A \left(\cos^{3}\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}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-24 B \left(\cos^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-10 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) \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-24 B \left(\cos^{3}\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}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-20 A \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+38 B \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+9 A \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-15 B \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-A +B \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*A*cos(1/2*d*x+1/2*c)^6+4*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)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*cos(1/2*d*x+1/2*c)^3+6*A*cos(1/2*d*x+1/2*c)^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)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-24*B*cos(1/2*d*x+1/2*c)^6-10*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)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*cos(1/2*d*x+1/2*c)^3-24*B*cos(1/2*d*x+1/2*c)^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)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-20*A*cos(1/2*d*x+1/2*c)^4+38*B*cos(1/2*d*x+1/2*c)^4+9*A*cos(1/2*d*x+1/2*c)^2-15*B*cos(1/2*d*x+1/2*c)^2-A+B)/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"
486,1,435,236,1.853000," ","int((A+B*cos(d*x+c))/(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(-16 B \left(\cos^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+24 A \left(\cos^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+10 A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+24 A \left(\cos^{3}\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}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-12 B \left(\cos^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-20 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) \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-42 B \left(\cos^{3}\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}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-38 A \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+48 B \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+15 A \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-21 B \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-A +B \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)*(-16*B*cos(1/2*d*x+1/2*c)^8+24*A*cos(1/2*d*x+1/2*c)^6+10*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)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*cos(1/2*d*x+1/2*c)^3+24*A*cos(1/2*d*x+1/2*c)^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)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-12*B*cos(1/2*d*x+1/2*c)^6-20*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)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*cos(1/2*d*x+1/2*c)^3-42*B*cos(1/2*d*x+1/2*c)^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)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-38*A*cos(1/2*d*x+1/2*c)^4+48*B*cos(1/2*d*x+1/2*c)^4+15*A*cos(1/2*d*x+1/2*c)^2-21*B*cos(1/2*d*x+1/2*c)^2-A+B)/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"
487,1,685,285,2.053000," ","int((A+B*cos(d*x+c))*sec(d*x+c)^(3/2)/(a+a*cos(d*x+c))^3,x)","-\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}}\, \sqrt{-2 \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(65 A \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-147 A \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-15 B \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+27 B \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^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \left(65 A \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-147 A \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-15 B \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+27 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) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-2 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \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(65 A \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-147 A \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-15 B \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+27 B \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)+12 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \left(49 A -9 B \right) \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-2 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \left(817 A -147 B \right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{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(248 A -43 B \right) \left(\sin^{4}\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(439 A -69 B \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{60 a^{3} \cos \left(\frac{d x}{2}+\frac{c}{2}\right)^{5} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-1/60*(-2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(65*A*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-147*A*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-15*B*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+27*B*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2)))*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4+4*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(65*A*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-147*A*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-15*B*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+27*B*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2)))*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)-2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(65*A*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-147*A*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-15*B*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+27*B*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2)))*cos(1/2*d*x+1/2*c)+12*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(49*A-9*B)*sin(1/2*d*x+1/2*c)^8-2*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(817*A-147*B)*sin(1/2*d*x+1/2*c)^6+6*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(248*A-43*B)*sin(1/2*d*x+1/2*c)^4-(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(439*A-69*B)*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"
488,1,451,250,1.651000," ","int((A+B*cos(d*x+c))*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(108 A \left(\cos^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-30 A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+54 A \left(\cos^{5}\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}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+12 B \left(\cos^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-10 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) \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+6 B \left(\cos^{5}\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}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-138 A \left(\cos^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-22 B \left(\cos^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+24 A \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+6 B \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+3 A \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+7 B \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+3 A -3 B \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)*(108*A*cos(1/2*d*x+1/2*c)^8-30*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)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*cos(1/2*d*x+1/2*c)^5+54*A*cos(1/2*d*x+1/2*c)^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)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+12*B*cos(1/2*d*x+1/2*c)^8-10*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)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*cos(1/2*d*x+1/2*c)^5+6*B*cos(1/2*d*x+1/2*c)^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)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-138*A*cos(1/2*d*x+1/2*c)^6-22*B*cos(1/2*d*x+1/2*c)^6+24*A*cos(1/2*d*x+1/2*c)^4+6*B*cos(1/2*d*x+1/2*c)^4+3*A*cos(1/2*d*x+1/2*c)^2+7*B*cos(1/2*d*x+1/2*c)^2+3*A-3*B)/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"
489,1,451,244,1.856000," ","int((A+B*cos(d*x+c))/(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 A \left(\cos^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-10 A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+6 A \left(\cos^{5}\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}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-12 B \left(\cos^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-10 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) \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-6 B \left(\cos^{5}\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}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-22 A \left(\cos^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+2 B \left(\cos^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+6 A \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+24 B \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+7 A \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-17 B \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-3 A +3 B \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*A*cos(1/2*d*x+1/2*c)^8-10*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)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*cos(1/2*d*x+1/2*c)^5+6*A*cos(1/2*d*x+1/2*c)^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)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-12*B*cos(1/2*d*x+1/2*c)^8-10*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)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*cos(1/2*d*x+1/2*c)^5-6*B*cos(1/2*d*x+1/2*c)^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)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-22*A*cos(1/2*d*x+1/2*c)^6+2*B*cos(1/2*d*x+1/2*c)^6+6*A*cos(1/2*d*x+1/2*c)^4+24*B*cos(1/2*d*x+1/2*c)^4+7*A*cos(1/2*d*x+1/2*c)^2-17*B*cos(1/2*d*x+1/2*c)^2-3*A+3*B)/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"
490,1,451,250,1.650000," ","int((A+B*cos(d*x+c))/(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 A \left(\cos^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+10 A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+6 A \left(\cos^{5}\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}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+108 B \left(\cos^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+30 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) \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+54 B \left(\cos^{5}\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}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-2 A \left(\cos^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-198 B \left(\cos^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-24 A \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+114 B \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+17 A \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-27 B \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-3 A +3 B \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*A*cos(1/2*d*x+1/2*c)^8+10*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)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*cos(1/2*d*x+1/2*c)^5+6*A*cos(1/2*d*x+1/2*c)^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)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+108*B*cos(1/2*d*x+1/2*c)^8+30*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)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*cos(1/2*d*x+1/2*c)^5+54*B*cos(1/2*d*x+1/2*c)^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)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-2*A*cos(1/2*d*x+1/2*c)^6-198*B*cos(1/2*d*x+1/2*c)^6-24*A*cos(1/2*d*x+1/2*c)^4+114*B*cos(1/2*d*x+1/2*c)^4+17*A*cos(1/2*d*x+1/2*c)^2-27*B*cos(1/2*d*x+1/2*c)^2-3*A+3*B)/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"
491,1,451,256,1.636000," ","int((A+B*cos(d*x+c))/(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(108 A \left(\cos^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+30 A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+54 A \left(\cos^{5}\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}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-348 B \left(\cos^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-130 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) \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-294 B \left(\cos^{5}\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}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-198 A \left(\cos^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+578 B \left(\cos^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+114 A \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-264 B \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-27 A \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+37 B \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+3 A -3 B \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)*(108*A*cos(1/2*d*x+1/2*c)^8+30*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)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*cos(1/2*d*x+1/2*c)^5+54*A*cos(1/2*d*x+1/2*c)^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)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-348*B*cos(1/2*d*x+1/2*c)^8-130*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)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*cos(1/2*d*x+1/2*c)^5-294*B*cos(1/2*d*x+1/2*c)^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)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-198*A*cos(1/2*d*x+1/2*c)^6+578*B*cos(1/2*d*x+1/2*c)^6+114*A*cos(1/2*d*x+1/2*c)^4-264*B*cos(1/2*d*x+1/2*c)^4-27*A*cos(1/2*d*x+1/2*c)^2+37*B*cos(1/2*d*x+1/2*c)^2+3*A-3*B)/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"
492,1,465,283,1.562000," ","int((A+B*cos(d*x+c))/(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(-160 B \left(\cos^{10}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+348 A \left(\cos^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+130 A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+294 A \left(\cos^{5}\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}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-468 B \left(\cos^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-330 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) \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-714 B \left(\cos^{5}\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}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-578 A \left(\cos^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1058 B \left(\cos^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+264 A \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-474 B \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-37 A \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+47 B \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+3 A -3 B \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)*(-160*B*cos(1/2*d*x+1/2*c)^10+348*A*cos(1/2*d*x+1/2*c)^8+130*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)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*cos(1/2*d*x+1/2*c)^5+294*A*cos(1/2*d*x+1/2*c)^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)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-468*B*cos(1/2*d*x+1/2*c)^8-330*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)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*cos(1/2*d*x+1/2*c)^5-714*B*cos(1/2*d*x+1/2*c)^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)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-578*A*cos(1/2*d*x+1/2*c)^6+1058*B*cos(1/2*d*x+1/2*c)^6+264*A*cos(1/2*d*x+1/2*c)^4-474*B*cos(1/2*d*x+1/2*c)^4-37*A*cos(1/2*d*x+1/2*c)^2+47*B*cos(1/2*d*x+1/2*c)^2+3*A-3*B)/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"
493,1,138,190,0.417000," ","int((A+B*cos(d*x+c))*sec(d*x+c)^(11/2)*(a+a*cos(d*x+c))^(1/2),x)","-\frac{2 \left(-1+\cos \left(d x +c \right)\right) \left(128 A \left(\cos^{4}\left(d x +c \right)\right)+144 B \left(\cos^{4}\left(d x +c \right)\right)+64 A \left(\cos^{3}\left(d x +c \right)\right)+72 B \left(\cos^{3}\left(d x +c \right)\right)+48 A \left(\cos^{2}\left(d x +c \right)\right)+54 B \left(\cos^{2}\left(d x +c \right)\right)+40 A \cos \left(d x +c \right)+45 B \cos \left(d x +c \right)+35 A \right) \cos \left(d x +c \right) \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{11}{2}} \sqrt{a \left(1+\cos \left(d x +c \right)\right)}}{315 d \sin \left(d x +c \right)}"," ",0,"-2/315/d*(-1+cos(d*x+c))*(128*A*cos(d*x+c)^4+144*B*cos(d*x+c)^4+64*A*cos(d*x+c)^3+72*B*cos(d*x+c)^3+48*A*cos(d*x+c)^2+54*B*cos(d*x+c)^2+40*A*cos(d*x+c)+45*B*cos(d*x+c)+35*A)*cos(d*x+c)*(1/cos(d*x+c))^(11/2)*(a*(1+cos(d*x+c)))^(1/2)/sin(d*x+c)","A"
494,1,116,151,0.377000," ","int((A+B*cos(d*x+c))*sec(d*x+c)^(9/2)*(a+a*cos(d*x+c))^(1/2),x)","-\frac{2 \left(-1+\cos \left(d x +c \right)\right) \left(48 A \left(\cos^{3}\left(d x +c \right)\right)+56 B \left(\cos^{3}\left(d x +c \right)\right)+24 A \left(\cos^{2}\left(d x +c \right)\right)+28 B \left(\cos^{2}\left(d x +c \right)\right)+18 A \cos \left(d x +c \right)+21 B \cos \left(d x +c \right)+15 A \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)}}{105 d \sin \left(d x +c \right)}"," ",0,"-2/105/d*(-1+cos(d*x+c))*(48*A*cos(d*x+c)^3+56*B*cos(d*x+c)^3+24*A*cos(d*x+c)^2+28*B*cos(d*x+c)^2+18*A*cos(d*x+c)+21*B*cos(d*x+c)+15*A)*cos(d*x+c)*(1/cos(d*x+c))^(9/2)*(a*(1+cos(d*x+c)))^(1/2)/sin(d*x+c)","A"
495,1,94,112,0.350000," ","int((A+B*cos(d*x+c))*sec(d*x+c)^(7/2)*(a+a*cos(d*x+c))^(1/2),x)","-\frac{2 \left(-1+\cos \left(d x +c \right)\right) \left(8 A \left(\cos^{2}\left(d x +c \right)\right)+10 B \left(\cos^{2}\left(d x +c \right)\right)+4 A \cos \left(d x +c \right)+5 B \cos \left(d x +c \right)+3 A \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*(-1+cos(d*x+c))*(8*A*cos(d*x+c)^2+10*B*cos(d*x+c)^2+4*A*cos(d*x+c)+5*B*cos(d*x+c)+3*A)*cos(d*x+c)*(1/cos(d*x+c))^(7/2)*(a*(1+cos(d*x+c)))^(1/2)/sin(d*x+c)","A"
496,1,70,73,0.376000," ","int((A+B*cos(d*x+c))*sec(d*x+c)^(5/2)*(a+a*cos(d*x+c))^(1/2),x)","-\frac{2 \left(-1+\cos \left(d x +c \right)\right) \left(2 A \cos \left(d x +c \right)+3 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{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*(-1+cos(d*x+c))*(2*A*cos(d*x+c)+3*B*cos(d*x+c)+A)*cos(d*x+c)*(1/cos(d*x+c))^(5/2)*(a*(1+cos(d*x+c)))^(1/2)/sin(d*x+c)","A"
497,1,171,82,0.391000," ","int((A+B*cos(d*x+c))*sec(d*x+c)^(3/2)*(a+a*cos(d*x+c))^(1/2),x)","\frac{2 \left(B \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)+B \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)+A \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)}}{d \left(1+\cos \left(d x +c \right)\right)}"," ",0,"2/d*(B*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))+B*(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*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))","B"
498,1,168,84,0.465000," ","int((A+B*cos(d*x+c))*(a+a*cos(d*x+c))^(1/2)*sec(d*x+c)^(1/2),x)","-\frac{\left(B \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+2 A \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)+B \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)}{d \sin \left(d x +c \right)^{2}}"," ",0,"-1/d*(B*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+2*A*arctan(sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)/cos(d*x+c))+B*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"
499,1,238,127,0.412000," ","int((A+B*cos(d*x+c))*(a+a*cos(d*x+c))^(1/2)/sec(d*x+c)^(1/2),x)","\frac{\left(-1+\cos \left(d x +c \right)\right)^{2} \left(2 B \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+4 A \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+3 B \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+4 A \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 B \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)}}{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*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+4*A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+3*B*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+4*A*arctan(sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)/cos(d*x+c))+3*B*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"
500,1,308,166,0.439000," ","int((A+B*cos(d*x+c))*(a+a*cos(d*x+c))^(1/2)/sec(d*x+c)^(3/2),x)","-\frac{\left(-1+\cos \left(d x +c \right)\right)^{3} \left(8 B \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+12 A \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+10 B \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+18 A \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+15 B \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+18 A \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)+15 B \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)}}{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*B*sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+12*A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+10*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+18*A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+15*B*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+18*A*arctan(sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)/cos(d*x+c))+15*B*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"
501,1,161,239,0.412000," ","int((a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))*sec(d*x+c)^(13/2),x)","-\frac{2 \left(-1+\cos \left(d x +c \right)\right) \left(2688 A \left(\cos^{5}\left(d x +c \right)\right)+2992 B \left(\cos^{5}\left(d x +c \right)\right)+1344 A \left(\cos^{4}\left(d x +c \right)\right)+1496 B \left(\cos^{4}\left(d x +c \right)\right)+1008 A \left(\cos^{3}\left(d x +c \right)\right)+1122 B \left(\cos^{3}\left(d x +c \right)\right)+840 A \left(\cos^{2}\left(d x +c \right)\right)+935 B \left(\cos^{2}\left(d x +c \right)\right)+735 A \cos \left(d x +c \right)+385 B \cos \left(d x +c \right)+315 A \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{13}{2}} a}{3465 d \sin \left(d x +c \right)}"," ",0,"-2/3465/d*(-1+cos(d*x+c))*(2688*A*cos(d*x+c)^5+2992*B*cos(d*x+c)^5+1344*A*cos(d*x+c)^4+1496*B*cos(d*x+c)^4+1008*A*cos(d*x+c)^3+1122*B*cos(d*x+c)^3+840*A*cos(d*x+c)^2+935*B*cos(d*x+c)^2+735*A*cos(d*x+c)+385*B*cos(d*x+c)+315*A)*cos(d*x+c)*(a*(1+cos(d*x+c)))^(1/2)*(1/cos(d*x+c))^(13/2)/sin(d*x+c)*a","A"
502,1,139,198,0.375000," ","int((a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))*sec(d*x+c)^(11/2),x)","-\frac{2 \left(-1+\cos \left(d x +c \right)\right) \left(272 A \left(\cos^{4}\left(d x +c \right)\right)+312 B \left(\cos^{4}\left(d x +c \right)\right)+136 A \left(\cos^{3}\left(d x +c \right)\right)+156 B \left(\cos^{3}\left(d x +c \right)\right)+102 A \left(\cos^{2}\left(d x +c \right)\right)+117 B \left(\cos^{2}\left(d x +c \right)\right)+85 A \cos \left(d x +c \right)+45 B \cos \left(d x +c \right)+35 A \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}{315 d \sin \left(d x +c \right)}"," ",0,"-2/315/d*(-1+cos(d*x+c))*(272*A*cos(d*x+c)^4+312*B*cos(d*x+c)^4+136*A*cos(d*x+c)^3+156*B*cos(d*x+c)^3+102*A*cos(d*x+c)^2+117*B*cos(d*x+c)^2+85*A*cos(d*x+c)+45*B*cos(d*x+c)+35*A)*cos(d*x+c)*(a*(1+cos(d*x+c)))^(1/2)*(1/cos(d*x+c))^(11/2)/sin(d*x+c)*a","A"
503,1,117,157,0.357000," ","int((a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))*sec(d*x+c)^(9/2),x)","-\frac{2 \left(-1+\cos \left(d x +c \right)\right) \left(104 A \left(\cos^{3}\left(d x +c \right)\right)+126 B \left(\cos^{3}\left(d x +c \right)\right)+52 A \left(\cos^{2}\left(d x +c \right)\right)+63 B \left(\cos^{2}\left(d x +c \right)\right)+39 A \cos \left(d x +c \right)+21 B \cos \left(d x +c \right)+15 A \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*(-1+cos(d*x+c))*(104*A*cos(d*x+c)^3+126*B*cos(d*x+c)^3+52*A*cos(d*x+c)^2+63*B*cos(d*x+c)^2+39*A*cos(d*x+c)+21*B*cos(d*x+c)+15*A)*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"
504,1,95,116,0.447000," ","int((a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))*sec(d*x+c)^(7/2),x)","-\frac{2 \left(-1+\cos \left(d x +c \right)\right) \left(18 A \left(\cos^{2}\left(d x +c \right)\right)+25 B \left(\cos^{2}\left(d x +c \right)\right)+9 A \cos \left(d x +c \right)+5 B \cos \left(d x +c \right)+3 A \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}{15 d \sin \left(d x +c \right)}"," ",0,"-2/15/d*(-1+cos(d*x+c))*(18*A*cos(d*x+c)^2+25*B*cos(d*x+c)^2+9*A*cos(d*x+c)+5*B*cos(d*x+c)+3*A)*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"
505,1,287,123,0.470000," ","int((a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))*sec(d*x+c)^(5/2),x)","-\frac{2 \left(3 B \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 B \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 B \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 A \cos \left(d x +c \right) \sin \left(d x +c \right)+3 B \cos \left(d x +c \right) \sin \left(d x +c \right)+A \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}{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*B*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*B*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*B*(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*A*cos(d*x+c)*sin(d*x+c)+3*B*cos(d*x+c)*sin(d*x+c)+A*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","B"
506,1,308,128,0.457000," ","int((a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))*sec(d*x+c)^(3/2),x)","\frac{\left(2 A \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)+3 B \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)+2 A \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)+B \cos \left(d x +c \right) \sin \left(d x +c \right)+3 B \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 A \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,"1/d*(2*A*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))+3*B*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))+2*A*(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))+B*cos(d*x+c)*sin(d*x+c)+3*B*(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*A*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"
507,1,233,129,0.387000," ","int((a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))*sec(d*x+c)^(1/2),x)","-\frac{\left(2 B \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+4 A \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+7 B \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+12 A \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)+7 B \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}{4 d \sin \left(d x +c \right)^{2}}"," ",0,"-1/4/d*(2*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+4*A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+7*B*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+12*A*arctan(sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)/cos(d*x+c))+7*B*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"
508,1,309,170,0.452000," ","int((a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))/sec(d*x+c)^(1/2),x)","\frac{\left(-1+\cos \left(d x +c \right)\right)^{2} \left(8 B \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+12 A \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+22 B \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+42 A \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+33 B \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+42 A \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)+33 B \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{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*B*sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+12*A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+22*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+42*A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+33*B*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+42*A*arctan(sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)/cos(d*x+c))+33*B*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"
509,1,381,211,0.359000," ","int((a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))/sec(d*x+c)^(3/2),x)","-\frac{\left(-1+\cos \left(d x +c \right)\right)^{3} \left(48 B \sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+64 A \left(\cos^{2}\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)+120 B \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+176 A \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+150 B \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+264 A \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+225 B \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+264 A \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)+225 B \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}{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*B*sin(d*x+c)*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+64*A*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+120*B*sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+176*A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+150*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+264*A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+225*B*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+264*A*arctan(sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)/cos(d*x+c))+225*B*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"
510,1,185,280,0.485000," ","int((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))*sec(d*x+c)^(15/2),x)","-\frac{2 \left(-1+\cos \left(d x +c \right)\right) \left(66944 A \left(\cos^{6}\left(d x +c \right)\right)+73840 B \left(\cos^{6}\left(d x +c \right)\right)+33472 A \left(\cos^{5}\left(d x +c \right)\right)+36920 B \left(\cos^{5}\left(d x +c \right)\right)+25104 A \left(\cos^{4}\left(d x +c \right)\right)+27690 B \left(\cos^{4}\left(d x +c \right)\right)+20920 A \left(\cos^{3}\left(d x +c \right)\right)+23075 B \left(\cos^{3}\left(d x +c \right)\right)+18305 A \left(\cos^{2}\left(d x +c \right)\right)+14560 B \left(\cos^{2}\left(d x +c \right)\right)+11970 A \cos \left(d x +c \right)+4095 B \cos \left(d x +c \right)+3465 A \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{15}{2}} a^{2}}{45045 d \sin \left(d x +c \right)}"," ",0,"-2/45045/d*(-1+cos(d*x+c))*(66944*A*cos(d*x+c)^6+73840*B*cos(d*x+c)^6+33472*A*cos(d*x+c)^5+36920*B*cos(d*x+c)^5+25104*A*cos(d*x+c)^4+27690*B*cos(d*x+c)^4+20920*A*cos(d*x+c)^3+23075*B*cos(d*x+c)^3+18305*A*cos(d*x+c)^2+14560*B*cos(d*x+c)^2+11970*A*cos(d*x+c)+4095*B*cos(d*x+c)+3465*A)*cos(d*x+c)*(a*(1+cos(d*x+c)))^(1/2)*(1/cos(d*x+c))^(15/2)/sin(d*x+c)*a^2","A"
511,1,163,239,0.462000," ","int((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))*sec(d*x+c)^(13/2),x)","-\frac{2 \left(-1+\cos \left(d x +c \right)\right) \left(5680 A \left(\cos^{5}\left(d x +c \right)\right)+6424 B \left(\cos^{5}\left(d x +c \right)\right)+2840 A \left(\cos^{4}\left(d x +c \right)\right)+3212 B \left(\cos^{4}\left(d x +c \right)\right)+2130 A \left(\cos^{3}\left(d x +c \right)\right)+2409 B \left(\cos^{3}\left(d x +c \right)\right)+1775 A \left(\cos^{2}\left(d x +c \right)\right)+1430 B \left(\cos^{2}\left(d x +c \right)\right)+1120 A \cos \left(d x +c \right)+385 B \cos \left(d x +c \right)+315 A \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{13}{2}} a^{2}}{3465 d \sin \left(d x +c \right)}"," ",0,"-2/3465/d*(-1+cos(d*x+c))*(5680*A*cos(d*x+c)^5+6424*B*cos(d*x+c)^5+2840*A*cos(d*x+c)^4+3212*B*cos(d*x+c)^4+2130*A*cos(d*x+c)^3+2409*B*cos(d*x+c)^3+1775*A*cos(d*x+c)^2+1430*B*cos(d*x+c)^2+1120*A*cos(d*x+c)+385*B*cos(d*x+c)+315*A)*cos(d*x+c)*(a*(1+cos(d*x+c)))^(1/2)*(1/cos(d*x+c))^(13/2)/sin(d*x+c)*a^2","A"
512,1,141,198,0.395000," ","int((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))*sec(d*x+c)^(11/2),x)","-\frac{2 \left(-1+\cos \left(d x +c \right)\right) \left(584 A \left(\cos^{4}\left(d x +c \right)\right)+690 B \left(\cos^{4}\left(d x +c \right)\right)+292 A \left(\cos^{3}\left(d x +c \right)\right)+345 B \left(\cos^{3}\left(d x +c \right)\right)+219 A \left(\cos^{2}\left(d x +c \right)\right)+180 B \left(\cos^{2}\left(d x +c \right)\right)+130 A \cos \left(d x +c \right)+45 B \cos \left(d x +c \right)+35 A \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*(-1+cos(d*x+c))*(584*A*cos(d*x+c)^4+690*B*cos(d*x+c)^4+292*A*cos(d*x+c)^3+345*B*cos(d*x+c)^3+219*A*cos(d*x+c)^2+180*B*cos(d*x+c)^2+130*A*cos(d*x+c)+45*B*cos(d*x+c)+35*A)*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"
513,1,119,157,0.354000," ","int((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))*sec(d*x+c)^(9/2),x)","-\frac{2 \left(-1+\cos \left(d x +c \right)\right) \left(230 A \left(\cos^{3}\left(d x +c \right)\right)+301 B \left(\cos^{3}\left(d x +c \right)\right)+115 A \left(\cos^{2}\left(d x +c \right)\right)+98 B \left(\cos^{2}\left(d x +c \right)\right)+60 A \cos \left(d x +c \right)+21 B \cos \left(d x +c \right)+15 A \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}}{105 d \sin \left(d x +c \right)}"," ",0,"-2/105/d*(-1+cos(d*x+c))*(230*A*cos(d*x+c)^3+301*B*cos(d*x+c)^3+115*A*cos(d*x+c)^2+98*B*cos(d*x+c)^2+60*A*cos(d*x+c)+21*B*cos(d*x+c)+15*A)*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"
514,1,389,164,0.464000," ","int((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))*sec(d*x+c)^(7/2),x)","\frac{2 \left(15 B \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)+45 B \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)+45 B \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)+15 B \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)+43 A \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+40 B \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right)+14 A \cos \left(d x +c \right) \sin \left(d x +c \right)+5 B \cos \left(d x +c \right) \sin \left(d x +c \right)+3 A \sin \left(d x +c \right)\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)}\, \left(\sin^{4}\left(d x +c \right)\right) a^{2}}{15 d \left(-1+\cos \left(d x +c \right)\right)^{2} \left(1+\cos \left(d x +c \right)\right)^{3}}"," ",0,"2/15/d*(15*B*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))+45*B*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))+45*B*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))+15*B*(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))+43*A*cos(d*x+c)^2*sin(d*x+c)+40*B*sin(d*x+c)*cos(d*x+c)^2+14*A*cos(d*x+c)*sin(d*x+c)+5*B*cos(d*x+c)*sin(d*x+c)+3*A*sin(d*x+c))*cos(d*x+c)*(1/cos(d*x+c))^(7/2)*(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*a^2","B"
515,1,492,167,0.426000," ","int((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))*sec(d*x+c)^(5/2),x)","-\frac{\left(6 A \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)+15 B \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)+12 A \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)+30 B \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)+6 A \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)+15 B \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 B \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right)+16 A \cos \left(d x +c \right) \sin \left(d x +c \right)+6 B \cos \left(d x +c \right) \sin \left(d x +c \right)+2 A \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,"-1/3/d*(6*A*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))+15*B*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))+12*A*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))+30*B*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))+6*A*(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))+15*B*(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*B*sin(d*x+c)*cos(d*x+c)^2+16*A*cos(d*x+c)*sin(d*x+c)+6*B*cos(d*x+c)*sin(d*x+c)+2*A*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"
516,1,344,170,0.441000," ","int((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))*sec(d*x+c)^(3/2),x)","\frac{\left(20 A \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)+19 B \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)+2 B \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right)+20 A \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)+4 A \cos \left(d x +c \right) \sin \left(d x +c \right)+19 B \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 B \cos \left(d x +c \right) \sin \left(d x +c \right)+8 A \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}}{4 d \left(1+\cos \left(d x +c \right)\right)}"," ",0,"1/4/d*(20*A*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))+19*B*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))+2*B*sin(d*x+c)*cos(d*x+c)^2+20*A*(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))+4*A*cos(d*x+c)*sin(d*x+c)+19*B*(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*B*cos(d*x+c)*sin(d*x+c)+8*A*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","B"
517,1,305,170,0.424000," ","int((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))*sec(d*x+c)^(1/2),x)","-\frac{\left(8 B \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+12 A \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+34 B \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+66 A \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+75 B \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+114 A \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)+75 B \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^{2}}{24 d \sin \left(d x +c \right)^{2}}"," ",0,"-1/24/d*(8*B*sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+12*A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+34*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+66*A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+75*B*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+114*A*arctan(sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)/cos(d*x+c))+75*B*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^2","A"
518,1,383,211,0.375000," ","int((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))/sec(d*x+c)^(1/2),x)","\frac{\left(-1+\cos \left(d x +c \right)\right)^{2} \left(48 B \sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+64 A \left(\cos^{2}\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)+184 B \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+272 A \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+326 B \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+600 A \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+489 B \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+600 A \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)+489 B \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{3}{2}} \sqrt{\frac{1}{\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)^{4}}"," ",0,"1/192/d*(-1+cos(d*x+c))^2*(48*B*sin(d*x+c)*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+64*A*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+184*B*sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+272*A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+326*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+600*A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+489*B*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+600*A*arctan(sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)/cos(d*x+c))+489*B*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"
519,1,455,252,0.347000," ","int((a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))/sec(d*x+c)^(3/2),x)","-\frac{\left(-1+\cos \left(d x +c \right)\right)^{3} \left(384 B \sin \left(d x +c \right) \left(\cos^{4}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+480 A \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)}}+1392 B \sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+1840 A \left(\cos^{2}\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)+2264 B \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+3260 A \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+2830 B \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+4890 A \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+4245 B \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+4890 A \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)+4245 B \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}}{1920 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,"-1/1920/d*(-1+cos(d*x+c))^3*(384*B*sin(d*x+c)*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+480*A*cos(d*x+c)^3*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+1392*B*sin(d*x+c)*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+1840*A*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+2264*B*sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+3260*A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+2830*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+4890*A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+4245*B*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+4890*A*arctan(sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)/cos(d*x+c))+4245*B*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"
520,1,793,250,0.368000," ","int((A+B*cos(d*x+c))*sec(d*x+c)^(11/2)/(a+a*cos(d*x+c))^(1/2),x)","\frac{\left(315 A \left(\cos^{5}\left(d x +c \right)\right) \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{9}{2}} \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)-315 B \left(\cos^{5}\left(d x +c \right)\right) \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{9}{2}} \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)+1575 A \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{9}{2}} \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)-1575 B \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{9}{2}} \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)+3150 A \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{9}{2}} \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)-3150 B \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{9}{2}} \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)+3150 A \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{9}{2}} \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)-3150 B \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{9}{2}} \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)+1575 A \cos \left(d x +c \right) \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{9}{2}} \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)-1575 B \cos \left(d x +c \right) \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{9}{2}} \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)+315 A \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{9}{2}} \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)-315 B \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{9}{2}} \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)+257 A \left(\cos^{4}\left(d x +c \right)\right) \sqrt{2}\, \sin \left(d x +c \right)-129 B \left(\cos^{4}\left(d x +c \right)\right) \sqrt{2}\, \sin \left(d x +c \right)-29 A \left(\cos^{3}\left(d x +c \right)\right) \sqrt{2}\, \sin \left(d x +c \right)+93 B \left(\cos^{3}\left(d x +c \right)\right) \sqrt{2}\, \sin \left(d x +c \right)+57 A \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}\, \sin \left(d x +c \right)-9 B \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}\, \sin \left(d x +c \right)-5 A \cos \left(d x +c \right) \sqrt{2}\, \sin \left(d x +c \right)+45 B \cos \left(d x +c \right) \sqrt{2}\, \sin \left(d x +c \right)+35 A \sqrt{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{11}{2}} \sqrt{a \left(1+\cos \left(d x +c \right)\right)}\, \left(\sin^{8}\left(d x +c \right)\right) \sqrt{2}}{315 d \left(-1+\cos \left(d x +c \right)\right)^{4} \left(1+\cos \left(d x +c \right)\right)^{5} a}"," ",0,"1/315/d*(315*A*cos(d*x+c)^5*(cos(d*x+c)/(1+cos(d*x+c)))^(9/2)*arcsin((-1+cos(d*x+c))/sin(d*x+c))-315*B*cos(d*x+c)^5*(cos(d*x+c)/(1+cos(d*x+c)))^(9/2)*arcsin((-1+cos(d*x+c))/sin(d*x+c))+1575*A*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(9/2)*arcsin((-1+cos(d*x+c))/sin(d*x+c))-1575*B*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(9/2)*arcsin((-1+cos(d*x+c))/sin(d*x+c))+3150*A*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(9/2)*arcsin((-1+cos(d*x+c))/sin(d*x+c))-3150*B*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(9/2)*arcsin((-1+cos(d*x+c))/sin(d*x+c))+3150*A*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(9/2)*arcsin((-1+cos(d*x+c))/sin(d*x+c))-3150*B*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(9/2)*arcsin((-1+cos(d*x+c))/sin(d*x+c))+1575*A*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(9/2)*arcsin((-1+cos(d*x+c))/sin(d*x+c))-1575*B*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(9/2)*arcsin((-1+cos(d*x+c))/sin(d*x+c))+315*A*(cos(d*x+c)/(1+cos(d*x+c)))^(9/2)*arcsin((-1+cos(d*x+c))/sin(d*x+c))-315*B*(cos(d*x+c)/(1+cos(d*x+c)))^(9/2)*arcsin((-1+cos(d*x+c))/sin(d*x+c))+257*A*cos(d*x+c)^4*2^(1/2)*sin(d*x+c)-129*B*cos(d*x+c)^4*2^(1/2)*sin(d*x+c)-29*A*cos(d*x+c)^3*2^(1/2)*sin(d*x+c)+93*B*cos(d*x+c)^3*2^(1/2)*sin(d*x+c)+57*A*cos(d*x+c)^2*2^(1/2)*sin(d*x+c)-9*B*cos(d*x+c)^2*2^(1/2)*sin(d*x+c)-5*A*cos(d*x+c)*2^(1/2)*sin(d*x+c)+45*B*cos(d*x+c)*2^(1/2)*sin(d*x+c)+35*A*2^(1/2)*sin(d*x+c))*cos(d*x+c)*(1/cos(d*x+c))^(11/2)*(a*(1+cos(d*x+c)))^(1/2)*sin(d*x+c)^8/(-1+cos(d*x+c))^4/(1+cos(d*x+c))^5*2^(1/2)/a","B"
521,1,657,211,0.495000," ","int((A+B*cos(d*x+c))*sec(d*x+c)^(9/2)/(a+a*cos(d*x+c))^(1/2),x)","\frac{\left(105 A \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) \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{7}{2}}-105 B \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) \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{7}{2}}+420 A \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{7}{2}}-420 B \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{7}{2}}+630 A \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{7}{2}}-630 B \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{7}{2}}+420 A \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{7}{2}}-420 B \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{7}{2}}+105 A \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}}-105 B \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}}+43 A \left(\cos^{3}\left(d x +c \right)\right) \sqrt{2}\, \sin \left(d x +c \right)-91 B \left(\cos^{3}\left(d x +c \right)\right) \sqrt{2}\, \sin \left(d x +c \right)-31 A \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}\, \sin \left(d x +c \right)+7 B \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}\, \sin \left(d x +c \right)+3 A \cos \left(d x +c \right) \sqrt{2}\, \sin \left(d x +c \right)-21 B \cos \left(d x +c \right) \sqrt{2}\, \sin \left(d x +c \right)-15 A \sqrt{2}\, \sin \left(d x +c \right)\right) \cos \left(d x +c \right) \left(\sin^{6}\left(d x +c \right)\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)}\, \sqrt{2}}{105 d \left(-1+\cos \left(d x +c \right)\right)^{3} \left(1+\cos \left(d x +c \right)\right)^{4} a}"," ",0,"1/105/d*(105*A*arcsin((-1+cos(d*x+c))/sin(d*x+c))*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(7/2)-105*B*arcsin((-1+cos(d*x+c))/sin(d*x+c))*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(7/2)+420*A*arcsin((-1+cos(d*x+c))/sin(d*x+c))*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(7/2)-420*B*arcsin((-1+cos(d*x+c))/sin(d*x+c))*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(7/2)+630*A*arcsin((-1+cos(d*x+c))/sin(d*x+c))*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(7/2)-630*B*arcsin((-1+cos(d*x+c))/sin(d*x+c))*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(7/2)+420*A*arcsin((-1+cos(d*x+c))/sin(d*x+c))*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(7/2)-420*B*arcsin((-1+cos(d*x+c))/sin(d*x+c))*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(7/2)+105*A*arcsin((-1+cos(d*x+c))/sin(d*x+c))*(cos(d*x+c)/(1+cos(d*x+c)))^(7/2)-105*B*arcsin((-1+cos(d*x+c))/sin(d*x+c))*(cos(d*x+c)/(1+cos(d*x+c)))^(7/2)+43*A*cos(d*x+c)^3*2^(1/2)*sin(d*x+c)-91*B*cos(d*x+c)^3*2^(1/2)*sin(d*x+c)-31*A*cos(d*x+c)^2*2^(1/2)*sin(d*x+c)+7*B*cos(d*x+c)^2*2^(1/2)*sin(d*x+c)+3*A*cos(d*x+c)*2^(1/2)*sin(d*x+c)-21*B*cos(d*x+c)*2^(1/2)*sin(d*x+c)-15*A*2^(1/2)*sin(d*x+c))*cos(d*x+c)*sin(d*x+c)^6*(1/cos(d*x+c))^(9/2)*(a*(1+cos(d*x+c)))^(1/2)/(-1+cos(d*x+c))^3/(1+cos(d*x+c))^4*2^(1/2)/a","B"
522,1,521,174,0.427000," ","int((A+B*cos(d*x+c))*sec(d*x+c)^(7/2)/(a+a*cos(d*x+c))^(1/2),x)","\frac{\left(15 A \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^{3}\left(d x +c \right)\right)-15 B \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^{3}\left(d x +c \right)\right)+45 A \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)-45 B \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)+45 A \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}} \cos \left(d x +c \right)-45 B \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}} \cos \left(d x +c \right)+15 A \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}}-15 B \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 A \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}\, \sin \left(d x +c \right)-5 B \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}\, \sin \left(d x +c \right)-A \cos \left(d x +c \right) \sqrt{2}\, \sin \left(d x +c \right)+5 B \cos \left(d x +c \right) \sqrt{2}\, \sin \left(d x +c \right)+3 A \sqrt{2}\, \sin \left(d x +c \right)\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*A*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)^3-15*B*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)^3+45*A*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)^2-45*B*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+45*A*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)-45*B*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)+15*A*arcsin((-1+cos(d*x+c))/sin(d*x+c))*(cos(d*x+c)/(1+cos(d*x+c)))^(5/2)-15*B*arcsin((-1+cos(d*x+c))/sin(d*x+c))*(cos(d*x+c)/(1+cos(d*x+c)))^(5/2)+13*A*cos(d*x+c)^2*2^(1/2)*sin(d*x+c)-5*B*cos(d*x+c)^2*2^(1/2)*sin(d*x+c)-A*cos(d*x+c)*2^(1/2)*sin(d*x+c)+5*B*cos(d*x+c)*2^(1/2)*sin(d*x+c)+3*A*2^(1/2)*sin(d*x+c))*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","B"
523,1,384,135,0.400000," ","int((A+B*cos(d*x+c))*sec(d*x+c)^(5/2)/(a+a*cos(d*x+c))^(1/2),x)","\frac{\left(3 A \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{3}{2}}-3 B \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{3}{2}}+6 A \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{3}{2}}-6 B \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{3}{2}}+3 A \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}}-3 B \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}}+A \cos \left(d x +c \right) \sqrt{2}\, \sin \left(d x +c \right)-3 B \cos \left(d x +c \right) \sqrt{2}\, \sin \left(d x +c \right)-A \sqrt{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{5}{2}} \sqrt{a \left(1+\cos \left(d x +c \right)\right)}\, \left(\sin^{2}\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*A*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)-3*B*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)+6*A*cos(d*x+c)*arcsin((-1+cos(d*x+c))/sin(d*x+c))*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)-6*B*cos(d*x+c)*arcsin((-1+cos(d*x+c))/sin(d*x+c))*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)+3*A*arcsin((-1+cos(d*x+c))/sin(d*x+c))*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)-3*B*arcsin((-1+cos(d*x+c))/sin(d*x+c))*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)+A*cos(d*x+c)*2^(1/2)*sin(d*x+c)-3*B*cos(d*x+c)*2^(1/2)*sin(d*x+c)-A*2^(1/2)*sin(d*x+c))*cos(d*x+c)*(1/cos(d*x+c))^(5/2)*(a*(1+cos(d*x+c)))^(1/2)*sin(d*x+c)^2/(-1+cos(d*x+c))/(1+cos(d*x+c))^2*2^(1/2)/a","B"
524,1,231,100,0.380000," ","int((A+B*cos(d*x+c))*sec(d*x+c)^(3/2)/(a+a*cos(d*x+c))^(1/2),x)","\frac{\left(A \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)}}-B \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)}}+A \sqrt{2}\, \sin \left(d x +c \right)+A \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)}}-B \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)}}\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*(A*cos(d*x+c)*arcsin((-1+cos(d*x+c))/sin(d*x+c))*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)-B*cos(d*x+c)*arcsin((-1+cos(d*x+c))/sin(d*x+c))*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+A*2^(1/2)*sin(d*x+c)+A*arcsin((-1+cos(d*x+c))/sin(d*x+c))*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)-B*arcsin((-1+cos(d*x+c))/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)*(a*(1+cos(d*x+c)))^(1/2)/(1+cos(d*x+c))*2^(1/2)/a","B"
525,1,153,115,0.385000," ","int((A+B*cos(d*x+c))*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)}\, \left(-B \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)+A \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)-B \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\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)*(-B*2^(1/2)*arctan(sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)/cos(d*x+c))+A*arcsin((-1+cos(d*x+c))/sin(d*x+c))-B*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"
526,1,232,152,0.397000," ","int((A+B*cos(d*x+c))/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(B \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+2 A \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)-B \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 A \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)-2 B \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \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} a}"," ",0,"1/2/d*(a*(1+cos(d*x+c)))^(1/2)*cos(d*x+c)*(-1+cos(d*x+c))^2*(B*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+2*A*2^(1/2)*arctan(sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)/cos(d*x+c))-B*2^(1/2)*arctan(sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)/cos(d*x+c))+2*A*arcsin((-1+cos(d*x+c))/sin(d*x+c))-2*B*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"
527,1,300,191,0.420000," ","int((A+B*cos(d*x+c))/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(-2 B \sin \left(d x +c \right) \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right)-4 A \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+B \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+4 A \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)-7 B \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 A \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)-8 B \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)\right) \sqrt{2}}{8 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,"1/8/d*(a*(1+cos(d*x+c)))^(1/2)*cos(d*x+c)*(-1+cos(d*x+c))^3*(-2*B*sin(d*x+c)*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)-4*A*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+B*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+4*A*2^(1/2)*arctan(sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)/cos(d*x+c))-7*B*2^(1/2)*arctan(sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)/cos(d*x+c))+8*A*arcsin((-1+cos(d*x+c))/sin(d*x+c))-8*B*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"
528,1,317,163,0.481000," ","int((a*A+(A*b+B*a)*cos(d*x+c)+b*B*cos(d*x+c)^2)*sec(d*x+c)^(1/2)/(a+a*cos(d*x+c))^(1/2),x)","-\frac{\left(B \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, b \sin \left(d x +c \right)+2 A \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) b +2 B \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) a -B \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) b -2 A \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) a +2 A \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) b +2 B \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) a -2 B \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) b \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) \sqrt{2}}{2 d \sin \left(d x +c \right)^{2} a}"," ",0,"-1/2/d*(B*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*b*sin(d*x+c)+2*A*2^(1/2)*arctan(sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)/cos(d*x+c))*b+2*B*2^(1/2)*arctan(sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)/cos(d*x+c))*a-B*2^(1/2)*arctan(sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)/cos(d*x+c))*b-2*A*arcsin((-1+cos(d*x+c))/sin(d*x+c))*a+2*A*arcsin((-1+cos(d*x+c))/sin(d*x+c))*b+2*B*arcsin((-1+cos(d*x+c))/sin(d*x+c))*a-2*B*arcsin((-1+cos(d*x+c))/sin(d*x+c))*b)*(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)*2^(1/2)/a","A"
529,1,731,270,0.554000," ","int((A+B*cos(d*x+c))*sec(d*x+c)^(9/2)/(a+a*cos(d*x+c))^(3/2),x)","-\frac{\left(-1995 A \sin \left(d x +c \right) \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) \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{7}{2}}+1575 B \sin \left(d x +c \right) \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) \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{7}{2}}-7980 A \sin \left(d x +c \right) \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{7}{2}}+6300 B \sin \left(d x +c \right) \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{7}{2}}-11970 A \sin \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) \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{7}{2}}+9450 B \sin \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) \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{7}{2}}-7980 A \sin \left(d x +c \right) \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{7}{2}}+6300 B \sin \left(d x +c \right) \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{7}{2}}-1995 A \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{7}{2}}+1575 B \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{7}{2}}+1201 A \sqrt{2}\, \left(\cos^{5}\left(d x +c \right)\right)-1029 B \sqrt{2}\, \left(\cos^{5}\left(d x +c \right)\right)-397 A \sqrt{2}\, \left(\cos^{4}\left(d x +c \right)\right)+273 B \sqrt{2}\, \left(\cos^{4}\left(d x +c \right)\right)-1000 A \sqrt{2}\, \left(\cos^{3}\left(d x +c \right)\right)+840 B \sqrt{2}\, \left(\cos^{3}\left(d x +c \right)\right)+232 A \sqrt{2}\, \left(\cos^{2}\left(d x +c \right)\right)-168 B \sqrt{2}\, \left(\cos^{2}\left(d x +c \right)\right)-96 A \sqrt{2}\, \cos \left(d x +c \right)+84 B \sqrt{2}\, \cos \left(d x +c \right)+60 A \sqrt{2}\right) \cos \left(d x +c \right) \left(\sin^{5}\left(d x +c \right)\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)}\, \sqrt{2}}{420 d \left(-1+\cos \left(d x +c \right)\right)^{3} \left(1+\cos \left(d x +c \right)\right)^{4} a^{2}}"," ",0,"-1/420/d*(-1995*A*sin(d*x+c)*arcsin((-1+cos(d*x+c))/sin(d*x+c))*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(7/2)+1575*B*sin(d*x+c)*arcsin((-1+cos(d*x+c))/sin(d*x+c))*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(7/2)-7980*A*sin(d*x+c)*arcsin((-1+cos(d*x+c))/sin(d*x+c))*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(7/2)+6300*B*sin(d*x+c)*arcsin((-1+cos(d*x+c))/sin(d*x+c))*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(7/2)-11970*A*sin(d*x+c)*arcsin((-1+cos(d*x+c))/sin(d*x+c))*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(7/2)+9450*B*sin(d*x+c)*arcsin((-1+cos(d*x+c))/sin(d*x+c))*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(7/2)-7980*A*sin(d*x+c)*arcsin((-1+cos(d*x+c))/sin(d*x+c))*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(7/2)+6300*B*sin(d*x+c)*arcsin((-1+cos(d*x+c))/sin(d*x+c))*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(7/2)-1995*A*sin(d*x+c)*arcsin((-1+cos(d*x+c))/sin(d*x+c))*(cos(d*x+c)/(1+cos(d*x+c)))^(7/2)+1575*B*sin(d*x+c)*arcsin((-1+cos(d*x+c))/sin(d*x+c))*(cos(d*x+c)/(1+cos(d*x+c)))^(7/2)+1201*A*2^(1/2)*cos(d*x+c)^5-1029*B*2^(1/2)*cos(d*x+c)^5-397*A*2^(1/2)*cos(d*x+c)^4+273*B*2^(1/2)*cos(d*x+c)^4-1000*A*2^(1/2)*cos(d*x+c)^3+840*B*2^(1/2)*cos(d*x+c)^3+232*A*2^(1/2)*cos(d*x+c)^2-168*B*2^(1/2)*cos(d*x+c)^2-96*A*2^(1/2)*cos(d*x+c)+84*B*2^(1/2)*cos(d*x+c)+60*A*2^(1/2))*cos(d*x+c)*sin(d*x+c)^5*(1/cos(d*x+c))^(9/2)*(a*(1+cos(d*x+c)))^(1/2)/(-1+cos(d*x+c))^3/(1+cos(d*x+c))^4*2^(1/2)/a^2","B"
530,1,595,229,0.562000," ","int((A+B*cos(d*x+c))*sec(d*x+c)^(7/2)/(a+a*cos(d*x+c))^(3/2),x)","\frac{\left(225 A \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^{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}}-165 B \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^{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}}+675 A \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) \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}}-495 B \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) \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}}+675 A \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) \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}}-495 B \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) \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}}+225 A \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \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}}-165 B \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \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}}-147 A \sqrt{2}\, \left(\cos^{4}\left(d x +c \right)\right)+95 B \sqrt{2}\, \left(\cos^{4}\left(d x +c \right)\right)+39 A \sqrt{2}\, \left(\cos^{3}\left(d x +c \right)\right)-35 B \sqrt{2}\, \left(\cos^{3}\left(d x +c \right)\right)+120 A \sqrt{2}\, \left(\cos^{2}\left(d x +c \right)\right)-80 B \sqrt{2}\, \left(\cos^{2}\left(d x +c \right)\right)-24 A \sqrt{2}\, \cos \left(d x +c \right)+20 B \sqrt{2}\, \cos \left(d x +c \right)+12 A \sqrt{2}\right) \cos \left(d x +c \right) \left(\sin^{3}\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}}{60 d \left(-1+\cos \left(d x +c \right)\right)^{2} \left(1+\cos \left(d x +c \right)\right)^{3} a^{2}}"," ",0,"1/60/d*(225*A*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)))^(5/2)-165*B*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)))^(5/2)+675*A*arcsin((-1+cos(d*x+c))/sin(d*x+c))*sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(5/2)-495*B*arcsin((-1+cos(d*x+c))/sin(d*x+c))*sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(5/2)+675*A*arcsin((-1+cos(d*x+c))/sin(d*x+c))*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(5/2)-495*B*arcsin((-1+cos(d*x+c))/sin(d*x+c))*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(5/2)+225*A*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)-165*B*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)-147*A*2^(1/2)*cos(d*x+c)^4+95*B*2^(1/2)*cos(d*x+c)^4+39*A*2^(1/2)*cos(d*x+c)^3-35*B*2^(1/2)*cos(d*x+c)^3+120*A*2^(1/2)*cos(d*x+c)^2-80*B*2^(1/2)*cos(d*x+c)^2-24*A*2^(1/2)*cos(d*x+c)+20*B*2^(1/2)*cos(d*x+c)+12*A*2^(1/2))*cos(d*x+c)*sin(d*x+c)^3*(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^2","B"
531,1,457,188,0.439000," ","int((A+B*cos(d*x+c))*sec(d*x+c)^(5/2)/(a+a*cos(d*x+c))^(3/2),x)","-\frac{\left(-33 A \sin \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(\cos^{2}\left(d x +c \right)\right)+21 B \sin \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(\cos^{2}\left(d x +c \right)\right)-66 A \sin \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) \cos \left(d x +c \right)+42 B \sin \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) \cos \left(d x +c \right)-33 A \sin \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)+21 B \sin \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)+19 A \sqrt{2}\, \left(\cos^{3}\left(d x +c \right)\right)-15 B \sqrt{2}\, \left(\cos^{3}\left(d x +c \right)\right)-7 A \sqrt{2}\, \left(\cos^{2}\left(d x +c \right)\right)+3 B \sqrt{2}\, \left(\cos^{2}\left(d x +c \right)\right)-16 A \sqrt{2}\, \cos \left(d x +c \right)+12 B \sqrt{2}\, \cos \left(d x +c \right)+4 A \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*A*sin(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)^2+21*B*sin(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)^2-66*A*sin(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)+42*B*sin(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)-33*A*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*arcsin((-1+cos(d*x+c))/sin(d*x+c))+21*B*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*arcsin((-1+cos(d*x+c))/sin(d*x+c))+19*A*2^(1/2)*cos(d*x+c)^3-15*B*2^(1/2)*cos(d*x+c)^3-7*A*2^(1/2)*cos(d*x+c)^2+3*B*2^(1/2)*cos(d*x+c)^2-16*A*2^(1/2)*cos(d*x+c)+12*B*2^(1/2)*cos(d*x+c)+4*A*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","B"
532,1,312,147,0.408000," ","int((A+B*cos(d*x+c))*sec(d*x+c)^(3/2)/(a+a*cos(d*x+c))^(3/2),x)","-\frac{\left(-7 A \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)+3 B \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)+5 A \sqrt{2}\, \left(\cos^{2}\left(d x +c \right)\right)-7 A \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)-B \sqrt{2}\, \left(\cos^{2}\left(d x +c \right)\right)+3 B \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)-A \sqrt{2}\, \cos \left(d x +c \right)+B \sqrt{2}\, \cos \left(d x +c \right)-4 A \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}}{4 d \sin \left(d x +c \right) \left(1+\cos \left(d x +c \right)\right) a^{2}}"," ",0,"-1/4/d*(-7*A*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)+3*B*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)+5*A*2^(1/2)*cos(d*x+c)^2-7*A*(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)-B*2^(1/2)*cos(d*x+c)^2+3*B*(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)-A*2^(1/2)*cos(d*x+c)+B*2^(1/2)*cos(d*x+c)-4*A*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)/(1+cos(d*x+c))*2^(1/2)/a^2","B"
533,1,235,104,0.366000," ","int((A+B*cos(d*x+c))*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(-A \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right)+B \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right)+3 A \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \sin \left(d x +c \right)+A \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+B \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \sin \left(d x +c \right)-B \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)*(-A*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)+B*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)+3*A*arcsin((-1+cos(d*x+c))/sin(d*x+c))*sin(d*x+c)+A*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+B*arcsin((-1+cos(d*x+c))/sin(d*x+c))*sin(d*x+c)-B*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","B"
534,1,288,152,0.383000," ","int((A+B*cos(d*x+c))/(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(A \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right)-4 B \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) \sin \left(d x +c \right)-B \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right)+A \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \sin \left(d x +c \right)-A \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}-5 B \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \sin \left(d x +c \right)+B \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \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*(A*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)-4*B*2^(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)-B*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)+A*arcsin((-1+cos(d*x+c))/sin(d*x+c))*sin(d*x+c)-A*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)-5*B*arcsin((-1+cos(d*x+c))/sin(d*x+c))*sin(d*x+c)+B*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)^5*2^(1/2)/a^2","A"
535,1,370,198,0.444000," ","int((A+B*cos(d*x+c))/(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)}\, \cos \left(d x +c \right) \left(-1+\cos \left(d x +c \right)\right)^{3} \left(-2 B \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)}}+A \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right)+4 A \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) \sin \left(d x +c \right)-B \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right)-6 B \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) \sin \left(d x +c \right)+5 A \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \sin \left(d x +c \right)-A \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}-9 B \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \sin \left(d x +c \right)+3 B \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)*cos(d*x+c)*(-1+cos(d*x+c))^3*(-2*B*cos(d*x+c)^2*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+A*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)+4*A*2^(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)-B*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)-6*B*2^(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)+5*A*arcsin((-1+cos(d*x+c))/sin(d*x+c))*sin(d*x+c)-A*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)-9*B*arcsin((-1+cos(d*x+c))/sin(d*x+c))*sin(d*x+c)+3*B*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"
536,1,729,270,0.520000," ","int((A+B*cos(d*x+c))*sec(d*x+c)^(7/2)/(a+a*cos(d*x+c))^(5/2),x)","-\frac{\left(4245 A \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^{4}\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}}-2445 B \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^{4}\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}}+16980 A \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^{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}}-9780 B \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^{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}}+25470 A \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) \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}}-14670 B \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) \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}}+16980 A \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) \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}}-9780 B \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) \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}}+4245 A \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \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}}-2445 B \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \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}}-2671 A \sqrt{2}\, \left(\cos^{5}\left(d x +c \right)\right)+1495 B \sqrt{2}\, \left(\cos^{5}\left(d x +c \right)\right)-1884 A \sqrt{2}\, \left(\cos^{4}\left(d x +c \right)\right)+1020 B \sqrt{2}\, \left(\cos^{4}\left(d x +c \right)\right)+2987 A \sqrt{2}\, \left(\cos^{3}\left(d x +c \right)\right)-1715 B \sqrt{2}\, \left(\cos^{3}\left(d x +c \right)\right)+1728 A \sqrt{2}\, \left(\cos^{2}\left(d x +c \right)\right)-960 B \sqrt{2}\, \left(\cos^{2}\left(d x +c \right)\right)-256 A \sqrt{2}\, \cos \left(d x +c \right)+160 B \sqrt{2}\, \cos \left(d x +c \right)+96 A \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{7}{2}} \sqrt{a \left(1+\cos \left(d x +c \right)\right)}\, \sqrt{2}}{480 d \left(-1+\cos \left(d x +c \right)\right) \left(1+\cos \left(d x +c \right)\right)^{3} a^{3}}"," ",0,"-1/480/d*(4245*A*arcsin((-1+cos(d*x+c))/sin(d*x+c))*sin(d*x+c)*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(5/2)-2445*B*arcsin((-1+cos(d*x+c))/sin(d*x+c))*sin(d*x+c)*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(5/2)+16980*A*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)))^(5/2)-9780*B*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)))^(5/2)+25470*A*arcsin((-1+cos(d*x+c))/sin(d*x+c))*sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(5/2)-14670*B*arcsin((-1+cos(d*x+c))/sin(d*x+c))*sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(5/2)+16980*A*arcsin((-1+cos(d*x+c))/sin(d*x+c))*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(5/2)-9780*B*arcsin((-1+cos(d*x+c))/sin(d*x+c))*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(5/2)+4245*A*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)-2445*B*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)-2671*A*2^(1/2)*cos(d*x+c)^5+1495*B*2^(1/2)*cos(d*x+c)^5-1884*A*2^(1/2)*cos(d*x+c)^4+1020*B*2^(1/2)*cos(d*x+c)^4+2987*A*2^(1/2)*cos(d*x+c)^3-1715*B*2^(1/2)*cos(d*x+c)^3+1728*A*2^(1/2)*cos(d*x+c)^2-960*B*2^(1/2)*cos(d*x+c)^2-256*A*2^(1/2)*cos(d*x+c)+160*B*2^(1/2)*cos(d*x+c)+96*A*2^(1/2))*cos(d*x+c)*sin(d*x+c)*(1/cos(d*x+c))^(7/2)*(a*(1+cos(d*x+c)))^(1/2)/(-1+cos(d*x+c))/(1+cos(d*x+c))^3*2^(1/2)/a^3","B"
537,1,585,229,0.513000," ","int((A+B*cos(d*x+c))*sec(d*x+c)^(5/2)/(a+a*cos(d*x+c))^(5/2),x)","\frac{\left(-489 A \sin \left(d x +c \right) \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{3}{2}}+225 B \sin \left(d x +c \right) \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{3}{2}}-1467 A \sin \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(\cos^{2}\left(d x +c \right)\right)+675 B \sin \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(\cos^{2}\left(d x +c \right)\right)-1467 A \sin \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) \cos \left(d x +c \right)+675 B \sin \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) \cos \left(d x +c \right)+299 A \sqrt{2}\, \left(\cos^{4}\left(d x +c \right)\right)-489 A \sin \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)-147 B \sqrt{2}\, \left(\cos^{4}\left(d x +c \right)\right)+225 B \sin \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)+204 A \sqrt{2}\, \left(\cos^{3}\left(d x +c \right)\right)-108 B \sqrt{2}\, \left(\cos^{3}\left(d x +c \right)\right)-343 A \sqrt{2}\, \left(\cos^{2}\left(d x +c \right)\right)+159 B \sqrt{2}\, \left(\cos^{2}\left(d x +c \right)\right)-192 A \sqrt{2}\, \cos \left(d x +c \right)+96 B \sqrt{2}\, \cos \left(d x +c \right)+32 A \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*A*sin(d*x+c)*arcsin((-1+cos(d*x+c))/sin(d*x+c))*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)+225*B*sin(d*x+c)*arcsin((-1+cos(d*x+c))/sin(d*x+c))*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)-1467*A*sin(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)^2+675*B*sin(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)^2-1467*A*sin(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)+675*B*sin(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)+299*A*2^(1/2)*cos(d*x+c)^4-489*A*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*arcsin((-1+cos(d*x+c))/sin(d*x+c))-147*B*2^(1/2)*cos(d*x+c)^4+225*B*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*arcsin((-1+cos(d*x+c))/sin(d*x+c))+204*A*2^(1/2)*cos(d*x+c)^3-108*B*2^(1/2)*cos(d*x+c)^3-343*A*2^(1/2)*cos(d*x+c)^2+159*B*2^(1/2)*cos(d*x+c)^2-192*A*2^(1/2)*cos(d*x+c)+96*B*2^(1/2)*cos(d*x+c)+32*A*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","B"
538,1,457,188,0.426000," ","int((A+B*cos(d*x+c))*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 A \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) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}-19 B \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) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+150 A \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)-49 A \sqrt{2}\, \left(\cos^{3}\left(d x +c \right)\right)-38 B \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)+9 B \sqrt{2}\, \left(\cos^{3}\left(d x +c \right)\right)+75 A \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 A \sqrt{2}\, \left(\cos^{2}\left(d x +c \right)\right)-19 B \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 B \sqrt{2}\, \left(\cos^{2}\left(d x +c \right)\right)+53 A \sqrt{2}\, \cos \left(d x +c \right)-13 B \sqrt{2}\, \cos \left(d x +c \right)+32 A \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*A*arcsin((-1+cos(d*x+c))/sin(d*x+c))*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)-19*B*arcsin((-1+cos(d*x+c))/sin(d*x+c))*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+150*A*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)-49*A*2^(1/2)*cos(d*x+c)^3-38*B*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)+9*B*2^(1/2)*cos(d*x+c)^3+75*A*(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*A*2^(1/2)*cos(d*x+c)^2-19*B*(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*B*2^(1/2)*cos(d*x+c)^2+53*A*2^(1/2)*cos(d*x+c)-13*B*2^(1/2)*cos(d*x+c)+32*A*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","B"
539,1,375,147,0.392000," ","int((A+B*cos(d*x+c))*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 A \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)}}+B \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 A \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)-4 A \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right)+5 B \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)+4 B \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right)+19 A \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \sin \left(d x +c \right)+13 A \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+5 B \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \sin \left(d x +c \right)-5 B \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*A*cos(d*x+c)^2*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+B*cos(d*x+c)^2*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+19*A*arcsin((-1+cos(d*x+c))/sin(d*x+c))*sin(d*x+c)*cos(d*x+c)-4*A*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)+5*B*arcsin((-1+cos(d*x+c))/sin(d*x+c))*sin(d*x+c)*cos(d*x+c)+4*B*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)+19*A*arcsin((-1+cos(d*x+c))/sin(d*x+c))*sin(d*x+c)+13*A*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+5*B*arcsin((-1+cos(d*x+c))/sin(d*x+c))*sin(d*x+c)-5*B*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","B"
540,1,375,145,0.468000," ","int((A+B*cos(d*x+c))/(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(A \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)}}+7 B \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)}}+5 A \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)+4 A \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right)+3 B \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)-4 B \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right)+5 A \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \sin \left(d x +c \right)-5 A \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+3 B \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \sin \left(d x +c \right)-3 B \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \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*(A*cos(d*x+c)^2*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+7*B*cos(d*x+c)^2*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+5*A*arcsin((-1+cos(d*x+c))/sin(d*x+c))*sin(d*x+c)*cos(d*x+c)+4*A*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)+3*B*arcsin((-1+cos(d*x+c))/sin(d*x+c))*sin(d*x+c)*cos(d*x+c)-4*B*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)+5*A*arcsin((-1+cos(d*x+c))/sin(d*x+c))*sin(d*x+c)-5*A*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+3*B*arcsin((-1+cos(d*x+c))/sin(d*x+c))*sin(d*x+c)-3*B*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)^7*2^(1/2)/a^3","B"
541,1,476,195,0.391000," ","int((A+B*cos(d*x+c))/(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 A \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)}}-15 B \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 B \cos \left(d x +c \right) \sqrt{2}\, \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)+3 A \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)-4 A \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right)-43 B \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)+4 B \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right)-32 B \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) \sin \left(d x +c \right)+3 A \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \sin \left(d x +c \right)-3 A \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}-43 B \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \sin \left(d x +c \right)+11 B \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{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*A*cos(d*x+c)^2*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)-15*B*cos(d*x+c)^2*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)-32*B*cos(d*x+c)*2^(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))+3*A*arcsin((-1+cos(d*x+c))/sin(d*x+c))*sin(d*x+c)*cos(d*x+c)-4*A*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)-43*B*arcsin((-1+cos(d*x+c))/sin(d*x+c))*sin(d*x+c)*cos(d*x+c)+4*B*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)-32*B*2^(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)+3*A*arcsin((-1+cos(d*x+c))/sin(d*x+c))*sin(d*x+c)-3*A*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)-43*B*arcsin((-1+cos(d*x+c))/sin(d*x+c))*sin(d*x+c)+11*B*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)^9*2^(1/2)/a^3","B"
542,1,609,241,0.434000," ","int((A+B*cos(d*x+c))/(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(-16 B \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \left(\cos^{3}\left(d x +c \right)\right)+15 A \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 A \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)-39 B \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 B \cos \left(d x +c \right) \sqrt{2}\, \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)+43 A \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)-4 A \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right)+32 A \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) \sin \left(d x +c \right)-115 B \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)+20 B \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right)-80 B \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) \sin \left(d x +c \right)+43 A \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \sin \left(d x +c \right)-11 A \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}-115 B \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \sin \left(d x +c \right)+35 B \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)*(-16*B*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^3+15*A*cos(d*x+c)^2*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+32*A*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)-39*B*cos(d*x+c)^2*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)-80*B*cos(d*x+c)*2^(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))+43*A*arcsin((-1+cos(d*x+c))/sin(d*x+c))*sin(d*x+c)*cos(d*x+c)-4*A*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)+32*A*2^(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)-115*B*arcsin((-1+cos(d*x+c))/sin(d*x+c))*sin(d*x+c)*cos(d*x+c)+20*B*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)-80*B*2^(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)+43*A*arcsin((-1+cos(d*x+c))/sin(d*x+c))*sin(d*x+c)-11*A*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)-115*B*arcsin((-1+cos(d*x+c))/sin(d*x+c))*sin(d*x+c)+35*B*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","B"
543,1,729,270,0.484000," ","int((A+B*cos(d*x+c))*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 A \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}}+1089 B \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 A \sin \left(d x +c \right) \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{3}{2}}+4356 B \sin \left(d x +c \right) \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{3}{2}}-18270 A \sin \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(\cos^{2}\left(d x +c \right)\right)+6534 B \sin \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(\cos^{2}\left(d x +c \right)\right)+1887 A \sqrt{2}\, \left(\cos^{5}\left(d x +c \right)\right)-12180 A \sin \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) \cos \left(d x +c \right)-691 B \sqrt{2}\, \left(\cos^{5}\left(d x +c \right)\right)+4356 B \sin \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) \cos \left(d x +c \right)+3195 A \sqrt{2}\, \left(\cos^{4}\left(d x +c \right)\right)-3045 A \sin \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)-1183 B \sqrt{2}\, \left(\cos^{4}\left(d x +c \right)\right)+1089 B \sin \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)-831 A \sqrt{2}\, \left(\cos^{3}\left(d x +c \right)\right)+275 B \sqrt{2}\, \left(\cos^{3}\left(d x +c \right)\right)-3355 A \sqrt{2}\, \left(\cos^{2}\left(d x +c \right)\right)+1215 B \sqrt{2}\, \left(\cos^{2}\left(d x +c \right)\right)-1024 A \sqrt{2}\, \cos \left(d x +c \right)+384 B \sqrt{2}\, \cos \left(d x +c \right)+128 A \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*A*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)+1089*B*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*A*sin(d*x+c)*arcsin((-1+cos(d*x+c))/sin(d*x+c))*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)+4356*B*sin(d*x+c)*arcsin((-1+cos(d*x+c))/sin(d*x+c))*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)-18270*A*sin(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)^2+6534*B*sin(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)^2+1887*A*2^(1/2)*cos(d*x+c)^5-12180*A*sin(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)-691*B*2^(1/2)*cos(d*x+c)^5+4356*B*sin(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)+3195*A*2^(1/2)*cos(d*x+c)^4-3045*A*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*arcsin((-1+cos(d*x+c))/sin(d*x+c))-1183*B*2^(1/2)*cos(d*x+c)^4+1089*B*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*arcsin((-1+cos(d*x+c))/sin(d*x+c))-831*A*2^(1/2)*cos(d*x+c)^3+275*B*2^(1/2)*cos(d*x+c)^3-3355*A*2^(1/2)*cos(d*x+c)^2+1215*B*2^(1/2)*cos(d*x+c)^2-1024*A*2^(1/2)*cos(d*x+c)+384*B*2^(1/2)*cos(d*x+c)+128*A*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","B"
544,1,595,229,0.419000," ","int((A+B*cos(d*x+c))*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 A \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) \left(\cos^{3}\left(d x +c \right)\right)-189 B \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) \left(\cos^{3}\left(d x +c \right)\right)+3267 A \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) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}-691 A \sqrt{2}\, \left(\cos^{4}\left(d x +c \right)\right)-567 B \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) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+103 B \sqrt{2}\, \left(\cos^{4}\left(d x +c \right)\right)+3267 A \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)-1183 A \sqrt{2}\, \left(\cos^{3}\left(d x +c \right)\right)-567 B \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)+163 B \sqrt{2}\, \left(\cos^{3}\left(d x +c \right)\right)+1089 A \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)+275 A \sqrt{2}\, \left(\cos^{2}\left(d x +c \right)\right)-189 B \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)-71 B \sqrt{2}\, \left(\cos^{2}\left(d x +c \right)\right)+1215 A \sqrt{2}\, \cos \left(d x +c \right)-195 B \sqrt{2}\, \cos \left(d x +c \right)+384 A \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*A*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)*cos(d*x+c)^3-189*B*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)*cos(d*x+c)^3+3267*A*arcsin((-1+cos(d*x+c))/sin(d*x+c))*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)-691*A*2^(1/2)*cos(d*x+c)^4-567*B*arcsin((-1+cos(d*x+c))/sin(d*x+c))*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+103*B*2^(1/2)*cos(d*x+c)^4+3267*A*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)-1183*A*2^(1/2)*cos(d*x+c)^3-567*B*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)+163*B*2^(1/2)*cos(d*x+c)^3+1089*A*(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)+275*A*2^(1/2)*cos(d*x+c)^2-189*B*(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)-71*B*2^(1/2)*cos(d*x+c)^2+1215*A*2^(1/2)*cos(d*x+c)-195*B*2^(1/2)*cos(d*x+c)+384*A*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","B"
545,1,512,188,0.391000," ","int((A+B*cos(d*x+c))*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 A \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \left(\cos^{3}\left(d x +c \right)\right)+5 B \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \left(\cos^{3}\left(d x +c \right)\right)+163 A \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)}}-189 A \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) \sin \left(d x +c \right)-7 B \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)}}-39 B \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) \sin \left(d x +c \right)-71 A \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right)-378 A \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)-37 B \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right)-78 B \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)-195 A \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}-189 A \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \sin \left(d x +c \right)+39 B \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}-39 B \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 \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*A*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^3+5*B*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^3+163*A*cos(d*x+c)^2*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)-189*A*cos(d*x+c)^2*arcsin((-1+cos(d*x+c))/sin(d*x+c))*sin(d*x+c)-7*B*cos(d*x+c)^2*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)-39*B*cos(d*x+c)^2*arcsin((-1+cos(d*x+c))/sin(d*x+c))*sin(d*x+c)-71*A*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)-378*A*arcsin((-1+cos(d*x+c))/sin(d*x+c))*sin(d*x+c)*cos(d*x+c)-37*B*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)-78*B*arcsin((-1+cos(d*x+c))/sin(d*x+c))*sin(d*x+c)*cos(d*x+c)-195*A*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)-189*A*arcsin((-1+cos(d*x+c))/sin(d*x+c))*sin(d*x+c)+39*B*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)-39*B*arcsin((-1+cos(d*x+c))/sin(d*x+c))*sin(d*x+c))/sin(d*x+c)^7/(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2)/a^4","B"
546,1,512,186,0.386000," ","int((A+B*cos(d*x+c))/(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 A \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \left(\cos^{3}\left(d x +c \right)\right)+17 B \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \left(\cos^{3}\left(d x +c \right)\right)+39 A \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) \sin \left(d x +c \right)+7 A \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 B \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) \sin \left(d x +c \right)+53 B \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 A \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)+37 A \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right)+42 B \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 B \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right)+39 A \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \sin \left(d x +c \right)-39 A \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+21 B \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \sin \left(d x +c \right)-21 B \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*A*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^3+17*B*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^3+39*A*cos(d*x+c)^2*arcsin((-1+cos(d*x+c))/sin(d*x+c))*sin(d*x+c)+7*A*cos(d*x+c)^2*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+21*B*cos(d*x+c)^2*arcsin((-1+cos(d*x+c))/sin(d*x+c))*sin(d*x+c)+53*B*cos(d*x+c)^2*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+78*A*arcsin((-1+cos(d*x+c))/sin(d*x+c))*sin(d*x+c)*cos(d*x+c)+37*A*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)+42*B*arcsin((-1+cos(d*x+c))/sin(d*x+c))*sin(d*x+c)*cos(d*x+c)-49*B*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)+39*A*arcsin((-1+cos(d*x+c))/sin(d*x+c))*sin(d*x+c)-39*A*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+21*B*arcsin((-1+cos(d*x+c))/sin(d*x+c))*sin(d*x+c)-21*B*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","B"
547,1,512,186,0.426000," ","int((A+B*cos(d*x+c))/(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 A \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \left(\cos^{3}\left(d x +c \right)\right)+67 B \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \left(\cos^{3}\left(d x +c \right)\right)+21 A \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) \sin \left(d x +c \right)+53 A \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)}}+15 B \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) \sin \left(d x +c \right)-17 B \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)}}+42 A \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 A \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right)+30 B \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)-35 B \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right)+21 A \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \sin \left(d x +c \right)-21 A \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+15 B \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \sin \left(d x +c \right)-15 B \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{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*A*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^3+67*B*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^3+21*A*cos(d*x+c)^2*arcsin((-1+cos(d*x+c))/sin(d*x+c))*sin(d*x+c)+53*A*cos(d*x+c)^2*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+15*B*cos(d*x+c)^2*arcsin((-1+cos(d*x+c))/sin(d*x+c))*sin(d*x+c)-17*B*cos(d*x+c)^2*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+42*A*arcsin((-1+cos(d*x+c))/sin(d*x+c))*sin(d*x+c)*cos(d*x+c)-49*A*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)+30*B*arcsin((-1+cos(d*x+c))/sin(d*x+c))*sin(d*x+c)*cos(d*x+c)-35*B*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)+21*A*arcsin((-1+cos(d*x+c))/sin(d*x+c))*sin(d*x+c)-21*A*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+15*B*arcsin((-1+cos(d*x+c))/sin(d*x+c))*sin(d*x+c)-15*B*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)^11*2^(1/2)/a^4","B"
548,1,667,236,0.414000," ","int((A+B*cos(d*x+c))/(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 A \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \left(\cos^{3}\left(d x +c \right)\right)-247 B \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \left(\cos^{3}\left(d x +c \right)\right)-384 B \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)+15 A \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) \sin \left(d x +c \right)-17 A \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 B \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) \sin \left(d x +c \right)-115 B \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)}}-768 B \cos \left(d x +c \right) \sqrt{2}\, \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)+30 A \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)-35 A \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right)-1062 B \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)+215 B \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right)-384 B \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) \sin \left(d x +c \right)+15 A \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \sin \left(d x +c \right)-15 A \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}-531 B \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \sin \left(d x +c \right)+147 B \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*A*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^3-247*B*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^3-384*B*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)+15*A*cos(d*x+c)^2*arcsin((-1+cos(d*x+c))/sin(d*x+c))*sin(d*x+c)-17*A*cos(d*x+c)^2*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)-531*B*cos(d*x+c)^2*arcsin((-1+cos(d*x+c))/sin(d*x+c))*sin(d*x+c)-115*B*cos(d*x+c)^2*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)-768*B*cos(d*x+c)*2^(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))+30*A*arcsin((-1+cos(d*x+c))/sin(d*x+c))*sin(d*x+c)*cos(d*x+c)-35*A*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)-1062*B*arcsin((-1+cos(d*x+c))/sin(d*x+c))*sin(d*x+c)*cos(d*x+c)+215*B*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)-384*B*2^(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)+15*A*arcsin((-1+cos(d*x+c))/sin(d*x+c))*sin(d*x+c)-15*A*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)-531*B*arcsin((-1+cos(d*x+c))/sin(d*x+c))*sin(d*x+c)+147*B*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","B"
549,1,855,282,0.440000," ","int((A+B*cos(d*x+c))/(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(-192 B \left(\cos^{4}\left(d x +c \right)\right) \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+247 A \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \left(\cos^{3}\left(d x +c \right)\right)+384 A \left(\cos^{2}\left(d x +c \right)\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)-907 B \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \left(\cos^{3}\left(d x +c \right)\right)-1344 B \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)+531 A \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) \sin \left(d x +c \right)+115 A \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)}}+768 A \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)-1911 B \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) \sin \left(d x +c \right)-343 B \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 B \cos \left(d x +c \right) \sqrt{2}\, \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)+1062 A \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)-215 A \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right)+384 A \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) \sin \left(d x +c \right)-3822 B \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)+875 B \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right)-1344 B \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) \sin \left(d x +c \right)+531 A \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \sin \left(d x +c \right)-147 A \sqrt{2}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}-1911 B \arcsin \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \sin \left(d x +c \right)+567 B \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{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)*(-192*B*cos(d*x+c)^4*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+247*A*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^3+384*A*cos(d*x+c)^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))-907*B*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^3-1344*B*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)+531*A*cos(d*x+c)^2*arcsin((-1+cos(d*x+c))/sin(d*x+c))*sin(d*x+c)+115*A*cos(d*x+c)^2*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+768*A*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)-1911*B*cos(d*x+c)^2*arcsin((-1+cos(d*x+c))/sin(d*x+c))*sin(d*x+c)-343*B*cos(d*x+c)^2*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)-2688*B*cos(d*x+c)*2^(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))+1062*A*arcsin((-1+cos(d*x+c))/sin(d*x+c))*sin(d*x+c)*cos(d*x+c)-215*A*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)+384*A*2^(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)-3822*B*arcsin((-1+cos(d*x+c))/sin(d*x+c))*sin(d*x+c)*cos(d*x+c)+875*B*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)-1344*B*2^(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)+531*A*arcsin((-1+cos(d*x+c))/sin(d*x+c))*sin(d*x+c)-147*A*2^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)-1911*B*arcsin((-1+cos(d*x+c))/sin(d*x+c))*sin(d*x+c)+567*B*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)^15*2^(1/2)/a^4","B"
550,1,663,208,4.511000," ","int((a+b*cos(d*x+c))*(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 B b \left(-\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+2 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right)^{2} \left(2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}-\frac{2 a 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 \left(A b +a 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)+\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*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)-2/5*a*A/(8*sin(1/2*d*x+1/2*c)^6-12*sin(1/2*d*x+1/2*c)^4+6*sin(1/2*d*x+1/2*c)^2-1)/sin(1/2*d*x+1/2*c)^2*(12*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^4-24*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6-12*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^2+24*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-8*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c))*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)+2*(A*b+B*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"
551,1,428,179,3.343000," ","int((a+b*cos(d*x+c))*(A+B*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(\frac{2 B b \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{2 \left(A b +a B \right) \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)}+2 a 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)\right)}{\sin \left(\frac{d 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*b*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+2*(A*b+B*a)*(-(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+2*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2)/sin(1/2*d*x+1/2*c)^2/(2*sin(1/2*d*x+1/2*c)^2-1)+2*a*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"
552,1,244,153,1.390000," ","int((a+b*cos(d*x+c))*(A+B*cos(d*x+c))*sec(d*x+c)^(3/2),x)","-\frac{2 \left(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)+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) a -2 A a \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+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)-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) 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*(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))+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))*a-2*A*a*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^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))-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)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
553,1,326,153,1.348000," ","int((a+b*cos(d*x+c))*(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 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 A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-3 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 +B 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{\frac{1}{2}-\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 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*b*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4+3*a*A*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-3*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+B*b*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-3*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*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*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"
554,1,371,180,1.425000," ","int((a+b*cos(d*x+c))*(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(-24 B 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 b +20 a B +24 B 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 b -10 a B -6 B 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 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 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) a +5 a B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-9 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) b \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*b*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6+(20*A*b+20*B*a+24*B*b)*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+(-10*A*b-10*B*a-6*B*b)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+5*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*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))*a+5*a*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-9*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)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
555,1,413,208,1.398000," ","int((a+b*cos(d*x+c))*(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(240 B 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 b -168 a B -360 B 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(140 a A +168 A b +168 a B +280 B 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(-70 a A -42 A b -42 a B -80 B 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)+35 a 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)-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) b +25 B 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)-63 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) a \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*b*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^8+(-168*A*b-168*B*a-360*B*b)*sin(1/2*d*x+1/2*c)^6*cos(1/2*d*x+1/2*c)+(140*A*a+168*A*b+168*B*a+280*B*b)*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+(-70*A*a-42*A*b-42*B*a-80*B*b)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+35*a*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))-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))*b+25*B*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))-63*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))*a)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
556,1,750,249,4.506000," ","int((a+b*cos(d*x+c))^2*(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 b^{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}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{2 b \left(A b +2 a B \right) \left(-\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+2 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right)^{2} \left(2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}-\frac{2 a^{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 a \left(2 A b +a 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)+\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^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))+2*b*(A*b+2*B*a)*(-(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+2*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2)/sin(1/2*d*x+1/2*c)^2/(2*sin(1/2*d*x+1/2*c)^2-1)-2/5*a^2*A/(8*sin(1/2*d*x+1/2*c)^6-12*sin(1/2*d*x+1/2*c)^4+6*sin(1/2*d*x+1/2*c)^2-1)/sin(1/2*d*x+1/2*c)^2*(12*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^4-24*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6-12*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^2+24*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-8*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c))*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)+2*a*(2*A*b+B*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"
557,1,677,211,3.472000," ","int((a+b*cos(d*x+c))^2*(A+B*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(\frac{2 b^{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}\, \left(\EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-\EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)\right)}{\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{2 A \,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}\, \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{4 B 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}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{2 b^{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}\, \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 \left(2 A b +a B \right) \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)}+2 a^{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)\right)}{\sin \left(\frac{d 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*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-EllipticE(cos(1/2*d*x+1/2*c),2^(1/2)))+2*A*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))+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)/(-2*sin(1/2*d*x+1/2*c)^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*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+2*a*(2*A*b+B*a)*(-(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+2*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2)/sin(1/2*d*x+1/2*c)^2/(2*sin(1/2*d*x+1/2*c)^2-1)+2*a^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"
558,1,404,197,1.539000," ","int((a+b*cos(d*x+c))^2*(A+B*cos(d*x+c))*sec(d*x+c)^(3/2),x)","-\frac{2 \left(4 B \,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)+6 A 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)+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) a^{2}-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^{2}-6 A \,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)+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} 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)-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) a b -2 B \,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 \sin \left(\frac{d 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*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4+6*A*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))+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))*a^2-3*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^2-6*A*a^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^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*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))-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))*a*b-2*B*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
559,1,487,203,1.395000," ","int((a+b*cos(d*x+c))^2*(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(-24 B \,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(20 A \,b^{2}+40 B a b +24 b^{2} B \right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\left(-10 A \,b^{2}-20 B a b -6 b^{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)+15 a^{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)+5 A \,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)-30 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) a b +10 B 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 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) a^{2}-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) 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*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6+(20*A*b^2+40*B*a*b+24*B*b^2)*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+(-10*A*b^2-20*B*a*b-6*B*b^2)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+15*a^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))+5*A*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))-30*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))*a*b+10*B*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*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))*a^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)/(-2*sin(1/2*d*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"
560,1,548,241,1.400000," ","int((a+b*cos(d*x+c))^2*(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(240 B \,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(-168 A \,b^{2}-336 B a b -360 b^{2} B \right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\left(280 A a b +168 A \,b^{2}+140 a^{2} B +336 B a b +280 b^{2} B \right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\left(-140 A a b -42 A \,b^{2}-70 a^{2} B -84 B a b -80 b^{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)+70 A 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)-105 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) a^{2}-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) b^{2}+35 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^{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)-126 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) 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*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^8+(-168*A*b^2-336*B*a*b-360*B*b^2)*sin(1/2*d*x+1/2*c)^6*cos(1/2*d*x+1/2*c)+(280*A*a*b+168*A*b^2+140*B*a^2+336*B*a*b+280*B*b^2)*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+(-140*A*a*b-42*A*b^2-70*B*a^2-84*B*a*b-80*B*b^2)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+70*A*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))-105*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))*a^2-63*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))*b^2+35*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^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))-126*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))*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"
561,1,944,319,6.091000," ","int((a+b*cos(d*x+c))^3*(A+B*cos(d*x+c))*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{2 b^{3} B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{2 a^{2} \left(3 A b +a B \right) \left(12 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \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(A b +3 a B \right) \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 b \left(A b +a 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)+\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 \,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)*(2*b^3*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-2/5*a^2*(3*A*b+B*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^2*(A*b+3*B*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*b*(A*b+B*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*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"
562,1,997,272,4.752000," ","int((a+b*cos(d*x+c))^3*(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 b^{3} B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \left(\EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-\EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)\right)}{\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{2 A \,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{6 B a \,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}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{2 b^{3} B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{6 a b \left(A b +a B \right) \left(-\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+2 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right)^{2} \left(2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}-\frac{2 A \,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}}+2 a^{2} \left(3 A b +a 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)+\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*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-EllipticE(cos(1/2*d*x+1/2*c),2^(1/2)))+2*A*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))+6*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+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^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*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))+6*a*b*(A*b+B*a)*(-(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+2*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2)/sin(1/2*d*x+1/2*c)^2/(2*sin(1/2*d*x+1/2*c)^2-1)-2/5*A*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)+2*a^2*(3*A*b+B*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"
563,1,1212,269,4.128000," ","int((a+b*cos(d*x+c))^3*(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(8 B \,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)+2 A \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, a^{3} \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+18 A \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, a \,b^{2} \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+18 A \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, a^{2} b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-6 A \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, b^{3} \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-36 A \,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)+18 B \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, a^{2} b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+2 B \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, b^{3} \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+6 B \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, a^{3} \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-18 B \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, a \,b^{2} \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-12 B \,a^{3} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-8 B \,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)-A \,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 A a \,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)-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) a^{2} b +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^{3}+2 A \,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 \,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)-9 a^{2} b 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} 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{\frac{1}{2}-\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 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) a \,b^{2}+6 B \,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 \,b^{3} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{3 \left(4 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-4 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \sin \left(\frac{d x}{2}+\frac{c}{2}\right)^{3} \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"2/3*(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)/(4*sin(1/2*d*x+1/2*c)^4-4*sin(1/2*d*x+1/2*c)^2+1)/sin(1/2*d*x+1/2*c)^3*(8*B*b^3*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6+2*A*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*a^3*sin(1/2*d*x+1/2*c)^2+18*A*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*a*b^2*sin(1/2*d*x+1/2*c)^2+18*A*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*a^2*b*sin(1/2*d*x+1/2*c)^2-6*A*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*b^3*sin(1/2*d*x+1/2*c)^2-36*A*a^2*b*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4+18*B*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*a^2*b*sin(1/2*d*x+1/2*c)^2+2*B*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*b^3*sin(1/2*d*x+1/2*c)^2+6*B*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*a^3*sin(1/2*d*x+1/2*c)^2-18*B*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*a*b^2*sin(1/2*d*x+1/2*c)^2-12*B*a^3*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4-8*B*b^3*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4-A*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*A*a*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))-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))*a^2*b+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^3+2*A*a^3*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2+18*A*a^2*b*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2-9*a^2*b*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*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-3*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*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*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))*a*b^2+6*B*a^3*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2+2*B*b^3*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
564,1,867,265,1.663000," ","int((a+b*cos(d*x+c))^3*(A+B*cos(d*x+c))*sec(d*x+c)^(3/2),x)","-\frac{2 \left(-24 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)}\, 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)+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)}\, b^{2} \left(5 A b +15 a B +6 B b \right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-2 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \left(15 A \,a^{3}+5 A \,b^{3}+15 B a \,b^{2}+3 b^{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)+45 A \,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) \sqrt{-2 \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 A \,b^{3} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}+15 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) a^{3}-45 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) a \,b^{2}+15 a^{3} B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}+15 B a \,b^{2} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}-45 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)}\, \sqrt{\frac{1}{2}-\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 -9 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)}\, \sqrt{\frac{1}{2}-\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)}{15 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-2/15*(-24*B*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*b^3*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6+4*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*b^2*(5*A*b+15*B*a+6*B*b)*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)-2*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(15*A*a^3+5*A*b^3+15*B*a*b^2+3*B*b^3)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+45*A*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))*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)+5*A*b^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)+15*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))*a^3-45*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))*a*b^2+15*a^3*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)+15*B*a*b^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)-45*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))*a^2*b-9*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))*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"
565,1,664,273,1.457000," ","int((a+b*cos(d*x+c))^3*(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(240 B \,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(-168 A \,b^{3}-504 B a \,b^{2}-360 b^{3} B \right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\left(420 A a \,b^{2}+168 A \,b^{3}+420 a^{2} b B +504 B a \,b^{2}+280 b^{3} 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(-210 A a \,b^{2}-42 A \,b^{3}-210 a^{2} b B -126 B a \,b^{2}-80 b^{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)-315 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) a^{2} b -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) b^{3}+105 A \,a^{3} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+105 A a \,b^{2} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-105 B \sqrt{\frac{1}{2}-\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 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) a \,b^{2}+105 a^{2} b 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} 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*b^3*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^8+(-168*A*b^3-504*B*a*b^2-360*B*b^3)*sin(1/2*d*x+1/2*c)^6*cos(1/2*d*x+1/2*c)+(420*A*a*b^2+168*A*b^3+420*B*a^2*b+504*B*a*b^2+280*B*b^3)*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+(-210*A*a*b^2-42*A*b^3-210*B*a^2*b-126*B*a*b^2-80*B*b^3)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)-315*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))*a^2*b-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))*b^3+105*A*a^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+105*A*a*b^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-105*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*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*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))*a*b^2+105*a^2*b*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*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"
566,1,745,319,1.595000," ","int((a+b*cos(d*x+c))^3*(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(-1120 B \,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(720 A \,b^{3}+2160 B a \,b^{2}+2240 b^{3} B \right) \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\left(-1512 A a \,b^{2}-1080 A \,b^{3}-1512 a^{2} b B -3240 B a \,b^{2}-2072 b^{3} B \right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\left(1260 A \,a^{2} b +1512 A a \,b^{2}+840 A \,b^{3}+420 a^{3} B +1512 a^{2} b B +2520 B a \,b^{2}+952 b^{3} 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(-630 A \,a^{2} b -378 A a \,b^{2}-240 A \,b^{3}-210 a^{3} B -378 a^{2} b B -720 B a \,b^{2}-168 b^{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)-315 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) a^{3}-567 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) a \,b^{2}+315 A \,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)+75 A \,b^{3} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-567 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) a^{2} b -147 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) b^{3}+105 a^{3} B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+225 B a \,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)\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*b^3*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^10+(720*A*b^3+2160*B*a*b^2+2240*B*b^3)*sin(1/2*d*x+1/2*c)^8*cos(1/2*d*x+1/2*c)+(-1512*A*a*b^2-1080*A*b^3-1512*B*a^2*b-3240*B*a*b^2-2072*B*b^3)*sin(1/2*d*x+1/2*c)^6*cos(1/2*d*x+1/2*c)+(1260*A*a^2*b+1512*A*a*b^2+840*A*b^3+420*B*a^3+1512*B*a^2*b+2520*B*a*b^2+952*B*b^3)*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+(-630*A*a^2*b-378*A*a*b^2-240*A*b^3-210*B*a^3-378*B*a^2*b-720*B*a*b^2-168*B*b^3)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)-315*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))*a^3-567*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))*a*b^2+315*A*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))+75*A*b^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-567*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))*a^2*b-147*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^3+105*a^3*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+225*B*a*b^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2)))/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
567,1,468,268,4.125000," ","int((A+B*cos(d*x+c))*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 \left(A b -a B \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}\, \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 \left(-A b +a B \right) \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{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)}{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*b-B*a)*b^2/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*b+B*a)/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/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"
568,1,327,168,2.865000," ","int((A+B*cos(d*x+c))*sec(d*x+c)^(3/2)/(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 \left(-A b +a B \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}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), -\frac{2 b}{a -b}, \sqrt{2}\right)}{a \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(-\sqrt{-2 \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 \sin \left(\frac{d x}{2}+\frac{c}{2}\right)^{2} \left(2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(-4*(-A*b+B*a)/a/(-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*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+2*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2)/sin(1/2*d*x+1/2*c)^2/(2*sin(1/2*d*x+1/2*c)^2-1))/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
569,1,217,145,1.499000," ","int((A+B*cos(d*x+c))*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}\, \left(A \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), -\frac{2 b}{a -b}, \sqrt{2}\right) b +B \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a -B \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) b -B \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), -\frac{2 b}{a -b}, \sqrt{2}\right) a \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)*(A*EllipticPi(cos(1/2*d*x+1/2*c),-2*b/(a-b),2^(1/2))*b+B*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*a-B*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*b-B*EllipticPi(cos(1/2*d*x+1/2*c),-2*b/(a-b),2^(1/2))*a)/(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"
570,1,295,215,1.586000," ","int((A+B*cos(d*x+c))/(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 \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), -\frac{2 b}{a -b}, \sqrt{2}\right) a b -A \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a b +A \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) b^{2}-B \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), -\frac{2 b}{a -b}, \sqrt{2}\right) a^{2}+B \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a^{2}-B \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a b +B \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a b -B \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) b^{2}\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)*(A*EllipticPi(cos(1/2*d*x+1/2*c),-2*b/(a-b),2^(1/2))*a*b-A*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*a*b+A*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*b^2-B*EllipticPi(cos(1/2*d*x+1/2*c),-2*b/(a-b),2^(1/2))*a^2+B*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*a^2-B*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*a*b+B*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a*b-B*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*b^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"
571,1,786,257,1.567000," ","int((A+B*cos(d*x+c))/(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(\left(-4 B a \,b^{2}+4 b^{3} B \right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(2 B a \,b^{2}-2 b^{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)+3 A \,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)-3 A a \,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)+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) a \,b^{2}-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^{3}-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}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), -\frac{2 b}{a -b}, \sqrt{2}\right) a^{2} b -3 a^{3} B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+3 a^{2} b 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 a \,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)+b^{3} B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-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) a^{2} b +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) a \,b^{2}+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}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), -\frac{2 b}{a -b}, \sqrt{2}\right) a^{3}\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*B*a*b^2+4*B*b^3)*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4+(2*B*a*b^2-2*B*b^3)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+3*A*a^2*b*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-3*A*a*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))+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))*a*b^2-3*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^3-3*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)*EllipticPi(cos(1/2*d*x+1/2*c),-2*b/(a-b),2^(1/2))*a^2*b-3*a^3*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+3*a^2*b*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*a*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))+b^3*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-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))*a^2*b+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))*a*b^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)*EllipticPi(cos(1/2*d*x+1/2*c),-2*b/(a-b),2^(1/2))*a^3)/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"
572,1,1031,461,6.901000," ","int((A+B*cos(d*x+c))*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{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)}{a^{2}}-\frac{4 b^{2} \left(2 A b -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}\, \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{2 \left(A b -a B \right) 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^{2}}+\frac{2 \left(-2 A b +a B \right) \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)}\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*A/a^2*(-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*(2*A*b-B*a)/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*b-B*a)*b/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)))+2*(-2*A*b+B*a)/a^3*(-(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+2*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2)/sin(1/2*d*x+1/2*c)^2/(2*sin(1/2*d*x+1/2*c)^2-1))/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
573,1,883,378,4.264000," ","int((A+B*cos(d*x+c))*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 A \,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 \left(-A b +a B \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)}-\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}+\frac{2 A \left(-\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+2 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}{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)}\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(4*A*b^2/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*b+B*a)/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)))+2*A/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))/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
574,1,721,324,3.646000," ","int((A+B*cos(d*x+c))*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{4 B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), -\frac{2 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 \left(A b -a B \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)}-\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*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))+2*(A*b-B*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"
575,1,808,322,3.802000," ","int((A+B*cos(d*x+c))/(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{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}\, \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{4 \left(A b -2 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}\, \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 \left(A b -a B \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)}-\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/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))-4/b*(A*b-2*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*a*(A*b-B*a)/b^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"
576,1,849,348,4.748000," ","int((A+B*cos(d*x+c))/(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(\sin^{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 -2 B \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) 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{4 a \left(2 A b -3 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}\, \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^{2} \left(A b -a B \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)}-\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)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(A*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*b-2*B*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))*b)+4*a/b^2*(2*A*b-3*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*a^2*(A*b-B*a)/b^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"
577,1,1066,421,5.323000," ","int((A+B*cos(d*x+c))/(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 \left(-4 B \,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)+6 A 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)+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^{2}-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^{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)-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) a b +2 B \,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 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{4 a^{2} \left(3 A b -4 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}\, \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^{3} \left(A b -a B \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)}-\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)*(-2/3/b^4/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(-4*B*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4+6*A*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))+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^2-9*a^2*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-b^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))-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))*a*b+2*B*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2)-4*a^2/b^3*(3*A*b-4*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*a^3*(A*b-B*a)/b^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"
578,1,2002,528,7.641000," ","int((A+B*cos(d*x+c))*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+B*a)/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)))+4*A*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*b/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)))+2/a^3*A*(-(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+2*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2)/sin(1/2*d*x+1/2*c)^2/(2*sin(1/2*d*x+1/2*c)^2-1))/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
579,1,1744,457,6.011000," ","int((A+B*cos(d*x+c))*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{2 \left(A b -a B \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)}}{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{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)}{b}\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*(A*b-B*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)))+2*B/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"
580,1,1850,454,6.468000," ","int((A+B*cos(d*x+c))/(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(A b -a B \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)}}{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 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)}{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 \left(A b -2 a B \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)}-\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*a*(A*b-B*a)/b^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/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))+2*(A*b-2*B*a)/b^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"
581,1,1937,452,6.605000," ","int((A+B*cos(d*x+c))/(a+b*cos(d*x+c))^3/sec(d*x+c)^(3/2),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/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*a^2*(A*b-B*a)/b^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)))-4/b^2*(A*b-3*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*a/b^3*(2*A*b-3*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"
582,1,1977,479,7.444000," ","int((A+B*cos(d*x+c))/(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^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)*(A*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*b-3*B*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))*b)-2*a^3*(A*b-B*a)/b^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)))+12/b^3*a*(A*b-2*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*a^2/b^4*(3*A*b-4*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"
583,1,2195,569,8.182000," ","int((A+B*cos(d*x+c))/(a+b*cos(d*x+c))^3/sec(d*x+c)^(7/2),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)*(-2/3/b^5/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(-4*B*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4+9*A*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))+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^2-18*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*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-9*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))*a*b+2*B*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2)-8*a^2/b^4*(3*A*b-5*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*a^4*(A*b-B*a)/b^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)))-2/b^5*a^3*(4*A*b-5*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"
584,1,214,80,1.301000," ","int((a*B+b*B*cos(d*x+c))*sec(d*x+c)^(5/2)/(a+b*cos(d*x+c)),x)","-\frac{2 \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)+\sqrt{\frac{1}{2}-\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 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right) B \sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\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)}\, \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)^{\frac{3}{2}} \sin \left(\frac{d x}{2}+\frac{c}{2}\right) d}"," ",0,"-2/3*(-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+(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-2*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c))*B*((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)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(2*cos(1/2*d*x+1/2*c)^2-1)^(3/2)/sin(1/2*d*x+1/2*c)/d","B"
585,1,102,80,1.507000," ","int((a*B+b*B*cos(d*x+c))*sec(d*x+c)^(3/2)/(a+b*cos(d*x+c)),x)","-\frac{2 B \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}\, \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*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)^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"
586,1,134,59,1.068000," ","int((a*B+b*B*cos(d*x+c))*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)}\, B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d 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)*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))/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
587,1,134,59,0.873000," ","int((a*B+b*B*cos(d*x+c))/(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)}\, 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)}{\sqrt{-2 \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)*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)*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"
588,1,180,80,1.426000," ","int((a*B+b*B*cos(d*x+c))/(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)}\, B \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)-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)*B*(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))-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"
589,1,203,80,1.225000," ","int((a*B+b*B*cos(d*x+c))/(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)}\, B \left(-8 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+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 \sqrt{\frac{1}{2}-\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)}{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)*B*(-8*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6+8*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)-3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-2*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+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"
590,1,3435,427,0.621000," ","int((A+B*cos(d*x+c))*sec(d*x+c)^(9/2)*(a+b*cos(d*x+c))^(1/2),x)","\text{output too large to display}"," ",0,"-2/105/d*(63*B*cos(d*x+c)^4*a^4-42*B*cos(d*x+c)^3*a^4-21*B*cos(d*x+c)*a^4+25*A*cos(d*x+c)^4*a^4-10*A*cos(d*x+c)^2*a^4+8*A*cos(d*x+c)^5*b^4-8*A*cos(d*x+c)^4*b^4-28*B*cos(d*x+c)^2*a^3*b+25*A*cos(d*x+c)^5*a^3*b+19*A*cos(d*x+c)^5*a^2*b^2-4*A*cos(d*x+c)^5*a*b^3+19*A*cos(d*x+c)^4*a^3*b-20*A*cos(d*x+c)^4*a^2*b^2+8*A*cos(d*x+c)^4*a*b^3-26*A*cos(d*x+c)^3*a^3*b-4*A*cos(d*x+c)^3*a*b^3+A*cos(d*x+c)^2*a^2*b^2-18*A*cos(d*x+c)*a^3*b+63*B*cos(d*x+c)^5*a^3*b+7*B*cos(d*x+c)^5*a^2*b^2-14*B*cos(d*x+c)^5*a*b^3-35*B*cos(d*x+c)^4*a^3*b-14*B*cos(d*x+c)^4*a^2*b^2+14*B*cos(d*x+c)^4*a*b^3+7*B*cos(d*x+c)^3*a^2*b^2+8*A*sin(d*x+c)*cos(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^3-8*A*sin(d*x+c)*cos(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))*b^4+25*A*sin(d*x+c)*cos(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^4-63*B*sin(d*x+c)*cos(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^4+63*B*sin(d*x+c)*cos(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^4-8*A*sin(d*x+c)*cos(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))*b^4+25*A*sin(d*x+c)*cos(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^4-63*B*sin(d*x+c)*cos(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+63*B*sin(d*x+c)*cos(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^4-15*A*a^4-63*B*sin(d*x+c)*cos(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^3*b+14*B*sin(d*x+c)*cos(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^2*b^2+14*B*sin(d*x+c)*cos(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^3+49*B*sin(d*x+c)*cos(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^3*b-14*B*sin(d*x+c)*cos(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^2-19*A*sin(d*x+c)*cos(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*b-19*A*sin(d*x+c)*cos(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^2-8*A*sin(d*x+c)*cos(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^3+19*A*sin(d*x+c)*cos(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^3*b+2*A*sin(d*x+c)*cos(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^2*b^2+8*A*sin(d*x+c)*cos(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^3-63*B*sin(d*x+c)*cos(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*b+14*B*sin(d*x+c)*cos(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^2+14*B*sin(d*x+c)*cos(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^3+49*B*sin(d*x+c)*cos(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^3*b-14*B*sin(d*x+c)*cos(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^2*b^2-19*A*sin(d*x+c)*cos(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^3*b-19*A*sin(d*x+c)*cos(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^2*b^2-8*A*sin(d*x+c)*cos(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^3+19*A*sin(d*x+c)*cos(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^3*b+2*A*sin(d*x+c)*cos(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^2)*cos(d*x+c)*(1/cos(d*x+c))^(9/2)/(a+b*cos(d*x+c))^(1/2)/sin(d*x+c)/a^3","B"
591,1,2489,350,0.456000," ","int((A+B*cos(d*x+c))*sec(d*x+c)^(7/2)*(a+b*cos(d*x+c))^(1/2),x)","\text{Expression too large to display}"," ",0,"2/15/d*(3*A*a^3-9*A*cos(d*x+c)^3*a^3-2*A*cos(d*x+c)^3*b^3+6*A*cos(d*x+c)^2*a^3-5*B*cos(d*x+c)^3*a^3-5*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)*sin(d*x+c)*cos(d*x+c)^3*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a^2*b+2*A*cos(d*x+c)^4*b^3+5*B*cos(d*x+c)*a^3+2*A*cos(d*x+c)^3*a*b^2-A*cos(d*x+c)^2*a*b^2+4*A*cos(d*x+c)*a^2*b-5*B*cos(d*x+c)^4*a*b^2-5*B*cos(d*x+c)^3*a^2*b+10*B*cos(d*x+c)^2*a^2*b+9*A*sin(d*x+c)*cos(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-2*A*sin(d*x+c)*cos(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^2-7*A*sin(d*x+c)*cos(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+2*A*sin(d*x+c)*cos(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+5*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)*sin(d*x+c)*cos(d*x+c)^2*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a^2*b+5*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)*sin(d*x+c)*cos(d*x+c)^2*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a*b^2-5*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)*sin(d*x+c)*cos(d*x+c)^2*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a^2*b+5*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)*sin(d*x+c)*cos(d*x+c)^3*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a*b^2+9*A*sin(d*x+c)*cos(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-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)*sin(d*x+c)*cos(d*x+c)^3*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a*b^2-7*A*sin(d*x+c)*cos(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^2*b+2*A*sin(d*x+c)*cos(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+5*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)*sin(d*x+c)*cos(d*x+c)^3*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a^2*b+5*B*cos(d*x+c)^3*a*b^2-9*A*cos(d*x+c)^4*a^2*b-A*cos(d*x+c)^4*a*b^2+5*A*cos(d*x+c)^3*a^2*b-5*B*cos(d*x+c)^4*a^2*b-5*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)*sin(d*x+c)*cos(d*x+c)^2*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a^3+9*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)*sin(d*x+c)*cos(d*x+c)^3*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a^3-2*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)*sin(d*x+c)*cos(d*x+c)^3*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*b^3-9*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)*sin(d*x+c)*cos(d*x+c)^3*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a^3-5*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)*sin(d*x+c)*cos(d*x+c)^3*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a^3+9*A*sin(d*x+c)*cos(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^3-2*A*sin(d*x+c)*cos(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^3-9*A*sin(d*x+c)*cos(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)*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"
592,1,1735,290,0.395000," ","int((A+B*cos(d*x+c))*sec(d*x+c)^(5/2)*(a+b*cos(d*x+c))^(1/2),x)","-\frac{2 \left(-A \left(\cos^{2}\left(d x +c \right)\right) b^{2}+A \left(\cos^{3}\left(d x +c \right)\right) b^{2}-3 B \cos \left(d x +c \right) a^{2}-a^{2} A +A \sin \left(d x +c \right) \cos \left(d x +c \right) \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{-\frac{a -b}{a +b}}\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \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}+3 B \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{-\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \cos \left(d x +c \right) a^{2}+A \left(\cos^{2}\left(d x +c \right)\right) a b +3 B \left(\cos^{3}\left(d x +c \right)\right) a b -3 B \left(\cos^{2}\left(d x +c \right)\right) a b +A \left(\cos^{2}\left(d x +c \right)\right) a^{2}-3 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) \cos \left(d x +c \right) a b +3 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) \cos \left(d x +c \right) a b -A \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{-\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \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 b +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)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{-\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) \cos \left(d x +c \right) a b +A \left(\cos^{3}\left(d x +c \right)\right) a b +3 B \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{-\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \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(\cos^{2}\left(d x +c \right)\right) a b -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) \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) a b -3 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) \left(\cos^{2}\left(d x +c \right)\right) a b +A \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\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{\cos \left(d x +c \right)}{1+\cos \left(d x +c \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 b +3 B \left(\cos^{2}\left(d x +c \right)\right) a^{2}-2 A \cos \left(d x +c \right) a b +A \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{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) a^{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)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{-\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) b^{2}+3 B \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{-\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \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(\cos^{2}\left(d x +c \right)\right) a^{2}-3 B \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{-\frac{a -b}{a +b}}\right) a^{2}-A \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{-\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \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}-3 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) \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*(3*B*cos(d*x+c)^2*a^2+3*B*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*cos(d*x+c)^2*a*b-3*B*cos(d*x+c)*a^2+A*cos(d*x+c)^3*b^2-A*cos(d*x+c)^2*b^2-a^2*A-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))*sin(d*x+c)*cos(d*x+c)^2*a*b+A*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((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-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))*sin(d*x+c)*cos(d*x+c)^2*b^2+3*B*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*cos(d*x+c)^2*a^2-3*B*sin(d*x+c)*cos(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+A*sin(d*x+c)*cos(d*x+c)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^2+3*B*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*cos(d*x+c)*a^2+A*cos(d*x+c)^2*a^2-3*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))*cos(d*x+c)*a*b+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))*cos(d*x+c)*a*b-A*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)*(cos(d*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+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)*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+A*cos(d*x+c)^3*a*b-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))*cos(d*x+c)^2*a*b+A*sin(d*x+c)*cos(d*x+c)^2*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a*b+A*cos(d*x+c)^2*a*b-2*A*cos(d*x+c)*a*b+3*B*cos(d*x+c)^3*a*b-3*B*cos(d*x+c)^2*a*b-A*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)*(cos(d*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^2-3*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))*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"
593,1,1361,375,0.459000," ","int((A+B*cos(d*x+c))*sec(d*x+c)^(3/2)*(a+b*cos(d*x+c))^(1/2),x)","-\frac{2 \left(A \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \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 +A \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \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 -A \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{-\frac{a -b}{a +b}}\right) a -A \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{-\frac{a -b}{a +b}}\right) b +B \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \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)}}\, a -B \cos \left(d x +c \right) \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{-\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \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 B \cos \left(d x +c \right) \EllipticPi \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, -1, \sqrt{-\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \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 +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)}}\, \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)+A \sin \left(d x +c \right) \sqrt{\frac{a +b \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{-\frac{a -b}{a +b}}\right) b -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)-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) b \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)-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) b \sin \left(d x +c \right)+2 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)}}\, \EllipticPi \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, -1, \sqrt{-\frac{a -b}{a +b}}\right) b \sin \left(d x +c \right)+A \left(\cos^{2}\left(d x +c \right)\right) b +A \cos \left(d x +c \right) a -A \cos \left(d x +c \right) b -a 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*(A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a+A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+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-A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a-A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+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+B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+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)*a-B*cos(d*x+c)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*b+2*B*cos(d*x+c)*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)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*b+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)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a*sin(d*x+c)+A*sin(d*x+c)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*b-A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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)-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))*b*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)-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))*b*sin(d*x+c)+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)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,(-(a-b)/(a+b))^(1/2))*b*sin(d*x+c)+A*cos(d*x+c)^2*b+A*cos(d*x+c)*a-A*cos(d*x+c)*b-a*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"
594,1,1369,405,0.492000," ","int((A+B*cos(d*x+c))*sec(d*x+c)^(1/2)*(a+b*cos(d*x+c))^(1/2),x)","-\frac{\sqrt{\frac{1}{\cos \left(d x +c \right)}}\, \left(2 A \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \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 A \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{-\frac{a -b}{a +b}}\right) b +4 A \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{a +b \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \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 B \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \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)}}\, a +2 B \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticPi \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, -1, \sqrt{-\frac{a -b}{a +b}}\right) \sqrt{\frac{a +b \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, a +B \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{-\frac{a -b}{a +b}}\right) a +B \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \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 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)}}\, \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 A \sin \left(d x +c \right) \sqrt{\frac{a +b \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{-\frac{a -b}{a +b}}\right) b +4 A \sin \left(d x +c \right) \sqrt{\frac{a +b \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \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 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)+2 B \sin \left(d x +c \right) \EllipticPi \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, -1, \sqrt{-\frac{a -b}{a +b}}\right) \sqrt{\frac{a +b \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, a +B \sin \left(d x +c \right) \sqrt{\frac{a +b \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \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{a +b \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{-\frac{a -b}{a +b}}\right) b +B \left(\cos^{3}\left(d x +c \right)\right) b +B \left(\cos^{2}\left(d x +c \right)\right) a -b B \left(\cos^{2}\left(d x +c \right)\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)}"," ",0,"-1/d*(1/cos(d*x+c))^(1/2)/(a+b*cos(d*x+c))^(1/2)*(2*A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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*A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+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*A*sin(d*x+c)*cos(d*x+c)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,(-(a-b)/(a+b))^(1/2))*b-2*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+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)*a+2*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*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)*a+B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a+B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*b+2*A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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)-2*A*sin(d*x+c)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*b+4*A*sin(d*x+c)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,(-(a-b)/(a+b))^(1/2))*b-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)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a*sin(d*x+c)+2*B*sin(d*x+c)*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)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*a+B*sin(d*x+c)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a+B*sin(d*x+c)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*b+B*cos(d*x+c)^3*b+B*cos(d*x+c)^2*a-b*B*cos(d*x+c)^2-B*cos(d*x+c)*a)/sin(d*x+c)","B"
595,1,2054,479,0.398000," ","int((A+B*cos(d*x+c))*(a+b*cos(d*x+c))^(1/2)/sec(d*x+c)^(1/2),x)","-\frac{\left(-4 A \left(\cos^{2}\left(d x +c \right)\right) b^{2}+4 A \left(\cos^{3}\left(d x +c \right)\right) b^{2}-B \cos \left(d x +c \right) a^{2}+4 A \left(\cos^{2}\left(d x +c \right)\right) a b +3 B \left(\cos^{3}\left(d x +c \right)\right) a b -B \left(\cos^{2}\left(d x +c \right)\right) a b +8 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) \cos \left(d x +c \right) a b +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) \cos \left(d x +c \right) a b +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)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{-\frac{a -b}{a +b}}\right) \cos \left(d x +c \right) a b +4 A \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{-\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \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 b -8 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)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{-\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) \cos \left(d x +c \right) a b +B \left(\cos^{2}\left(d x +c \right)\right) a^{2}-2 B \left(\cos^{2}\left(d x +c \right)\right) b^{2}+2 B \left(\cos^{4}\left(d x +c \right)\right) b^{2}-4 A \cos \left(d x +c \right) a b -2 B \cos \left(d x +c \right) a b +4 A \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{-\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \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 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)}}\, \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 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)}}\, \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}+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^{2}-4 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}+4 A \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{-\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \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 b -8 A \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{-\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \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 b +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 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) a b +4 A \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{-\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \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 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)}}\, \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) a^{2}+8 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)}}\, \EllipticPi \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, -1, \sqrt{-\frac{a -b}{a +b}}\right) \cos \left(d x +c \right) b^{2}+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) \cos \left(d x +c \right) a^{2}-4 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) \cos \left(d x +c \right) b^{2}+8 A \EllipticPi \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, -1, \sqrt{-\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \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 b \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)}\, b}"," ",0,"-1/4/d*(4*A*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*b^2+B*cos(d*x+c)^2*a^2+2*B*cos(d*x+c)^4*b^2-2*B*cos(d*x+c)^2*b^2-B*cos(d*x+c)*a^2+4*A*cos(d*x+c)^3*b^2-4*A*cos(d*x+c)^2*b^2+8*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)*a*b+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))*cos(d*x+c)*a*b+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)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*cos(d*x+c)*a*b+4*A*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)*(cos(d*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-8*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)*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-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)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,(-(a-b)/(a+b))^(1/2))*a^2+4*A*cos(d*x+c)^2*a*b-4*A*cos(d*x+c)*a*b+3*B*cos(d*x+c)^3*a*b-B*cos(d*x+c)^2*a*b-2*B*cos(d*x+c)*a*b-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)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,(-(a-b)/(a+b))^(1/2))*cos(d*x+c)*a^2+8*A*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)/(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*A*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a*b-8*A*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a*b+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*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*b+4*A*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)*(cos(d*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+8*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)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,(-(a-b)/(a+b))^(1/2))*cos(d*x+c)*b^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))*cos(d*x+c)*a^2-4*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))*cos(d*x+c)*b^2+8*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)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,(-(a-b)/(a+b))^(1/2))*b^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^2-4*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))*b^2)*(1/cos(d*x+c))^(1/2)/sin(d*x+c)/(a+b*cos(d*x+c))^(1/2)/b","B"
596,1,2956,560,0.468000," ","int((A+B*cos(d*x+c))*(a+b*cos(d*x+c))^(1/2)/sec(d*x+c)^(3/2),x)","\text{output too large to display}"," ",0,"1/24/d*(12*A*sin(d*x+c)*cos(d*x+c)*(cos(d*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-6*A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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-6*A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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+28*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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^2-24*B*sin(d*x+c)*cos(d*x+c)*(cos(d*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*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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-12*A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a*b^2-16*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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^2-12*A*cos(d*x+c)^4*b^3+12*A*cos(d*x+c)^2*b^3-8*B*cos(d*x+c)^5*b^3-8*B*cos(d*x+c)^3*b^3+3*B*cos(d*x+c)^2*a^3+16*B*cos(d*x+c)^2*b^3-3*B*cos(d*x+c)*a^3-18*A*cos(d*x+c)^3*a*b^2-6*A*cos(d*x+c)^2*a^2*b+6*A*cos(d*x+c)^2*a*b^2+6*A*cos(d*x+c)*a^2*b+12*A*cos(d*x+c)*a*b^2-10*B*cos(d*x+c)^4*a*b^2+B*cos(d*x+c)^3*a^2*b-3*B*cos(d*x+c)^2*a^2*b-6*B*cos(d*x+c)^2*a*b^2+2*B*cos(d*x+c)*a^2*b+16*B*cos(d*x+c)*a*b^2-48*A*sin(d*x+c)*cos(d*x+c)*(cos(d*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^3-6*B*sin(d*x+c)*cos(d*x+c)*(cos(d*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+3*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+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^3-12*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))*a*b^2+12*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)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,(-(a-b)/(a+b))^(1/2))*a^2*b-6*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^2*b-6*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*b^2-2*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)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a^2*b+28*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*b^2-24*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)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,(-(a-b)/(a+b))^(1/2))*a*b^2+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-16*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+24*A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+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+24*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^3-48*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)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,(-(a-b)/(a+b))^(1/2))*b^3-6*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)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,(-(a-b)/(a+b))^(1/2))*a^3+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^3-16*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^3)*cos(d*x+c)*(1/cos(d*x+c))^(3/2)/sin(d*x+c)/(a+b*cos(d*x+c))^(1/2)/b^2","B"
597,1,4400,510,0.720000," ","int((a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))*sec(d*x+c)^(11/2),x)","\text{output too large to display}"," ",0,"2/315/d*(-33*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)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)^4*a^3*b^2-2*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)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)^4*a^2*b^3-8*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)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)^4*a*b^4+246*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))*sin(d*x+c)*cos(d*x+c)^4*a^4*b+246*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))*sin(d*x+c)*cos(d*x+c)^4*a^3*b^2-18*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))*sin(d*x+c)*cos(d*x+c)^4*a^2*b^3-18*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))*sin(d*x+c)*cos(d*x+c)^4*a*b^4-246*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)^4*a^4*b-153*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)^4*a^3*b^2+18*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)^4*a^2*b^3+147*A*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(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)*a^4*b+33*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))*sin(d*x+c)*cos(d*x+c)^5*a^3*b^2+33*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))*sin(d*x+c)*cos(d*x+c)^5*a^2*b^3+8*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))*sin(d*x+c)*cos(d*x+c)^5*a*b^4-186*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)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)^5*a^4*b-33*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)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)^5*a^3*b^2-2*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)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)^5*a^2*b^3-8*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)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)^5*a*b^4+246*B*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(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)*a^4*b+246*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))*sin(d*x+c)*cos(d*x+c)^5*a^3*b^2-18*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))*sin(d*x+c)*cos(d*x+c)^5*a^2*b^3-18*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))*sin(d*x+c)*cos(d*x+c)^5*a*b^4-246*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)^5*a^4*b-153*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)^5*a^3*b^2+18*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)^5*a^2*b^3+147*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))*sin(d*x+c)*cos(d*x+c)^4*a^4*b-186*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)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)^4*a^4*b+117*B*cos(d*x+c)^2*a^4*b-75*B*cos(d*x+c)^6*a^4*b-246*B*cos(d*x+c)^6*a^3*b^2-9*B*cos(d*x+c)^6*a^2*b^3+18*B*cos(d*x+c)^6*a*b^4-246*B*cos(d*x+c)^5*a^4*b+165*B*cos(d*x+c)^5*a^3*b^2+18*B*cos(d*x+c)^5*a^2*b^3-18*B*cos(d*x+c)^5*a*b^4+204*B*cos(d*x+c)^4*a^4*b+35*A*a^5-147*A*cos(d*x+c)^6*a^4*b-88*A*cos(d*x+c)^6*a^3*b^2-33*A*cos(d*x+c)^6*a^2*b^3+4*A*cos(d*x+c)^6*a*b^4+10*A*cos(d*x+c)^5*a^4*b-33*A*cos(d*x+c)^5*a^3*b^2+34*A*cos(d*x+c)^5*a^2*b^3-8*A*cos(d*x+c)^5*a*b^4+68*A*cos(d*x+c)^4*a^3*b^2+4*A*cos(d*x+c)^4*a*b^4+52*A*cos(d*x+c)^3*a^4*b-A*cos(d*x+c)^3*a^2*b^3+53*A*cos(d*x+c)^2*a^3*b^2+85*A*cos(d*x+c)*a^4*b-9*B*cos(d*x+c)^4*a^2*b^3+81*B*cos(d*x+c)^3*a^3*b^2-8*A*cos(d*x+c)^6*b^5-147*A*cos(d*x+c)^5*a^5+8*A*cos(d*x+c)^5*b^5+98*A*cos(d*x+c)^4*a^5+14*A*cos(d*x+c)^2*a^5-75*B*cos(d*x+c)^5*a^5+30*B*cos(d*x+c)^3*a^5+45*B*cos(d*x+c)*a^5+147*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))*sin(d*x+c)*cos(d*x+c)^5*a^5+8*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))*sin(d*x+c)*cos(d*x+c)^5*b^5-147*A*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(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)*a^5-75*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)^5*a^5+147*A*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(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)*a^5+8*A*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(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)*b^5-147*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)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)^4*a^5-75*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)^4*a^5+33*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))*sin(d*x+c)*cos(d*x+c)^4*a^3*b^2+33*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))*sin(d*x+c)*cos(d*x+c)^4*a^2*b^3+8*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))*sin(d*x+c)*cos(d*x+c)^4*a*b^4)*cos(d*x+c)/(a+b*cos(d*x+c))^(1/2)*(1/cos(d*x+c))^(11/2)/sin(d*x+c)/a^3","B"
598,1,3421,427,0.513000," ","int((a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))*sec(d*x+c)^(9/2),x)","\text{output too large to display}"," ",0,"-2/105/d*(63*B*cos(d*x+c)^4*a^4-42*B*cos(d*x+c)^3*a^4-21*B*cos(d*x+c)*a^4+25*A*cos(d*x+c)^4*a^4-10*A*cos(d*x+c)^2*a^4-6*A*cos(d*x+c)^5*b^4+6*A*cos(d*x+c)^4*b^4-63*B*cos(d*x+c)^2*a^3*b+25*A*cos(d*x+c)^5*a^3*b+82*A*cos(d*x+c)^5*a^2*b^2+3*A*cos(d*x+c)^5*a*b^3+82*A*cos(d*x+c)^4*a^3*b-55*A*cos(d*x+c)^4*a^2*b^2-6*A*cos(d*x+c)^4*a*b^3-68*A*cos(d*x+c)^3*a^3*b+3*A*cos(d*x+c)^3*a*b^3-27*A*cos(d*x+c)^2*a^2*b^2-39*A*cos(d*x+c)*a^3*b+63*B*cos(d*x+c)^5*a^3*b+42*B*cos(d*x+c)^5*a^2*b^2+21*B*cos(d*x+c)^5*a*b^3+21*B*cos(d*x+c)^4*a^2*b^2-21*B*cos(d*x+c)^4*a*b^3-63*B*cos(d*x+c)^3*a^2*b^2-6*A*sin(d*x+c)*cos(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^3+6*A*sin(d*x+c)*cos(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))*b^4+25*A*sin(d*x+c)*cos(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^4-63*B*sin(d*x+c)*cos(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^4+63*B*sin(d*x+c)*cos(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^4+6*A*sin(d*x+c)*cos(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))*b^4+25*A*sin(d*x+c)*cos(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^4-63*B*sin(d*x+c)*cos(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+63*B*sin(d*x+c)*cos(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^4-15*A*a^4-63*B*sin(d*x+c)*cos(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^3*b-21*B*sin(d*x+c)*cos(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^2*b^2-21*B*sin(d*x+c)*cos(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^3+84*B*sin(d*x+c)*cos(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^3*b+21*B*sin(d*x+c)*cos(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^2-82*A*sin(d*x+c)*cos(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*b-82*A*sin(d*x+c)*cos(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^2+6*A*sin(d*x+c)*cos(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^3+82*A*sin(d*x+c)*cos(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^3*b+51*A*sin(d*x+c)*cos(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^2*b^2-6*A*sin(d*x+c)*cos(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^3-63*B*sin(d*x+c)*cos(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*b-21*B*sin(d*x+c)*cos(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^2-21*B*sin(d*x+c)*cos(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^3+84*B*sin(d*x+c)*cos(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^3*b+21*B*sin(d*x+c)*cos(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^2*b^2-82*A*sin(d*x+c)*cos(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^3*b-82*A*sin(d*x+c)*cos(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^2*b^2+6*A*sin(d*x+c)*cos(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^3+82*A*sin(d*x+c)*cos(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^3*b+51*A*sin(d*x+c)*cos(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^2)*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"
599,1,2674,353,0.409000," ","int((a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))*sec(d*x+c)^(7/2),x)","\text{Expression too large to display}"," ",0,"-2/15/d*(-3*A*a^3+9*A*cos(d*x+c)^3*a^3-3*A*cos(d*x+c)^3*b^3-6*A*cos(d*x+c)^2*a^3+5*B*cos(d*x+c)^3*a^3+20*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)*sin(d*x+c)*cos(d*x+c)^3*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a^2*b+15*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)*sin(d*x+c)*cos(d*x+c)^2*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a*b^2+3*A*cos(d*x+c)^4*b^3-5*B*cos(d*x+c)*a^3+3*A*cos(d*x+c)^3*a*b^2-9*A*cos(d*x+c)^2*a*b^2-9*A*cos(d*x+c)*a^2*b+20*B*cos(d*x+c)^4*a*b^2+20*B*cos(d*x+c)^3*a^2*b-25*B*cos(d*x+c)^2*a^2*b-9*A*sin(d*x+c)*cos(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*A*sin(d*x+c)*cos(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+12*A*sin(d*x+c)*cos(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*A*sin(d*x+c)*cos(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^2-20*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)*sin(d*x+c)*cos(d*x+c)^2*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a^2*b-20*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)*sin(d*x+c)*cos(d*x+c)^2*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a*b^2+20*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)*sin(d*x+c)*cos(d*x+c)^2*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a^2*b-20*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)*sin(d*x+c)*cos(d*x+c)^3*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a*b^2-9*A*sin(d*x+c)*cos(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-3*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)*sin(d*x+c)*cos(d*x+c)^3*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a*b^2+12*A*sin(d*x+c)*cos(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^2*b+3*A*sin(d*x+c)*cos(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^2-20*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)*sin(d*x+c)*cos(d*x+c)^3*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a^2*b+15*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)*sin(d*x+c)*cos(d*x+c)^3*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a*b^2-20*B*cos(d*x+c)^3*a*b^2+9*A*cos(d*x+c)^4*a^2*b+6*A*cos(d*x+c)^4*a*b^2+5*B*cos(d*x+c)^4*a^2*b+5*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)*sin(d*x+c)*cos(d*x+c)^2*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a^3-9*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)*sin(d*x+c)*cos(d*x+c)^3*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a^3-3*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)*sin(d*x+c)*cos(d*x+c)^3*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*b^3+9*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)*sin(d*x+c)*cos(d*x+c)^3*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a^3+5*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)*sin(d*x+c)*cos(d*x+c)^3*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a^3-9*A*sin(d*x+c)*cos(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^3-3*A*sin(d*x+c)*cos(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+9*A*sin(d*x+c)*cos(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)*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"
600,1,2326,433,0.358000," ","int((a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))*sec(d*x+c)^(5/2),x)","\text{Expression too large to display}"," ",0,"-2/3/d*(3*B*cos(d*x+c)^2*a^2+3*A*sin(d*x+c)*cos(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))*b^2+6*B*sin(d*x+c)*cos(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^2-3*B*sin(d*x+c)*cos(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))*b^2+6*B*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*cos(d*x+c)^2*a*b-3*B*cos(d*x+c)*a^2+4*A*cos(d*x+c)^3*b^2-4*A*cos(d*x+c)^2*b^2-a^2*A-4*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))*sin(d*x+c)*cos(d*x+c)^2*a*b+A*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((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^2-4*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))*sin(d*x+c)*cos(d*x+c)^2*b^2+3*B*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*cos(d*x+c)^2*a^2-3*B*sin(d*x+c)*cos(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+A*sin(d*x+c)*cos(d*x+c)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^2+3*B*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*cos(d*x+c)*a^2+A*cos(d*x+c)^2*a^2-3*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))*cos(d*x+c)*a*b+6*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))*cos(d*x+c)*a*b-4*A*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)*(cos(d*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*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)*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+A*cos(d*x+c)^3*a*b-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))*cos(d*x+c)^2*a*b+4*A*sin(d*x+c)*cos(d*x+c)^2*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a*b+3*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)*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^2+4*A*cos(d*x+c)^2*a*b-5*A*cos(d*x+c)*a*b+3*B*cos(d*x+c)^3*a*b-3*B*cos(d*x+c)^2*a*b-4*A*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)*(cos(d*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*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)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,(-(a-b)/(a+b))^(1/2))*cos(d*x+c)*b^2-3*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))*cos(d*x+c)*a^2-3*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))*cos(d*x+c)*b^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"
601,1,2196,465,0.365000," ","int((a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))*sec(d*x+c)^(3/2),x)","\text{Expression too large to display}"," ",0,"1/d*(-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))*a^2-2*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)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a^2+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)*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^2-4*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)*b^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))*sin(d*x+c)*cos(d*x+c)*b^2-6*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)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*a*b+B*cos(d*x+c)^2*b^2-6*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)*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)*a*b+2*a^2*A-2*A*sin(d*x+c)*cos(d*x+c)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^2-2*B*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*cos(d*x+c)*a^2-2*A*cos(d*x+c)*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))*cos(d*x+c)*a*b+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))*cos(d*x+c)*a*b+2*A*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)*(cos(d*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*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)*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+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)*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^2-B*cos(d*x+c)^3*b^2-2*A*cos(d*x+c)^2*a*b+2*A*cos(d*x+c)*a*b-B*cos(d*x+c)^2*a*b+B*cos(d*x+c)*a*b+2*A*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a*b-4*A*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a*b-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+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*b+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)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*b^2+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)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*a^2-4*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)*b^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))*sin(d*x+c)*b^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"
602,1,2432,478,0.368000," ","int((a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))*sec(d*x+c)^(1/2),x)","\text{Expression too large to display}"," ",0,"-1/4/d*(1/cos(d*x+c))^(1/2)/(a+b*cos(d*x+c))^(1/2)*(8*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))*a^2+4*A*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*b^2+5*B*cos(d*x+c)^2*a^2-8*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+2*B*cos(d*x+c)^4*b^2-2*B*cos(d*x+c)^2*b^2-5*B*cos(d*x+c)*a^2+4*A*cos(d*x+c)^3*b^2-4*A*cos(d*x+c)^2*b^2+24*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)*a*b+8*A*sin(d*x+c)*cos(d*x+c)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^2-8*B*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*cos(d*x+c)*a^2+5*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))*cos(d*x+c)*a*b+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)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*cos(d*x+c)*a*b+4*A*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)*(cos(d*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-16*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)*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+6*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)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,(-(a-b)/(a+b))^(1/2))*a^2+4*A*cos(d*x+c)^2*a*b-4*A*cos(d*x+c)*a*b+7*B*cos(d*x+c)^3*a*b-5*B*cos(d*x+c)^2*a*b-2*B*cos(d*x+c)*a*b+6*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)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,(-(a-b)/(a+b))^(1/2))*cos(d*x+c)*a^2+24*A*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)/(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*A*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a*b-16*A*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a*b+5*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*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*b+4*A*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)*(cos(d*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+8*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)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,(-(a-b)/(a+b))^(1/2))*cos(d*x+c)*b^2+5*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))*cos(d*x+c)*a^2-4*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))*cos(d*x+c)*b^2+8*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)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,(-(a-b)/(a+b))^(1/2))*b^2+5*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^2-4*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))*b^2)/sin(d*x+c)","B"
603,1,3141,566,0.483000," ","int((a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))/sec(d*x+c)^(1/2),x)","\text{output too large to display}"," ",0,"-1/24/d*(36*A*sin(d*x+c)*cos(d*x+c)*(cos(d*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+30*A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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+30*A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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+72*B*sin(d*x+c)*cos(d*x+c)*(cos(d*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*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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+12*A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a*b^2+16*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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^2-48*A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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+12*A*cos(d*x+c)^4*b^3-12*A*cos(d*x+c)^2*b^3+8*B*cos(d*x+c)^5*b^3+8*B*cos(d*x+c)^3*b^3+3*B*cos(d*x+c)^2*a^3-16*B*cos(d*x+c)^2*b^3-3*B*cos(d*x+c)*a^3+42*A*cos(d*x+c)^3*a*b^2+30*A*cos(d*x+c)^2*a^2*b-30*A*cos(d*x+c)^2*a*b^2-30*A*cos(d*x+c)*a^2*b-12*A*cos(d*x+c)*a*b^2+22*B*cos(d*x+c)^4*a*b^2+17*B*cos(d*x+c)^3*a^2*b-3*B*cos(d*x+c)^2*a^2*b-6*B*cos(d*x+c)^2*a*b^2-14*B*cos(d*x+c)*a^2*b-16*B*cos(d*x+c)*a*b^2+48*A*sin(d*x+c)*cos(d*x+c)*(cos(d*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^3-6*B*sin(d*x+c)*cos(d*x+c)*(cos(d*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+3*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+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+12*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))*a*b^2+36*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)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,(-(a-b)/(a+b))^(1/2))*a^2*b+30*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^2*b+30*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*b^2+14*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-52*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*b^2+72*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)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,(-(a-b)/(a+b))^(1/2))*a*b^2+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+16*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^2-24*A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+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^3-48*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))*a^2*b-24*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^3+48*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)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,(-(a-b)/(a+b))^(1/2))*b^3-6*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)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,(-(a-b)/(a+b))^(1/2))*a^3+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^3+16*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^3)*(1/cos(d*x+c))^(1/2)/sin(d*x+c)/(a+b*cos(d*x+c))^(1/2)/b","B"
604,1,4056,664,0.615000," ","int((a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))/sec(d*x+c)^(3/2),x)","\text{output too large to display}"," ",0,"-1/192/d*(136*A*cos(d*x+c)^3*a^2*b^2-3*B*cos(d*x+c)^3*a^3*b+108*B*cos(d*x+c)^3*a*b^3+78*B*cos(d*x+c)^2*a^2*b^2-156*B*cos(d*x+c)^2*a*b^3-6*B*cos(d*x+c)*a^3*b-156*B*cos(d*x+c)*a^2*b^2-72*B*cos(d*x+c)*a*b^3+24*A*cos(d*x+c)^2*a^3*b-48*A*cos(d*x+c)^2*a*b^3-112*A*cos(d*x+c)*a^2*b^2-128*A*cos(d*x+c)*a*b^3+128*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^4-9*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^4+18*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)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,(-(a-b)/(a+b))^(1/2))*a^4+288*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)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,(-(a-b)/(a+b))^(1/2))*b^4-144*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^4+48*B*cos(d*x+c)^6*b^4+64*A*cos(d*x+c)^3*b^4-128*A*cos(d*x+c)^2*b^4+24*B*cos(d*x+c)^4*b^4-72*B*cos(d*x+c)^2*b^4-9*B*cos(d*x+c)^2*a^4+9*B*cos(d*x+c)*a^4+64*A*cos(d*x+c)^5*b^4+9*B*cos(d*x+c)^2*a^3*b+176*A*cos(d*x+c)^4*a*b^3-24*A*cos(d*x+c)^2*a^2*b^2-24*A*cos(d*x+c)*a^3*b+120*B*cos(d*x+c)^5*a*b^3+78*B*cos(d*x+c)^4*a^2*b^2+24*A*sin(d*x+c)*cos(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-9*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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+18*B*sin(d*x+c)*cos(d*x+c)*(cos(d*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+288*B*sin(d*x+c)*cos(d*x+c)*(cos(d*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*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+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+24*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^3*b+24*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^2*b^2+128*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*b^3-48*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)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,(-(a-b)/(a+b))^(1/2))*a^3*b+576*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)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,(-(a-b)/(a+b))^(1/2))*a*b^3+112*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))*a^2*b^2-416*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))*a*b^3-9*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^3*b+156*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+156*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^3+144*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)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,(-(a-b)/(a+b))^(1/2))*a^2*b^2+6*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-228*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+72*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*b^3+128*A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+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+24*A*sin(d*x+c)*cos(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^2+128*A*sin(d*x+c)*cos(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^3-48*A*sin(d*x+c)*cos(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+576*A*sin(d*x+c)*cos(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^3+112*A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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^2-416*A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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^3-9*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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+156*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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+156*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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+144*B*sin(d*x+c)*cos(d*x+c)*(cos(d*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+6*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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-228*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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)*(1/cos(d*x+c))^(3/2)/sin(d*x+c)/(a+b*cos(d*x+c))^(1/2)/b^2","B"
605,1,5381,604,0.938000," ","int((a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))*sec(d*x+c)^(13/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
606,1,4400,510,0.703000," ","int((a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))*sec(d*x+c)^(11/2),x)","\text{output too large to display}"," ",0,"2/315/d*(-279*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)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)^4*a^3*b^2-155*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)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)^4*a^2*b^3+10*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)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)^4*a*b^4+435*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))*sin(d*x+c)*cos(d*x+c)^4*a^4*b+435*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))*sin(d*x+c)*cos(d*x+c)^4*a^3*b^2+45*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))*sin(d*x+c)*cos(d*x+c)^4*a^2*b^3+45*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))*sin(d*x+c)*cos(d*x+c)^4*a*b^4-435*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)^4*a^4*b-405*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)^4*a^3*b^2-45*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)^4*a^2*b^3+147*A*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(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)*a^4*b+279*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))*sin(d*x+c)*cos(d*x+c)^5*a^3*b^2+279*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))*sin(d*x+c)*cos(d*x+c)^5*a^2*b^3-10*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))*sin(d*x+c)*cos(d*x+c)^5*a*b^4-261*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)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)^5*a^4*b-279*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)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)^5*a^3*b^2-155*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)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)^5*a^2*b^3+10*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)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)^5*a*b^4+435*B*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(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)*a^4*b+435*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))*sin(d*x+c)*cos(d*x+c)^5*a^3*b^2+45*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))*sin(d*x+c)*cos(d*x+c)^5*a^2*b^3+45*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))*sin(d*x+c)*cos(d*x+c)^5*a*b^4-435*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)^5*a^4*b-405*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)^5*a^3*b^2-45*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)^5*a^2*b^3+147*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))*sin(d*x+c)*cos(d*x+c)^4*a^4*b-261*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)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)^4*a^4*b+180*B*cos(d*x+c)^2*a^4*b-75*B*cos(d*x+c)^6*a^4*b-435*B*cos(d*x+c)^6*a^3*b^2-135*B*cos(d*x+c)^6*a^2*b^3-45*B*cos(d*x+c)^6*a*b^4-435*B*cos(d*x+c)^5*a^4*b+165*B*cos(d*x+c)^5*a^3*b^2-45*B*cos(d*x+c)^5*a^2*b^3+45*B*cos(d*x+c)^5*a*b^4+330*B*cos(d*x+c)^4*a^4*b+35*A*a^5-147*A*cos(d*x+c)^6*a^4*b-163*A*cos(d*x+c)^6*a^3*b^2-279*A*cos(d*x+c)^6*a^2*b^3-5*A*cos(d*x+c)^6*a*b^4-65*A*cos(d*x+c)^5*a^4*b-279*A*cos(d*x+c)^5*a^3*b^2+199*A*cos(d*x+c)^5*a^2*b^3+10*A*cos(d*x+c)^5*a*b^4+272*A*cos(d*x+c)^4*a^3*b^2-5*A*cos(d*x+c)^4*a*b^4+82*A*cos(d*x+c)^3*a^4*b+80*A*cos(d*x+c)^3*a^2*b^3+170*A*cos(d*x+c)^2*a^3*b^2+130*A*cos(d*x+c)*a^4*b+180*B*cos(d*x+c)^4*a^2*b^3+270*B*cos(d*x+c)^3*a^3*b^2+10*A*cos(d*x+c)^6*b^5-147*A*cos(d*x+c)^5*a^5-10*A*cos(d*x+c)^5*b^5+98*A*cos(d*x+c)^4*a^5+14*A*cos(d*x+c)^2*a^5-75*B*cos(d*x+c)^5*a^5+30*B*cos(d*x+c)^3*a^5+45*B*cos(d*x+c)*a^5+147*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))*sin(d*x+c)*cos(d*x+c)^5*a^5-10*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))*sin(d*x+c)*cos(d*x+c)^5*b^5-147*A*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(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)*a^5-75*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)^5*a^5+147*A*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(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)*a^5-10*A*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(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)*b^5-147*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)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)^4*a^5-75*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)^4*a^5+279*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))*sin(d*x+c)*cos(d*x+c)^4*a^3*b^2+279*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))*sin(d*x+c)*cos(d*x+c)^4*a^2*b^3-10*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))*sin(d*x+c)*cos(d*x+c)^4*a*b^4)*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"
607,1,3636,428,0.535000," ","int((a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))*sec(d*x+c)^(9/2),x)","\text{output too large to display}"," ",0,"-2/105/d*(105*B*sin(d*x+c)*cos(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^3+63*B*cos(d*x+c)^4*a^4-42*B*cos(d*x+c)^3*a^4-21*B*cos(d*x+c)*a^4+25*A*cos(d*x+c)^4*a^4-10*A*cos(d*x+c)^2*a^4+15*A*cos(d*x+c)^5*b^4-15*A*cos(d*x+c)^4*b^4-98*B*cos(d*x+c)^2*a^3*b+25*A*cos(d*x+c)^5*a^3*b+145*A*cos(d*x+c)^5*a^2*b^2+45*A*cos(d*x+c)^5*a*b^3+145*A*cos(d*x+c)^4*a^3*b-55*A*cos(d*x+c)^4*a^2*b^2+15*A*cos(d*x+c)^4*a*b^3-110*A*cos(d*x+c)^3*a^3*b-60*A*cos(d*x+c)^3*a*b^3-90*A*cos(d*x+c)^2*a^2*b^2-60*A*cos(d*x+c)*a^3*b+63*B*cos(d*x+c)^5*a^3*b+77*B*cos(d*x+c)^5*a^2*b^2+161*B*cos(d*x+c)^5*a*b^3+35*B*cos(d*x+c)^4*a^3*b+161*B*cos(d*x+c)^4*a^2*b^2-161*B*cos(d*x+c)^4*a*b^3-238*B*cos(d*x+c)^3*a^2*b^2+15*A*sin(d*x+c)*cos(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^3+105*B*sin(d*x+c)*cos(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^3-15*A*sin(d*x+c)*cos(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))*b^4+25*A*sin(d*x+c)*cos(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^4-63*B*sin(d*x+c)*cos(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^4+63*B*sin(d*x+c)*cos(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^4-15*A*sin(d*x+c)*cos(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))*b^4+25*A*sin(d*x+c)*cos(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^4-63*B*sin(d*x+c)*cos(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+63*B*sin(d*x+c)*cos(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^4-15*A*a^4-63*B*sin(d*x+c)*cos(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^3*b-161*B*sin(d*x+c)*cos(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^2*b^2-161*B*sin(d*x+c)*cos(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^3+119*B*sin(d*x+c)*cos(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^3*b+161*B*sin(d*x+c)*cos(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^2-145*A*sin(d*x+c)*cos(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*b-145*A*sin(d*x+c)*cos(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^2-15*A*sin(d*x+c)*cos(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^3+145*A*sin(d*x+c)*cos(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^3*b+135*A*sin(d*x+c)*cos(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^2*b^2+15*A*sin(d*x+c)*cos(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^3-63*B*sin(d*x+c)*cos(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*b-161*B*sin(d*x+c)*cos(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^2-161*B*sin(d*x+c)*cos(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^3+119*B*sin(d*x+c)*cos(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^3*b+161*B*sin(d*x+c)*cos(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^2*b^2-145*A*sin(d*x+c)*cos(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^3*b-145*A*sin(d*x+c)*cos(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^2*b^2-15*A*sin(d*x+c)*cos(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^3+145*A*sin(d*x+c)*cos(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^3*b+135*A*sin(d*x+c)*cos(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^2)*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"
608,1,3282,501,0.449000," ","int((a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))*sec(d*x+c)^(7/2),x)","\text{output too large to display}"," ",0,"-2/15/d*(-3*A*a^3+9*A*cos(d*x+c)^3*a^3-23*A*cos(d*x+c)^3*b^3-6*A*cos(d*x+c)^2*a^3+5*B*cos(d*x+c)^3*a^3+35*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)*sin(d*x+c)*cos(d*x+c)^3*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a^2*b+45*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)*sin(d*x+c)*cos(d*x+c)^2*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a*b^2+23*A*cos(d*x+c)^4*b^3-5*B*cos(d*x+c)*a^3+23*A*cos(d*x+c)^3*a*b^2-34*A*cos(d*x+c)^2*a*b^2-14*A*cos(d*x+c)*a^2*b+35*B*cos(d*x+c)^4*a*b^2+35*B*cos(d*x+c)^3*a^2*b-40*B*cos(d*x+c)^2*a^2*b-9*A*sin(d*x+c)*cos(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-23*A*sin(d*x+c)*cos(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+17*A*sin(d*x+c)*cos(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+23*A*sin(d*x+c)*cos(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^2-35*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)*sin(d*x+c)*cos(d*x+c)^2*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a^2*b-35*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)*sin(d*x+c)*cos(d*x+c)^2*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a*b^2+35*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)*sin(d*x+c)*cos(d*x+c)^2*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a^2*b-35*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)*sin(d*x+c)*cos(d*x+c)^3*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a*b^2-9*A*sin(d*x+c)*cos(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-23*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)*sin(d*x+c)*cos(d*x+c)^3*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a*b^2+17*A*sin(d*x+c)*cos(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^2*b+23*A*sin(d*x+c)*cos(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^2-35*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)*sin(d*x+c)*cos(d*x+c)^3*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a^2*b+45*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)*sin(d*x+c)*cos(d*x+c)^3*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a*b^2-35*B*cos(d*x+c)^3*a*b^2+9*A*cos(d*x+c)^4*a^2*b+11*A*cos(d*x+c)^4*a*b^2+5*A*cos(d*x+c)^3*a^2*b+5*B*cos(d*x+c)^4*a^2*b+15*A*sin(d*x+c)*cos(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))*b^3-15*B*sin(d*x+c)*cos(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))*b^3+30*B*sin(d*x+c)*cos(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)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,(-(a-b)/(a+b))^(1/2))*b^3-15*B*sin(d*x+c)*cos(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))*b^3+30*B*sin(d*x+c)*cos(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^3+15*A*sin(d*x+c)*cos(d*x+c)^2*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*b^3+5*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)*sin(d*x+c)*cos(d*x+c)^2*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a^3-9*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)*sin(d*x+c)*cos(d*x+c)^3*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a^3-23*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)*sin(d*x+c)*cos(d*x+c)^3*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*b^3+9*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)*sin(d*x+c)*cos(d*x+c)^3*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a^3+5*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)*sin(d*x+c)*cos(d*x+c)^3*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a^3-9*A*sin(d*x+c)*cos(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^3-23*A*sin(d*x+c)*cos(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+9*A*sin(d*x+c)*cos(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)*cos(d*x+c)/(a+b*cos(d*x+c))^(1/2)*(1/cos(d*x+c))^(7/2)/sin(d*x+c)","B"
609,1,3212,540,0.411000," ","int((a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))*sec(d*x+c)^(5/2),x)","\text{output too large to display}"," ",0,"-1/3/d*(-2*A*a^3+2*A*cos(d*x+c)^2*a^3-14*A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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-14*A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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+18*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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-18*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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+30*B*sin(d*x+c)*cos(d*x+c)*(cos(d*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^2-6*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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+18*A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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^2-18*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)*sin(d*x+c)*cos(d*x+c)^2*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a*b^2+14*A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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*B*cos(d*x+c)^3*b^3+6*B*cos(d*x+c)^2*a^3-6*B*cos(d*x+c)*a^3+14*A*cos(d*x+c)^3*a*b^2+14*A*cos(d*x+c)^2*a^2*b-14*A*cos(d*x+c)^2*a*b^2-16*A*cos(d*x+c)*a^2*b+6*B*cos(d*x+c)^3*a^2*b-6*B*cos(d*x+c)^2*a^2*b-3*B*cos(d*x+c)^2*a*b^2+3*B*cos(d*x+c)^4*b^3+12*A*sin(d*x+c)*cos(d*x+c)*(cos(d*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^3-6*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+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*A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+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^3-14*A*sin(d*x+c)*cos(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-14*A*sin(d*x+c)*cos(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+14*A*sin(d*x+c)*cos(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+18*A*sin(d*x+c)*cos(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^2-6*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)*sin(d*x+c)*cos(d*x+c)^2*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a^2*b+3*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)*sin(d*x+c)*cos(d*x+c)^2*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a*b^2+18*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)*sin(d*x+c)*cos(d*x+c)^2*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a^2*b+30*B*sin(d*x+c)*cos(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*b^2+3*B*cos(d*x+c)^3*a*b^2+2*A*cos(d*x+c)^3*a^2*b+2*A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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*B*sin(d*x+c)*cos(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^3+3*B*sin(d*x+c)*cos(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^3-6*A*sin(d*x+c)*cos(d*x+c)^2*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*b^3+12*A*sin(d*x+c)*cos(d*x+c)^2*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,(-(a-b)/(a+b))^(1/2))*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*b^3+6*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)*sin(d*x+c)*cos(d*x+c)^2*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a^3+2*A*sin(d*x+c)*cos(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)*cos(d*x+c)/(a+b*cos(d*x+c))^(1/2)*(1/cos(d*x+c))^(5/2)/sin(d*x+c)","B"
610,1,3278,549,0.435000," ","int((a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))*sec(d*x+c)^(3/2),x)","\text{output too large to display}"," ",0,"-1/4/d*(-8*A*a^3+8*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+30*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)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*a^2*b-8*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))*sin(d*x+c)*cos(d*x+c)*a^3+4*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))*sin(d*x+c)*cos(d*x+c)*b^3-4*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)*b^3+8*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)*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)*b^3+40*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)*a*b^2+40*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)*a*b^2+30*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)*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)*a^2*b+4*A*cos(d*x+c)^3*b^3+8*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))*a^3-8*A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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*A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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^2-24*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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-24*A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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+24*A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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*A*cos(d*x+c)^2*b^3-2*B*cos(d*x+c)^2*b^3+8*A*cos(d*x+c)^2*a^2*b+4*A*cos(d*x+c)^2*a*b^2-8*A*cos(d*x+c)*a^2*b-4*A*cos(d*x+c)*a*b^2+9*B*cos(d*x+c)^2*a^2*b-9*B*cos(d*x+c)^2*a*b^2-9*B*cos(d*x+c)*a^2*b-2*B*cos(d*x+c)*a*b^2+8*A*cos(d*x+c)*a^3+2*B*cos(d*x+c)^4*b^3-24*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))*a*b^2-8*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^2*b+4*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*b^2-24*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*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*b^2+9*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+9*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+24*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))*a^2*b+11*B*cos(d*x+c)^3*a*b^2+8*A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a^3+8*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a^3-8*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))*sin(d*x+c)*a^3+4*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))*sin(d*x+c)*b^3-4*B*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*b^3+8*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)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*b^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"
611,1,3514,564,0.474000," ","int((a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))*sec(d*x+c)^(1/2),x)","\text{output too large to display}"," ",0,"-1/24/d*(1/cos(d*x+c))^(1/2)/(a+b*cos(d*x+c))^(1/2)*(-48*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+48*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))*a^3+180*A*sin(d*x+c)*cos(d*x+c)*(cos(d*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+54*A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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+54*A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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+120*B*sin(d*x+c)*cos(d*x+c)*(cos(d*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*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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+12*A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a*b^2+16*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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^2-144*A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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+12*A*cos(d*x+c)^4*b^3-12*A*cos(d*x+c)^2*b^3+8*B*cos(d*x+c)^5*b^3+8*B*cos(d*x+c)^3*b^3+33*B*cos(d*x+c)^2*a^3-16*B*cos(d*x+c)^2*b^3-33*B*cos(d*x+c)*a^3+66*A*cos(d*x+c)^3*a*b^2+54*A*cos(d*x+c)^2*a^2*b-54*A*cos(d*x+c)^2*a*b^2-54*A*cos(d*x+c)*a^2*b-12*A*cos(d*x+c)*a*b^2+34*B*cos(d*x+c)^4*a*b^2+59*B*cos(d*x+c)^3*a^2*b-33*B*cos(d*x+c)^2*a^2*b-18*B*cos(d*x+c)^2*a*b^2-26*B*cos(d*x+c)*a^2*b-16*B*cos(d*x+c)*a*b^2+48*A*sin(d*x+c)*cos(d*x+c)*(cos(d*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+30*B*sin(d*x+c)*cos(d*x+c)*(cos(d*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+33*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+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+12*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))*a*b^2+180*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)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,(-(a-b)/(a+b))^(1/2))*a^2*b+54*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^2*b+54*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*b^2+26*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-76*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*b^2+120*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)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,(-(a-b)/(a+b))^(1/2))*a*b^2+33*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+16*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^2-24*A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+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^3-144*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))*a^2*b-24*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^3+48*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)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,(-(a-b)/(a+b))^(1/2))*b^3+30*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)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,(-(a-b)/(a+b))^(1/2))*a^3+33*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^3+16*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^3+48*A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a^3-48*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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)","B"
612,1,4240,658,0.620000," ","int((a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))/sec(d*x+c)^(1/2),x)","\text{output too large to display}"," ",0,"-1/192/d*(472*A*cos(d*x+c)^3*a^2*b^2+133*B*cos(d*x+c)^3*a^3*b+172*B*cos(d*x+c)^3*a*b^3+30*B*cos(d*x+c)^2*a^2*b^2-284*B*cos(d*x+c)^2*a*b^3-118*B*cos(d*x+c)*a^3*b-284*B*cos(d*x+c)*a^2*b^2-72*B*cos(d*x+c)*a*b^3+264*A*cos(d*x+c)^2*a^3*b-144*A*cos(d*x+c)^2*a*b^3-208*A*cos(d*x+c)*a^2*b^2-128*A*cos(d*x+c)*a*b^3+128*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^4+15*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^4-30*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)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,(-(a-b)/(a+b))^(1/2))*a^4+288*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)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,(-(a-b)/(a+b))^(1/2))*b^4-144*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^4+48*B*cos(d*x+c)^6*b^4+64*A*cos(d*x+c)^3*b^4-128*A*cos(d*x+c)^2*b^4+24*B*cos(d*x+c)^4*b^4-72*B*cos(d*x+c)^2*b^4+15*B*cos(d*x+c)^2*a^4-15*B*cos(d*x+c)*a^4+64*A*cos(d*x+c)^5*b^4-15*B*cos(d*x+c)^2*a^3*b+272*A*cos(d*x+c)^4*a*b^3-264*A*cos(d*x+c)^2*a^2*b^2-264*A*cos(d*x+c)*a^3*b+184*B*cos(d*x+c)^5*a*b^3+254*B*cos(d*x+c)^4*a^2*b^2+264*A*sin(d*x+c)*cos(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+15*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a^4-30*B*sin(d*x+c)*cos(d*x+c)*(cos(d*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+288*B*sin(d*x+c)*cos(d*x+c)*(cos(d*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*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+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+264*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^3*b+264*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^2*b^2+128*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*b^3+240*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)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,(-(a-b)/(a+b))^(1/2))*a^3*b+960*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)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,(-(a-b)/(a+b))^(1/2))*a*b^3+208*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))*a^2*b^2-608*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))*a*b^3+15*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^3*b+284*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+284*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^3+720*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)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,(-(a-b)/(a+b))^(1/2))*a^2*b^2+118*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-644*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+72*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*b^3+128*A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+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+264*A*sin(d*x+c)*cos(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^2+128*A*sin(d*x+c)*cos(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^3+240*A*sin(d*x+c)*cos(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+960*A*sin(d*x+c)*cos(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^3+208*A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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^2-608*A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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+720*B*sin(d*x+c)*cos(d*x+c)*(cos(d*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+118*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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^3-384*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))*a^3*b-384*A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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)*(1/cos(d*x+c))^(1/2)/sin(d*x+c)/(a+b*cos(d*x+c))^(1/2)/b","B"
613,1,5172,767,0.838000," ","int((a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))/sec(d*x+c)^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
614,1,2488,363,0.414000," ","int((A+B*cos(d*x+c))*sec(d*x+c)^(7/2)/(a+b*cos(d*x+c))^(1/2),x)","\text{Expression too large to display}"," ",0,"-2/15/d*(-3*A*a^3+9*A*cos(d*x+c)^3*a^3-8*A*cos(d*x+c)^3*b^3-6*A*cos(d*x+c)^2*a^3+5*B*cos(d*x+c)^3*a^3-10*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)*sin(d*x+c)*cos(d*x+c)^3*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a^2*b+8*A*cos(d*x+c)^4*b^3-5*B*cos(d*x+c)*a^3+8*A*cos(d*x+c)^3*a*b^2-4*A*cos(d*x+c)^2*a*b^2+A*cos(d*x+c)*a^2*b-10*B*cos(d*x+c)^4*a*b^2-10*B*cos(d*x+c)^3*a^2*b+5*B*cos(d*x+c)^2*a^2*b-9*A*sin(d*x+c)*cos(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-8*A*sin(d*x+c)*cos(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+2*A*sin(d*x+c)*cos(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+8*A*sin(d*x+c)*cos(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+10*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)*sin(d*x+c)*cos(d*x+c)^2*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a^2*b+10*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)*sin(d*x+c)*cos(d*x+c)^2*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a*b^2-10*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)*sin(d*x+c)*cos(d*x+c)^2*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a^2*b+10*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)*sin(d*x+c)*cos(d*x+c)^3*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a*b^2-9*A*sin(d*x+c)*cos(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-8*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)*sin(d*x+c)*cos(d*x+c)^3*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a*b^2+2*A*sin(d*x+c)*cos(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^2*b+8*A*sin(d*x+c)*cos(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+10*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)*sin(d*x+c)*cos(d*x+c)^3*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a^2*b+10*B*cos(d*x+c)^3*a*b^2+9*A*cos(d*x+c)^4*a^2*b-4*A*cos(d*x+c)^4*a*b^2-10*A*cos(d*x+c)^3*a^2*b+5*B*cos(d*x+c)^4*a^2*b+5*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)*sin(d*x+c)*cos(d*x+c)^2*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a^3-9*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)*sin(d*x+c)*cos(d*x+c)^3*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a^3-8*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)*sin(d*x+c)*cos(d*x+c)^3*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*b^3+9*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)*sin(d*x+c)*cos(d*x+c)^3*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a^3+5*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)*sin(d*x+c)*cos(d*x+c)^3*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a^3-9*A*sin(d*x+c)*cos(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^3-8*A*sin(d*x+c)*cos(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+9*A*sin(d*x+c)*cos(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)*cos(d*x+c)*(1/cos(d*x+c))^(7/2)/(a+b*cos(d*x+c))^(1/2)/sin(d*x+c)/a^3","B"
615,1,1544,296,0.472000," ","int((A+B*cos(d*x+c))*sec(d*x+c)^(5/2)/(a+b*cos(d*x+c))^(1/2),x)","-\frac{2 \left(2 A \left(\cos^{2}\left(d x +c \right)\right) b^{2}-2 A \left(\cos^{3}\left(d x +c \right)\right) b^{2}-3 B \cos \left(d x +c \right) a^{2}-a^{2} A +A \sin \left(d x +c \right) \cos \left(d x +c \right) \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{-\frac{a -b}{a +b}}\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \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}+3 B \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{-\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \cos \left(d x +c \right) a^{2}-2 A \left(\cos^{2}\left(d x +c \right)\right) a b +3 B \left(\cos^{3}\left(d x +c \right)\right) a b -3 B \left(\cos^{2}\left(d x +c \right)\right) a b +A \left(\cos^{2}\left(d x +c \right)\right) a^{2}-3 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) \cos \left(d x +c \right) a b +2 A \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{-\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \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 b -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)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{-\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) \cos \left(d x +c \right) a b +A \left(\cos^{3}\left(d x +c \right)\right) a b +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)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{-\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) a b -3 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) \left(\cos^{2}\left(d x +c \right)\right) a b -2 A \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\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{\cos \left(d x +c \right)}{1+\cos \left(d x +c \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 b +3 B \left(\cos^{2}\left(d x +c \right)\right) a^{2}+A \cos \left(d x +c \right) a b +A \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{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) a^{2}+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)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{-\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) b^{2}+3 B \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{-\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \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(\cos^{2}\left(d x +c \right)\right) a^{2}-3 B \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \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 A \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{-\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \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}-3 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) \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*(3*B*cos(d*x+c)^2*a^2-3*B*cos(d*x+c)*a^2-2*A*cos(d*x+c)^3*b^2+2*A*cos(d*x+c)^2*b^2-a^2*A+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)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)^2*a*b+A*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((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+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)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)^2*b^2+3*B*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*cos(d*x+c)^2*a^2-3*B*sin(d*x+c)*cos(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+A*sin(d*x+c)*cos(d*x+c)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^2+3*B*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*cos(d*x+c)*a^2+A*cos(d*x+c)^2*a^2-3*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))*cos(d*x+c)*a*b+2*A*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)*(cos(d*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-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)*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+A*cos(d*x+c)^3*a*b-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))*cos(d*x+c)^2*a*b-2*A*sin(d*x+c)*cos(d*x+c)^2*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a*b-2*A*cos(d*x+c)^2*a*b+A*cos(d*x+c)*a*b+3*B*cos(d*x+c)^3*a*b-3*B*cos(d*x+c)^2*a*b+2*A*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)*(cos(d*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^2-3*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))*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"
616,1,812,246,0.398000," ","int((A+B*cos(d*x+c))*sec(d*x+c)^(3/2)/(a+b*cos(d*x+c))^(1/2),x)","-\frac{2 \left(A \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \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 -A \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{-\frac{a -b}{a +b}}\right) a -A \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{-\frac{a -b}{a +b}}\right) b +B \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \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)}}\, a +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)}}\, \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)-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)-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) b \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)+A \left(\cos^{2}\left(d x +c \right)\right) b +A \cos \left(d x +c \right) a -A \cos \left(d x +c \right) b -a 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*(A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a-A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a-A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+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+B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+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)*a+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)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a*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)-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))*b*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)+A*cos(d*x+c)^2*b+A*cos(d*x+c)*a-A*cos(d*x+c)*b-a*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"
617,1,199,244,0.376000," ","int((A+B*cos(d*x+c))*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)}}\, \left(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 \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{-\frac{a -b}{a +b}}\right)+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)*(A*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))-B*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))+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"
618,1,1004,443,0.459000," ","int((A+B*cos(d*x+c))/sec(d*x+c)^(1/2)/(a+b*cos(d*x+c))^(1/2),x)","-\frac{\left(4 A \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{a +b \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \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 A \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \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 B \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticPi \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, -1, \sqrt{-\frac{a -b}{a +b}}\right) \sqrt{\frac{a +b \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, a +B \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{-\frac{a -b}{a +b}}\right) a +B \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \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 A \sin \left(d x +c \right) \sqrt{\frac{a +b \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \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 A \sin \left(d x +c \right) \sqrt{\frac{a +b \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \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 \sin \left(d x +c \right) \EllipticPi \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, -1, \sqrt{-\frac{a -b}{a +b}}\right) \sqrt{\frac{a +b \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, a +B \sin \left(d x +c \right) \sqrt{\frac{a +b \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \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{a +b \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{-\frac{a -b}{a +b}}\right) b +B \left(\cos^{3}\left(d x +c \right)\right) b +B \left(\cos^{2}\left(d x +c \right)\right) a -b B \left(\cos^{2}\left(d x +c \right)\right)-B \cos \left(d x +c \right) a \right) \sqrt{\frac{1}{\cos \left(d x +c \right)}}}{d \sqrt{a +b \cos \left(d x +c \right)}\, \sin \left(d x +c \right) b}"," ",0,"-1/d*(4*A*sin(d*x+c)*cos(d*x+c)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,(-(a-b)/(a+b))^(1/2))*b-2*A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+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*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*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)*a+B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a+B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+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*sin(d*x+c)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,(-(a-b)/(a+b))^(1/2))*b-2*A*sin(d*x+c)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*b-2*B*sin(d*x+c)*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)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*a+B*sin(d*x+c)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a+B*sin(d*x+c)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*b+B*cos(d*x+c)^3*b+B*cos(d*x+c)^2*a-b*B*cos(d*x+c)^2-B*cos(d*x+c)*a)*(1/cos(d*x+c))^(1/2)/(a+b*cos(d*x+c))^(1/2)/sin(d*x+c)/b","B"
619,1,1878,485,0.390000," ","int((A+B*cos(d*x+c))/sec(d*x+c)^(3/2)/(a+b*cos(d*x+c))^(1/2),x)","\frac{\left(4 A \left(\cos^{2}\left(d x +c \right)\right) b^{2}-4 A \left(\cos^{3}\left(d x +c \right)\right) b^{2}-3 B \cos \left(d x +c \right) a^{2}-4 A \left(\cos^{2}\left(d x +c \right)\right) a b +B \left(\cos^{3}\left(d x +c \right)\right) a b -3 B \left(\cos^{2}\left(d x +c \right)\right) a b +8 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) \cos \left(d x +c \right) a b +3 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) \cos \left(d x +c \right) a b -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)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{-\frac{a -b}{a +b}}\right) \cos \left(d x +c \right) a b -4 A \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{-\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \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 b +3 B \left(\cos^{2}\left(d x +c \right)\right) a^{2}+2 B \left(\cos^{2}\left(d x +c \right)\right) b^{2}-2 B \left(\cos^{4}\left(d x +c \right)\right) b^{2}+4 A \cos \left(d x +c \right) a b +2 B \cos \left(d x +c \right) a b -4 A \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{-\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \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 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)}}\, \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 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)}}\, \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}+3 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^{2}+4 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}-4 A \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{-\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \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 b +3 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 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) a b -4 A \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{-\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \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 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)}}\, \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) a^{2}-8 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)}}\, \EllipticPi \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, -1, \sqrt{-\frac{a -b}{a +b}}\right) \cos \left(d x +c \right) b^{2}+3 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) \cos \left(d x +c \right) a^{2}+4 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) \cos \left(d x +c \right) b^{2}+8 A \EllipticPi \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, -1, \sqrt{-\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \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 b \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^{2}}"," ",0,"1/4/d*(-4*A*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*b^2+3*B*cos(d*x+c)^2*a^2-2*B*cos(d*x+c)^4*b^2+2*B*cos(d*x+c)^2*b^2-3*B*cos(d*x+c)*a^2-4*A*cos(d*x+c)^3*b^2+4*A*cos(d*x+c)^2*b^2+8*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)*a*b+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))*cos(d*x+c)*a*b-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)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*cos(d*x+c)*a*b-4*A*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)*(cos(d*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*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)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,(-(a-b)/(a+b))^(1/2))*a^2-4*A*cos(d*x+c)^2*a*b+4*A*cos(d*x+c)*a*b+B*cos(d*x+c)^3*a*b-3*B*cos(d*x+c)^2*a*b+2*B*cos(d*x+c)*a*b-6*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)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,(-(a-b)/(a+b))^(1/2))*cos(d*x+c)*a^2+8*A*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)/(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*A*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a*b+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*b-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)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a*b-4*A*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)*(cos(d*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^2-8*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)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,(-(a-b)/(a+b))^(1/2))*cos(d*x+c)*b^2+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))*cos(d*x+c)*a^2+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))*cos(d*x+c)*b^2-8*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)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,(-(a-b)/(a+b))^(1/2))*b^2+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+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))*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^2","B"
620,1,3343,395,0.402000," ","int((A+B*cos(d*x+c))*sec(d*x+c)^(5/2)/(a+b*cos(d*x+c))^(3/2),x)","\text{output too large to display}"," ",0,"-2/3/d*(-5*A*cos(d*x+c)^3*a^2*b^2+3*B*cos(d*x+c)^3*a^3*b-6*B*cos(d*x+c)^3*a*b^3-6*B*cos(d*x+c)^2*a^2*b^2+6*B*cos(d*x+c)^2*a*b^3+3*B*cos(d*x+c)*a^2*b^2-5*A*cos(d*x+c)^2*a^3*b+8*A*cos(d*x+c)^2*a*b^3-4*A*cos(d*x+c)*a*b^3+A*a^2*b^2+8*A*cos(d*x+c)^3*b^4-8*A*cos(d*x+c)^2*b^4+3*B*cos(d*x+c)^2*a^4-3*B*cos(d*x+c)*a^4+A*cos(d*x+c)^2*a^4-3*B*cos(d*x+c)^2*a^3*b+A*cos(d*x+c)^3*a^3*b-4*A*cos(d*x+c)^3*a*b^3+4*A*cos(d*x+c)^2*a^2*b^2+4*A*cos(d*x+c)*a^3*b+3*B*cos(d*x+c)^3*a^2*b^2+5*A*sin(d*x+c)*cos(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-3*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a^4-8*A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+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*a^4+5*A*sin(d*x+c)*cos(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^2-8*A*sin(d*x+c)*cos(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^3+2*A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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*A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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+6*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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+6*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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-6*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a^2*b^2+5*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))*sin(d*x+c)*cos(d*x+c)^2*a^3*b+5*A*sin(d*x+c)*cos(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^2-8*A*sin(d*x+c)*cos(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^3-5*A*sin(d*x+c)*cos(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*b+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)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)^2*a^2*b^2+8*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)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)^2*a*b^3-3*B*sin(d*x+c)*cos(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^3*b+6*B*sin(d*x+c)*cos(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^2+6*B*sin(d*x+c)*cos(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^3-3*B*sin(d*x+c)*cos(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*b-6*B*sin(d*x+c)*cos(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^2+3*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^4-8*A*sin(d*x+c)*cos(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^4+A*sin(d*x+c)*cos(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^4-3*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))*sin(d*x+c)*cos(d*x+c)^2*a^4+3*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)^2*a^4+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)*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^4-5*A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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)*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"
621,1,2291,317,0.441000," ","int((A+B*cos(d*x+c))*sec(d*x+c)^(3/2)/(a+b*cos(d*x+c))^(3/2),x)","\text{Expression too large to display}"," ",0,"-2/d*(-A*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^3-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))*sin(d*x+c)*cos(d*x+c)*a^3+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)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)*b^3+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))*a^3+A*a*b^2-A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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*A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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+B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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-B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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*A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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-B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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-A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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*A*cos(d*x+c)^2*b^3+A*cos(d*x+c)^2*a^2*b+A*cos(d*x+c)^2*a*b^2-A*cos(d*x+c)*a^2*b-2*A*cos(d*x+c)*a*b^2-B*cos(d*x+c)^2*a^2*b+B*cos(d*x+c)^2*a*b^2+B*cos(d*x+c)*a^2*b-B*cos(d*x+c)*a*b^2+A*cos(d*x+c)*a^3-2*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))*a*b^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^2*b+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*b^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)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a^2*b-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-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+2*A*cos(d*x+c)*b^3-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))*a^2*b+A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+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+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)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*b^3)*cos(d*x+c)*(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"
622,1,1636,296,0.454000," ","int((A+B*cos(d*x+c))*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(A \sin \left(d x +c \right) \cos \left(d x +c \right) \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{-\frac{a -b}{a +b}}\right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \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}+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)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{-\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) \cos \left(d x +c \right) a b -A \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{-\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \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 b -A \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{-\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \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}-B \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{-\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \cos \left(d x +c \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)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{-\frac{a -b}{a +b}}\right) \cos \left(d x +c \right) a b +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) \cos \left(d x +c \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) \cos \left(d x +c \right) a b +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) a^{2}+A \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{-\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \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 b -A \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{-\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \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 b -A \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{-\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \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}-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) 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)}}\, \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 +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^{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 -A \left(\cos^{2}\left(d x +c \right)\right) a b +A \left(\cos^{2}\left(d x +c \right)\right) b^{2}+B \left(\cos^{2}\left(d x +c \right)\right) a^{2}-B \left(\cos^{2}\left(d x +c \right)\right) a b +A \cos \left(d x +c \right) a b -A \cos \left(d x +c \right) b^{2}-B \cos \left(d x +c \right) a^{2}+B \cos \left(d x +c \right) a b \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)*(A*sin(d*x+c)*cos(d*x+c)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^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)*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-A*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)*(cos(d*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-A*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)*(cos(d*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-B*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*cos(d*x+c)*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)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*cos(d*x+c)*a*b+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))*cos(d*x+c)*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))*cos(d*x+c)*a*b+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))*a^2+A*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a*b-A*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a*b-A*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*b^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)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a^2-B*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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+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*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a*b-A*cos(d*x+c)^2*a*b+A*cos(d*x+c)^2*b^2+B*cos(d*x+c)^2*a^2-B*cos(d*x+c)^2*a*b+A*cos(d*x+c)*a*b-A*cos(d*x+c)*b^2-B*cos(d*x+c)*a^2+B*cos(d*x+c)*a*b)/sin(d*x+c)/(a+b)/(a-b)/a","B"
623,1,2016,436,0.424000," ","int((A+B*cos(d*x+c))/(a+b*cos(d*x+c))^(3/2)/sec(d*x+c)^(1/2),x)","\frac{2 \left(A \left(\cos^{2}\left(d x +c \right)\right) b^{2}-B \cos \left(d x +c \right) a^{2}-A \left(\cos^{2}\left(d x +c \right)\right) a b -B \left(\cos^{2}\left(d x +c \right)\right) a b -A \cos \left(d x +c \right) b^{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) \cos \left(d x +c \right) a b -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) \cos \left(d x +c \right) a b -A \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{-\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \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 b +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)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{-\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) \cos \left(d x +c \right) a b +B \left(\cos^{2}\left(d x +c \right)\right) a^{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)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{-\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) \cos \left(d x +c \right) b^{2}+A \cos \left(d x +c \right) a b +B \cos \left(d x +c \right) a b -A \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{-\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \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 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)}}\, \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 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)}}\, \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}+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^{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)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{-\frac{a -b}{a +b}}\right) b^{2}+A \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a +b \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{-\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) b^{2}-A \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{-\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \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 b +A \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{-\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \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 b +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 -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) a b -A \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{-\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \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 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)}}\, \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) a^{2}+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)}}\, \EllipticPi \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, -1, \sqrt{-\frac{a -b}{a +b}}\right) \cos \left(d x +c \right) b^{2}+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) \cos \left(d x +c \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)}}\, \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) b^{2}\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) b}"," ",0,"2/d*(-A*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*b^2+B*cos(d*x+c)^2*a^2-B*cos(d*x+c)*a^2+A*cos(d*x+c)^2*b^2-A*cos(d*x+c)*b^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))*cos(d*x+c)*a*b-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))*cos(d*x+c)*a*b-A*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)*(cos(d*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+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)*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-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)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,(-(a-b)/(a+b))^(1/2))*a^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)*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^2-A*cos(d*x+c)^2*a*b+A*cos(d*x+c)*a*b-B*cos(d*x+c)^2*a*b+B*cos(d*x+c)*a*b-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)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,(-(a-b)/(a+b))^(1/2))*cos(d*x+c)*a^2-A*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a*b+A*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a*b+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-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*b+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)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*b^2-A*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)*(cos(d*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+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)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,(-(a-b)/(a+b))^(1/2))*cos(d*x+c)*b^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))*cos(d*x+c)*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)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*cos(d*x+c)*b^2+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)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,(-(a-b)/(a+b))^(1/2))*b^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^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)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*b^2)*(1/cos(d*x+c))^(1/2)/sin(d*x+c)/(a+b*cos(d*x+c))^(1/2)/(a+b)/(a-b)/b","B"
624,1,2890,516,0.382000," ","int((A+B*cos(d*x+c))/(a+b*cos(d*x+c))^(3/2)/sec(d*x+c)^(3/2),x)","\text{output too large to display}"," ",0,"1/d*(-4*A*sin(d*x+c)*cos(d*x+c)*(cos(d*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*A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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*A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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^2-6*B*sin(d*x+c)*cos(d*x+c)*(cos(d*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*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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*A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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+B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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+B*cos(d*x+c)^3*b^3-3*B*cos(d*x+c)^2*a^3-B*cos(d*x+c)^2*b^3+3*B*cos(d*x+c)*a^3+2*A*cos(d*x+c)^2*a^2*b-2*A*cos(d*x+c)^2*a*b^2-2*A*cos(d*x+c)*a^2*b+2*A*cos(d*x+c)*a*b^2-B*cos(d*x+c)^3*a^2*b+3*B*cos(d*x+c)^2*a^2*b+B*cos(d*x+c)^2*a*b^2-2*B*cos(d*x+c)*a^2*b-B*cos(d*x+c)*a*b^2+4*A*sin(d*x+c)*cos(d*x+c)*(cos(d*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+6*B*sin(d*x+c)*cos(d*x+c)*(cos(d*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^3-3*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a^3+B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*b^3-2*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))*a*b^2-4*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)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,(-(a-b)/(a+b))^(1/2))*a^2*b+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^2*b+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*b^2+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)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a^2*b+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)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a*b^2-6*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)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,(-(a-b)/(a+b))^(1/2))*a*b^2-3*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+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^2-2*A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*b^3-2*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^3+4*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)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,(-(a-b)/(a+b))^(1/2))*b^3+6*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)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,(-(a-b)/(a+b))^(1/2))*a^3-3*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^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))*b^3)*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^2","B"
625,1,8101,561,0.601000," ","int((A+B*cos(d*x+c))*sec(d*x+c)^(5/2)/(a+b*cos(d*x+c))^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
626,1,6506,456,0.630000," ","int((A+B*cos(d*x+c))*sec(d*x+c)^(3/2)/(a+b*cos(d*x+c))^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
627,1,5202,429,0.503000," ","int((A+B*cos(d*x+c))*sec(d*x+c)^(1/2)/(a+b*cos(d*x+c))^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
628,1,4243,391,0.470000," ","int((A+B*cos(d*x+c))/(a+b*cos(d*x+c))^(5/2)/sec(d*x+c)^(1/2),x)","\text{output too large to display}"," ",0,"2/3/d*(-3*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))*sin(d*x+c)*a^4+3*A*cos(d*x+c)^3*a^2*b^2-4*B*cos(d*x+c)^3*a*b^3-8*B*cos(d*x+c)^2*a^2*b^2+4*B*cos(d*x+c)^2*a*b^3-4*B*cos(d*x+c)*a^3*b+3*B*cos(d*x+c)*a^2*b^2+6*A*cos(d*x+c)^2*a^3*b+2*A*cos(d*x+c)^2*a*b^3+A*cos(d*x+c)*a^2*b^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)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*a^4+A*cos(d*x+c)^3*b^4-A*cos(d*x+c)^2*b^4-B*cos(d*x+c)^3*a^4+B*cos(d*x+c)*a^4-3*A*cos(d*x+c)^2*a^4+3*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)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*a^4+4*B*cos(d*x+c)^2*a^3*b-2*A*cos(d*x+c)^3*a^3*b-2*A*cos(d*x+c)^3*a*b^3-4*A*cos(d*x+c)^2*a^2*b^2-4*A*cos(d*x+c)*a^3*b+5*B*cos(d*x+c)^3*a^2*b^2-6*A*sin(d*x+c)*cos(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-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))*cos(d*x+c)^2*a*b^3-3*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^3*b-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^2*b^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*b^3+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))*a^2*b^2+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)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a^3*b+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)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*a^2*b^2-4*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-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-A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+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^4-4*A*sin(d*x+c)*cos(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^2-2*A*sin(d*x+c)*cos(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^3+5*A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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+A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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+4*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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+8*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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+4*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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-7*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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*A*cos(d*x+c)*a^4-3*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))*sin(d*x+c)*cos(d*x+c)^2*a^3*b-3*A*sin(d*x+c)*cos(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^2-A*sin(d*x+c)*cos(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^3+3*A*sin(d*x+c)*cos(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*b+4*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)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)^2*a^2*b^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)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),(-(a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)^2*a*b^3+4*B*sin(d*x+c)*cos(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^2+4*B*sin(d*x+c)*cos(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^3-B*sin(d*x+c)*cos(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*b-4*B*sin(d*x+c)*cos(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^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)*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+4*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))*a^3*b-A*sin(d*x+c)*cos(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^4+3*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)*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+7*A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((a+b*cos(d*x+c))/(1+cos(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*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))*sin(d*x+c)*cos(d*x+c)*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"
629,1,5757,550,0.433000," ","int((A+B*cos(d*x+c))/(a+b*cos(d*x+c))^(5/2)/sec(d*x+c)^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
630,1,8621,675,0.563000," ","int((A+B*cos(d*x+c))/(a+b*cos(d*x+c))^(5/2)/sec(d*x+c)^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
631,1,621,242,0.333000," ","int((a*B+b*B*cos(d*x+c))*sec(d*x+c)^(3/2)/(a+b*cos(d*x+c))^(3/2),x)","-\frac{2 B \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*B/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)/(a+b*cos(d*x+c))^(1/2)*(1/cos(d*x+c))^(3/2)/sin(d*x+c)/a","B"
632,1,126,118,0.318000," ","int((a*B+b*B*cos(d*x+c))*sec(d*x+c)^(1/2)/(a+b*cos(d*x+c))^(3/2),x)","\frac{2 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) \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*B/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"
633,1,144,125,0.299000," ","int((a*B+b*B*cos(d*x+c))/(a+b*cos(d*x+c))^(3/2)/sec(d*x+c)^(1/2),x)","\frac{2 B \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*B/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"
634,1,631,435,0.352000," ","int((a*B+b*B*cos(d*x+c))/(a+b*cos(d*x+c))^(3/2)/sec(d*x+c)^(3/2),x)","-\frac{B \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,"-B/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"
635,0,0,58,3.111000," ","int((a+b*cos(f*x+e))^n*(A+B*cos(f*x+e))*(c*sec(f*x+e))^m,x)","\int \left(a +b \cos \left(f x +e \right)\right)^{n} \left(A +B \cos \left(f x +e \right)\right) \left(c \sec \left(f x +e \right)\right)^{m}\, dx"," ",0,"int((a+b*cos(f*x+e))^n*(A+B*cos(f*x+e))*(c*sec(f*x+e))^m,x)","F"
636,0,0,604,2.793000," ","int((a+b*cos(f*x+e))^4*(A+B*cos(f*x+e))*(c*sec(f*x+e))^m,x)","\int \left(a +b \cos \left(f x +e \right)\right)^{4} \left(A +B \cos \left(f x +e \right)\right) \left(c \sec \left(f x +e \right)\right)^{m}\, dx"," ",0,"int((a+b*cos(f*x+e))^4*(A+B*cos(f*x+e))*(c*sec(f*x+e))^m,x)","F"
637,0,0,419,2.228000," ","int((a+b*cos(f*x+e))^3*(A+B*cos(f*x+e))*(c*sec(f*x+e))^m,x)","\int \left(a +b \cos \left(f x +e \right)\right)^{3} \left(A +B \cos \left(f x +e \right)\right) \left(c \sec \left(f x +e \right)\right)^{m}\, dx"," ",0,"int((a+b*cos(f*x+e))^3*(A+B*cos(f*x+e))*(c*sec(f*x+e))^m,x)","F"
638,0,0,295,1.801000," ","int((a+b*cos(f*x+e))^2*(A+B*cos(f*x+e))*(c*sec(f*x+e))^m,x)","\int \left(a +b \cos \left(f x +e \right)\right)^{2} \left(A +B \cos \left(f x +e \right)\right) \left(c \sec \left(f x +e \right)\right)^{m}\, dx"," ",0,"int((a+b*cos(f*x+e))^2*(A+B*cos(f*x+e))*(c*sec(f*x+e))^m,x)","F"
639,0,0,193,1.942000," ","int((a+b*cos(f*x+e))*(A+B*cos(f*x+e))*(c*sec(f*x+e))^m,x)","\int \left(a +b \cos \left(f x +e \right)\right) \left(A +B \cos \left(f x +e \right)\right) \left(c \sec \left(f x +e \right)\right)^{m}\, dx"," ",0,"int((a+b*cos(f*x+e))*(A+B*cos(f*x+e))*(c*sec(f*x+e))^m,x)","F"
640,0,0,273,1.270000," ","int((A+B*cos(f*x+e))*(c*sec(f*x+e))^m/(a+b*cos(f*x+e)),x)","\int \frac{\left(A +B \cos \left(f x +e \right)\right) \left(c \sec \left(f x +e \right)\right)^{m}}{a +b \cos \left(f x +e \right)}\, dx"," ",0,"int((A+B*cos(f*x+e))*(c*sec(f*x+e))^m/(a+b*cos(f*x+e)),x)","F"
641,0,0,197,0.457000," ","int((a+b*cos(f*x+e))^(3/2)*(A+B*cos(f*x+e))*(c*sec(f*x+e))^m,x)","\int \left(a +b \cos \left(f x +e \right)\right)^{\frac{3}{2}} \left(A +B \cos \left(f x +e \right)\right) \left(c \sec \left(f x +e \right)\right)^{m}\, dx"," ",0,"int((a+b*cos(f*x+e))^(3/2)*(A+B*cos(f*x+e))*(c*sec(f*x+e))^m,x)","F"
642,0,0,58,0.421000," ","int((a+b*cos(f*x+e))^(1/2)*(A+B*cos(f*x+e))*(c*sec(f*x+e))^m,x)","\int \sqrt{a +b \cos \left(f x +e \right)}\, \left(A +B \cos \left(f x +e \right)\right) \left(c \sec \left(f x +e \right)\right)^{m}\, dx"," ",0,"int((a+b*cos(f*x+e))^(1/2)*(A+B*cos(f*x+e))*(c*sec(f*x+e))^m,x)","F"
643,0,0,58,0.409000," ","int((A+B*cos(f*x+e))*(c*sec(f*x+e))^m/(a+b*cos(f*x+e))^(1/2),x)","\int \frac{\left(A +B \cos \left(f x +e \right)\right) \left(c \sec \left(f x +e \right)\right)^{m}}{\sqrt{a +b \cos \left(f x +e \right)}}\, dx"," ",0,"int((A+B*cos(f*x+e))*(c*sec(f*x+e))^m/(a+b*cos(f*x+e))^(1/2),x)","F"
644,0,0,202,0.387000," ","int((A+B*cos(f*x+e))*(c*sec(f*x+e))^m/(a+b*cos(f*x+e))^(3/2),x)","\int \frac{\left(A +B \cos \left(f x +e \right)\right) \left(c \sec \left(f x +e \right)\right)^{m}}{\left(a +b \cos \left(f x +e \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int((A+B*cos(f*x+e))*(c*sec(f*x+e))^m/(a+b*cos(f*x+e))^(3/2),x)","F"