1,1,78,79,1.264000," ","int(sec(d*x+c)^6*(A+C*sec(d*x+c)^2),x)","\frac{-A \left(-\frac{8}{15}-\frac{\left(\sec^{4}\left(d x +c \right)\right)}{5}-\frac{4 \left(\sec^{2}\left(d x +c \right)\right)}{15}\right) \tan \left(d x +c \right)-C \left(-\frac{16}{35}-\frac{\left(\sec^{6}\left(d x +c \right)\right)}{7}-\frac{6 \left(\sec^{4}\left(d x +c \right)\right)}{35}-\frac{8 \left(\sec^{2}\left(d x +c \right)\right)}{35}\right) \tan \left(d x +c \right)}{d}"," ",0,"1/d*(-A*(-8/15-1/5*sec(d*x+c)^4-4/15*sec(d*x+c)^2)*tan(d*x+c)-C*(-16/35-1/7*sec(d*x+c)^6-6/35*sec(d*x+c)^4-8/35*sec(d*x+c)^2)*tan(d*x+c))","A"
2,1,138,90,1.442000," ","int(sec(d*x+c)^5*(A+C*sec(d*x+c)^2),x)","\frac{A \left(\sec^{3}\left(d x +c \right)\right) \tan \left(d x +c \right)}{4 d}+\frac{3 A \sec \left(d x +c \right) \tan \left(d x +c \right)}{8 d}+\frac{3 A \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}+\frac{C \left(\sec^{5}\left(d x +c \right)\right) \tan \left(d x +c \right)}{6 d}+\frac{5 C \tan \left(d x +c \right) \left(\sec^{3}\left(d x +c \right)\right)}{24 d}+\frac{5 C \tan \left(d x +c \right) \sec \left(d x +c \right)}{16 d}+\frac{5 C \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{16 d}"," ",0,"1/4*A*sec(d*x+c)^3*tan(d*x+c)/d+3/8*A*sec(d*x+c)*tan(d*x+c)/d+3/8/d*A*ln(sec(d*x+c)+tan(d*x+c))+1/6*C*sec(d*x+c)^5*tan(d*x+c)/d+5/24/d*C*tan(d*x+c)*sec(d*x+c)^3+5/16/d*C*tan(d*x+c)*sec(d*x+c)+5/16/d*C*ln(sec(d*x+c)+tan(d*x+c))","A"
3,1,58,59,1.291000," ","int(sec(d*x+c)^4*(A+C*sec(d*x+c)^2),x)","\frac{-A \left(-\frac{2}{3}-\frac{\left(\sec^{2}\left(d x +c \right)\right)}{3}\right) \tan \left(d x +c \right)-C \left(-\frac{8}{15}-\frac{\left(\sec^{4}\left(d x +c \right)\right)}{5}-\frac{4 \left(\sec^{2}\left(d x +c \right)\right)}{15}\right) \tan \left(d x +c \right)}{d}"," ",0,"1/d*(-A*(-2/3-1/3*sec(d*x+c)^2)*tan(d*x+c)-C*(-8/15-1/5*sec(d*x+c)^4-4/15*sec(d*x+c)^2)*tan(d*x+c))","A"
4,1,98,64,1.102000," ","int(sec(d*x+c)^3*(A+C*sec(d*x+c)^2),x)","\frac{A \sec \left(d x +c \right) \tan \left(d x +c \right)}{2 d}+\frac{A \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}+\frac{C \tan \left(d x +c \right) \left(\sec^{3}\left(d x +c \right)\right)}{4 d}+\frac{3 C \tan \left(d x +c \right) \sec \left(d x +c \right)}{8 d}+\frac{3 C \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}"," ",0,"1/2*A*sec(d*x+c)*tan(d*x+c)/d+1/2/d*A*ln(sec(d*x+c)+tan(d*x+c))+1/4/d*C*tan(d*x+c)*sec(d*x+c)^3+3/8/d*C*tan(d*x+c)*sec(d*x+c)+3/8/d*C*ln(sec(d*x+c)+tan(d*x+c))","A"
5,1,35,39,1.342000," ","int(sec(d*x+c)^2*(A+C*sec(d*x+c)^2),x)","\frac{A \tan \left(d x +c \right)-C \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*(A*tan(d*x+c)-C*(-2/3-1/3*sec(d*x+c)^2)*tan(d*x+c))","A"
6,1,59,36,0.895000," ","int(sec(d*x+c)*(A+C*sec(d*x+c)^2),x)","\frac{A \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{C \tan \left(d x +c \right) \sec \left(d x +c \right)}{2 d}+\frac{C \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}"," ",0,"1/d*A*ln(sec(d*x+c)+tan(d*x+c))+1/2/d*C*tan(d*x+c)*sec(d*x+c)+1/2/d*C*ln(sec(d*x+c)+tan(d*x+c))","A"
7,1,16,15,0.979000," ","int(A+C*sec(d*x+c)^2,x)","A x +\frac{C \tan \left(d x +c \right)}{d}"," ",0,"A*x+C*tan(d*x+c)/d","A"
8,1,32,24,0.936000," ","int(cos(d*x+c)*(A+C*sec(d*x+c)^2),x)","\frac{A \sin \left(d x +c \right)}{d}+\frac{C \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}"," ",0,"A*sin(d*x+c)/d+1/d*C*ln(sec(d*x+c)+tan(d*x+c))","A"
9,1,37,27,1.075000," ","int(cos(d*x+c)^2*(A+C*sec(d*x+c)^2),x)","\frac{A \left(\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{2}+\frac{d x}{2}+\frac{c}{2}\right)+C \left(d x +c \right)}{d}"," ",0,"1/d*(A*(1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c)+C*(d*x+c))","A"
10,1,33,28,1.360000," ","int(cos(d*x+c)^3*(A+C*sec(d*x+c)^2),x)","\frac{\frac{A \left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3}+C \sin \left(d x +c \right)}{d}"," ",0,"1/d*(1/3*A*(2+cos(d*x+c)^2)*sin(d*x+c)+C*sin(d*x+c))","A"
11,1,65,55,1.549000," ","int(cos(d*x+c)^4*(A+C*sec(d*x+c)^2),x)","\frac{A \left(\frac{\left(\cos^{3}\left(d x +c \right)+\frac{3 \cos \left(d x +c \right)}{2}\right) \sin \left(d x +c \right)}{4}+\frac{3 d x}{8}+\frac{3 c}{8}\right)+C \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*(1/4*(cos(d*x+c)^3+3/2*cos(d*x+c))*sin(d*x+c)+3/8*d*x+3/8*c)+C*(1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c))","A"
12,1,54,46,1.497000," ","int(cos(d*x+c)^5*(A+C*sec(d*x+c)^2),x)","\frac{\frac{A \left(\frac{8}{3}+\cos^{4}\left(d x +c \right)+\frac{4 \left(\cos^{2}\left(d x +c \right)\right)}{3}\right) \sin \left(d x +c \right)}{5}+\frac{C \left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3}}{d}"," ",0,"1/d*(1/5*A*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c)+1/3*C*(2+cos(d*x+c)^2)*sin(d*x+c))","A"
13,1,86,81,1.947000," ","int(cos(d*x+c)^6*(A+C*sec(d*x+c)^2),x)","\frac{A \left(\frac{\left(\cos^{5}\left(d x +c \right)+\frac{5 \left(\cos^{3}\left(d x +c \right)\right)}{4}+\frac{15 \cos \left(d x +c \right)}{8}\right) \sin \left(d x +c \right)}{6}+\frac{5 d x}{16}+\frac{5 c}{16}\right)+C \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*(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)+C*(1/4*(cos(d*x+c)^3+3/2*cos(d*x+c))*sin(d*x+c)+3/8*d*x+3/8*c))","A"
14,1,512,26,2.066000," ","int(sec(d*x+c)^m*(-C*m/(1+m)+C*sec(d*x+c)^2),x)","-\frac{i C \left(\left({\mathrm e}^{2 i \left(d x +c \right)}+1\right)^{-m} \left({\mathrm e}^{i \left(\Re \left(d x \right)+\Re \left(c \right)\right)}\right)^{m} 2^{m} {\mathrm e}^{-m \Im \left(d x \right)-m \Im \left(c \right)} {\mathrm e}^{-\frac{i \pi  \mathrm{csgn}\left(\frac{i {\mathrm e}^{i \left(d x +c \right)}}{{\mathrm e}^{2 i \left(d x +c \right)}+1}\right)^{3} m}{2}} {\mathrm e}^{\frac{i \pi  \mathrm{csgn}\left(\frac{i {\mathrm e}^{i \left(d x +c \right)}}{{\mathrm e}^{2 i \left(d x +c \right)}+1}\right)^{2} \mathrm{csgn}\left(i {\mathrm e}^{i \left(d x +c \right)}\right) m}{2}} {\mathrm e}^{\frac{i \pi  \mathrm{csgn}\left(\frac{i {\mathrm e}^{i \left(d x +c \right)}}{{\mathrm e}^{2 i \left(d x +c \right)}+1}\right)^{2} \mathrm{csgn}\left(\frac{i}{{\mathrm e}^{2 i \left(d x +c \right)}+1}\right) m}{2}} {\mathrm e}^{-\frac{i \pi  \,\mathrm{csgn}\left(\frac{i {\mathrm e}^{i \left(d x +c \right)}}{{\mathrm e}^{2 i \left(d x +c \right)}+1}\right) \mathrm{csgn}\left(i {\mathrm e}^{i \left(d x +c \right)}\right) \mathrm{csgn}\left(\frac{i}{{\mathrm e}^{2 i \left(d x +c \right)}+1}\right) m}{2}} {\mathrm e}^{2 i d x} {\mathrm e}^{2 i c}-\left({\mathrm e}^{2 i \left(d x +c \right)}+1\right)^{-m} \left({\mathrm e}^{i \left(\Re \left(d x \right)+\Re \left(c \right)\right)}\right)^{m} 2^{m} {\mathrm e}^{-\frac{m \left(i \pi  \mathrm{csgn}\left(\frac{i {\mathrm e}^{i \left(d x +c \right)}}{{\mathrm e}^{2 i \left(d x +c \right)}+1}\right)^{3}-i \pi  \mathrm{csgn}\left(\frac{i {\mathrm e}^{i \left(d x +c \right)}}{{\mathrm e}^{2 i \left(d x +c \right)}+1}\right)^{2} \mathrm{csgn}\left(i {\mathrm e}^{i \left(d x +c \right)}\right)-i \pi  \mathrm{csgn}\left(\frac{i {\mathrm e}^{i \left(d x +c \right)}}{{\mathrm e}^{2 i \left(d x +c \right)}+1}\right)^{2} \mathrm{csgn}\left(\frac{i}{{\mathrm e}^{2 i \left(d x +c \right)}+1}\right)+i \pi  \,\mathrm{csgn}\left(\frac{i {\mathrm e}^{i \left(d x +c \right)}}{{\mathrm e}^{2 i \left(d x +c \right)}+1}\right) \mathrm{csgn}\left(i {\mathrm e}^{i \left(d x +c \right)}\right) \mathrm{csgn}\left(\frac{i}{{\mathrm e}^{2 i \left(d x +c \right)}+1}\right)+2 \Im \left(d x \right)+2 \Im \left(c \right)\right)}{2}}\right)}{\left(1+m \right) d \left({\mathrm e}^{2 i \left(d x +c \right)}+1\right)}"," ",0,"-I*C/(1+m)/d/(exp(2*I*(d*x+c))+1)*(1/((exp(2*I*(d*x+c))+1)^m)*exp(I*(Re(d*x)+Re(c)))^m*2^m*exp(-m*Im(d*x)-m*Im(c))*exp(-1/2*I*Pi*csgn(I*exp(I*(d*x+c))/(exp(2*I*(d*x+c))+1))^3*m)*exp(1/2*I*Pi*csgn(I*exp(I*(d*x+c))/(exp(2*I*(d*x+c))+1))^2*csgn(I*exp(I*(d*x+c)))*m)*exp(1/2*I*Pi*csgn(I*exp(I*(d*x+c))/(exp(2*I*(d*x+c))+1))^2*csgn(I/(exp(2*I*(d*x+c))+1))*m)*exp(-1/2*I*Pi*csgn(I*exp(I*(d*x+c))/(exp(2*I*(d*x+c))+1))*csgn(I*exp(I*(d*x+c)))*csgn(I/(exp(2*I*(d*x+c))+1))*m)*exp(2*I*d*x)*exp(2*I*c)-1/((exp(2*I*(d*x+c))+1)^m)*exp(I*(Re(d*x)+Re(c)))^m*2^m*exp(-1/2*m*(I*Pi*csgn(I*exp(I*(d*x+c))/(exp(2*I*(d*x+c))+1))^3-I*Pi*csgn(I*exp(I*(d*x+c))/(exp(2*I*(d*x+c))+1))^2*csgn(I*exp(I*(d*x+c)))-I*Pi*csgn(I*exp(I*(d*x+c))/(exp(2*I*(d*x+c))+1))^2*csgn(I/(exp(2*I*(d*x+c))+1))+I*Pi*csgn(I*exp(I*(d*x+c))/(exp(2*I*(d*x+c))+1))*csgn(I*exp(I*(d*x+c)))*csgn(I/(exp(2*I*(d*x+c))+1))+2*Im(d*x)+2*Im(c))))","C"
15,1,510,25,1.415000," ","int(sec(d*x+c)^m*(A-A*(1+m)*sec(d*x+c)^2/m),x)","\frac{i A \left(\left({\mathrm e}^{2 i \left(d x +c \right)}+1\right)^{-m} \left({\mathrm e}^{i \left(\Re \left(d x \right)+\Re \left(c \right)\right)}\right)^{m} 2^{m} {\mathrm e}^{-m \Im \left(d x \right)-m \Im \left(c \right)} {\mathrm e}^{-\frac{i \pi  \mathrm{csgn}\left(\frac{i {\mathrm e}^{i \left(d x +c \right)}}{{\mathrm e}^{2 i \left(d x +c \right)}+1}\right)^{3} m}{2}} {\mathrm e}^{\frac{i \pi  \mathrm{csgn}\left(\frac{i {\mathrm e}^{i \left(d x +c \right)}}{{\mathrm e}^{2 i \left(d x +c \right)}+1}\right)^{2} \mathrm{csgn}\left(i {\mathrm e}^{i \left(d x +c \right)}\right) m}{2}} {\mathrm e}^{\frac{i \pi  \mathrm{csgn}\left(\frac{i {\mathrm e}^{i \left(d x +c \right)}}{{\mathrm e}^{2 i \left(d x +c \right)}+1}\right)^{2} \mathrm{csgn}\left(\frac{i}{{\mathrm e}^{2 i \left(d x +c \right)}+1}\right) m}{2}} {\mathrm e}^{-\frac{i \pi  \,\mathrm{csgn}\left(\frac{i {\mathrm e}^{i \left(d x +c \right)}}{{\mathrm e}^{2 i \left(d x +c \right)}+1}\right) \mathrm{csgn}\left(i {\mathrm e}^{i \left(d x +c \right)}\right) \mathrm{csgn}\left(\frac{i}{{\mathrm e}^{2 i \left(d x +c \right)}+1}\right) m}{2}} {\mathrm e}^{2 i d x} {\mathrm e}^{2 i c}-\left({\mathrm e}^{2 i \left(d x +c \right)}+1\right)^{-m} \left({\mathrm e}^{i \left(\Re \left(d x \right)+\Re \left(c \right)\right)}\right)^{m} 2^{m} {\mathrm e}^{-\frac{m \left(i \pi  \mathrm{csgn}\left(\frac{i {\mathrm e}^{i \left(d x +c \right)}}{{\mathrm e}^{2 i \left(d x +c \right)}+1}\right)^{3}-i \pi  \mathrm{csgn}\left(\frac{i {\mathrm e}^{i \left(d x +c \right)}}{{\mathrm e}^{2 i \left(d x +c \right)}+1}\right)^{2} \mathrm{csgn}\left(i {\mathrm e}^{i \left(d x +c \right)}\right)-i \pi  \mathrm{csgn}\left(\frac{i {\mathrm e}^{i \left(d x +c \right)}}{{\mathrm e}^{2 i \left(d x +c \right)}+1}\right)^{2} \mathrm{csgn}\left(\frac{i}{{\mathrm e}^{2 i \left(d x +c \right)}+1}\right)+i \pi  \,\mathrm{csgn}\left(\frac{i {\mathrm e}^{i \left(d x +c \right)}}{{\mathrm e}^{2 i \left(d x +c \right)}+1}\right) \mathrm{csgn}\left(i {\mathrm e}^{i \left(d x +c \right)}\right) \mathrm{csgn}\left(\frac{i}{{\mathrm e}^{2 i \left(d x +c \right)}+1}\right)+2 \Im \left(d x \right)+2 \Im \left(c \right)\right)}{2}}\right)}{d m \left({\mathrm e}^{2 i \left(d x +c \right)}+1\right)}"," ",0,"I*A/d/m/(exp(2*I*(d*x+c))+1)*(1/((exp(2*I*(d*x+c))+1)^m)*exp(I*(Re(d*x)+Re(c)))^m*2^m*exp(-m*Im(d*x)-m*Im(c))*exp(-1/2*I*Pi*csgn(I*exp(I*(d*x+c))/(exp(2*I*(d*x+c))+1))^3*m)*exp(1/2*I*Pi*csgn(I*exp(I*(d*x+c))/(exp(2*I*(d*x+c))+1))^2*csgn(I*exp(I*(d*x+c)))*m)*exp(1/2*I*Pi*csgn(I*exp(I*(d*x+c))/(exp(2*I*(d*x+c))+1))^2*csgn(I/(exp(2*I*(d*x+c))+1))*m)*exp(-1/2*I*Pi*csgn(I*exp(I*(d*x+c))/(exp(2*I*(d*x+c))+1))*csgn(I*exp(I*(d*x+c)))*csgn(I/(exp(2*I*(d*x+c))+1))*m)*exp(2*I*d*x)*exp(2*I*c)-1/((exp(2*I*(d*x+c))+1)^m)*exp(I*(Re(d*x)+Re(c)))^m*2^m*exp(-1/2*m*(I*Pi*csgn(I*exp(I*(d*x+c))/(exp(2*I*(d*x+c))+1))^3-I*Pi*csgn(I*exp(I*(d*x+c))/(exp(2*I*(d*x+c))+1))^2*csgn(I*exp(I*(d*x+c)))-I*Pi*csgn(I*exp(I*(d*x+c))/(exp(2*I*(d*x+c))+1))^2*csgn(I/(exp(2*I*(d*x+c))+1))+I*Pi*csgn(I*exp(I*(d*x+c))/(exp(2*I*(d*x+c))+1))*csgn(I*exp(I*(d*x+c)))*csgn(I/(exp(2*I*(d*x+c))+1))+2*Im(d*x)+2*Im(c))))","C"
16,1,251,122,1.450000," ","int((b*sec(d*x+c))^(5/2)*(A+C*sec(d*x+c)^2),x)","-\frac{2 \left(1+\cos \left(d x +c \right)\right)^{2} \left(-1+\cos \left(d x +c \right)\right) \left(7 i A \sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \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)}{\sin \left(d x +c \right)}, i\right)+5 i C \sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \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)}{\sin \left(d x +c \right)}, i\right)-7 A \left(\cos^{3}\left(d x +c \right)\right)-5 C \left(\cos^{3}\left(d x +c \right)\right)+7 A \left(\cos^{2}\left(d x +c \right)\right)+5 C \left(\cos^{2}\left(d x +c \right)\right)-3 C \cos \left(d x +c \right)+3 C \right) \left(\frac{b}{\cos \left(d x +c \right)}\right)^{\frac{5}{2}}}{21 d \sin \left(d x +c \right)^{3} \cos \left(d x +c \right)}"," ",0,"-2/21/d*(1+cos(d*x+c))^2*(-1+cos(d*x+c))*(7*I*A*sin(d*x+c)*cos(d*x+c)^3*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)+5*I*C*sin(d*x+c)*cos(d*x+c)^3*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)-7*A*cos(d*x+c)^3-5*C*cos(d*x+c)^3+7*A*cos(d*x+c)^2+5*C*cos(d*x+c)^2-3*C*cos(d*x+c)+3*C)*(b/cos(d*x+c))^(5/2)/sin(d*x+c)^3/cos(d*x+c)","C"
17,1,670,122,1.417000," ","int((b*sec(d*x+c))^(3/2)*(A+C*sec(d*x+c)^2),x)","-\frac{2 \left(1+\cos \left(d x +c \right)\right)^{2} \left(-1+\cos \left(d x +c \right)\right)^{2} \left(5 i A \sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \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)}{\sin \left(d x +c \right)}, i\right)-5 i A \sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \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)}{\sin \left(d x +c \right)}, i\right)+3 i C \sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \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)}{\sin \left(d x +c \right)}, i\right)-3 i C \sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \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)}{\sin \left(d x +c \right)}, i\right)+5 i A \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \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)}{\sin \left(d x +c \right)}, i\right) \sin \left(d x +c \right)-5 i A \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \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)}{\sin \left(d x +c \right)}, i\right)+3 i C \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \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)}{\sin \left(d x +c \right)}, i\right)-3 i C \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \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)}{\sin \left(d x +c \right)}, i\right)+5 A \left(\cos^{3}\left(d x +c \right)\right)+3 C \left(\cos^{3}\left(d x +c \right)\right)-5 A \left(\cos^{2}\left(d x +c \right)\right)-2 C \left(\cos^{2}\left(d x +c \right)\right)-C \right) \left(\frac{b}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}}}{5 d \sin \left(d x +c \right)^{5} \cos \left(d x +c \right)}"," ",0,"-2/5/d*(1+cos(d*x+c))^2*(-1+cos(d*x+c))^2*(5*I*A*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*sin(d*x+c)*cos(d*x+c)^3-5*I*A*sin(d*x+c)*cos(d*x+c)^3*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)+3*I*C*sin(d*x+c)*cos(d*x+c)^3*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)-3*I*C*sin(d*x+c)*cos(d*x+c)^3*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)+5*I*A*cos(d*x+c)^2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*sin(d*x+c)-5*I*A*sin(d*x+c)*cos(d*x+c)^2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)+3*I*C*sin(d*x+c)*cos(d*x+c)^2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)-3*I*C*sin(d*x+c)*cos(d*x+c)^2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)+5*A*cos(d*x+c)^3+3*C*cos(d*x+c)^3-5*A*cos(d*x+c)^2-2*C*cos(d*x+c)^2-C)*(b/cos(d*x+c))^(3/2)/sin(d*x+c)^5/cos(d*x+c)","C"
18,1,201,88,1.721000," ","int((b*sec(d*x+c))^(1/2)*(A+C*sec(d*x+c)^2),x)","-\frac{2 \sqrt{\frac{b}{\cos \left(d x +c \right)}}\, \left(-1+\cos \left(d x +c \right)\right) \left(3 i A \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \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)}{\sin \left(d x +c \right)}, i\right)+i C \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \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)}{\sin \left(d x +c \right)}, i\right)-C \cos \left(d x +c \right)+C \right) \left(1+\cos \left(d x +c \right)\right)^{2}}{3 d \sin \left(d x +c \right)^{3} \cos \left(d x +c \right)}"," ",0,"-2/3/d*(b/cos(d*x+c))^(1/2)*(-1+cos(d*x+c))*(3*I*A*sin(d*x+c)*cos(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)+I*C*sin(d*x+c)*cos(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)-C*cos(d*x+c)+C)*(1+cos(d*x+c))^2/sin(d*x+c)^3/cos(d*x+c)","C"
19,1,588,88,1.805000," ","int((A+C*sec(d*x+c)^2)/(b*sec(d*x+c))^(1/2),x)","-\frac{2 \left(i A \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \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)}{\sin \left(d x +c \right)}, i\right) \sin \left(d x +c \right) \cos \left(d x +c \right)-i A \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \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)}{\sin \left(d x +c \right)}, i\right)-i C \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \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)}{\sin \left(d x +c \right)}, i\right) \sin \left(d x +c \right) \cos \left(d x +c \right)+i C \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \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)}{\sin \left(d x +c \right)}, i\right)+i A \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \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)}{\sin \left(d x +c \right)}, i\right)-i A \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \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)}{\sin \left(d x +c \right)}, i\right)-i C \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \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)}{\sin \left(d x +c \right)}, i\right)+i C \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \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)}{\sin \left(d x +c \right)}, i\right)+A \left(\cos^{2}\left(d x +c \right)\right)-A \cos \left(d x +c \right)+C \cos \left(d x +c \right)-C \right) \sqrt{\frac{b}{\cos \left(d x +c \right)}}}{d \sin \left(d x +c \right) b}"," ",0,"-2/d*(I*A*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)*sin(d*x+c)*cos(d*x+c)-I*A*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*sin(d*x+c)*cos(d*x+c)-I*C*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)*sin(d*x+c)*cos(d*x+c)+I*C*sin(d*x+c)*cos(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)+I*A*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)-I*A*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)-I*C*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)+I*C*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)+A*cos(d*x+c)^2-A*cos(d*x+c)+C*cos(d*x+c)-C)*(b/cos(d*x+c))^(1/2)/sin(d*x+c)/b","C"
20,1,198,91,1.701000," ","int((A+C*sec(d*x+c)^2)/(b*sec(d*x+c))^(3/2),x)","-\frac{2 \left(1+\cos \left(d x +c \right)\right)^{2} \left(-1+\cos \left(d x +c \right)\right) \left(i A \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \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)}{\sin \left(d x +c \right)}, i\right)+3 i C \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \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)}{\sin \left(d x +c \right)}, i\right)-A \left(\cos^{2}\left(d x +c \right)\right)+A \cos \left(d x +c \right)\right)}{3 d \sin \left(d x +c \right)^{3} \cos \left(d x +c \right)^{2} \left(\frac{b}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}}}"," ",0,"-2/3/d*(1+cos(d*x+c))^2*(-1+cos(d*x+c))*(I*A*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+3*I*C*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)-A*cos(d*x+c)^2+A*cos(d*x+c))/sin(d*x+c)^3/cos(d*x+c)^2/(b/cos(d*x+c))^(3/2)","C"
21,1,614,93,1.433000," ","int((A+C*sec(d*x+c)^2)/(b*sec(d*x+c))^(5/2),x)","\frac{\frac{6 i A \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \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)}{\sin \left(d x +c \right)}, i\right)}{5}-\frac{6 i A \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \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)}{\sin \left(d x +c \right)}, i\right) \sin \left(d x +c \right) \cos \left(d x +c \right)}{5}+2 i C \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \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)}{\sin \left(d x +c \right)}, i\right)-2 i C \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \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)}{\sin \left(d x +c \right)}, i\right) \sin \left(d x +c \right) \cos \left(d x +c \right)+\frac{6 i A \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \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)}{\sin \left(d x +c \right)}, i\right)}{5}-\frac{6 i A \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \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)}{\sin \left(d x +c \right)}, i\right)}{5}+2 i C \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \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)}{\sin \left(d x +c \right)}, i\right)-2 i C \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \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)}{\sin \left(d x +c \right)}, i\right)-\frac{2 A \left(\cos^{4}\left(d x +c \right)\right)}{5}-\frac{4 A \left(\cos^{2}\left(d x +c \right)\right)}{5}-2 C \left(\cos^{2}\left(d x +c \right)\right)+\frac{6 A \cos \left(d x +c \right)}{5}+2 C \cos \left(d x +c \right)}{d \sin \left(d x +c \right) \cos \left(d x +c \right)^{3} \left(\frac{b}{\cos \left(d x +c \right)}\right)^{\frac{5}{2}}}"," ",0,"2/5/d*(3*I*A*sin(d*x+c)*cos(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)-3*I*A*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)*sin(d*x+c)*cos(d*x+c)+5*I*C*sin(d*x+c)*cos(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)-5*I*C*sin(d*x+c)*cos(d*x+c)*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+3*I*A*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)-3*I*A*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)+5*I*C*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)-5*I*C*sin(d*x+c)*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)-A*cos(d*x+c)^4-2*A*cos(d*x+c)^2-5*C*cos(d*x+c)^2+3*A*cos(d*x+c)+5*C*cos(d*x+c))/sin(d*x+c)/cos(d*x+c)^3/(b/cos(d*x+c))^(5/2)","C"
22,1,241,124,1.759000," ","int((A+C*sec(d*x+c)^2)/(b*sec(d*x+c))^(7/2),x)","-\frac{2 \left(1+\cos \left(d x +c \right)\right)^{2} \left(-1+\cos \left(d x +c \right)\right) \left(5 i A \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \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)}{\sin \left(d x +c \right)}, i\right)+7 i C \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \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)}{\sin \left(d x +c \right)}, i\right)-3 A \left(\cos^{4}\left(d x +c \right)\right)+3 A \left(\cos^{3}\left(d x +c \right)\right)-5 A \left(\cos^{2}\left(d x +c \right)\right)-7 C \left(\cos^{2}\left(d x +c \right)\right)+5 A \cos \left(d x +c \right)+7 C \cos \left(d x +c \right)\right)}{21 d \cos \left(d x +c \right)^{4} \left(\frac{b}{\cos \left(d x +c \right)}\right)^{\frac{7}{2}} \sin \left(d x +c \right)^{3}}"," ",0,"-2/21/d*(1+cos(d*x+c))^2*(-1+cos(d*x+c))*(5*I*A*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*sin(d*x+c)+7*I*C*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*sin(d*x+c)-3*A*cos(d*x+c)^4+3*A*cos(d*x+c)^3-5*A*cos(d*x+c)^2-7*C*cos(d*x+c)^2+5*A*cos(d*x+c)+7*C*cos(d*x+c))/cos(d*x+c)^4/(b/cos(d*x+c))^(7/2)/sin(d*x+c)^3","C"
23,1,636,124,1.566000," ","int((A+C*sec(d*x+c)^2)/(b*sec(d*x+c))^(9/2),x)","-\frac{2 \left(5 A \left(\cos^{6}\left(d x +c \right)\right)-21 i A \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \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)}{\sin \left(d x +c \right)}, i\right)+21 i A \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \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)}{\sin \left(d x +c \right)}, i\right) \sin \left(d x +c \right) \cos \left(d x +c \right)-27 i C \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \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)}{\sin \left(d x +c \right)}, i\right)+27 i C \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \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)}{\sin \left(d x +c \right)}, i\right) \sin \left(d x +c \right) \cos \left(d x +c \right)-21 i A \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \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)}{\sin \left(d x +c \right)}, i\right)+21 i A \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \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)}{\sin \left(d x +c \right)}, i\right)-27 i C \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \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)}{\sin \left(d x +c \right)}, i\right)+27 i C \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \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)}{\sin \left(d x +c \right)}, i\right)+2 A \left(\cos^{4}\left(d x +c \right)\right)+9 C \left(\cos^{4}\left(d x +c \right)\right)+14 A \left(\cos^{2}\left(d x +c \right)\right)+18 C \left(\cos^{2}\left(d x +c \right)\right)-21 A \cos \left(d x +c \right)-27 C \cos \left(d x +c \right)\right)}{45 d \cos \left(d x +c \right)^{5} \left(\frac{b}{\cos \left(d x +c \right)}\right)^{\frac{9}{2}} \sin \left(d x +c \right)}"," ",0,"-2/45/d*(5*A*cos(d*x+c)^6-21*I*A*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)+21*I*A*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)*sin(d*x+c)*cos(d*x+c)-27*I*C*sin(d*x+c)*cos(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)+27*I*C*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)-21*I*A*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)+21*I*A*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)-27*I*C*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)+27*I*C*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)+2*A*cos(d*x+c)^4+9*C*cos(d*x+c)^4+14*A*cos(d*x+c)^2+18*C*cos(d*x+c)^2-21*A*cos(d*x+c)-27*C*cos(d*x+c))/cos(d*x+c)^5/(b/cos(d*x+c))^(9/2)/sin(d*x+c)","C"
24,1,41,19,2.576000," ","int((3+3*sec(d*x+c)^2)/sec(d*x+c)^(1/2),x)","\frac{12 \sin \left(\frac{d x}{2}+\frac{c}{2}\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,"12*sin(1/2*d*x+1/2*c)*cos(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
25,1,506,21,1.533000," ","int(sec(f*x+e)^m*(m-(1+m)*sec(f*x+e)^2),x)","\frac{i \left(\left({\mathrm e}^{2 i \left(f x +e \right)}+1\right)^{-m} \left({\mathrm e}^{i \left(\Re \left(f x \right)+\Re \left(e \right)\right)}\right)^{m} 2^{m} {\mathrm e}^{-m \Im \left(f x \right)-m \Im \left(e \right)} {\mathrm e}^{-\frac{i \pi  \mathrm{csgn}\left(\frac{i {\mathrm e}^{i \left(f x +e \right)}}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right)^{3} m}{2}} {\mathrm e}^{\frac{i \pi  \mathrm{csgn}\left(\frac{i {\mathrm e}^{i \left(f x +e \right)}}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right)^{2} \mathrm{csgn}\left(i {\mathrm e}^{i \left(f x +e \right)}\right) m}{2}} {\mathrm e}^{\frac{i \pi  \mathrm{csgn}\left(\frac{i {\mathrm e}^{i \left(f x +e \right)}}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right)^{2} \mathrm{csgn}\left(\frac{i}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right) m}{2}} {\mathrm e}^{-\frac{i \pi  \,\mathrm{csgn}\left(\frac{i {\mathrm e}^{i \left(f x +e \right)}}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right) \mathrm{csgn}\left(i {\mathrm e}^{i \left(f x +e \right)}\right) \mathrm{csgn}\left(\frac{i}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right) m}{2}} {\mathrm e}^{2 i f x} {\mathrm e}^{2 i e}-\left({\mathrm e}^{2 i \left(f x +e \right)}+1\right)^{-m} \left({\mathrm e}^{i \left(\Re \left(f x \right)+\Re \left(e \right)\right)}\right)^{m} 2^{m} {\mathrm e}^{-\frac{m \left(i \pi  \mathrm{csgn}\left(\frac{i {\mathrm e}^{i \left(f x +e \right)}}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right)^{3}-i \pi  \mathrm{csgn}\left(\frac{i {\mathrm e}^{i \left(f x +e \right)}}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right)^{2} \mathrm{csgn}\left(i {\mathrm e}^{i \left(f x +e \right)}\right)-i \pi  \mathrm{csgn}\left(\frac{i {\mathrm e}^{i \left(f x +e \right)}}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right)^{2} \mathrm{csgn}\left(\frac{i}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right)+i \pi  \,\mathrm{csgn}\left(\frac{i {\mathrm e}^{i \left(f x +e \right)}}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right) \mathrm{csgn}\left(i {\mathrm e}^{i \left(f x +e \right)}\right) \mathrm{csgn}\left(\frac{i}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right)+2 \Im \left(e \right)+2 \Im \left(f x \right)\right)}{2}}\right)}{f \left({\mathrm e}^{2 i \left(f x +e \right)}+1\right)}"," ",0,"I/f/(exp(2*I*(f*x+e))+1)*(1/((exp(2*I*(f*x+e))+1)^m)*exp(I*(Re(f*x)+Re(e)))^m*2^m*exp(-m*Im(f*x)-m*Im(e))*exp(-1/2*I*Pi*csgn(I*exp(I*(f*x+e))/(exp(2*I*(f*x+e))+1))^3*m)*exp(1/2*I*Pi*csgn(I*exp(I*(f*x+e))/(exp(2*I*(f*x+e))+1))^2*csgn(I*exp(I*(f*x+e)))*m)*exp(1/2*I*Pi*csgn(I*exp(I*(f*x+e))/(exp(2*I*(f*x+e))+1))^2*csgn(I/(exp(2*I*(f*x+e))+1))*m)*exp(-1/2*I*Pi*csgn(I*exp(I*(f*x+e))/(exp(2*I*(f*x+e))+1))*csgn(I*exp(I*(f*x+e)))*csgn(I/(exp(2*I*(f*x+e))+1))*m)*exp(2*I*f*x)*exp(2*I*e)-1/((exp(2*I*(f*x+e))+1)^m)*exp(I*(Re(f*x)+Re(e)))^m*2^m*exp(-1/2*m*(I*Pi*csgn(I*exp(I*(f*x+e))/(exp(2*I*(f*x+e))+1))^3-I*Pi*csgn(I*exp(I*(f*x+e))/(exp(2*I*(f*x+e))+1))^2*csgn(I*exp(I*(f*x+e)))-I*Pi*csgn(I*exp(I*(f*x+e))/(exp(2*I*(f*x+e))+1))^2*csgn(I/(exp(2*I*(f*x+e))+1))+I*Pi*csgn(I*exp(I*(f*x+e))/(exp(2*I*(f*x+e))+1))*csgn(I*exp(I*(f*x+e)))*csgn(I/(exp(2*I*(f*x+e))+1))+2*Im(e)+2*Im(f*x))))","C"
26,1,70,19,1.564000," ","int(sec(f*x+e)^5*(5-6*sec(f*x+e)^2),x)","\frac{-5 \left(-\frac{\left(\sec^{3}\left(f x +e \right)\right)}{4}-\frac{3 \sec \left(f x +e \right)}{8}\right) \tan \left(f x +e \right)+6 \left(-\frac{\left(\sec^{5}\left(f x +e \right)\right)}{6}-\frac{5 \left(\sec^{3}\left(f x +e \right)\right)}{24}-\frac{5 \sec \left(f x +e \right)}{16}\right) \tan \left(f x +e \right)}{f}"," ",0,"1/f*(-5*(-1/4*sec(f*x+e)^3-3/8*sec(f*x+e))*tan(f*x+e)+6*(-1/6*sec(f*x+e)^5-5/24*sec(f*x+e)^3-5/16*sec(f*x+e))*tan(f*x+e))","B"
27,1,56,19,1.174000," ","int(sec(f*x+e)^4*(4-5*sec(f*x+e)^2),x)","\frac{-4 \left(-\frac{2}{3}-\frac{\left(\sec^{2}\left(f x +e \right)\right)}{3}\right) \tan \left(f x +e \right)+5 \left(-\frac{8}{15}-\frac{\left(\sec^{4}\left(f x +e \right)\right)}{5}-\frac{4 \left(\sec^{2}\left(f x +e \right)\right)}{15}\right) \tan \left(f x +e \right)}{f}"," ",0,"1/f*(-4*(-2/3-1/3*sec(f*x+e)^2)*tan(f*x+e)+5*(-8/15-1/5*sec(f*x+e)^4-4/15*sec(f*x+e)^2)*tan(f*x+e))","B"
28,1,47,19,1.289000," ","int(sec(f*x+e)^3*(3-4*sec(f*x+e)^2),x)","\frac{\frac{3 \sec \left(f x +e \right) \tan \left(f x +e \right)}{2}+4 \left(-\frac{\left(\sec^{3}\left(f x +e \right)\right)}{4}-\frac{3 \sec \left(f x +e \right)}{8}\right) \tan \left(f x +e \right)}{f}"," ",0,"1/f*(3/2*sec(f*x+e)*tan(f*x+e)+4*(-1/4*sec(f*x+e)^3-3/8*sec(f*x+e))*tan(f*x+e))","B"
29,1,34,19,1.083000," ","int(sec(f*x+e)^2*(2-3*sec(f*x+e)^2),x)","\frac{2 \tan \left(f x +e \right)+3 \left(-\frac{2}{3}-\frac{\left(\sec^{2}\left(f x +e \right)\right)}{3}\right) \tan \left(f x +e \right)}{f}"," ",0,"1/f*(2*tan(f*x+e)+3*(-2/3-1/3*sec(f*x+e)^2)*tan(f*x+e))","A"
30,1,18,17,0.941000," ","int(sec(f*x+e)*(1-2*sec(f*x+e)^2),x)","-\frac{\sec \left(f x +e \right) \tan \left(f x +e \right)}{f}"," ",0,"-sec(f*x+e)*tan(f*x+e)/f","A"
31,1,12,11,0.847000," ","int(-sec(f*x+e)^2,x)","-\frac{\tan \left(f x +e \right)}{f}"," ",0,"-tan(f*x+e)/f","A"
32,1,12,11,0.201000," ","int(-cos(f*x+e),x)","-\frac{\sin \left(f x +e \right)}{f}"," ",0,"-sin(f*x+e)/f","A"
33,1,18,17,1.033000," ","int(cos(f*x+e)^2*(-2+sec(f*x+e)^2),x)","-\frac{\cos \left(f x +e \right) \sin \left(f x +e \right)}{f}"," ",0,"-cos(f*x+e)*sin(f*x+e)/f","A"
34,1,32,19,1.724000," ","int(cos(f*x+e)^3*(-3+2*sec(f*x+e)^2),x)","\frac{-\left(2+\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+2 \sin \left(f x +e \right)}{f}"," ",0,"1/f*(-(2+cos(f*x+e)^2)*sin(f*x+e)+2*sin(f*x+e))","A"
35,1,45,19,1.452000," ","int(cos(f*x+e)^4*(-4+3*sec(f*x+e)^2),x)","\frac{-\left(\cos^{3}\left(f x +e \right)+\frac{3 \cos \left(f x +e \right)}{2}\right) \sin \left(f x +e \right)+\frac{3 \sin \left(f x +e \right) \cos \left(f x +e \right)}{2}}{f}"," ",0,"1/f*(-(cos(f*x+e)^3+3/2*cos(f*x+e))*sin(f*x+e)+3/2*sin(f*x+e)*cos(f*x+e))","B"
36,1,52,19,2.008000," ","int(cos(f*x+e)^5*(-5+4*sec(f*x+e)^2),x)","\frac{-\left(\frac{8}{3}+\cos^{4}\left(f x +e \right)+\frac{4 \left(\cos^{2}\left(f x +e \right)\right)}{3}\right) \sin \left(f x +e \right)+\frac{4 \left(2+\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)}{3}}{f}"," ",0,"1/f*(-(8/3+cos(f*x+e)^4+4/3*cos(f*x+e)^2)*sin(f*x+e)+4/3*(2+cos(f*x+e)^2)*sin(f*x+e))","B"
37,1,92,77,1.043000," ","int(sec(d*x+c)^3*(B*sec(d*x+c)+C*sec(d*x+c)^2),x)","\frac{2 B \tan \left(d x +c \right)}{3 d}+\frac{B \tan \left(d x +c \right) \left(\sec^{2}\left(d x +c \right)\right)}{3 d}+\frac{C \tan \left(d x +c \right) \left(\sec^{3}\left(d x +c \right)\right)}{4 d}+\frac{3 C \tan \left(d x +c \right) \sec \left(d x +c \right)}{8 d}+\frac{3 C \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}"," ",0,"2/3*B*tan(d*x+c)/d+1/3/d*B*tan(d*x+c)*sec(d*x+c)^2+1/4/d*C*tan(d*x+c)*sec(d*x+c)^3+3/8/d*C*tan(d*x+c)*sec(d*x+c)+3/8/d*C*ln(sec(d*x+c)+tan(d*x+c))","A"
38,1,72,57,1.221000," ","int(sec(d*x+c)^2*(B*sec(d*x+c)+C*sec(d*x+c)^2),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}+\frac{2 C \tan \left(d x +c \right)}{3 d}+\frac{C \left(\sec^{2}\left(d x +c \right)\right) \tan \left(d x +c \right)}{3 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))+2/3*C*tan(d*x+c)/d+1/3*C*sec(d*x+c)^2*tan(d*x+c)/d","A"
39,1,51,43,1.134000," ","int(sec(d*x+c)*(B*sec(d*x+c)+C*sec(d*x+c)^2),x)","\frac{B \tan \left(d x +c \right)}{d}+\frac{C \tan \left(d x +c \right) \sec \left(d x +c \right)}{2 d}+\frac{C \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}"," ",0,"B*tan(d*x+c)/d+1/2/d*C*tan(d*x+c)*sec(d*x+c)+1/2/d*C*ln(sec(d*x+c)+tan(d*x+c))","A"
40,1,32,24,0.939000," ","int(B*sec(d*x+c)+C*sec(d*x+c)^2,x)","\frac{B \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{C \tan \left(d x +c \right)}{d}"," ",0,"1/d*B*ln(sec(d*x+c)+tan(d*x+c))+C*tan(d*x+c)/d","A"
41,1,30,16,0.808000," ","int(cos(d*x+c)*(B*sec(d*x+c)+C*sec(d*x+c)^2),x)","B x +\frac{B c}{d}+\frac{C \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}"," ",0,"B*x+1/d*B*c+1/d*C*ln(sec(d*x+c)+tan(d*x+c))","A"
42,1,21,15,0.939000," ","int(cos(d*x+c)^2*(B*sec(d*x+c)+C*sec(d*x+c)^2),x)","\frac{B \sin \left(d x +c \right)+C \left(d x +c \right)}{d}"," ",0,"1/d*(B*sin(d*x+c)+C*(d*x+c))","A"
43,1,38,34,1.134000," ","int(cos(d*x+c)^3*(B*sec(d*x+c)+C*sec(d*x+c)^2),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)+C \sin \left(d x +c \right)}{d}"," ",0,"1/d*(B*(1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c)+C*sin(d*x+c))","A"
44,1,49,48,1.422000," ","int(cos(d*x+c)^4*(B*sec(d*x+c)+C*sec(d*x+c)^2),x)","\frac{\frac{B \left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3}+C \left(\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{2}+\frac{d x}{2}+\frac{c}{2}\right)}{d}"," ",0,"1/d*(1/3*B*(2+cos(d*x+c)^2)*sin(d*x+c)+C*(1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c))","A"
45,1,60,68,1.429000," ","int(cos(d*x+c)^5*(B*sec(d*x+c)+C*sec(d*x+c)^2),x)","\frac{B \left(\frac{\left(\cos^{3}\left(d x +c \right)+\frac{3 \cos \left(d x +c \right)}{2}\right) \sin \left(d x +c \right)}{4}+\frac{3 d x}{8}+\frac{3 c}{8}\right)+\frac{C \left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3}}{d}"," ",0,"1/d*(B*(1/4*(cos(d*x+c)^3+3/2*cos(d*x+c))*sin(d*x+c)+3/8*d*x+3/8*c)+1/3*C*(2+cos(d*x+c)^2)*sin(d*x+c))","A"
46,1,70,82,1.898000," ","int(cos(d*x+c)^6*(B*sec(d*x+c)+C*sec(d*x+c)^2),x)","\frac{\frac{B \left(\frac{8}{3}+\cos^{4}\left(d x +c \right)+\frac{4 \left(\cos^{2}\left(d x +c \right)\right)}{3}\right) \sin \left(d x +c \right)}{5}+C \left(\frac{\left(\cos^{3}\left(d x +c \right)+\frac{3 \cos \left(d x +c \right)}{2}\right) \sin \left(d x +c \right)}{4}+\frac{3 d x}{8}+\frac{3 c}{8}\right)}{d}"," ",0,"1/d*(1/5*B*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c)+C*(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"
47,1,526,197,1.367000," ","int((b*sec(d*x+c))^(3/2)*(B*sec(d*x+c)+C*sec(d*x+c)^2),x)","\frac{2 \left(1+\cos \left(d x +c \right)\right)^{2} \left(-1+\cos \left(d x +c \right)\right)^{2} \left(5 i B \sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \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)}{\sin \left(d x +c \right)}, i\right)+9 i C \sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \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)}{\sin \left(d x +c \right)}, i\right)-9 i C \sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \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)}{\sin \left(d x +c \right)}, i\right)+5 i B \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \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)}{\sin \left(d x +c \right)}, i\right)+9 i C \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \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)}{\sin \left(d x +c \right)}, i\right)-9 i C \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \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)}{\sin \left(d x +c \right)}, i\right)-5 B \left(\cos^{3}\left(d x +c \right)\right)-9 C \left(\cos^{3}\left(d x +c \right)\right)+6 C \left(\cos^{2}\left(d x +c \right)\right)+5 B \cos \left(d x +c \right)+3 C \right) \left(\frac{b}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}}}{15 d \sin \left(d x +c \right)^{5} \cos \left(d x +c \right)}"," ",0,"2/15/d*(1+cos(d*x+c))^2*(-1+cos(d*x+c))^2*(5*I*B*sin(d*x+c)*cos(d*x+c)^3*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)+9*I*C*sin(d*x+c)*cos(d*x+c)^3*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)-9*I*C*sin(d*x+c)*cos(d*x+c)^3*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)+5*I*B*sin(d*x+c)*cos(d*x+c)^2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)+9*I*C*sin(d*x+c)*cos(d*x+c)^2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)-9*I*C*sin(d*x+c)*cos(d*x+c)^2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)-5*B*cos(d*x+c)^3-9*C*cos(d*x+c)^3+6*C*cos(d*x+c)^2+5*B*cos(d*x+c)+3*C)*(b/cos(d*x+c))^(3/2)/sin(d*x+c)^5/cos(d*x+c)","C"
48,1,508,171,1.794000," ","int((b*sec(d*x+c))^(1/2)*(B*sec(d*x+c)+C*sec(d*x+c)^2),x)","-\frac{2 \sqrt{\frac{b}{\cos \left(d x +c \right)}}\, \left(-1+\cos \left(d x +c \right)\right)^{2} \left(3 i B \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \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)}{\sin \left(d x +c \right)}, i\right)-3 i B \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \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)}{\sin \left(d x +c \right)}, i\right)-i C \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \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)}{\sin \left(d x +c \right)}, i\right)+3 i B \cos \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \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)}{\sin \left(d x +c \right)}, i\right) \sin \left(d x +c \right)-3 i B \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \EllipticE \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \cos \left(d x +c \right)-i C \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \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)}{\sin \left(d x +c \right)}, i\right)+3 B \left(\cos^{2}\left(d x +c \right)\right)+C \left(\cos^{2}\left(d x +c \right)\right)-3 B \cos \left(d x +c \right)-C \right) \left(1+\cos \left(d x +c \right)\right)^{2}}{3 d \cos \left(d x +c \right) \sin \left(d x +c \right)^{5}}"," ",0,"-2/3/d*(b/cos(d*x+c))^(1/2)*(-1+cos(d*x+c))^2*(3*I*B*cos(d*x+c)^2*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)-3*I*B*cos(d*x+c)^2*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)-I*C*cos(d*x+c)^2*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)+3*I*B*cos(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*sin(d*x+c)-3*I*B*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)*cos(d*x+c)-I*C*sin(d*x+c)*cos(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)+3*B*cos(d*x+c)^2+C*cos(d*x+c)^2-3*B*cos(d*x+c)-C)*(1+cos(d*x+c))^2/cos(d*x+c)/sin(d*x+c)^5","C"
49,1,456,151,1.534000," ","int((B*sec(d*x+c)+C*sec(d*x+c)^2)/(b*sec(d*x+c))^(1/2),x)","\frac{2 \left(1+\cos \left(d x +c \right)\right)^{2} \left(-1+\cos \left(d x +c \right)\right)^{2} \left(i B \cos \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \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)}{\sin \left(d x +c \right)}, i\right) \sin \left(d x +c \right)-i C \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \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)}{\sin \left(d x +c \right)}, i\right)+i C \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \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)}{\sin \left(d x +c \right)}, i\right) \sin \left(d x +c \right) \cos \left(d x +c \right)+i B \sin \left(d x +c \right) \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}-i C \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \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)}{\sin \left(d x +c \right)}, i\right)+i C \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \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)}{\sin \left(d x +c \right)}, i\right)-C \cos \left(d x +c \right)+C \right) \sqrt{\frac{b}{\cos \left(d x +c \right)}}}{d b \sin \left(d x +c \right)^{5}}"," ",0,"2/d*(1+cos(d*x+c))^2*(-1+cos(d*x+c))^2*(I*B*cos(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*sin(d*x+c)-I*C*sin(d*x+c)*cos(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)+I*C*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)*cos(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+I*B*sin(d*x+c)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)-I*C*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)+I*C*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-C*cos(d*x+c)+C)*(b/cos(d*x+c))^(1/2)/b/sin(d*x+c)^5","C"
50,1,450,129,1.669000," ","int((B*sec(d*x+c)+C*sec(d*x+c)^2)/(b*sec(d*x+c))^(3/2),x)","\frac{2 i B \cos \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \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)}{\sin \left(d x +c \right)}, i\right) \sin \left(d x +c \right)-2 i B \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \EllipticE \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \cos \left(d x +c \right)+2 i C \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \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)}{\sin \left(d x +c \right)}, i\right)+2 i B \sin \left(d x +c \right) \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}-2 i B \sin \left(d x +c \right) \EllipticE \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+2 i C \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \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)}{\sin \left(d x +c \right)}, i\right)-2 B \left(\cos^{2}\left(d x +c \right)\right)+2 B \cos \left(d x +c \right)}{d \cos \left(d x +c \right)^{2} \left(\frac{b}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sin \left(d x +c \right)}"," ",0,"2/d*(I*B*cos(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*sin(d*x+c)-I*B*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)*sin(d*x+c)*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)+I*C*sin(d*x+c)*cos(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)+I*B*sin(d*x+c)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)-I*B*sin(d*x+c)*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+I*C*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)-B*cos(d*x+c)^2+B*cos(d*x+c))/cos(d*x+c)^2/(b/cos(d*x+c))^(3/2)/sin(d*x+c)","C"
51,1,470,154,1.347000," ","int((B*sec(d*x+c)+C*sec(d*x+c)^2)/(b*sec(d*x+c))^(5/2),x)","\frac{\frac{2 i B \cos \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \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)}{\sin \left(d x +c \right)}, i\right) \sin \left(d x +c \right)}{3}+2 i C \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \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)}{\sin \left(d x +c \right)}, i\right)-2 i C \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \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)}{\sin \left(d x +c \right)}, i\right) \sin \left(d x +c \right) \cos \left(d x +c \right)+\frac{2 i B \sin \left(d x +c \right) \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}{3}+2 i C \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \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)}{\sin \left(d x +c \right)}, i\right)-2 i C \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \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)}{\sin \left(d x +c \right)}, i\right)-\frac{2 B \left(\cos^{3}\left(d x +c \right)\right)}{3}-2 C \left(\cos^{2}\left(d x +c \right)\right)+\frac{2 B \cos \left(d x +c \right)}{3}+2 C \cos \left(d x +c \right)}{d \sin \left(d x +c \right) \cos \left(d x +c \right)^{3} \left(\frac{b}{\cos \left(d x +c \right)}\right)^{\frac{5}{2}}}"," ",0,"2/3/d*(I*B*cos(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*sin(d*x+c)+3*I*C*sin(d*x+c)*cos(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)-3*I*C*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)*cos(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+I*B*sin(d*x+c)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+3*I*C*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)-3*I*C*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-B*cos(d*x+c)^3-3*C*cos(d*x+c)^2+B*cos(d*x+c)+3*C*cos(d*x+c))/sin(d*x+c)/cos(d*x+c)^3/(b/cos(d*x+c))^(5/2)","C"
52,1,482,179,2.161000," ","int((B*sec(d*x+c)+C*sec(d*x+c)^2)/(b*sec(d*x+c))^(7/2),x)","-\frac{2 \left(9 i B \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \EllipticE \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \cos \left(d x +c \right)-9 i B \cos \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \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)}{\sin \left(d x +c \right)}, i\right) \sin \left(d x +c \right)-5 i C \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \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)}{\sin \left(d x +c \right)}, i\right)+9 i B \sin \left(d x +c \right) \EllipticE \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}-9 i B \sin \left(d x +c \right) \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}-5 i C \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \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)}{\sin \left(d x +c \right)}, i\right)+3 B \left(\cos^{4}\left(d x +c \right)\right)+5 C \left(\cos^{3}\left(d x +c \right)\right)+6 B \left(\cos^{2}\left(d x +c \right)\right)-9 B \cos \left(d x +c \right)-5 C \cos \left(d x +c \right)\right)}{15 d \cos \left(d x +c \right)^{4} \left(\frac{b}{\cos \left(d x +c \right)}\right)^{\frac{7}{2}} \sin \left(d x +c \right)}"," ",0,"-2/15/d*(9*I*B*cos(d*x+c)*sin(d*x+c)*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)-9*I*B*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*cos(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-5*I*C*sin(d*x+c)*cos(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)+9*I*B*sin(d*x+c)*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)-9*I*B*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-5*I*C*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)+3*B*cos(d*x+c)^4+5*C*cos(d*x+c)^3+6*B*cos(d*x+c)^2-9*B*cos(d*x+c)-5*C*cos(d*x+c))/cos(d*x+c)^4/(b/cos(d*x+c))^(7/2)/sin(d*x+c)","C"
53,1,493,204,1.520000," ","int((B*sec(d*x+c)+C*sec(d*x+c)^2)/(b*sec(d*x+c))^(9/2),x)","-\frac{2 \left(-25 i B \cos \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \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)}{\sin \left(d x +c \right)}, i\right) \sin \left(d x +c \right)-63 i C \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \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)}{\sin \left(d x +c \right)}, i\right)+63 i C \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \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)}{\sin \left(d x +c \right)}, i\right) \sin \left(d x +c \right) \cos \left(d x +c \right)+15 B \left(\cos^{5}\left(d x +c \right)\right)-25 i B \sin \left(d x +c \right) \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}-63 i C \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \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)}{\sin \left(d x +c \right)}, i\right)+63 i C \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \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)}{\sin \left(d x +c \right)}, i\right)+21 C \left(\cos^{4}\left(d x +c \right)\right)+10 B \left(\cos^{3}\left(d x +c \right)\right)+42 C \left(\cos^{2}\left(d x +c \right)\right)-25 B \cos \left(d x +c \right)-63 C \cos \left(d x +c \right)\right)}{105 d \cos \left(d x +c \right)^{5} \left(\frac{b}{\cos \left(d x +c \right)}\right)^{\frac{9}{2}} \sin \left(d x +c \right)}"," ",0,"-2/105/d*(-25*I*B*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*cos(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-63*I*C*sin(d*x+c)*cos(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)+63*I*C*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)*cos(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+15*B*cos(d*x+c)^5-25*I*B*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-63*I*C*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)+63*I*C*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+21*C*cos(d*x+c)^4+10*B*cos(d*x+c)^3+42*C*cos(d*x+c)^2-25*B*cos(d*x+c)-63*C*cos(d*x+c))/cos(d*x+c)^5/(b/cos(d*x+c))^(9/2)/sin(d*x+c)","C"
54,1,144,110,1.710000," ","int(sec(d*x+c)^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x)","\frac{2 A \tan \left(d x +c \right)}{3 d}+\frac{A \left(\sec^{2}\left(d x +c \right)\right) \tan \left(d x +c \right)}{3 d}+\frac{B \left(\sec^{3}\left(d x +c \right)\right) \tan \left(d x +c \right)}{4 d}+\frac{3 B \sec \left(d x +c \right) \tan \left(d x +c \right)}{8 d}+\frac{3 B \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}+\frac{8 C \tan \left(d x +c \right)}{15 d}+\frac{C \left(\sec^{4}\left(d x +c \right)\right) \tan \left(d x +c \right)}{5 d}+\frac{4 C \left(\sec^{2}\left(d x +c \right)\right) \tan \left(d x +c \right)}{15 d}"," ",0,"2/3*A*tan(d*x+c)/d+1/3*A*sec(d*x+c)^2*tan(d*x+c)/d+1/4*B*sec(d*x+c)^3*tan(d*x+c)/d+3/8*B*sec(d*x+c)*tan(d*x+c)/d+3/8/d*B*ln(sec(d*x+c)+tan(d*x+c))+8/15*C*tan(d*x+c)/d+1/5*C*sec(d*x+c)^4*tan(d*x+c)/d+4/15*C*sec(d*x+c)^2*tan(d*x+c)/d","A"
55,1,130,89,1.371000," ","int(sec(d*x+c)^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x)","\frac{A \sec \left(d x +c \right) \tan \left(d x +c \right)}{2 d}+\frac{A \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}+\frac{2 B \tan \left(d x +c \right)}{3 d}+\frac{B \tan \left(d x +c \right) \left(\sec^{2}\left(d x +c \right)\right)}{3 d}+\frac{C \tan \left(d x +c \right) \left(\sec^{3}\left(d x +c \right)\right)}{4 d}+\frac{3 C \tan \left(d x +c \right) \sec \left(d x +c \right)}{8 d}+\frac{3 C \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}"," ",0,"1/2*A*sec(d*x+c)*tan(d*x+c)/d+1/2/d*A*ln(sec(d*x+c)+tan(d*x+c))+2/3*B*tan(d*x+c)/d+1/3/d*B*tan(d*x+c)*sec(d*x+c)^2+1/4/d*C*tan(d*x+c)*sec(d*x+c)^3+3/8/d*C*tan(d*x+c)*sec(d*x+c)+3/8/d*C*ln(sec(d*x+c)+tan(d*x+c))","A"
56,1,83,70,1.523000," ","int(sec(d*x+c)^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x)","\frac{A \tan \left(d x +c \right)}{d}+\frac{B \sec \left(d x +c \right) \tan \left(d x +c \right)}{2 d}+\frac{B \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}+\frac{2 C \tan \left(d x +c \right)}{3 d}+\frac{C \left(\sec^{2}\left(d x +c \right)\right) \tan \left(d x +c \right)}{3 d}"," ",0,"A*tan(d*x+c)/d+1/2*B*sec(d*x+c)*tan(d*x+c)/d+1/2/d*B*ln(sec(d*x+c)+tan(d*x+c))+2/3*C*tan(d*x+c)/d+1/3*C*sec(d*x+c)^2*tan(d*x+c)/d","A"
57,1,70,47,1.088000," ","int(sec(d*x+c)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x)","\frac{A \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{B \tan \left(d x +c \right)}{d}+\frac{C \tan \left(d x +c \right) \sec \left(d x +c \right)}{2 d}+\frac{C \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}"," ",0,"1/d*A*ln(sec(d*x+c)+tan(d*x+c))+B*tan(d*x+c)/d+1/2/d*C*tan(d*x+c)*sec(d*x+c)+1/2/d*C*ln(sec(d*x+c)+tan(d*x+c))","A"
58,1,35,27,0.945000," ","int(A+B*sec(d*x+c)+C*sec(d*x+c)^2,x)","A x +\frac{B \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{C \tan \left(d x +c \right)}{d}"," ",0,"A*x+1/d*B*ln(sec(d*x+c)+tan(d*x+c))+C*tan(d*x+c)/d","A"
59,1,41,27,0.777000," ","int(cos(d*x+c)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x)","B x +\frac{A \sin \left(d x +c \right)}{d}+\frac{B c}{d}+\frac{C \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}"," ",0,"B*x+A*sin(d*x+c)/d+1/d*B*c+1/d*C*ln(sec(d*x+c)+tan(d*x+c))","A"
60,1,45,38,0.903000," ","int(cos(d*x+c)^2*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x)","\frac{A \left(\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{2}+\frac{d x}{2}+\frac{c}{2}\right)+B \sin \left(d x +c \right)+C \left(d x +c \right)}{d}"," ",0,"1/d*(A*(1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c)+B*sin(d*x+c)+C*(d*x+c))","A"
61,1,57,50,1.359000," ","int(cos(d*x+c)^3*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x)","\frac{\frac{A \left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3}+B \left(\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{2}+\frac{d x}{2}+\frac{c}{2}\right)+C \sin \left(d x +c \right)}{d}"," ",0,"1/d*(1/3*A*(2+cos(d*x+c)^2)*sin(d*x+c)+B*(1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c)+C*sin(d*x+c))","A"
62,1,84,80,1.729000," ","int(cos(d*x+c)^4*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x)","\frac{A \left(\frac{\left(\cos^{3}\left(d x +c \right)+\frac{3 \cos \left(d x +c \right)}{2}\right) \sin \left(d x +c \right)}{4}+\frac{3 d x}{8}+\frac{3 c}{8}\right)+\frac{B \left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3}+C \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*(1/4*(cos(d*x+c)^3+3/2*cos(d*x+c))*sin(d*x+c)+3/8*d*x+3/8*c)+1/3*B*(2+cos(d*x+c)^2)*sin(d*x+c)+C*(1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c))","A"
63,1,89,88,1.693000," ","int(cos(d*x+c)^5*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x)","\frac{\frac{A \left(\frac{8}{3}+\cos^{4}\left(d x +c \right)+\frac{4 \left(\cos^{2}\left(d x +c \right)\right)}{3}\right) \sin \left(d x +c \right)}{5}+B \left(\frac{\left(\cos^{3}\left(d x +c \right)+\frac{3 \cos \left(d x +c \right)}{2}\right) \sin \left(d x +c \right)}{4}+\frac{3 d x}{8}+\frac{3 c}{8}\right)+\frac{C \left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3}}{d}"," ",0,"1/d*(1/5*A*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c)+B*(1/4*(cos(d*x+c)^3+3/2*cos(d*x+c))*sin(d*x+c)+3/8*d*x+3/8*c)+1/3*C*(2+cos(d*x+c)^2)*sin(d*x+c))","A"
64,1,115,120,2.173000," ","int(cos(d*x+c)^6*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x)","\frac{A \left(\frac{\left(\cos^{5}\left(d x +c \right)+\frac{5 \left(\cos^{3}\left(d x +c \right)\right)}{4}+\frac{15 \cos \left(d x +c \right)}{8}\right) \sin \left(d x +c \right)}{6}+\frac{5 d x}{16}+\frac{5 c}{16}\right)+\frac{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}+C \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*(1/6*(cos(d*x+c)^5+5/4*cos(d*x+c)^3+15/8*cos(d*x+c))*sin(d*x+c)+5/16*d*x+5/16*c)+1/5*B*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c)+C*(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"
65,1,832,206,1.403000," ","int((b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x)","\frac{2 \left(1+\cos \left(d x +c \right)\right)^{2} \left(-1+\cos \left(d x +c \right)\right)^{2} \left(-9 i C \sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \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)}{\sin \left(d x +c \right)}, i\right)+15 i A \sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \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)}{\sin \left(d x +c \right)}, i\right)-9 i C \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \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)}{\sin \left(d x +c \right)}, i\right)+15 i A \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \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)}{\sin \left(d x +c \right)}, i\right)+9 i C \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \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)}{\sin \left(d x +c \right)}, i\right)+5 i B \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \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)}{\sin \left(d x +c \right)}, i\right)-15 i A \sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \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)}{\sin \left(d x +c \right)}, i\right)+9 i C \sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \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)}{\sin \left(d x +c \right)}, i\right)+5 i B \sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \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)}{\sin \left(d x +c \right)}, i\right)-15 i A \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \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)}{\sin \left(d x +c \right)}, i\right)-15 A \left(\cos^{3}\left(d x +c \right)\right)-5 B \left(\cos^{3}\left(d x +c \right)\right)-9 C \left(\cos^{3}\left(d x +c \right)\right)+15 A \left(\cos^{2}\left(d x +c \right)\right)+6 C \left(\cos^{2}\left(d x +c \right)\right)+5 B \cos \left(d x +c \right)+3 C \right) \left(\frac{b}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}}}{15 d \sin \left(d x +c \right)^{5} \cos \left(d x +c \right)}"," ",0,"2/15/d*(1+cos(d*x+c))^2*(-1+cos(d*x+c))^2*(15*I*A*sin(d*x+c)*cos(d*x+c)^2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)-15*I*A*sin(d*x+c)*cos(d*x+c)^3*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)+9*I*C*sin(d*x+c)*cos(d*x+c)^3*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)-9*I*C*sin(d*x+c)*cos(d*x+c)^3*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)+5*I*B*sin(d*x+c)*cos(d*x+c)^2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)+15*I*A*sin(d*x+c)*cos(d*x+c)^3*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)-9*I*C*sin(d*x+c)*cos(d*x+c)^2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)-15*I*A*sin(d*x+c)*cos(d*x+c)^2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)+5*I*B*sin(d*x+c)*cos(d*x+c)^3*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)+9*I*C*sin(d*x+c)*cos(d*x+c)^2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)-15*A*cos(d*x+c)^3-5*B*cos(d*x+c)^3-9*C*cos(d*x+c)^3+15*A*cos(d*x+c)^2+6*C*cos(d*x+c)^2+5*B*cos(d*x+c)+3*C)*(b/cos(d*x+c))^(3/2)/sin(d*x+c)^5/cos(d*x+c)","C"
66,1,647,172,1.797000," ","int((b*sec(d*x+c))^(1/2)*(A+B*sec(d*x+c)+C*sec(d*x+c)^2),x)","\frac{2 \sqrt{\frac{b}{\cos \left(d x +c \right)}}\, \left(-1+\cos \left(d x +c \right)\right)^{2} \left(3 i A \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \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)}{\sin \left(d x +c \right)}, i\right)-3 i B \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \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)}{\sin \left(d x +c \right)}, i\right)+3 i B \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \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)}{\sin \left(d x +c \right)}, i\right)+i C \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \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)}{\sin \left(d x +c \right)}, i\right)+3 i A \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \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)}{\sin \left(d x +c \right)}, i\right)-3 i B \cos \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \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)}{\sin \left(d x +c \right)}, i\right) \sin \left(d x +c \right)+3 i B \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \EllipticE \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \cos \left(d x +c \right)+i C \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \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)}{\sin \left(d x +c \right)}, i\right)-3 B \left(\cos^{2}\left(d x +c \right)\right)-C \left(\cos^{2}\left(d x +c \right)\right)+3 B \cos \left(d x +c \right)+C \right) \left(1+\cos \left(d x +c \right)\right)^{2}}{3 d \cos \left(d x +c \right) \sin \left(d x +c \right)^{5}}"," ",0,"2/3/d*(b/cos(d*x+c))^(1/2)*(-1+cos(d*x+c))^2*(3*I*A*cos(d*x+c)^2*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)-3*I*B*cos(d*x+c)^2*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)+3*I*B*cos(d*x+c)^2*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)+I*C*cos(d*x+c)^2*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)+3*I*A*sin(d*x+c)*cos(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)-3*I*B*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*cos(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+3*I*B*cos(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)*sin(d*x+c)+I*C*sin(d*x+c)*cos(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)-3*B*cos(d*x+c)^2-C*cos(d*x+c)^2+3*B*cos(d*x+c)+C)*(1+cos(d*x+c))^2/cos(d*x+c)/sin(d*x+c)^5","C"
67,1,719,152,1.569000," ","int((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(b*sec(d*x+c))^(1/2),x)","\frac{2 \left(i A \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \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)}{\sin \left(d x +c \right)}, i\right)-i A \EllipticE \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+i B \cos \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \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)}{\sin \left(d x +c \right)}, i\right) \sin \left(d x +c \right)-i C \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \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)}{\sin \left(d x +c \right)}, i\right)+i C \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \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)}{\sin \left(d x +c \right)}, i\right) \sin \left(d x +c \right) \cos \left(d x +c \right)+i A \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \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)}{\sin \left(d x +c \right)}, i\right)-i A \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \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)}{\sin \left(d x +c \right)}, i\right)+i B \sin \left(d x +c \right) \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}-i C \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \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)}{\sin \left(d x +c \right)}, i\right)+i C \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \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)}{\sin \left(d x +c \right)}, i\right)-A \left(\cos^{2}\left(d x +c \right)\right)+A \cos \left(d x +c \right)-C \cos \left(d x +c \right)+C \right) \sqrt{\frac{b}{\cos \left(d x +c \right)}}}{d \sin \left(d x +c \right) b}"," ",0,"2/d*(I*A*sin(d*x+c)*cos(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)-I*A*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)*cos(d*x+c)*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+I*B*cos(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*sin(d*x+c)-I*C*sin(d*x+c)*cos(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)+I*C*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)*cos(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+I*A*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)-I*A*sin(d*x+c)*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+I*B*sin(d*x+c)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)-I*C*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)+I*C*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-A*cos(d*x+c)^2+A*cos(d*x+c)-C*cos(d*x+c)+C)*(b/cos(d*x+c))^(1/2)/sin(d*x+c)/b","C"
68,1,602,155,1.740000," ","int((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(b*sec(d*x+c))^(3/2),x)","\frac{\frac{2 i A \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \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)}{\sin \left(d x +c \right)}, i\right)}{3}+2 i B \cos \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \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)}{\sin \left(d x +c \right)}, i\right) \sin \left(d x +c \right)-2 i B \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \EllipticE \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \cos \left(d x +c \right)+2 i C \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \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)}{\sin \left(d x +c \right)}, i\right)+\frac{2 i A \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \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)}{\sin \left(d x +c \right)}, i\right)}{3}+2 i B \sin \left(d x +c \right) \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}-2 i B \EllipticE \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+2 i C \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \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)}{\sin \left(d x +c \right)}, i\right)-\frac{2 A \left(\cos^{3}\left(d x +c \right)\right)}{3}-2 B \left(\cos^{2}\left(d x +c \right)\right)+\frac{2 A \cos \left(d x +c \right)}{3}+2 B \cos \left(d x +c \right)}{d \cos \left(d x +c \right)^{2} \left(\frac{b}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sin \left(d x +c \right)}"," ",0,"2/3/d*(I*A*sin(d*x+c)*cos(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)+3*I*B*cos(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*sin(d*x+c)-3*I*B*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)*cos(d*x+c)+3*I*C*sin(d*x+c)*cos(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)+I*A*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+3*I*B*sin(d*x+c)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)-3*I*B*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+3*I*C*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)-A*cos(d*x+c)^3-3*B*cos(d*x+c)^2+A*cos(d*x+c)+3*B*cos(d*x+c))/cos(d*x+c)^2/(b/cos(d*x+c))^(3/2)/sin(d*x+c)","C"
69,1,766,182,1.358000," ","int((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(b*sec(d*x+c))^(5/2),x)","\frac{-\frac{6 i A \EllipticE \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}{5}-2 i C \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \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)}{\sin \left(d x +c \right)}, i\right)+\frac{6 i A \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \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)}{\sin \left(d x +c \right)}, i\right)}{5}+\frac{6 i A \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \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)}{\sin \left(d x +c \right)}, i\right)}{5}+\frac{2 i B \sin \left(d x +c \right) \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}{3}+\frac{2 i B \cos \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \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)}{\sin \left(d x +c \right)}, i\right) \sin \left(d x +c \right)}{3}-\frac{6 i A \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \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)}{\sin \left(d x +c \right)}, i\right)}{5}+2 i C \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \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)}{\sin \left(d x +c \right)}, i\right)+2 i C \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \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)}{\sin \left(d x +c \right)}, i\right)-2 i C \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \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)}{\sin \left(d x +c \right)}, i\right) \sin \left(d x +c \right) \cos \left(d x +c \right)-\frac{2 A \left(\cos^{4}\left(d x +c \right)\right)}{5}-\frac{2 B \left(\cos^{3}\left(d x +c \right)\right)}{3}-\frac{4 A \left(\cos^{2}\left(d x +c \right)\right)}{5}-2 C \left(\cos^{2}\left(d x +c \right)\right)+\frac{6 A \cos \left(d x +c \right)}{5}+\frac{2 B \cos \left(d x +c \right)}{3}+2 C \cos \left(d x +c \right)}{d \sin \left(d x +c \right) \cos \left(d x +c \right)^{3} \left(\frac{b}{\cos \left(d x +c \right)}\right)^{\frac{5}{2}}}"," ",0,"2/15/d*(-15*I*C*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+9*I*A*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+5*I*B*sin(d*x+c)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)-9*I*A*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)*sin(d*x+c)+15*I*C*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)+9*I*A*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*cos(d*x+c)+5*I*B*cos(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*sin(d*x+c)-15*I*C*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)*cos(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+15*I*C*sin(d*x+c)*cos(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)-9*I*A*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-3*A*cos(d*x+c)^4-5*B*cos(d*x+c)^3-6*A*cos(d*x+c)^2-15*C*cos(d*x+c)^2+9*A*cos(d*x+c)+5*B*cos(d*x+c)+15*C*cos(d*x+c))/sin(d*x+c)/cos(d*x+c)^3/(b/cos(d*x+c))^(5/2)","C"
70,1,645,213,1.716000," ","int((A+B*sec(d*x+c)+C*sec(d*x+c)^2)/(b*sec(d*x+c))^(7/2),x)","\frac{\frac{6 i B \sin \left(d x +c \right) \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}{5}+\frac{6 i B \cos \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \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)}{\sin \left(d x +c \right)}, i\right) \sin \left(d x +c \right)}{5}-\frac{6 i B \EllipticE \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}{5}+\frac{10 i A \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \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)}{\sin \left(d x +c \right)}, i\right)}{21}+\frac{10 i A \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \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)}{\sin \left(d x +c \right)}, i\right)}{21}-\frac{2 A \left(\cos^{5}\left(d x +c \right)\right)}{7}+\frac{2 i C \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \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)}{\sin \left(d x +c \right)}, i\right)}{3}+\frac{2 i C \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \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)}{\sin \left(d x +c \right)}, i\right)}{3}-\frac{6 i B \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \EllipticE \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \cos \left(d x +c \right)}{5}-\frac{2 B \left(\cos^{4}\left(d x +c \right)\right)}{5}-\frac{4 A \left(\cos^{3}\left(d x +c \right)\right)}{21}-\frac{2 C \left(\cos^{3}\left(d x +c \right)\right)}{3}-\frac{4 B \left(\cos^{2}\left(d x +c \right)\right)}{5}+\frac{10 A \cos \left(d x +c \right)}{21}+\frac{6 B \cos \left(d x +c \right)}{5}+\frac{2 C \cos \left(d x +c \right)}{3}}{d \cos \left(d x +c \right)^{4} \left(\frac{b}{\cos \left(d x +c \right)}\right)^{\frac{7}{2}} \sin \left(d x +c \right)}"," ",0,"2/105/d*(35*I*C*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)+25*I*A*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)+35*I*C*sin(d*x+c)*cos(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)+25*I*A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)-63*I*B*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)*cos(d*x+c)*sin(d*x+c)-15*A*cos(d*x+c)^5+63*I*B*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*cos(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+63*I*B*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-63*I*B*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)*sin(d*x+c)-21*B*cos(d*x+c)^4-10*A*cos(d*x+c)^3-35*C*cos(d*x+c)^3-42*B*cos(d*x+c)^2+25*A*cos(d*x+c)+63*B*cos(d*x+c)+35*C*cos(d*x+c))/cos(d*x+c)^4/(b/cos(d*x+c))^(7/2)/sin(d*x+c)","C"