1,1,19,11,0.028000," ","int(sec(b*x+a),x)","\frac{\ln \left(\sec \left(b x +a \right)+\tan \left(b x +a \right)\right)}{b}"," ",0,"1/b*ln(sec(b*x+a)+tan(b*x+a))","A"
2,1,11,10,0.540000," ","int(sec(b*x+a)^2,x)","\frac{\tan \left(b x +a \right)}{b}"," ",0,"tan(b*x+a)/b","A"
3,1,38,30,0.560000," ","int(sec(b*x+a)^3,x)","\frac{\sec \left(b x +a \right) \tan \left(b x +a \right)}{2 b}+\frac{\ln \left(\sec \left(b x +a \right)+\tan \left(b x +a \right)\right)}{2 b}"," ",0,"1/2*sec(b*x+a)*tan(b*x+a)/b+1/2/b*ln(sec(b*x+a)+tan(b*x+a))","A"
4,1,24,24,0.518000," ","int(sec(b*x+a)^4,x)","-\frac{\left(-\frac{2}{3}-\frac{\left(\sec^{2}\left(b x +a \right)\right)}{3}\right) \tan \left(b x +a \right)}{b}"," ",0,"-1/b*(-2/3-1/3*sec(b*x+a)^2)*tan(b*x+a)","A"
5,1,57,49,0.538000," ","int(sec(b*x+a)^5,x)","\frac{\left(\sec^{3}\left(b x +a \right)\right) \tan \left(b x +a \right)}{4 b}+\frac{3 \sec \left(b x +a \right) \tan \left(b x +a \right)}{8 b}+\frac{3 \ln \left(\sec \left(b x +a \right)+\tan \left(b x +a \right)\right)}{8 b}"," ",0,"1/4*sec(b*x+a)^3*tan(b*x+a)/b+3/8*sec(b*x+a)*tan(b*x+a)/b+3/8/b*ln(sec(b*x+a)+tan(b*x+a))","A"
6,1,34,37,0.523000," ","int(sec(b*x+a)^6,x)","-\frac{\left(-\frac{8}{15}-\frac{\left(\sec^{4}\left(b x +a \right)\right)}{5}-\frac{4 \left(\sec^{2}\left(b x +a \right)\right)}{15}\right) \tan \left(b x +a \right)}{b}"," ",0,"-1/b*(-8/15-1/5*sec(b*x+a)^4-4/15*sec(b*x+a)^2)*tan(b*x+a)","A"
7,1,76,68,0.532000," ","int(sec(b*x+a)^7,x)","\frac{\left(\sec^{5}\left(b x +a \right)\right) \tan \left(b x +a \right)}{6 b}+\frac{5 \left(\sec^{3}\left(b x +a \right)\right) \tan \left(b x +a \right)}{24 b}+\frac{5 \sec \left(b x +a \right) \tan \left(b x +a \right)}{16 b}+\frac{5 \ln \left(\sec \left(b x +a \right)+\tan \left(b x +a \right)\right)}{16 b}"," ",0,"1/6*sec(b*x+a)^5*tan(b*x+a)/b+5/24*sec(b*x+a)^3*tan(b*x+a)/b+5/16*sec(b*x+a)*tan(b*x+a)/b+5/16/b*ln(sec(b*x+a)+tan(b*x+a))","A"
8,1,44,49,0.516000," ","int(sec(b*x+a)^8,x)","-\frac{\left(-\frac{16}{35}-\frac{\left(\sec^{6}\left(b x +a \right)\right)}{7}-\frac{6 \left(\sec^{4}\left(b x +a \right)\right)}{35}-\frac{8 \left(\sec^{2}\left(b x +a \right)\right)}{35}\right) \tan \left(b x +a \right)}{b}"," ",0,"-1/b*(-16/35-1/7*sec(b*x+a)^6-6/35*sec(b*x+a)^4-8/35*sec(b*x+a)^2)*tan(b*x+a)","A"
9,1,358,97,5.094000," ","int(sec(b*x+a)^(7/2),x)","\frac{2 \sqrt{-\left(-2 \left(\cos^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)}\, \left(12 \EllipticE \left(\cos \left(\frac{b x}{2}+\frac{a}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(b x +a \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1}\, \left(\sin^{4}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-24 \cos \left(\frac{b x}{2}+\frac{a}{2}\right) \left(\sin^{6}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-12 \EllipticE \left(\cos \left(\frac{b x}{2}+\frac{a}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(b x +a \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1}\, \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+24 \left(\sin^{4}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) \cos \left(\frac{b x}{2}+\frac{a}{2}\right)+3 \sqrt{\frac{1}{2}-\frac{\cos \left(b x +a \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{b x}{2}+\frac{a}{2}\right), \sqrt{2}\right)-8 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) \cos \left(\frac{b x}{2}+\frac{a}{2}\right)\right) \sqrt{-2 \left(\sin^{4}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)}}{5 \left(8 \left(\sin^{6}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-12 \left(\sin^{4}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+6 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1\right) \sin \left(\frac{b x}{2}+\frac{a}{2}\right)^{3} \sqrt{2 \left(\cos^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1}\, b}"," ",0,"2/5*(-(-2*cos(1/2*b*x+1/2*a)^2+1)*sin(1/2*b*x+1/2*a)^2)^(1/2)/(8*sin(1/2*b*x+1/2*a)^6-12*sin(1/2*b*x+1/2*a)^4+6*sin(1/2*b*x+1/2*a)^2-1)/sin(1/2*b*x+1/2*a)^3*(12*EllipticE(cos(1/2*b*x+1/2*a),2^(1/2))*(sin(1/2*b*x+1/2*a)^2)^(1/2)*(2*sin(1/2*b*x+1/2*a)^2-1)^(1/2)*sin(1/2*b*x+1/2*a)^4-24*cos(1/2*b*x+1/2*a)*sin(1/2*b*x+1/2*a)^6-12*EllipticE(cos(1/2*b*x+1/2*a),2^(1/2))*(sin(1/2*b*x+1/2*a)^2)^(1/2)*(2*sin(1/2*b*x+1/2*a)^2-1)^(1/2)*sin(1/2*b*x+1/2*a)^2+24*sin(1/2*b*x+1/2*a)^4*cos(1/2*b*x+1/2*a)+3*(sin(1/2*b*x+1/2*a)^2)^(1/2)*(2*sin(1/2*b*x+1/2*a)^2-1)^(1/2)*EllipticE(cos(1/2*b*x+1/2*a),2^(1/2))-8*sin(1/2*b*x+1/2*a)^2*cos(1/2*b*x+1/2*a))*(-2*sin(1/2*b*x+1/2*a)^4+sin(1/2*b*x+1/2*a)^2)^(1/2)/(2*cos(1/2*b*x+1/2*a)^2-1)^(1/2)/b","B"
10,1,213,78,3.073000," ","int(sec(b*x+a)^(5/2),x)","-\frac{2 \left(-2 \sqrt{\frac{1}{2}-\frac{\cos \left(b x +a \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{b x}{2}+\frac{a}{2}\right), \sqrt{2}\right) \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+\sqrt{\frac{1}{2}-\frac{\cos \left(b x +a \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{b x}{2}+\frac{a}{2}\right), \sqrt{2}\right)-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) \cos \left(\frac{b x}{2}+\frac{a}{2}\right)\right) \sqrt{\left(2 \left(\cos^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)}}{3 \sqrt{-2 \left(\sin^{4}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)}\, \left(2 \left(\cos^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1\right)^{\frac{3}{2}} \sin \left(\frac{b x}{2}+\frac{a}{2}\right) b}"," ",0,"-2/3*(-2*(sin(1/2*b*x+1/2*a)^2)^(1/2)*(2*sin(1/2*b*x+1/2*a)^2-1)^(1/2)*EllipticF(cos(1/2*b*x+1/2*a),2^(1/2))*sin(1/2*b*x+1/2*a)^2+(sin(1/2*b*x+1/2*a)^2)^(1/2)*(2*sin(1/2*b*x+1/2*a)^2-1)^(1/2)*EllipticF(cos(1/2*b*x+1/2*a),2^(1/2))-2*sin(1/2*b*x+1/2*a)^2*cos(1/2*b*x+1/2*a))*((2*cos(1/2*b*x+1/2*a)^2-1)*sin(1/2*b*x+1/2*a)^2)^(1/2)/(-2*sin(1/2*b*x+1/2*a)^4+sin(1/2*b*x+1/2*a)^2)^(1/2)/(2*cos(1/2*b*x+1/2*a)^2-1)^(3/2)/sin(1/2*b*x+1/2*a)/b","B"
11,1,101,78,3.227000," ","int(sec(b*x+a)^(3/2),x)","-\frac{2 \left(\sqrt{\frac{1}{2}-\frac{\cos \left(b x +a \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{b x}{2}+\frac{a}{2}\right), \sqrt{2}\right)-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) \cos \left(\frac{b x}{2}+\frac{a}{2}\right)\right)}{\sin \left(\frac{b x}{2}+\frac{a}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1}\, b}"," ",0,"-2*((sin(1/2*b*x+1/2*a)^2)^(1/2)*(2*sin(1/2*b*x+1/2*a)^2-1)^(1/2)*EllipticE(cos(1/2*b*x+1/2*a),2^(1/2))-2*sin(1/2*b*x+1/2*a)^2*cos(1/2*b*x+1/2*a))/sin(1/2*b*x+1/2*a)/(2*cos(1/2*b*x+1/2*a)^2-1)^(1/2)/b","A"
12,1,133,58,2.433000," ","int(sec(b*x+a)^(1/2),x)","-\frac{2 \sqrt{\left(2 \left(\cos^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)}\, \sqrt{\frac{1}{2}-\frac{\cos \left(b x +a \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{b x}{2}+\frac{a}{2}\right), \sqrt{2}\right)}{\sqrt{-2 \left(\sin^{4}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)}\, \sin \left(\frac{b x}{2}+\frac{a}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1}\, b}"," ",0,"-2*((2*cos(1/2*b*x+1/2*a)^2-1)*sin(1/2*b*x+1/2*a)^2)^(1/2)*(sin(1/2*b*x+1/2*a)^2)^(1/2)*(-2*cos(1/2*b*x+1/2*a)^2+1)^(1/2)/(-2*sin(1/2*b*x+1/2*a)^4+sin(1/2*b*x+1/2*a)^2)^(1/2)*EllipticF(cos(1/2*b*x+1/2*a),2^(1/2))/sin(1/2*b*x+1/2*a)/(2*cos(1/2*b*x+1/2*a)^2-1)^(1/2)/b","B"
13,1,133,58,2.403000," ","int(1/sec(b*x+a)^(1/2),x)","\frac{2 \sqrt{\left(2 \left(\cos^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)}\, \sqrt{\frac{1}{2}-\frac{\cos \left(b x +a \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+1}\, \EllipticE \left(\cos \left(\frac{b x}{2}+\frac{a}{2}\right), \sqrt{2}\right)}{\sqrt{-2 \left(\sin^{4}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)}\, \sin \left(\frac{b x}{2}+\frac{a}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1}\, b}"," ",0,"2*((2*cos(1/2*b*x+1/2*a)^2-1)*sin(1/2*b*x+1/2*a)^2)^(1/2)*(sin(1/2*b*x+1/2*a)^2)^(1/2)*(-2*cos(1/2*b*x+1/2*a)^2+1)^(1/2)*EllipticE(cos(1/2*b*x+1/2*a),2^(1/2))/(-2*sin(1/2*b*x+1/2*a)^4+sin(1/2*b*x+1/2*a)^2)^(1/2)/sin(1/2*b*x+1/2*a)/(2*cos(1/2*b*x+1/2*a)^2-1)^(1/2)/b","B"
14,1,179,78,2.851000," ","int(1/sec(b*x+a)^(3/2),x)","-\frac{2 \sqrt{\left(2 \left(\cos^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)}\, \left(4 \left(\sin^{4}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) \cos \left(\frac{b x}{2}+\frac{a}{2}\right)+\sqrt{\frac{1}{2}-\frac{\cos \left(b x +a \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{b x}{2}+\frac{a}{2}\right), \sqrt{2}\right)-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) \cos \left(\frac{b x}{2}+\frac{a}{2}\right)\right)}{3 \sqrt{-2 \left(\sin^{4}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)}\, \sin \left(\frac{b x}{2}+\frac{a}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1}\, b}"," ",0,"-2/3*((2*cos(1/2*b*x+1/2*a)^2-1)*sin(1/2*b*x+1/2*a)^2)^(1/2)*(4*sin(1/2*b*x+1/2*a)^4*cos(1/2*b*x+1/2*a)+(sin(1/2*b*x+1/2*a)^2)^(1/2)*(2*sin(1/2*b*x+1/2*a)^2-1)^(1/2)*EllipticF(cos(1/2*b*x+1/2*a),2^(1/2))-2*sin(1/2*b*x+1/2*a)^2*cos(1/2*b*x+1/2*a))/(-2*sin(1/2*b*x+1/2*a)^4+sin(1/2*b*x+1/2*a)^2)^(1/2)/sin(1/2*b*x+1/2*a)/(2*cos(1/2*b*x+1/2*a)^2-1)^(1/2)/b","B"
15,1,202,78,2.987000," ","int(1/sec(b*x+a)^(5/2),x)","-\frac{2 \sqrt{\left(2 \left(\cos^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)}\, \left(-8 \cos \left(\frac{b x}{2}+\frac{a}{2}\right) \left(\sin^{6}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+8 \left(\sin^{4}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) \cos \left(\frac{b x}{2}+\frac{a}{2}\right)-3 \sqrt{\frac{1}{2}-\frac{\cos \left(b x +a \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{b x}{2}+\frac{a}{2}\right), \sqrt{2}\right)-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) \cos \left(\frac{b x}{2}+\frac{a}{2}\right)\right)}{5 \sqrt{-2 \left(\sin^{4}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)}\, \sin \left(\frac{b x}{2}+\frac{a}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1}\, b}"," ",0,"-2/5*((2*cos(1/2*b*x+1/2*a)^2-1)*sin(1/2*b*x+1/2*a)^2)^(1/2)*(-8*cos(1/2*b*x+1/2*a)*sin(1/2*b*x+1/2*a)^6+8*sin(1/2*b*x+1/2*a)^4*cos(1/2*b*x+1/2*a)-3*(sin(1/2*b*x+1/2*a)^2)^(1/2)*(2*sin(1/2*b*x+1/2*a)^2-1)^(1/2)*EllipticE(cos(1/2*b*x+1/2*a),2^(1/2))-2*sin(1/2*b*x+1/2*a)^2*cos(1/2*b*x+1/2*a))/(-2*sin(1/2*b*x+1/2*a)^4+sin(1/2*b*x+1/2*a)^2)^(1/2)/sin(1/2*b*x+1/2*a)/(2*cos(1/2*b*x+1/2*a)^2-1)^(1/2)/b","B"
16,1,199,97,3.018000," ","int(1/sec(b*x+a)^(7/2),x)","-\frac{2 \sqrt{\left(2 \left(\cos^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)}\, \left(48 \left(\cos^{9}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-120 \left(\cos^{7}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+128 \left(\cos^{5}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-72 \left(\cos^{3}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+5 \sqrt{\frac{1}{2}-\frac{\cos \left(b x +a \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{b x}{2}+\frac{a}{2}\right), \sqrt{2}\right)+16 \cos \left(\frac{b x}{2}+\frac{a}{2}\right)\right)}{21 \sqrt{-2 \left(\sin^{4}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)}\, \sin \left(\frac{b x}{2}+\frac{a}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1}\, b}"," ",0,"-2/21*((2*cos(1/2*b*x+1/2*a)^2-1)*sin(1/2*b*x+1/2*a)^2)^(1/2)*(48*cos(1/2*b*x+1/2*a)^9-120*cos(1/2*b*x+1/2*a)^7+128*cos(1/2*b*x+1/2*a)^5-72*cos(1/2*b*x+1/2*a)^3+5*(sin(1/2*b*x+1/2*a)^2)^(1/2)*(-2*cos(1/2*b*x+1/2*a)^2+1)^(1/2)*EllipticF(cos(1/2*b*x+1/2*a),2^(1/2))+16*cos(1/2*b*x+1/2*a))/(-2*sin(1/2*b*x+1/2*a)^4+sin(1/2*b*x+1/2*a)^2)^(1/2)/sin(1/2*b*x+1/2*a)/(2*cos(1/2*b*x+1/2*a)^2-1)^(1/2)/b","B"
17,1,354,110,1.007000," ","int((c*sec(b*x+a))^(7/2),x)","-\frac{2 \left(-1+\cos \left(b x +a \right)\right)^{2} \left(3 i \sin \left(b x +a \right) \EllipticF \left(\frac{i \left(-1+\cos \left(b x +a \right)\right)}{\sin \left(b x +a \right)}, i\right) \left(\cos^{3}\left(b x +a \right)\right) \sqrt{\frac{1}{\cos \left(b x +a \right)+1}}\, \sqrt{\frac{\cos \left(b x +a \right)}{\cos \left(b x +a \right)+1}}-3 i \sin \left(b x +a \right) \left(\cos^{3}\left(b x +a \right)\right) \sqrt{\frac{1}{\cos \left(b x +a \right)+1}}\, \sqrt{\frac{\cos \left(b x +a \right)}{\cos \left(b x +a \right)+1}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(b x +a \right)\right)}{\sin \left(b x +a \right)}, i\right)+3 i \sin \left(b x +a \right) \EllipticF \left(\frac{i \left(-1+\cos \left(b x +a \right)\right)}{\sin \left(b x +a \right)}, i\right) \left(\cos^{2}\left(b x +a \right)\right) \sqrt{\frac{1}{\cos \left(b x +a \right)+1}}\, \sqrt{\frac{\cos \left(b x +a \right)}{\cos \left(b x +a \right)+1}}-3 i \sin \left(b x +a \right) \left(\cos^{2}\left(b x +a \right)\right) \sqrt{\frac{1}{\cos \left(b x +a \right)+1}}\, \sqrt{\frac{\cos \left(b x +a \right)}{\cos \left(b x +a \right)+1}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(b x +a \right)\right)}{\sin \left(b x +a \right)}, i\right)+3 \left(\cos^{3}\left(b x +a \right)\right)-2 \left(\cos^{2}\left(b x +a \right)\right)-1\right) \cos \left(b x +a \right) \left(\cos \left(b x +a \right)+1\right)^{2} \left(\frac{c}{\cos \left(b x +a \right)}\right)^{\frac{7}{2}}}{5 b \sin \left(b x +a \right)^{5}}"," ",0,"-2/5/b*(-1+cos(b*x+a))^2*(3*I*sin(b*x+a)*EllipticF(I*(-1+cos(b*x+a))/sin(b*x+a),I)*cos(b*x+a)^3*(1/(cos(b*x+a)+1))^(1/2)*(cos(b*x+a)/(cos(b*x+a)+1))^(1/2)-3*I*sin(b*x+a)*cos(b*x+a)^3*(1/(cos(b*x+a)+1))^(1/2)*(cos(b*x+a)/(cos(b*x+a)+1))^(1/2)*EllipticE(I*(-1+cos(b*x+a))/sin(b*x+a),I)+3*I*sin(b*x+a)*EllipticF(I*(-1+cos(b*x+a))/sin(b*x+a),I)*cos(b*x+a)^2*(1/(cos(b*x+a)+1))^(1/2)*(cos(b*x+a)/(cos(b*x+a)+1))^(1/2)-3*I*sin(b*x+a)*cos(b*x+a)^2*(1/(cos(b*x+a)+1))^(1/2)*(cos(b*x+a)/(cos(b*x+a)+1))^(1/2)*EllipticE(I*(-1+cos(b*x+a))/sin(b*x+a),I)+3*cos(b*x+a)^3-2*cos(b*x+a)^2-1)*cos(b*x+a)*(cos(b*x+a)+1)^2*(c/cos(b*x+a))^(7/2)/sin(b*x+a)^5","C"
18,1,128,86,0.836000," ","int((c*sec(b*x+a))^(5/2),x)","-\frac{2 \left(-1+\cos \left(b x +a \right)\right) \left(i \cos \left(b x +a \right) \sin \left(b x +a \right) \sqrt{\frac{1}{\cos \left(b x +a \right)+1}}\, \sqrt{\frac{\cos \left(b x +a \right)}{\cos \left(b x +a \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(b x +a \right)\right)}{\sin \left(b x +a \right)}, i\right)-\cos \left(b x +a \right)+1\right) \cos \left(b x +a \right) \left(\cos \left(b x +a \right)+1\right)^{2} \left(\frac{c}{\cos \left(b x +a \right)}\right)^{\frac{5}{2}}}{3 b \sin \left(b x +a \right)^{3}}"," ",0,"-2/3/b*(-1+cos(b*x+a))*(I*cos(b*x+a)*sin(b*x+a)*(1/(cos(b*x+a)+1))^(1/2)*(cos(b*x+a)/(cos(b*x+a)+1))^(1/2)*EllipticF(I*(-1+cos(b*x+a))/sin(b*x+a),I)-cos(b*x+a)+1)*cos(b*x+a)*(cos(b*x+a)+1)^2*(c/cos(b*x+a))^(5/2)/sin(b*x+a)^3","C"
19,1,322,86,0.982000," ","int((c*sec(b*x+a))^(3/2),x)","\frac{2 \left(\cos \left(b x +a \right)+1\right)^{2} \left(-1+\cos \left(b x +a \right)\right)^{2} \left(i \cos \left(b x +a \right) \sin \left(b x +a \right) \EllipticE \left(\frac{i \left(-1+\cos \left(b x +a \right)\right)}{\sin \left(b x +a \right)}, i\right) \sqrt{\frac{1}{\cos \left(b x +a \right)+1}}\, \sqrt{\frac{\cos \left(b x +a \right)}{\cos \left(b x +a \right)+1}}-i \cos \left(b x +a \right) \sin \left(b x +a \right) \sqrt{\frac{1}{\cos \left(b x +a \right)+1}}\, \sqrt{\frac{\cos \left(b x +a \right)}{\cos \left(b x +a \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(b x +a \right)\right)}{\sin \left(b x +a \right)}, i\right)+i \sin \left(b x +a \right) \EllipticE \left(\frac{i \left(-1+\cos \left(b x +a \right)\right)}{\sin \left(b x +a \right)}, i\right) \sqrt{\frac{1}{\cos \left(b x +a \right)+1}}\, \sqrt{\frac{\cos \left(b x +a \right)}{\cos \left(b x +a \right)+1}}-i \sin \left(b x +a \right) \EllipticF \left(\frac{i \left(-1+\cos \left(b x +a \right)\right)}{\sin \left(b x +a \right)}, i\right) \sqrt{\frac{1}{\cos \left(b x +a \right)+1}}\, \sqrt{\frac{\cos \left(b x +a \right)}{\cos \left(b x +a \right)+1}}-\cos \left(b x +a \right)+1\right) \cos \left(b x +a \right) \left(\frac{c}{\cos \left(b x +a \right)}\right)^{\frac{3}{2}}}{b \sin \left(b x +a \right)^{5}}"," ",0,"2/b*(cos(b*x+a)+1)^2*(-1+cos(b*x+a))^2*(I*cos(b*x+a)*sin(b*x+a)*EllipticE(I*(-1+cos(b*x+a))/sin(b*x+a),I)*(1/(cos(b*x+a)+1))^(1/2)*(cos(b*x+a)/(cos(b*x+a)+1))^(1/2)-I*cos(b*x+a)*sin(b*x+a)*(1/(cos(b*x+a)+1))^(1/2)*(cos(b*x+a)/(cos(b*x+a)+1))^(1/2)*EllipticF(I*(-1+cos(b*x+a))/sin(b*x+a),I)+I*sin(b*x+a)*EllipticE(I*(-1+cos(b*x+a))/sin(b*x+a),I)*(1/(cos(b*x+a)+1))^(1/2)*(cos(b*x+a)/(cos(b*x+a)+1))^(1/2)-I*sin(b*x+a)*EllipticF(I*(-1+cos(b*x+a))/sin(b*x+a),I)*(1/(cos(b*x+a)+1))^(1/2)*(cos(b*x+a)/(cos(b*x+a)+1))^(1/2)-cos(b*x+a)+1)*cos(b*x+a)*(c/cos(b*x+a))^(3/2)/sin(b*x+a)^5","C"
20,1,98,60,0.915000," ","int((c*sec(b*x+a))^(1/2),x)","-\frac{2 i \sqrt{\frac{c}{\cos \left(b x +a \right)}}\, \left(-1+\cos \left(b x +a \right)\right) \sqrt{\frac{1}{\cos \left(b x +a \right)+1}}\, \sqrt{\frac{\cos \left(b x +a \right)}{\cos \left(b x +a \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(b x +a \right)\right)}{\sin \left(b x +a \right)}, i\right) \left(\cos \left(b x +a \right)+1\right)^{2}}{b \sin \left(b x +a \right)^{2}}"," ",0,"-2*I/b*(c/cos(b*x+a))^(1/2)*(-1+cos(b*x+a))*(1/(cos(b*x+a)+1))^(1/2)*(cos(b*x+a)/(cos(b*x+a)+1))^(1/2)*EllipticF(I*(-1+cos(b*x+a))/sin(b*x+a),I)*(cos(b*x+a)+1)^2/sin(b*x+a)^2","C"
21,1,306,60,1.059000," ","int(1/(c*sec(b*x+a))^(1/2),x)","\frac{2 \left(i \cos \left(b x +a \right) \sin \left(b x +a \right) \sqrt{\frac{1}{\cos \left(b x +a \right)+1}}\, \sqrt{\frac{\cos \left(b x +a \right)}{\cos \left(b x +a \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(b x +a \right)\right)}{\sin \left(b x +a \right)}, i\right)-i \cos \left(b x +a \right) \sin \left(b x +a \right) \EllipticE \left(\frac{i \left(-1+\cos \left(b x +a \right)\right)}{\sin \left(b x +a \right)}, i\right) \sqrt{\frac{1}{\cos \left(b x +a \right)+1}}\, \sqrt{\frac{\cos \left(b x +a \right)}{\cos \left(b x +a \right)+1}}+i \sin \left(b x +a \right) \EllipticF \left(\frac{i \left(-1+\cos \left(b x +a \right)\right)}{\sin \left(b x +a \right)}, i\right) \sqrt{\frac{1}{\cos \left(b x +a \right)+1}}\, \sqrt{\frac{\cos \left(b x +a \right)}{\cos \left(b x +a \right)+1}}-i \sin \left(b x +a \right) \EllipticE \left(\frac{i \left(-1+\cos \left(b x +a \right)\right)}{\sin \left(b x +a \right)}, i\right) \sqrt{\frac{1}{\cos \left(b x +a \right)+1}}\, \sqrt{\frac{\cos \left(b x +a \right)}{\cos \left(b x +a \right)+1}}-\left(\cos^{2}\left(b x +a \right)\right)+\cos \left(b x +a \right)\right) \sqrt{\frac{c}{\cos \left(b x +a \right)}}}{b \sin \left(b x +a \right) c}"," ",0,"2/b*(I*cos(b*x+a)*sin(b*x+a)*(1/(cos(b*x+a)+1))^(1/2)*(cos(b*x+a)/(cos(b*x+a)+1))^(1/2)*EllipticF(I*(-1+cos(b*x+a))/sin(b*x+a),I)-I*cos(b*x+a)*sin(b*x+a)*EllipticE(I*(-1+cos(b*x+a))/sin(b*x+a),I)*(1/(cos(b*x+a)+1))^(1/2)*(cos(b*x+a)/(cos(b*x+a)+1))^(1/2)+I*sin(b*x+a)*EllipticF(I*(-1+cos(b*x+a))/sin(b*x+a),I)*(1/(cos(b*x+a)+1))^(1/2)*(cos(b*x+a)/(cos(b*x+a)+1))^(1/2)-I*sin(b*x+a)*EllipticE(I*(-1+cos(b*x+a))/sin(b*x+a),I)*(1/(cos(b*x+a)+1))^(1/2)*(cos(b*x+a)/(cos(b*x+a)+1))^(1/2)-cos(b*x+a)^2+cos(b*x+a))*(c/cos(b*x+a))^(1/2)/sin(b*x+a)/c","C"
22,1,131,88,0.817000," ","int(1/(c*sec(b*x+a))^(3/2),x)","-\frac{2 \left(\cos \left(b x +a \right)+1\right)^{2} \left(-1+\cos \left(b x +a \right)\right) \left(i \sin \left(b x +a \right) \EllipticF \left(\frac{i \left(-1+\cos \left(b x +a \right)\right)}{\sin \left(b x +a \right)}, i\right) \sqrt{\frac{1}{\cos \left(b x +a \right)+1}}\, \sqrt{\frac{\cos \left(b x +a \right)}{\cos \left(b x +a \right)+1}}-\left(\cos^{2}\left(b x +a \right)\right)+\cos \left(b x +a \right)\right)}{3 b \left(\frac{c}{\cos \left(b x +a \right)}\right)^{\frac{3}{2}} \cos \left(b x +a \right)^{2} \sin \left(b x +a \right)^{3}}"," ",0,"-2/3/b*(cos(b*x+a)+1)^2*(-1+cos(b*x+a))*(I*sin(b*x+a)*EllipticF(I*(-1+cos(b*x+a))/sin(b*x+a),I)*(1/(cos(b*x+a)+1))^(1/2)*(cos(b*x+a)/(cos(b*x+a)+1))^(1/2)-cos(b*x+a)^2+cos(b*x+a))/(c/cos(b*x+a))^(3/2)/cos(b*x+a)^2/sin(b*x+a)^3","C"
23,1,321,88,0.973000," ","int(1/(c*sec(b*x+a))^(5/2),x)","-\frac{2 \left(-3 i \cos \left(b x +a \right) \sin \left(b x +a \right) \sqrt{\frac{1}{\cos \left(b x +a \right)+1}}\, \sqrt{\frac{\cos \left(b x +a \right)}{\cos \left(b x +a \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(b x +a \right)\right)}{\sin \left(b x +a \right)}, i\right)+3 i \cos \left(b x +a \right) \sin \left(b x +a \right) \EllipticE \left(\frac{i \left(-1+\cos \left(b x +a \right)\right)}{\sin \left(b x +a \right)}, i\right) \sqrt{\frac{1}{\cos \left(b x +a \right)+1}}\, \sqrt{\frac{\cos \left(b x +a \right)}{\cos \left(b x +a \right)+1}}-3 i \sin \left(b x +a \right) \EllipticF \left(\frac{i \left(-1+\cos \left(b x +a \right)\right)}{\sin \left(b x +a \right)}, i\right) \sqrt{\frac{1}{\cos \left(b x +a \right)+1}}\, \sqrt{\frac{\cos \left(b x +a \right)}{\cos \left(b x +a \right)+1}}+3 i \sin \left(b x +a \right) \EllipticE \left(\frac{i \left(-1+\cos \left(b x +a \right)\right)}{\sin \left(b x +a \right)}, i\right) \sqrt{\frac{1}{\cos \left(b x +a \right)+1}}\, \sqrt{\frac{\cos \left(b x +a \right)}{\cos \left(b x +a \right)+1}}+\cos^{4}\left(b x +a \right)+2 \left(\cos^{2}\left(b x +a \right)\right)-3 \cos \left(b x +a \right)\right)}{5 b \left(\frac{c}{\cos \left(b x +a \right)}\right)^{\frac{5}{2}} \cos \left(b x +a \right)^{3} \sin \left(b x +a \right)}"," ",0,"-2/5/b*(-3*I*cos(b*x+a)*sin(b*x+a)*(1/(cos(b*x+a)+1))^(1/2)*(cos(b*x+a)/(cos(b*x+a)+1))^(1/2)*EllipticF(I*(-1+cos(b*x+a))/sin(b*x+a),I)+3*I*cos(b*x+a)*sin(b*x+a)*EllipticE(I*(-1+cos(b*x+a))/sin(b*x+a),I)*(1/(cos(b*x+a)+1))^(1/2)*(cos(b*x+a)/(cos(b*x+a)+1))^(1/2)-3*I*sin(b*x+a)*EllipticF(I*(-1+cos(b*x+a))/sin(b*x+a),I)*(1/(cos(b*x+a)+1))^(1/2)*(cos(b*x+a)/(cos(b*x+a)+1))^(1/2)+3*I*sin(b*x+a)*EllipticE(I*(-1+cos(b*x+a))/sin(b*x+a),I)*(1/(cos(b*x+a)+1))^(1/2)*(cos(b*x+a)/(cos(b*x+a)+1))^(1/2)+cos(b*x+a)^4+2*cos(b*x+a)^2-3*cos(b*x+a))/(c/cos(b*x+a))^(5/2)/cos(b*x+a)^3/sin(b*x+a)","C"
24,1,153,112,0.939000," ","int(1/(c*sec(b*x+a))^(7/2),x)","\frac{2 \left(\cos \left(b x +a \right)+1\right)^{2} \left(-1+\cos \left(b x +a \right)\right) \left(-5 i \sin \left(b x +a \right) \EllipticF \left(\frac{i \left(-1+\cos \left(b x +a \right)\right)}{\sin \left(b x +a \right)}, i\right) \sqrt{\frac{1}{\cos \left(b x +a \right)+1}}\, \sqrt{\frac{\cos \left(b x +a \right)}{\cos \left(b x +a \right)+1}}+3 \left(\cos^{4}\left(b x +a \right)\right)-3 \left(\cos^{3}\left(b x +a \right)\right)+5 \left(\cos^{2}\left(b x +a \right)\right)-5 \cos \left(b x +a \right)\right)}{21 b \left(\frac{c}{\cos \left(b x +a \right)}\right)^{\frac{7}{2}} \cos \left(b x +a \right)^{4} \sin \left(b x +a \right)^{3}}"," ",0,"2/21/b*(cos(b*x+a)+1)^2*(-1+cos(b*x+a))*(-5*I*sin(b*x+a)*EllipticF(I*(-1+cos(b*x+a))/sin(b*x+a),I)*(1/(cos(b*x+a)+1))^(1/2)*(cos(b*x+a)/(cos(b*x+a)+1))^(1/2)+3*cos(b*x+a)^4-3*cos(b*x+a)^3+5*cos(b*x+a)^2-5*cos(b*x+a))/(c/cos(b*x+a))^(7/2)/cos(b*x+a)^4/sin(b*x+a)^3","C"
25,0,0,43,0.634000," ","int(sec(b*x+a)^(4/3),x)","\int \sec^{\frac{4}{3}}\left(b x +a \right)\, dx"," ",0,"int(sec(b*x+a)^(4/3),x)","F"
26,0,0,43,0.611000," ","int(sec(b*x+a)^(2/3),x)","\int \sec^{\frac{2}{3}}\left(b x +a \right)\, dx"," ",0,"int(sec(b*x+a)^(2/3),x)","F"
27,0,0,43,0.675000," ","int(sec(b*x+a)^(1/3),x)","\int \sec^{\frac{1}{3}}\left(b x +a \right)\, dx"," ",0,"int(sec(b*x+a)^(1/3),x)","F"
28,0,0,43,0.553000," ","int(1/sec(b*x+a)^(1/3),x)","\int \frac{1}{\sec \left(b x +a \right)^{\frac{1}{3}}}\, dx"," ",0,"int(1/sec(b*x+a)^(1/3),x)","F"
29,0,0,43,0.599000," ","int(1/sec(b*x+a)^(2/3),x)","\int \frac{1}{\sec \left(b x +a \right)^{\frac{2}{3}}}\, dx"," ",0,"int(1/sec(b*x+a)^(2/3),x)","F"
30,0,0,43,0.538000," ","int(1/sec(b*x+a)^(4/3),x)","\int \frac{1}{\sec \left(b x +a \right)^{\frac{4}{3}}}\, dx"," ",0,"int(1/sec(b*x+a)^(4/3),x)","F"
31,0,0,46,0.536000," ","int((c*sec(b*x+a))^(4/3),x)","\int \left(c \sec \left(b x +a \right)\right)^{\frac{4}{3}}\, dx"," ",0,"int((c*sec(b*x+a))^(4/3),x)","F"
32,0,0,46,0.594000," ","int((c*sec(b*x+a))^(2/3),x)","\int \left(c \sec \left(b x +a \right)\right)^{\frac{2}{3}}\, dx"," ",0,"int((c*sec(b*x+a))^(2/3),x)","F"
33,0,0,46,0.745000," ","int((c*sec(b*x+a))^(1/3),x)","\int \left(c \sec \left(b x +a \right)\right)^{\frac{1}{3}}\, dx"," ",0,"int((c*sec(b*x+a))^(1/3),x)","F"
34,0,0,46,0.532000," ","int(1/(c*sec(b*x+a))^(1/3),x)","\int \frac{1}{\left(c \sec \left(b x +a \right)\right)^{\frac{1}{3}}}\, dx"," ",0,"int(1/(c*sec(b*x+a))^(1/3),x)","F"
35,0,0,46,0.538000," ","int(1/(c*sec(b*x+a))^(2/3),x)","\int \frac{1}{\left(c \sec \left(b x +a \right)\right)^{\frac{2}{3}}}\, dx"," ",0,"int(1/(c*sec(b*x+a))^(2/3),x)","F"
36,0,0,46,0.447000," ","int(1/(c*sec(b*x+a))^(4/3),x)","\int \frac{1}{\left(c \sec \left(b x +a \right)\right)^{\frac{4}{3}}}\, dx"," ",0,"int(1/(c*sec(b*x+a))^(4/3),x)","F"
37,0,0,60,1.458000," ","int(sec(b*x+a)^n,x)","\int \sec^{n}\left(b x +a \right)\, dx"," ",0,"int(sec(b*x+a)^n,x)","F"
38,0,0,63,1.317000," ","int((c*sec(b*x+a))^n,x)","\int \left(c \sec \left(b x +a \right)\right)^{n}\, dx"," ",0,"int((c*sec(b*x+a))^n,x)","F"
39,1,72,36,0.437000," ","int((sec(x)^2)^(7/2),x)","-\frac{\left(15 \left(\cos^{6}\left(x \right)\right) \ln \left(-\frac{-1+\cos \left(x \right)+\sin \left(x \right)}{\sin \left(x \right)}\right)-15 \left(\cos^{6}\left(x \right)\right) \ln \left(-\frac{-\sin \left(x \right)-1+\cos \left(x \right)}{\sin \left(x \right)}\right)-15 \left(\cos^{4}\left(x \right)\right) \sin \left(x \right)-10 \left(\cos^{2}\left(x \right)\right) \sin \left(x \right)-8 \sin \left(x \right)\right) \cos \left(x \right) \sqrt{2}\, \sqrt{\frac{1}{\cos \left(2 x \right)+1}}}{6 \left(\cos \left(2 x \right)+1\right)^{3}}"," ",0,"-1/48*(15*cos(x)^6*ln(-(-1+cos(x)+sin(x))/sin(x))-15*cos(x)^6*ln(-(-sin(x)-1+cos(x))/sin(x))-15*cos(x)^4*sin(x)-10*cos(x)^2*sin(x)-8*sin(x))*cos(x)*(1/cos(x)^2)^(7/2)","A"
40,1,64,26,0.353000," ","int((sec(x)^2)^(5/2),x)","-\frac{\left(3 \left(\cos^{4}\left(x \right)\right) \ln \left(-\frac{-1+\cos \left(x \right)+\sin \left(x \right)}{\sin \left(x \right)}\right)-3 \left(\cos^{4}\left(x \right)\right) \ln \left(-\frac{-\sin \left(x \right)-1+\cos \left(x \right)}{\sin \left(x \right)}\right)-3 \left(\cos^{2}\left(x \right)\right) \sin \left(x \right)-2 \sin \left(x \right)\right) \cos \left(x \right) \sqrt{2}\, \sqrt{\frac{1}{\cos \left(2 x \right)+1}}}{2 \left(\cos \left(2 x \right)+1\right)^{2}}"," ",0,"-1/8*(3*cos(x)^4*ln(-(-1+cos(x)+sin(x))/sin(x))-3*cos(x)^4*ln(-(-sin(x)-1+cos(x))/sin(x))-3*cos(x)^2*sin(x)-2*sin(x))*cos(x)*(1/cos(x)^2)^(5/2)","B"
41,1,55,16,0.292000," ","int((sec(x)^2)^(3/2),x)","-\frac{\left(\left(\cos^{2}\left(x \right)\right) \ln \left(-\frac{-1+\cos \left(x \right)+\sin \left(x \right)}{\sin \left(x \right)}\right)-\left(\cos^{2}\left(x \right)\right) \ln \left(-\frac{-\sin \left(x \right)-1+\cos \left(x \right)}{\sin \left(x \right)}\right)-\sin \left(x \right)\right) \cos \left(x \right) \sqrt{2}\, \sqrt{\frac{1}{\cos \left(2 x \right)+1}}}{\cos \left(2 x \right)+1}"," ",0,"-1/2*(cos(x)^2*ln(-(-1+cos(x)+sin(x))/sin(x))-cos(x)^2*ln(-(-sin(x)-1+cos(x))/sin(x))-sin(x))*cos(x)*(1/cos(x)^2)^(3/2)","B"
42,1,21,3,0.367000," ","int((sec(x)^2)^(1/2),x)","-2 \cos \left(x \right) \sqrt{2}\, \sqrt{\frac{1}{\cos \left(2 x \right)+1}}\, \arctanh \left(\frac{-1+\cos \left(x \right)}{\sin \left(x \right)}\right)"," ",0,"-2*cos(x)*(1/cos(x)^2)^(1/2)*arctanh((-1+cos(x))/sin(x))","B"
43,1,14,9,0.397000," ","int(1/(sec(x)^2)^(1/2),x)","\frac{\sin \left(x \right) \sqrt{2}}{2 \sqrt{\frac{1}{\cos \left(2 x \right)+1}}\, \cos \left(x \right)}"," ",0,"sin(x)/(1/cos(x)^2)^(1/2)/cos(x)","A"
44,1,21,21,0.341000," ","int(1/(sec(x)^2)^(3/2),x)","\frac{\sin \left(x \right) \left(\cos^{2}\left(x \right)+2\right) \left(\cos \left(2 x \right)+1\right) \sqrt{2}}{12 \cos \left(x \right)^{3} \sqrt{\frac{1}{\cos \left(2 x \right)+1}}}"," ",0,"1/3*sin(x)*(cos(x)^2+2)/cos(x)^3/(1/cos(x)^2)^(3/2)","A"
45,1,29,31,0.316000," ","int(1/(sec(x)^2)^(5/2),x)","\frac{\sin \left(x \right) \left(3 \left(\cos^{4}\left(x \right)\right)+4 \left(\cos^{2}\left(x \right)\right)+8\right) \left(\cos \left(2 x \right)+1\right)^{2} \sqrt{2}}{120 \cos \left(x \right)^{5} \sqrt{\frac{1}{\cos \left(2 x \right)+1}}}"," ",0,"1/15*sin(x)*(3*cos(x)^4+4*cos(x)^2+8)/cos(x)^5/(1/cos(x)^2)^(5/2)","A"
46,1,35,41,0.362000," ","int(1/(sec(x)^2)^(7/2),x)","\frac{\sin \left(x \right) \left(5 \left(\cos^{6}\left(x \right)\right)+6 \left(\cos^{4}\left(x \right)\right)+8 \left(\cos^{2}\left(x \right)\right)+16\right) \left(\cos \left(2 x \right)+1\right)^{3} \sqrt{2}}{560 \cos \left(x \right)^{7} \sqrt{\frac{1}{\cos \left(2 x \right)+1}}}"," ",0,"1/35*sin(x)*(5*cos(x)^6+6*cos(x)^4+8*cos(x)^2+16)/cos(x)^7/(1/cos(x)^2)^(7/2)","A"
47,1,74,64,0.448000," ","int((a*sec(x)^2)^(7/2),x)","-\frac{\left(15 \left(\cos^{6}\left(x \right)\right) \ln \left(-\frac{-1+\cos \left(x \right)+\sin \left(x \right)}{\sin \left(x \right)}\right)-15 \left(\cos^{6}\left(x \right)\right) \ln \left(-\frac{-\sin \left(x \right)-1+\cos \left(x \right)}{\sin \left(x \right)}\right)-15 \left(\cos^{4}\left(x \right)\right) \sin \left(x \right)-10 \left(\cos^{2}\left(x \right)\right) \sin \left(x \right)-8 \sin \left(x \right)\right) \cos \left(x \right) \left(\frac{a}{\cos \left(x \right)^{2}}\right)^{\frac{7}{2}}}{48}"," ",0,"-1/48*(15*cos(x)^6*ln(-(-1+cos(x)+sin(x))/sin(x))-15*cos(x)^6*ln(-(-sin(x)-1+cos(x))/sin(x))-15*cos(x)^4*sin(x)-10*cos(x)^2*sin(x)-8*sin(x))*cos(x)*(a/cos(x)^2)^(7/2)","A"
48,1,66,49,0.360000," ","int((a*sec(x)^2)^(5/2),x)","-\frac{\left(3 \left(\cos^{4}\left(x \right)\right) \ln \left(-\frac{-1+\cos \left(x \right)+\sin \left(x \right)}{\sin \left(x \right)}\right)-3 \left(\cos^{4}\left(x \right)\right) \ln \left(-\frac{-\sin \left(x \right)-1+\cos \left(x \right)}{\sin \left(x \right)}\right)-3 \left(\cos^{2}\left(x \right)\right) \sin \left(x \right)-2 \sin \left(x \right)\right) \cos \left(x \right) \left(\frac{a}{\cos \left(x \right)^{2}}\right)^{\frac{5}{2}}}{8}"," ",0,"-1/8*(3*cos(x)^4*ln(-(-1+cos(x)+sin(x))/sin(x))-3*cos(x)^4*ln(-(-sin(x)-1+cos(x))/sin(x))-3*cos(x)^2*sin(x)-2*sin(x))*cos(x)*(a/cos(x)^2)^(5/2)","A"
49,1,57,34,0.297000," ","int((a*sec(x)^2)^(3/2),x)","-\frac{\left(\left(\cos^{2}\left(x \right)\right) \ln \left(-\frac{-1+\cos \left(x \right)+\sin \left(x \right)}{\sin \left(x \right)}\right)-\left(\cos^{2}\left(x \right)\right) \ln \left(-\frac{-\sin \left(x \right)-1+\cos \left(x \right)}{\sin \left(x \right)}\right)-\sin \left(x \right)\right) \cos \left(x \right) \left(\frac{a}{\cos \left(x \right)^{2}}\right)^{\frac{3}{2}}}{2}"," ",0,"-1/2*(cos(x)^2*ln(-(-1+cos(x)+sin(x))/sin(x))-cos(x)^2*ln(-(-sin(x)-1+cos(x))/sin(x))-sin(x))*cos(x)*(a/cos(x)^2)^(3/2)","A"
50,1,23,19,0.385000," ","int((a*sec(x)^2)^(1/2),x)","-2 \cos \left(x \right) \sqrt{\frac{a}{\cos \left(x \right)^{2}}}\, \arctanh \left(\frac{-1+\cos \left(x \right)}{\sin \left(x \right)}\right)"," ",0,"-2*cos(x)*(a/cos(x)^2)^(1/2)*arctanh((-1+cos(x))/sin(x))","A"
51,1,16,11,0.396000," ","int(1/(a*sec(x)^2)^(1/2),x)","\frac{\sin \left(x \right)}{\sqrt{\frac{a}{\cos \left(x \right)^{2}}}\, \cos \left(x \right)}"," ",0,"sin(x)/(a/cos(x)^2)^(1/2)/cos(x)","A"
52,1,23,28,0.299000," ","int(1/(a*sec(x)^2)^(3/2),x)","\frac{\sin \left(x \right) \left(\cos^{2}\left(x \right)+2\right)}{3 \cos \left(x \right)^{3} \left(\frac{a}{\cos \left(x \right)^{2}}\right)^{\frac{3}{2}}}"," ",0,"1/3*sin(x)*(cos(x)^2+2)/cos(x)^3/(a/cos(x)^2)^(3/2)","A"
53,1,31,43,0.311000," ","int(1/(a*sec(x)^2)^(5/2),x)","\frac{\sin \left(x \right) \left(3 \left(\cos^{4}\left(x \right)\right)+4 \left(\cos^{2}\left(x \right)\right)+8\right)}{15 \cos \left(x \right)^{5} \left(\frac{a}{\cos \left(x \right)^{2}}\right)^{\frac{5}{2}}}"," ",0,"1/15*sin(x)*(3*cos(x)^4+4*cos(x)^2+8)/cos(x)^5/(a/cos(x)^2)^(5/2)","A"
54,1,37,58,0.339000," ","int(1/(a*sec(x)^2)^(7/2),x)","\frac{\sin \left(x \right) \left(5 \left(\cos^{6}\left(x \right)\right)+6 \left(\cos^{4}\left(x \right)\right)+8 \left(\cos^{2}\left(x \right)\right)+16\right)}{35 \cos \left(x \right)^{7} \left(\frac{a}{\cos \left(x \right)^{2}}\right)^{\frac{7}{2}}}"," ",0,"1/35*sin(x)*(5*cos(x)^6+6*cos(x)^4+8*cos(x)^2+16)/cos(x)^7/(a/cos(x)^2)^(7/2)","A"
55,1,223,110,0.758000," ","int((a*sec(x)^3)^(5/2),x)","\frac{2 \left(\cos \left(x \right)+1\right)^{2} \left(-1+\cos \left(x \right)\right)^{2} \left(231 i \left(\cos^{7}\left(x \right)\right) \sin \left(x \right) \sqrt{\frac{1}{\cos \left(x \right)+1}}\, \sqrt{\frac{\cos \left(x \right)}{\cos \left(x \right)+1}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(x \right)\right)}{\sin \left(x \right)}, i\right)-231 i \left(\cos^{7}\left(x \right)\right) \sin \left(x \right) \sqrt{\frac{1}{\cos \left(x \right)+1}}\, \sqrt{\frac{\cos \left(x \right)}{\cos \left(x \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(x \right)\right)}{\sin \left(x \right)}, i\right)+231 i \left(\cos^{6}\left(x \right)\right) \sin \left(x \right) \sqrt{\frac{1}{\cos \left(x \right)+1}}\, \sqrt{\frac{\cos \left(x \right)}{\cos \left(x \right)+1}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(x \right)\right)}{\sin \left(x \right)}, i\right)-231 i \left(\cos^{6}\left(x \right)\right) \sin \left(x \right) \sqrt{\frac{1}{\cos \left(x \right)+1}}\, \sqrt{\frac{\cos \left(x \right)}{\cos \left(x \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(x \right)\right)}{\sin \left(x \right)}, i\right)-231 \left(\cos^{7}\left(x \right)\right)+154 \left(\cos^{6}\left(x \right)\right)+22 \left(\cos^{4}\left(x \right)\right)+10 \left(\cos^{2}\left(x \right)\right)+45\right) \cos \left(x \right) \left(\frac{a}{\cos \left(x \right)^{3}}\right)^{\frac{5}{2}}}{585 \sin \left(x \right)^{5}}"," ",0,"2/585*(cos(x)+1)^2*(-1+cos(x))^2*(231*I*cos(x)^7*sin(x)*(1/(cos(x)+1))^(1/2)*(cos(x)/(cos(x)+1))^(1/2)*EllipticE(I*(-1+cos(x))/sin(x),I)-231*I*cos(x)^7*sin(x)*(1/(cos(x)+1))^(1/2)*(cos(x)/(cos(x)+1))^(1/2)*EllipticF(I*(-1+cos(x))/sin(x),I)+231*I*cos(x)^6*sin(x)*(1/(cos(x)+1))^(1/2)*(cos(x)/(cos(x)+1))^(1/2)*EllipticE(I*(-1+cos(x))/sin(x),I)-231*I*cos(x)^6*sin(x)*(1/(cos(x)+1))^(1/2)*(cos(x)/(cos(x)+1))^(1/2)*EllipticF(I*(-1+cos(x))/sin(x),I)-231*cos(x)^7+154*cos(x)^6+22*cos(x)^4+10*cos(x)^2+45)*cos(x)*(a/cos(x)^3)^(5/2)/sin(x)^5","C"
56,1,87,66,0.549000," ","int((a*sec(x)^3)^(3/2),x)","-\frac{2 \left(\cos \left(x \right)+1\right)^{2} \left(-1+\cos \left(x \right)\right) \left(5 i \left(\cos^{3}\left(x \right)\right) \sin \left(x \right) \sqrt{\frac{1}{\cos \left(x \right)+1}}\, \sqrt{\frac{\cos \left(x \right)}{\cos \left(x \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(x \right)\right)}{\sin \left(x \right)}, i\right)-5 \left(\cos^{3}\left(x \right)\right)+5 \left(\cos^{2}\left(x \right)\right)-3 \cos \left(x \right)+3\right) \cos \left(x \right) \left(\frac{a}{\cos \left(x \right)^{3}}\right)^{\frac{3}{2}}}{21 \sin \left(x \right)^{3}}"," ",0,"-2/21*(cos(x)+1)^2*(-1+cos(x))*(5*I*cos(x)^3*sin(x)*(1/(cos(x)+1))^(1/2)*(cos(x)/(cos(x)+1))^(1/2)*EllipticF(I*(-1+cos(x))/sin(x),I)-5*cos(x)^3+5*cos(x)^2-3*cos(x)+3)*cos(x)*(a/cos(x)^3)^(3/2)/sin(x)^3","C"
57,1,191,51,0.706000," ","int((a*sec(x)^3)^(1/2),x)","\frac{2 \left(\cos \left(x \right)+1\right)^{2} \left(-1+\cos \left(x \right)\right)^{2} \left(i \cos \left(x \right) \sin \left(x \right) \EllipticE \left(\frac{i \left(-1+\cos \left(x \right)\right)}{\sin \left(x \right)}, i\right) \sqrt{\frac{1}{\cos \left(x \right)+1}}\, \sqrt{\frac{\cos \left(x \right)}{\cos \left(x \right)+1}}-i \cos \left(x \right) \sin \left(x \right) \EllipticF \left(\frac{i \left(-1+\cos \left(x \right)\right)}{\sin \left(x \right)}, i\right) \sqrt{\frac{1}{\cos \left(x \right)+1}}\, \sqrt{\frac{\cos \left(x \right)}{\cos \left(x \right)+1}}+i \sin \left(x \right) \EllipticE \left(\frac{i \left(-1+\cos \left(x \right)\right)}{\sin \left(x \right)}, i\right) \sqrt{\frac{1}{\cos \left(x \right)+1}}\, \sqrt{\frac{\cos \left(x \right)}{\cos \left(x \right)+1}}-i \sin \left(x \right) \EllipticF \left(\frac{i \left(-1+\cos \left(x \right)\right)}{\sin \left(x \right)}, i\right) \sqrt{\frac{1}{\cos \left(x \right)+1}}\, \sqrt{\frac{\cos \left(x \right)}{\cos \left(x \right)+1}}-\cos \left(x \right)+1\right) \cos \left(x \right) \sqrt{\frac{a}{\cos \left(x \right)^{3}}}}{\sin \left(x \right)^{5}}"," ",0,"2*(cos(x)+1)^2*(-1+cos(x))^2*(I*cos(x)*sin(x)*EllipticE(I*(-1+cos(x))/sin(x),I)*(1/(cos(x)+1))^(1/2)*(cos(x)/(cos(x)+1))^(1/2)-I*cos(x)*sin(x)*EllipticF(I*(-1+cos(x))/sin(x),I)*(1/(cos(x)+1))^(1/2)*(cos(x)/(cos(x)+1))^(1/2)+I*sin(x)*EllipticE(I*(-1+cos(x))/sin(x),I)*(1/(cos(x)+1))^(1/2)*(cos(x)/(cos(x)+1))^(1/2)-I*sin(x)*EllipticF(I*(-1+cos(x))/sin(x),I)*(1/(cos(x)+1))^(1/2)*(cos(x)/(cos(x)+1))^(1/2)-cos(x)+1)*cos(x)*(a/cos(x)^3)^(1/2)/sin(x)^5","C"
58,1,76,49,0.577000," ","int(1/(a*sec(x)^3)^(1/2),x)","\frac{2 \left(-1+\cos \left(x \right)\right) \left(-i \sin \left(x \right) \EllipticF \left(\frac{i \left(-1+\cos \left(x \right)\right)}{\sin \left(x \right)}, i\right) \sqrt{\frac{1}{\cos \left(x \right)+1}}\, \sqrt{\frac{\cos \left(x \right)}{\cos \left(x \right)+1}}+\cos^{2}\left(x \right)-\cos \left(x \right)\right) \left(\cos \left(x \right)+1\right)^{2}}{3 \cos \left(x \right)^{2} \sin \left(x \right)^{3} \sqrt{\frac{a}{\cos \left(x \right)^{3}}}}"," ",0,"2/3*(-1+cos(x))*(-I*sin(x)*EllipticF(I*(-1+cos(x))/sin(x),I)*(1/(cos(x)+1))^(1/2)*(cos(x)/(cos(x)+1))^(1/2)+cos(x)^2-cos(x))*(cos(x)+1)^2/cos(x)^2/sin(x)^3/(a/cos(x)^3)^(1/2)","C"
59,1,198,74,0.546000," ","int(1/(a*sec(x)^3)^(3/2),x)","-\frac{2 \left(5 \left(\cos^{6}\left(x \right)\right)-21 i \cos \left(x \right) \sin \left(x \right) \EllipticF \left(\frac{i \left(-1+\cos \left(x \right)\right)}{\sin \left(x \right)}, i\right) \sqrt{\frac{1}{\cos \left(x \right)+1}}\, \sqrt{\frac{\cos \left(x \right)}{\cos \left(x \right)+1}}+21 i \cos \left(x \right) \sin \left(x \right) \EllipticE \left(\frac{i \left(-1+\cos \left(x \right)\right)}{\sin \left(x \right)}, i\right) \sqrt{\frac{1}{\cos \left(x \right)+1}}\, \sqrt{\frac{\cos \left(x \right)}{\cos \left(x \right)+1}}-21 i \sin \left(x \right) \EllipticF \left(\frac{i \left(-1+\cos \left(x \right)\right)}{\sin \left(x \right)}, i\right) \sqrt{\frac{1}{\cos \left(x \right)+1}}\, \sqrt{\frac{\cos \left(x \right)}{\cos \left(x \right)+1}}+21 i \sin \left(x \right) \EllipticE \left(\frac{i \left(-1+\cos \left(x \right)\right)}{\sin \left(x \right)}, i\right) \sqrt{\frac{1}{\cos \left(x \right)+1}}\, \sqrt{\frac{\cos \left(x \right)}{\cos \left(x \right)+1}}+2 \left(\cos^{4}\left(x \right)\right)+14 \left(\cos^{2}\left(x \right)\right)-21 \cos \left(x \right)\right)}{45 \cos \left(x \right)^{5} \sin \left(x \right) \left(\frac{a}{\cos \left(x \right)^{3}}\right)^{\frac{3}{2}}}"," ",0,"-2/45*(5*cos(x)^6-21*I*cos(x)*sin(x)*EllipticF(I*(-1+cos(x))/sin(x),I)*(1/(cos(x)+1))^(1/2)*(cos(x)/(cos(x)+1))^(1/2)+21*I*cos(x)*sin(x)*EllipticE(I*(-1+cos(x))/sin(x),I)*(1/(cos(x)+1))^(1/2)*(cos(x)/(cos(x)+1))^(1/2)-21*I*sin(x)*EllipticF(I*(-1+cos(x))/sin(x),I)*(1/(cos(x)+1))^(1/2)*(cos(x)/(cos(x)+1))^(1/2)+21*I*sin(x)*EllipticE(I*(-1+cos(x))/sin(x),I)*(1/(cos(x)+1))^(1/2)*(cos(x)/(cos(x)+1))^(1/2)+2*cos(x)^4+14*cos(x)^2-21*cos(x))/cos(x)^5/sin(x)/(a/cos(x)^3)^(3/2)","C"
60,1,114,110,0.523000," ","int(1/(a*sec(x)^3)^(5/2),x)","\frac{2 \left(-1+\cos \left(x \right)\right) \left(77 \left(\cos^{8}\left(x \right)\right)-77 \left(\cos^{7}\left(x \right)\right)+91 \left(\cos^{6}\left(x \right)\right)-91 \left(\cos^{5}\left(x \right)\right)-195 i \sin \left(x \right) \EllipticF \left(\frac{i \left(-1+\cos \left(x \right)\right)}{\sin \left(x \right)}, i\right) \sqrt{\frac{1}{\cos \left(x \right)+1}}\, \sqrt{\frac{\cos \left(x \right)}{\cos \left(x \right)+1}}+117 \left(\cos^{4}\left(x \right)\right)-117 \left(\cos^{3}\left(x \right)\right)+195 \left(\cos^{2}\left(x \right)\right)-195 \cos \left(x \right)\right) \left(\cos \left(x \right)+1\right)^{2}}{1155 \cos \left(x \right)^{8} \sin \left(x \right)^{3} \left(\frac{a}{\cos \left(x \right)^{3}}\right)^{\frac{5}{2}}}"," ",0,"2/1155*(-1+cos(x))*(77*cos(x)^8-77*cos(x)^7+91*cos(x)^6-91*cos(x)^5-195*I*sin(x)*EllipticF(I*(-1+cos(x))/sin(x),I)*(1/(cos(x)+1))^(1/2)*(cos(x)/(cos(x)+1))^(1/2)+117*cos(x)^4-117*cos(x)^3+195*cos(x)^2-195*cos(x))*(cos(x)+1)^2/cos(x)^8/sin(x)^3/(a/cos(x)^3)^(5/2)","C"
61,1,53,141,0.557000," ","int((a*sec(x)^4)^(7/2),x)","\frac{\left(1024 \left(\cos^{12}\left(x \right)\right)+512 \left(\cos^{10}\left(x \right)\right)+384 \left(\cos^{8}\left(x \right)\right)+320 \left(\cos^{6}\left(x \right)\right)+280 \left(\cos^{4}\left(x \right)\right)+252 \left(\cos^{2}\left(x \right)\right)+231\right) \left(\frac{a}{\cos \left(x \right)^{4}}\right)^{\frac{7}{2}} \sin \left(x \right) \cos \left(x \right)}{3003}"," ",0,"1/3003*(1024*cos(x)^12+512*cos(x)^10+384*cos(x)^8+320*cos(x)^6+280*cos(x)^4+252*cos(x)^2+231)*(a/cos(x)^4)^(7/2)*sin(x)*cos(x)","A"
62,1,41,99,0.360000," ","int((a*sec(x)^4)^(5/2),x)","\frac{\left(128 \left(\cos^{8}\left(x \right)\right)+64 \left(\cos^{6}\left(x \right)\right)+48 \left(\cos^{4}\left(x \right)\right)+40 \left(\cos^{2}\left(x \right)\right)+35\right) \cos \left(x \right) \sin \left(x \right) \left(\frac{a}{\cos \left(x \right)^{4}}\right)^{\frac{5}{2}}}{315}"," ",0,"1/315*(128*cos(x)^8+64*cos(x)^6+48*cos(x)^4+40*cos(x)^2+35)*cos(x)*sin(x)*(a/cos(x)^4)^(5/2)","A"
63,1,29,51,0.295000," ","int((a*sec(x)^4)^(3/2),x)","\frac{\left(8 \left(\cos^{4}\left(x \right)\right)+4 \left(\cos^{2}\left(x \right)\right)+3\right) \cos \left(x \right) \sin \left(x \right) \left(\frac{a}{\cos \left(x \right)^{4}}\right)^{\frac{3}{2}}}{15}"," ",0,"1/15*(8*cos(x)^4+4*cos(x)^2+3)*cos(x)*sin(x)*(a/cos(x)^4)^(3/2)","A"
64,1,14,13,0.395000," ","int((a*sec(x)^4)^(1/2),x)","\cos \left(x \right) \sin \left(x \right) \sqrt{\frac{a}{\cos \left(x \right)^{4}}}"," ",0,"cos(x)*sin(x)*(a/cos(x)^4)^(1/2)","A"
65,1,22,28,0.413000," ","int(1/(a*sec(x)^4)^(1/2),x)","\frac{\cos \left(x \right) \sin \left(x \right)+x}{2 \cos \left(x \right)^{2} \sqrt{\frac{a}{\cos \left(x \right)^{4}}}}"," ",0,"1/2*(cos(x)*sin(x)+x)/cos(x)^2/(a/cos(x)^4)^(1/2)","A"
66,1,41,70,0.378000," ","int(1/(a*sec(x)^4)^(3/2),x)","\frac{8 \sin \left(x \right) \left(\cos^{5}\left(x \right)\right)+10 \left(\cos^{3}\left(x \right)\right) \sin \left(x \right)+15 \cos \left(x \right) \sin \left(x \right)+15 x}{48 \cos \left(x \right)^{6} \left(\frac{a}{\cos \left(x \right)^{4}}\right)^{\frac{3}{2}}}"," ",0,"1/48*(8*sin(x)*cos(x)^5+10*cos(x)^3*sin(x)+15*cos(x)*sin(x)+15*x)/cos(x)^6/(a/cos(x)^4)^(3/2)","A"
67,1,57,108,0.597000," ","int(1/(a*sec(x)^4)^(5/2),x)","\frac{128 \sin \left(x \right) \left(\cos^{9}\left(x \right)\right)+144 \sin \left(x \right) \left(\cos^{7}\left(x \right)\right)+168 \sin \left(x \right) \left(\cos^{5}\left(x \right)\right)+210 \left(\cos^{3}\left(x \right)\right) \sin \left(x \right)+315 \cos \left(x \right) \sin \left(x \right)+315 x}{1280 \cos \left(x \right)^{10} \left(\frac{a}{\cos \left(x \right)^{4}}\right)^{\frac{5}{2}}}"," ",0,"1/1280*(128*sin(x)*cos(x)^9+144*sin(x)*cos(x)^7+168*sin(x)*cos(x)^5+210*cos(x)^3*sin(x)+315*cos(x)*sin(x)+315*x)/cos(x)^10/(a/cos(x)^4)^(5/2)","A"
68,0,0,71,1.832000," ","int(((b*sec(d*x+c))^p)^n,x)","\int \left(\left(b \sec \left(d x +c \right)\right)^{p}\right)^{n}\, dx"," ",0,"int(((b*sec(d*x+c))^p)^n,x)","F"
69,0,0,73,1.656000," ","int((a*(b*sec(d*x+c))^p)^n,x)","\int \left(a \left(b \sec \left(d x +c \right)\right)^{p}\right)^{n}\, dx"," ",0,"int((a*(b*sec(d*x+c))^p)^n,x)","F"
70,1,152,109,1.201000," ","int(sec(d*x+c)^4*(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) \left(5 i \left(\cos^{3}\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)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)-5 \left(\cos^{3}\left(d x +c \right)\right)+5 \left(\cos^{2}\left(d x +c \right)\right)-3 \cos \left(d x +c \right)+3\right) \sqrt{\frac{b}{\cos \left(d x +c \right)}}}{21 d \sin \left(d x +c \right)^{3} \cos \left(d x +c \right)^{3}}"," ",0,"-2/21/d*(1+cos(d*x+c))^2*(-1+cos(d*x+c))*(5*I*cos(d*x+c)^3*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*cos(d*x+c)^3+5*cos(d*x+c)^2-3*cos(d*x+c)+3)*(b/cos(d*x+c))^(1/2)/sin(d*x+c)^3/cos(d*x+c)^3","C"
71,1,356,107,0.915000," ","int(sec(d*x+c)^3*(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(3 i \left(\cos^{3}\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)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)-3 i \left(\cos^{3}\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)+3 i \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)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)-3 i \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)+3 \left(\cos^{3}\left(d x +c \right)\right)-2 \left(\cos^{2}\left(d x +c \right)\right)-1\right) \sqrt{\frac{b}{\cos \left(d x +c \right)}}}{5 d \cos \left(d x +c \right)^{2} \sin \left(d x +c \right)^{5}}"," ",0,"-2/5/d*(1+cos(d*x+c))^2*(-1+cos(d*x+c))^2*(3*I*cos(d*x+c)^3*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*cos(d*x+c)^3*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)+3*I*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*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)+3*cos(d*x+c)^3-2*cos(d*x+c)^2-1)*(b/cos(d*x+c))^(1/2)/cos(d*x+c)^2/sin(d*x+c)^5","C"
72,1,130,85,0.786000," ","int(sec(d*x+c)^2*(b*sec(d*x+c))^(1/2),x)","-\frac{2 \sqrt{\frac{b}{\cos \left(d x +c \right)}}\, \left(-1+\cos \left(d x +c \right)\right) \left(i \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{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)}}-\cos \left(d x +c \right)+1\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))*(I*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*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)*(1+cos(d*x+c))^2/sin(d*x+c)^3/cos(d*x+c)","C"
73,1,314,83,0.915000," ","int(sec(d*x+c)*(b*sec(d*x+c))^(1/2),x)","-\frac{2 \sqrt{\frac{b}{\cos \left(d x +c \right)}}\, \left(1+\cos \left(d x +c \right)\right)^{2} \left(-1+\cos \left(d x +c \right)\right)^{2} \left(i \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{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)}}-i \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) \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 \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 \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)}}+\cos \left(d x +c \right)-1\right)}{d \sin \left(d x +c \right)^{5}}"," ",0,"-2/d*(b/cos(d*x+c))^(1/2)*(1+cos(d*x+c))^2*(-1+cos(d*x+c))^2*(I*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*(1/(1+cos(d*x+c)))^(1/2)-I*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)+I*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*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)+cos(d*x+c)-1)/sin(d*x+c)^5","C"
74,1,98,60,0.812000," ","int((b*sec(d*x+c))^(1/2),x)","-\frac{2 i \sqrt{\frac{b}{\cos \left(d x +c \right)}}\, \left(-1+\cos \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) \left(1+\cos \left(d x +c \right)\right)^{2}}{d \sin \left(d x +c \right)^{2}}"," ",0,"-2*I/d*(b/cos(d*x+c))^(1/2)*(-1+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)*(1+cos(d*x+c))^2/sin(d*x+c)^2","C"
75,1,303,61,0.874000," ","int(cos(d*x+c)*(b*sec(d*x+c))^(1/2),x)","\frac{2 \left(i \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{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)}}-i \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) \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 \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 \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)}}-\left(\cos^{2}\left(d x +c \right)\right)+\cos \left(d x +c \right)\right) \sqrt{\frac{b}{\cos \left(d x +c \right)}}}{d \sin \left(d x +c \right)}"," ",0,"2/d*(I*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*(1/(1+cos(d*x+c)))^(1/2)-I*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)+I*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*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)-cos(d*x+c)^2+cos(d*x+c))*(b/cos(d*x+c))^(1/2)/sin(d*x+c)","C"
76,1,123,83,0.894000," ","int(cos(d*x+c)^2*(b*sec(d*x+c))^(1/2),x)","-\frac{2 \left(-1+\cos \left(d x +c \right)\right) \left(i \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)}}-\left(\cos^{2}\left(d x +c \right)\right)+\cos \left(d x +c \right)\right) \left(1+\cos \left(d x +c \right)\right)^{2} \sqrt{\frac{b}{\cos \left(d x +c \right)}}}{3 d \sin \left(d x +c \right)^{3}}"," ",0,"-2/3/d*(-1+cos(d*x+c))*(I*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)-cos(d*x+c)^2+cos(d*x+c))*(1+cos(d*x+c))^2*(b/cos(d*x+c))^(1/2)/sin(d*x+c)^3","C"
77,1,315,86,0.961000," ","int(cos(d*x+c)^3*(b*sec(d*x+c))^(1/2),x)","\frac{2 \sqrt{\frac{b}{\cos \left(d x +c \right)}}\, \left(3 i \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{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)}}-3 i \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) \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 i \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 i \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)}}-\left(\cos^{4}\left(d x +c \right)\right)-2 \left(\cos^{2}\left(d x +c \right)\right)+3 \cos \left(d x +c \right)\right)}{5 d \sin \left(d x +c \right)}"," ",0,"2/5/d*(b/cos(d*x+c))^(1/2)*(3*I*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*(1/(1+cos(d*x+c)))^(1/2)-3*I*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)+3*I*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*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)-cos(d*x+c)^4-2*cos(d*x+c)^2+3*cos(d*x+c))/sin(d*x+c)","C"
78,1,145,107,1.000000," ","int(cos(d*x+c)^4*(b*sec(d*x+c))^(1/2),x)","-\frac{2 \left(-1+\cos \left(d x +c \right)\right) \left(5 i \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 \left(\cos^{4}\left(d x +c \right)\right)+3 \left(\cos^{3}\left(d x +c \right)\right)-5 \left(\cos^{2}\left(d x +c \right)\right)+5 \cos \left(d x +c \right)\right) \left(1+\cos \left(d x +c \right)\right)^{2} \sqrt{\frac{b}{\cos \left(d x +c \right)}}}{21 d \sin \left(d x +c \right)^{3}}"," ",0,"-2/21/d*(-1+cos(d*x+c))*(5*I*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*cos(d*x+c)^4+3*cos(d*x+c)^3-5*cos(d*x+c)^2+5*cos(d*x+c))*(1+cos(d*x+c))^2*(b/cos(d*x+c))^(1/2)/sin(d*x+c)^3","C"
79,1,325,110,0.940000," ","int(cos(d*x+c)^5*(b*sec(d*x+c))^(1/2),x)","\frac{2 \sqrt{\frac{b}{\cos \left(d x +c \right)}}\, \left(21 i \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{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)}}-21 i \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) \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 \left(\cos^{6}\left(d x +c \right)\right)+21 i \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)}}-21 i \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 \left(\cos^{4}\left(d x +c \right)\right)-14 \left(\cos^{2}\left(d x +c \right)\right)+21 \cos \left(d x +c \right)\right)}{45 d \sin \left(d x +c \right)}"," ",0,"2/45/d*(b/cos(d*x+c))^(1/2)*(21*I*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*(1/(1+cos(d*x+c)))^(1/2)-21*I*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)-5*cos(d*x+c)^6+21*I*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)-21*I*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)-2*cos(d*x+c)^4-14*cos(d*x+c)^2+21*cos(d*x+c))/sin(d*x+c)","C"
80,1,152,107,0.768000," ","int(sec(d*x+c)^3*(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(5 i \left(\cos^{3}\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)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)-5 \left(\cos^{3}\left(d x +c \right)\right)+5 \left(\cos^{2}\left(d x +c \right)\right)-3 \cos \left(d x +c \right)+3\right) \left(\frac{b}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}}}{21 d \sin \left(d x +c \right)^{3} \cos \left(d x +c \right)^{2}}"," ",0,"-2/21/d*(1+cos(d*x+c))^2*(-1+cos(d*x+c))*(5*I*cos(d*x+c)^3*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*cos(d*x+c)^3+5*cos(d*x+c)^2-3*cos(d*x+c)+3)*(b/cos(d*x+c))^(3/2)/sin(d*x+c)^3/cos(d*x+c)^2","C"
81,1,356,110,0.762000," ","int(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)^{2} \left(3 i \left(\cos^{3}\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)-3 i \left(\cos^{3}\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)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)+3 i \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)-3 i \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)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)-3 \left(\cos^{3}\left(d x +c \right)\right)+2 \left(\cos^{2}\left(d x +c \right)\right)+1\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*(3*I*cos(d*x+c)^3*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)-3*I*cos(d*x+c)^3*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*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)-3*I*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*cos(d*x+c)^3+2*cos(d*x+c)^2+1)*(b/cos(d*x+c))^(3/2)/sin(d*x+c)^5/cos(d*x+c)","C"
82,1,122,83,0.663000," ","int(sec(d*x+c)*(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 \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{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)}}-\cos \left(d x +c \right)+1\right) \left(\frac{b}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}}}{3 d \sin \left(d x +c \right)^{3}}"," ",0,"-2/3/d*(1+cos(d*x+c))^2*(-1+cos(d*x+c))*(I*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*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)*(b/cos(d*x+c))^(3/2)/sin(d*x+c)^3","C"
83,1,320,86,0.844000," ","int((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)^{2} \left(i \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{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)}}-i \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) \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 \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 \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)}}+\cos \left(d x +c \right)-1\right) \cos \left(d x +c \right) \left(\frac{b}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}}}{d \sin \left(d x +c \right)^{5}}"," ",0,"-2/d*(1+cos(d*x+c))^2*(-1+cos(d*x+c))^2*(I*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*(1/(1+cos(d*x+c)))^(1/2)-I*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)+I*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*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)+cos(d*x+c)-1)*cos(d*x+c)*(b/cos(d*x+c))^(3/2)/sin(d*x+c)^5","C"
84,1,98,61,0.746000," ","int(cos(d*x+c)*(b*sec(d*x+c))^(3/2),x)","-\frac{2 i \left(\frac{b}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \left(-1+\cos \left(d x +c \right)\right) \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \left(1+\cos \left(d x +c \right)\right)^{3} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}}{d \sin \left(d x +c \right)^{2}}"," ",0,"-2*I/d*(b/cos(d*x+c))^(3/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*(-1+cos(d*x+c))*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*(1+cos(d*x+c))^3*(1/(1+cos(d*x+c)))^(1/2)/sin(d*x+c)^2","C"
85,1,309,63,0.770000," ","int(cos(d*x+c)^2*(b*sec(d*x+c))^(3/2),x)","\frac{2 \left(i \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{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)}}-i \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) \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 \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 \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)}}-\left(\cos^{2}\left(d x +c \right)\right)+\cos \left(d x +c \right)\right) \cos \left(d x +c \right) \left(\frac{b}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}}}{d \sin \left(d x +c \right)}"," ",0,"2/d*(I*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*(1/(1+cos(d*x+c)))^(1/2)-I*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)+I*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*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)-cos(d*x+c)^2+cos(d*x+c))*cos(d*x+c)*(b/cos(d*x+c))^(3/2)/sin(d*x+c)","C"
86,1,129,86,0.824000," ","int(cos(d*x+c)^3*(b*sec(d*x+c))^(3/2),x)","\frac{2 \left(1+\cos \left(d x +c \right)\right)^{2} \left(\frac{b}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \left(-1+\cos \left(d x +c \right)\right) \cos \left(d x +c \right) \left(-i \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)}}+\cos^{2}\left(d x +c \right)-\cos \left(d x +c \right)\right)}{3 d \sin \left(d x +c \right)^{3}}"," ",0,"2/3/d*(1+cos(d*x+c))^2*(b/cos(d*x+c))^(3/2)*(-1+cos(d*x+c))*cos(d*x+c)*(-I*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)+cos(d*x+c)^2-cos(d*x+c))/sin(d*x+c)^3","C"
87,1,319,88,0.843000," ","int(cos(d*x+c)^4*(b*sec(d*x+c))^(3/2),x)","-\frac{2 \left(-3 i \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{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)}}+3 i \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) \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 i \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 i \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)}}+\cos^{4}\left(d x +c \right)+2 \left(\cos^{2}\left(d x +c \right)\right)-3 \cos \left(d x +c \right)\right) \cos \left(d x +c \right) \left(\frac{b}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}}}{5 d \sin \left(d x +c \right)}"," ",0,"-2/5/d*(-3*I*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*(1/(1+cos(d*x+c)))^(1/2)+3*I*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)-3*I*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*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)+cos(d*x+c)^4+2*cos(d*x+c)^2-3*cos(d*x+c))*cos(d*x+c)*(b/cos(d*x+c))^(3/2)/sin(d*x+c)","C"
88,1,151,110,0.944000," ","int(cos(d*x+c)^5*(b*sec(d*x+c))^(3/2),x)","\frac{2 \left(1+\cos \left(d x +c \right)\right)^{2} \left(\frac{b}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \left(-1+\cos \left(d x +c \right)\right) \cos \left(d x +c \right) \left(-5 i \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 \left(\cos^{4}\left(d x +c \right)\right)-3 \left(\cos^{3}\left(d x +c \right)\right)+5 \left(\cos^{2}\left(d x +c \right)\right)-5 \cos \left(d x +c \right)\right)}{21 d \sin \left(d x +c \right)^{3}}"," ",0,"2/21/d*(1+cos(d*x+c))^2*(b/cos(d*x+c))^(3/2)*(-1+cos(d*x+c))*cos(d*x+c)*(-5*I*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*cos(d*x+c)^4-3*cos(d*x+c)^3+5*cos(d*x+c)^2-5*cos(d*x+c))/sin(d*x+c)^3","C"
89,1,331,112,0.946000," ","int(cos(d*x+c)^6*(b*sec(d*x+c))^(3/2),x)","\frac{2 \left(21 i \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{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)}}-21 i \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) \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 \left(\cos^{6}\left(d x +c \right)\right)+21 i \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)}}-21 i \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 \left(\cos^{4}\left(d x +c \right)\right)-14 \left(\cos^{2}\left(d x +c \right)\right)+21 \cos \left(d x +c \right)\right) \cos \left(d x +c \right) \left(\frac{b}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}}}{45 d \sin \left(d x +c \right)}"," ",0,"2/45/d*(21*I*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*(1/(1+cos(d*x+c)))^(1/2)-21*I*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)-5*cos(d*x+c)^6+21*I*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)-21*I*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)-2*cos(d*x+c)^4-14*cos(d*x+c)^2+21*cos(d*x+c))*cos(d*x+c)*(b/cos(d*x+c))^(3/2)/sin(d*x+c)","C"
90,1,152,110,0.805000," ","int(sec(d*x+c)^2*(b*sec(d*x+c))^(5/2),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 \left(\cos^{3}\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)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)-5 \left(\cos^{3}\left(d x +c \right)\right)+5 \left(\cos^{2}\left(d x +c \right)\right)-3 \cos \left(d x +c \right)+3\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))*(5*I*cos(d*x+c)^3*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*cos(d*x+c)^3+5*cos(d*x+c)^2-3*cos(d*x+c)+3)*(b/cos(d*x+c))^(5/2)/sin(d*x+c)^3/cos(d*x+c)","C"
91,1,348,109,0.823000," ","int(sec(d*x+c)*(b*sec(d*x+c))^(5/2),x)","\frac{2 \left(1+\cos \left(d x +c \right)\right)^{2} \left(-1+\cos \left(d x +c \right)\right)^{2} \left(3 i \left(\cos^{3}\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)-3 i \left(\cos^{3}\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)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)+3 i \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)-3 i \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)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)-3 \left(\cos^{3}\left(d x +c \right)\right)+2 \left(\cos^{2}\left(d x +c \right)\right)+1\right) \left(\frac{b}{\cos \left(d x +c \right)}\right)^{\frac{5}{2}}}{5 d \sin \left(d x +c \right)^{5}}"," ",0,"2/5/d*(1+cos(d*x+c))^2*(-1+cos(d*x+c))^2*(3*I*cos(d*x+c)^3*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)-3*I*cos(d*x+c)^3*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*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)-3*I*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*cos(d*x+c)^3+2*cos(d*x+c)^2+1)*(b/cos(d*x+c))^(5/2)/sin(d*x+c)^5","C"
92,1,128,86,0.786000," ","int((b*sec(d*x+c))^(5/2),x)","-\frac{2 \left(-1+\cos \left(d x +c \right)\right) \left(i \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{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)}}-\cos \left(d x +c \right)+1\right) \cos \left(d x +c \right) \left(1+\cos \left(d x +c \right)\right)^{2} \left(\frac{b}{\cos \left(d x +c \right)}\right)^{\frac{5}{2}}}{3 d \sin \left(d x +c \right)^{3}}"," ",0,"-2/3/d*(-1+cos(d*x+c))*(I*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*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+cos(d*x+c))^2*(b/cos(d*x+c))^(5/2)/sin(d*x+c)^3","C"
93,1,324,88,0.957000," ","int(cos(d*x+c)*(b*sec(d*x+c))^(5/2),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 \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) \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 \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{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)}}+i \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)}}-i \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)}}-\cos \left(d x +c \right)+1\right) \left(\cos^{2}\left(d x +c \right)\right) \left(\frac{b}{\cos \left(d x +c \right)}\right)^{\frac{5}{2}}}{d \sin \left(d x +c \right)^{5}}"," ",0,"2/d*(1+cos(d*x+c))^2*(-1+cos(d*x+c))^2*(I*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)-I*cos(d*x+c)*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*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*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)-cos(d*x+c)+1)*cos(d*x+c)^2*(b/cos(d*x+c))^(5/2)/sin(d*x+c)^5","C"
94,1,98,63,0.813000," ","int(cos(d*x+c)^2*(b*sec(d*x+c))^(5/2),x)","-\frac{2 i \left(\frac{b}{\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \left(-1+\cos \left(d x +c \right)\right) \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \left(1+\cos \left(d x +c \right)\right)^{5} \left(\frac{1}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}}}{d \sin \left(d x +c \right)^{2}}"," ",0,"-2*I/d*(b/cos(d*x+c))^(5/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*(-1+cos(d*x+c))*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*(1+cos(d*x+c))^5*(1/(1+cos(d*x+c)))^(3/2)/sin(d*x+c)^2","C"
95,1,311,63,0.820000," ","int(cos(d*x+c)^3*(b*sec(d*x+c))^(5/2),x)","-\frac{2 \left(-i \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{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)}}+i \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) \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 \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 \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)}}+\cos^{2}\left(d x +c \right)-\cos \left(d x +c \right)\right) \left(\cos^{2}\left(d x +c \right)\right) \left(\frac{b}{\cos \left(d x +c \right)}\right)^{\frac{5}{2}}}{d \sin \left(d x +c \right)}"," ",0,"-2/d*(-I*cos(d*x+c)*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*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)-I*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*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)+cos(d*x+c)^2-cos(d*x+c))*cos(d*x+c)^2*(b/cos(d*x+c))^(5/2)/sin(d*x+c)","C"
96,1,131,88,0.824000," ","int(cos(d*x+c)^4*(b*sec(d*x+c))^(5/2),x)","\frac{2 \left(1+\cos \left(d x +c \right)\right)^{2} \left(\frac{b}{\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \left(-1+\cos \left(d x +c \right)\right) \left(\cos^{2}\left(d x +c \right)\right) \left(-i \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)}}+\cos^{2}\left(d x +c \right)-\cos \left(d x +c \right)\right)}{3 d \sin \left(d x +c \right)^{3}}"," ",0,"2/3/d*(1+cos(d*x+c))^2*(b/cos(d*x+c))^(5/2)*(-1+cos(d*x+c))*cos(d*x+c)^2*(-I*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)+cos(d*x+c)^2-cos(d*x+c))/sin(d*x+c)^3","C"
97,1,321,88,0.945000," ","int(cos(d*x+c)^5*(b*sec(d*x+c))^(5/2),x)","-\frac{2 \left(\frac{b}{\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \left(\cos^{2}\left(d x +c \right)\right) \left(-3 i \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{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)}}+3 i \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) \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 i \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 i \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)}}+\cos^{4}\left(d x +c \right)+2 \left(\cos^{2}\left(d x +c \right)\right)-3 \cos \left(d x +c \right)\right)}{5 d \sin \left(d x +c \right)}"," ",0,"-2/5/d*(b/cos(d*x+c))^(5/2)*cos(d*x+c)^2*(-3*I*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*(1/(1+cos(d*x+c)))^(1/2)+3*I*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)-3*I*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*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)+cos(d*x+c)^4+2*cos(d*x+c)^2-3*cos(d*x+c))/sin(d*x+c)","C"
98,1,153,112,0.974000," ","int(cos(d*x+c)^6*(b*sec(d*x+c))^(5/2),x)","-\frac{2 \left(1+\cos \left(d x +c \right)\right)^{2} \left(\frac{b}{\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \left(-1+\cos \left(d x +c \right)\right) \left(\cos^{2}\left(d x +c \right)\right) \left(5 i \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 \left(\cos^{4}\left(d x +c \right)\right)+3 \left(\cos^{3}\left(d x +c \right)\right)-5 \left(\cos^{2}\left(d x +c \right)\right)+5 \cos \left(d x +c \right)\right)}{21 d \sin \left(d x +c \right)^{3}}"," ",0,"-2/21/d*(1+cos(d*x+c))^2*(b/cos(d*x+c))^(5/2)*(-1+cos(d*x+c))*cos(d*x+c)^2*(5*I*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*cos(d*x+c)^4+3*cos(d*x+c)^3-5*cos(d*x+c)^2+5*cos(d*x+c))/sin(d*x+c)^3","C"
99,1,333,112,1.033000," ","int(cos(d*x+c)^7*(b*sec(d*x+c))^(5/2),x)","-\frac{2 \left(\frac{b}{\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \left(\cos^{2}\left(d x +c \right)\right) \left(5 \left(\cos^{6}\left(d x +c \right)\right)+21 i \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) \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)}}-21 i \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{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)}}+21 i \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)}}-21 i \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 \left(\cos^{4}\left(d x +c \right)\right)+14 \left(\cos^{2}\left(d x +c \right)\right)-21 \cos \left(d x +c \right)\right)}{45 d \sin \left(d x +c \right)}"," ",0,"-2/45/d*(b/cos(d*x+c))^(5/2)*cos(d*x+c)^2*(5*cos(d*x+c)^6+21*I*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)-21*I*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*(1/(1+cos(d*x+c)))^(1/2)+21*I*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)-21*I*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)+2*cos(d*x+c)^4+14*cos(d*x+c)^2-21*cos(d*x+c))/sin(d*x+c)","C"
100,1,354,110,0.915000," ","int((b*sec(d*x+c))^(7/2),x)","\frac{2 \left(-1+\cos \left(d x +c \right)\right)^{2} \left(3 i \left(\cos^{3}\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)-3 i \left(\cos^{3}\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)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)+3 i \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)-3 i \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)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)-3 \left(\cos^{3}\left(d x +c \right)\right)+2 \left(\cos^{2}\left(d x +c \right)\right)+1\right) \cos \left(d x +c \right) \left(1+\cos \left(d x +c \right)\right)^{2} \left(\frac{b}{\cos \left(d x +c \right)}\right)^{\frac{7}{2}}}{5 d \sin \left(d x +c \right)^{5}}"," ",0,"2/5/d*(-1+cos(d*x+c))^2*(3*I*cos(d*x+c)^3*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)-3*I*cos(d*x+c)^3*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*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)-3*I*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*cos(d*x+c)^3+2*cos(d*x+c)^2+1)*cos(d*x+c)*(1+cos(d*x+c))^2*(b/cos(d*x+c))^(7/2)/sin(d*x+c)^5","C"
101,1,152,112,0.992000," ","int(sec(d*x+c)^5/(b*sec(d*x+c))^(1/2),x)","-\frac{2 \left(-1+\cos \left(d x +c \right)\right) \left(5 i \left(\cos^{3}\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)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)-5 \left(\cos^{3}\left(d x +c \right)\right)+5 \left(\cos^{2}\left(d x +c \right)\right)-3 \cos \left(d x +c \right)+3\right) \left(1+\cos \left(d x +c \right)\right)^{2}}{21 d \cos \left(d x +c \right)^{4} \sqrt{\frac{b}{\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)^{3}}"," ",0,"-2/21/d*(-1+cos(d*x+c))*(5*I*cos(d*x+c)^3*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*cos(d*x+c)^3+5*cos(d*x+c)^2-3*cos(d*x+c)+3)*(1+cos(d*x+c))^2/cos(d*x+c)^4/(b/cos(d*x+c))^(1/2)/sin(d*x+c)^3","C"
102,1,356,109,1.050000," ","int(sec(d*x+c)^4/(b*sec(d*x+c))^(1/2),x)","-\frac{2 \left(-1+\cos \left(d x +c \right)\right)^{2} \left(3 i \left(\cos^{3}\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)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)-3 i \left(\cos^{3}\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)+3 i \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)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)-3 i \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)+3 \left(\cos^{3}\left(d x +c \right)\right)-2 \left(\cos^{2}\left(d x +c \right)\right)-1\right) \left(1+\cos \left(d x +c \right)\right)^{2}}{5 d \sin \left(d x +c \right)^{5} \cos \left(d x +c \right)^{3} \sqrt{\frac{b}{\cos \left(d x +c \right)}}}"," ",0,"-2/5/d*(-1+cos(d*x+c))^2*(3*I*cos(d*x+c)^3*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*cos(d*x+c)^3*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)+3*I*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*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)+3*cos(d*x+c)^3-2*cos(d*x+c)^2-1)*(1+cos(d*x+c))^2/sin(d*x+c)^5/cos(d*x+c)^3/(b/cos(d*x+c))^(1/2)","C"
103,1,130,88,0.892000," ","int(sec(d*x+c)^3/(b*sec(d*x+c))^(1/2),x)","-\frac{2 \left(-1+\cos \left(d x +c \right)\right) \left(i \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{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)}}-\cos \left(d x +c \right)+1\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)^{2} \sqrt{\frac{b}{\cos \left(d x +c \right)}}}"," ",0,"-2/3/d*(-1+cos(d*x+c))*(I*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*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)*(1+cos(d*x+c))^2/sin(d*x+c)^3/cos(d*x+c)^2/(b/cos(d*x+c))^(1/2)","C"
104,1,319,85,0.963000," ","int(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 \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) \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 \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{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)}}+i \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)}}-i \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)}}-\cos \left(d x +c \right)+1\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*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)-I*cos(d*x+c)*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*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*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)-cos(d*x+c)+1)*(b/cos(d*x+c))^(1/2)/b/sin(d*x+c)^5","C"
105,1,98,63,0.846000," ","int(sec(d*x+c)/(b*sec(d*x+c))^(1/2),x)","-\frac{2 i \left(\frac{1}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \left(-1+\cos \left(d x +c \right)\right) \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \left(1+\cos \left(d x +c \right)\right)^{2}}{d \sqrt{\frac{b}{\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)^{2}}"," ",0,"-2*I/d*(1/(1+cos(d*x+c)))^(3/2)*(-1+cos(d*x+c))*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*(1+cos(d*x+c))^2/(b/cos(d*x+c))^(1/2)/(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)/sin(d*x+c)^2","C"
106,1,306,60,0.905000," ","int(1/(b*sec(d*x+c))^(1/2),x)","\frac{2 \left(i \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{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)}}-i \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) \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 \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 \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)}}-\left(\cos^{2}\left(d x +c \right)\right)+\cos \left(d x +c \right)\right) \sqrt{\frac{b}{\cos \left(d x +c \right)}}}{d \sin \left(d x +c \right) b}"," ",0,"2/d*(I*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*(1/(1+cos(d*x+c)))^(1/2)-I*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)+I*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*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)-cos(d*x+c)^2+cos(d*x+c))*(b/cos(d*x+c))^(1/2)/sin(d*x+c)/b","C"
107,1,126,85,1.020000," ","int(cos(d*x+c)/(b*sec(d*x+c))^(1/2),x)","-\frac{2 \left(-1+\cos \left(d x +c \right)\right) \left(i \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)}}-\left(\cos^{2}\left(d x +c \right)\right)+\cos \left(d x +c \right)\right) \left(1+\cos \left(d x +c \right)\right)^{2} \sqrt{\frac{b}{\cos \left(d x +c \right)}}}{3 d \sin \left(d x +c \right)^{3} b}"," ",0,"-2/3/d*(-1+cos(d*x+c))*(I*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)-cos(d*x+c)^2+cos(d*x+c))*(1+cos(d*x+c))^2*(b/cos(d*x+c))^(1/2)/sin(d*x+c)^3/b","C"
108,1,318,83,1.168000," ","int(cos(d*x+c)^2/(b*sec(d*x+c))^(1/2),x)","\frac{2 \left(3 i \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\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) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-3 i \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) \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 i \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 i \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)}}-\left(\cos^{4}\left(d x +c \right)\right)-2 \left(\cos^{2}\left(d x +c \right)\right)+3 \cos \left(d x +c \right)\right) \sqrt{\frac{b}{\cos \left(d x +c \right)}}}{5 d \sin \left(d x +c \right) b}"," ",0,"2/5/d*(3*I*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*(1/(1+cos(d*x+c)))^(1/2)-3*I*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)+3*I*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*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)-cos(d*x+c)^4-2*cos(d*x+c)^2+3*cos(d*x+c))*(b/cos(d*x+c))^(1/2)/sin(d*x+c)/b","C"
109,1,148,109,0.978000," ","int(cos(d*x+c)^3/(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) \left(5 i \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 \left(\cos^{4}\left(d x +c \right)\right)+3 \left(\cos^{3}\left(d x +c \right)\right)-5 \left(\cos^{2}\left(d x +c \right)\right)+5 \cos \left(d x +c \right)\right) \sqrt{\frac{b}{\cos \left(d x +c \right)}}}{21 d \sin \left(d x +c \right)^{3} b}"," ",0,"-2/21/d*(1+cos(d*x+c))^2*(-1+cos(d*x+c))*(5*I*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*cos(d*x+c)^4+3*cos(d*x+c)^3-5*cos(d*x+c)^2+5*cos(d*x+c))*(b/cos(d*x+c))^(1/2)/sin(d*x+c)^3/b","C"
110,1,328,107,0.986000," ","int(cos(d*x+c)^4/(b*sec(d*x+c))^(1/2),x)","\frac{2 \left(21 i \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{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)}}-21 i \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) \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 \left(\cos^{6}\left(d x +c \right)\right)+21 i \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)}}-21 i \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 \left(\cos^{4}\left(d x +c \right)\right)-14 \left(\cos^{2}\left(d x +c \right)\right)+21 \cos \left(d x +c \right)\right) \sqrt{\frac{b}{\cos \left(d x +c \right)}}}{45 d \sin \left(d x +c \right) b}"," ",0,"2/45/d*(21*I*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*(1/(1+cos(d*x+c)))^(1/2)-21*I*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)-5*cos(d*x+c)^6+21*I*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)-21*I*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)-2*cos(d*x+c)^4-14*cos(d*x+c)^2+21*cos(d*x+c))*(b/cos(d*x+c))^(1/2)/sin(d*x+c)/b","C"
111,1,152,112,0.893000," ","int(sec(d*x+c)^6/(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(5 i \left(\cos^{3}\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)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)-5 \left(\cos^{3}\left(d x +c \right)\right)+5 \left(\cos^{2}\left(d x +c \right)\right)-3 \cos \left(d x +c \right)+3\right)}{21 d \sin \left(d x +c \right)^{3} \cos \left(d x +c \right)^{5} \left(\frac{b}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}}}"," ",0,"-2/21/d*(1+cos(d*x+c))^2*(-1+cos(d*x+c))*(5*I*cos(d*x+c)^3*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*cos(d*x+c)^3+5*cos(d*x+c)^2-3*cos(d*x+c)+3)/sin(d*x+c)^3/cos(d*x+c)^5/(b/cos(d*x+c))^(3/2)","C"
112,1,356,112,0.964000," ","int(sec(d*x+c)^5/(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)^{2} \left(3 i \left(\cos^{3}\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)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)-3 i \left(\cos^{3}\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)+3 i \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)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)-3 i \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)+3 \left(\cos^{3}\left(d x +c \right)\right)-2 \left(\cos^{2}\left(d x +c \right)\right)-1\right)}{5 d \sin \left(d x +c \right)^{5} \cos \left(d x +c \right)^{4} \left(\frac{b}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}}}"," ",0,"-2/5/d*(1+cos(d*x+c))^2*(-1+cos(d*x+c))^2*(3*I*cos(d*x+c)^3*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*cos(d*x+c)^3*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)+3*I*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*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)+3*cos(d*x+c)^3-2*cos(d*x+c)^2-1)/sin(d*x+c)^5/cos(d*x+c)^4/(b/cos(d*x+c))^(3/2)","C"
113,1,125,88,0.862000," ","int(sec(d*x+c)^4/(b*sec(d*x+c))^(3/2),x)","-\frac{2 \left(-1+\cos \left(d x +c \right)\right) \left(i \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{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)}}-\cos \left(d x +c \right)+1\right) \left(1+\cos \left(d x +c \right)\right)^{2} \left(\frac{b}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}}}{3 d \,b^{3} \sin \left(d x +c \right)^{3}}"," ",0,"-2/3/d*(-1+cos(d*x+c))*(I*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*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)*(1+cos(d*x+c))^2*(b/cos(d*x+c))^(3/2)/b^3/sin(d*x+c)^3","C"
114,1,324,88,1.019000," ","int(sec(d*x+c)^3/(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)^{2} \left(i \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) \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 \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{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)}}+i \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)}}-i \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)}}-\cos \left(d x +c \right)+1\right)}{d \cos \left(d x +c \right)^{2} \sin \left(d x +c \right)^{5} \left(\frac{b}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}}}"," ",0,"2/d*(1+cos(d*x+c))^2*(-1+cos(d*x+c))^2*(I*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)-I*cos(d*x+c)*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*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*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)-cos(d*x+c)+1)/cos(d*x+c)^2/sin(d*x+c)^5/(b/cos(d*x+c))^(3/2)","C"
115,1,98,63,0.738000," ","int(sec(d*x+c)^2/(b*sec(d*x+c))^(3/2),x)","-\frac{2 i \left(\frac{1}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \left(-1+\cos \left(d x +c \right)\right) \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \left(1+\cos \left(d x +c \right)\right)^{2}}{d \left(\frac{b}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sin \left(d x +c \right)^{2}}"," ",0,"-2*I/d*(1/(1+cos(d*x+c)))^(5/2)*(-1+cos(d*x+c))*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*(1+cos(d*x+c))^2/(b/cos(d*x+c))^(3/2)/(cos(d*x+c)/(1+cos(d*x+c)))^(3/2)/sin(d*x+c)^2","C"
116,1,311,63,0.778000," ","int(sec(d*x+c)/(b*sec(d*x+c))^(3/2),x)","-\frac{2 \left(-i \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{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)}}+i \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) \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 \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 \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)}}+\cos^{2}\left(d x +c \right)-\cos \left(d x +c \right)\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*cos(d*x+c)*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*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)-I*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*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)+cos(d*x+c)^2-cos(d*x+c))/cos(d*x+c)^2/(b/cos(d*x+c))^(3/2)/sin(d*x+c)","C"
117,1,131,88,0.789000," ","int(1/(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 \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)}}-\left(\cos^{2}\left(d x +c \right)\right)+\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*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)-cos(d*x+c)^2+cos(d*x+c))/sin(d*x+c)^3/cos(d*x+c)^2/(b/cos(d*x+c))^(3/2)","C"
118,1,323,85,0.953000," ","int(cos(d*x+c)/(b*sec(d*x+c))^(3/2),x)","\frac{\frac{6 i \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{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)}}}{5}-\frac{6 i \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) \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 \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 \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)}}}{5}-\frac{2 \left(\cos^{4}\left(d x +c \right)\right)}{5}-\frac{4 \left(\cos^{2}\left(d x +c \right)\right)}{5}+\frac{6 \cos \left(d x +c \right)}{5}}{d \sin \left(d x +c \right) \cos \left(d x +c \right)^{2} \left(\frac{b}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}}}"," ",0,"2/5/d*(3*I*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*(1/(1+cos(d*x+c)))^(1/2)-3*I*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)+3*I*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*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)-cos(d*x+c)^4-2*cos(d*x+c)^2+3*cos(d*x+c))/sin(d*x+c)/cos(d*x+c)^2/(b/cos(d*x+c))^(3/2)","C"
119,1,153,110,0.897000," ","int(cos(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(5 i \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 \left(\cos^{4}\left(d x +c \right)\right)+3 \left(\cos^{3}\left(d x +c \right)\right)-5 \left(\cos^{2}\left(d x +c \right)\right)+5 \cos \left(d x +c \right)\right)}{21 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,"-2/21/d*(1+cos(d*x+c))^2*(-1+cos(d*x+c))*(5*I*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*cos(d*x+c)^4+3*cos(d*x+c)^3-5*cos(d*x+c)^2+5*cos(d*x+c))/sin(d*x+c)^3/cos(d*x+c)^2/(b/cos(d*x+c))^(3/2)","C"
120,1,333,109,0.978000," ","int(cos(d*x+c)^3/(b*sec(d*x+c))^(3/2),x)","\frac{\frac{14 i \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{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)}}}{15}-\frac{14 i \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) \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)}}}{15}-\frac{2 \left(\cos^{6}\left(d x +c \right)\right)}{9}+\frac{14 i \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)}}}{15}-\frac{14 i \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)}}}{15}-\frac{4 \left(\cos^{4}\left(d x +c \right)\right)}{45}-\frac{28 \left(\cos^{2}\left(d x +c \right)\right)}{45}+\frac{14 \cos \left(d x +c \right)}{15}}{d \sin \left(d x +c \right) \cos \left(d x +c \right)^{2} \left(\frac{b}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}}}"," ",0,"2/45/d*(21*I*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*(1/(1+cos(d*x+c)))^(1/2)-21*I*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)-5*cos(d*x+c)^6+21*I*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)-21*I*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)-2*cos(d*x+c)^4-14*cos(d*x+c)^2+21*cos(d*x+c))/sin(d*x+c)/cos(d*x+c)^2/(b/cos(d*x+c))^(3/2)","C"
121,1,152,112,0.899000," ","int(sec(d*x+c)^7/(b*sec(d*x+c))^(5/2),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 \left(\cos^{3}\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)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)-5 \left(\cos^{3}\left(d x +c \right)\right)+5 \left(\cos^{2}\left(d x +c \right)\right)-3 \cos \left(d x +c \right)+3\right)}{21 d \sin \left(d x +c \right)^{3} \cos \left(d x +c \right)^{6} \left(\frac{b}{\cos \left(d x +c \right)}\right)^{\frac{5}{2}}}"," ",0,"-2/21/d*(1+cos(d*x+c))^2*(-1+cos(d*x+c))*(5*I*cos(d*x+c)^3*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*cos(d*x+c)^3+5*cos(d*x+c)^2-3*cos(d*x+c)+3)/sin(d*x+c)^3/cos(d*x+c)^6/(b/cos(d*x+c))^(5/2)","C"
122,1,351,112,1.029000," ","int(sec(d*x+c)^6/(b*sec(d*x+c))^(5/2),x)","-\frac{2 \left(1+\cos \left(d x +c \right)\right)^{2} \left(-1+\cos \left(d x +c \right)\right)^{2} \left(3 i \left(\cos^{3}\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)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)-3 i \left(\cos^{3}\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)+3 i \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)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)-3 i \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)+3 \left(\cos^{3}\left(d x +c \right)\right)-2 \left(\cos^{2}\left(d x +c \right)\right)-1\right) \left(\frac{b}{\cos \left(d x +c \right)}\right)^{\frac{5}{2}}}{5 d \,b^{5} \sin \left(d x +c \right)^{5}}"," ",0,"-2/5/d*(1+cos(d*x+c))^2*(-1+cos(d*x+c))^2*(3*I*cos(d*x+c)^3*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*cos(d*x+c)^3*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)+3*I*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*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)+3*cos(d*x+c)^3-2*cos(d*x+c)^2-1)*(b/cos(d*x+c))^(5/2)/b^5/sin(d*x+c)^5","C"
123,1,130,88,0.879000," ","int(sec(d*x+c)^5/(b*sec(d*x+c))^(5/2),x)","-\frac{2 \left(-1+\cos \left(d x +c \right)\right) \left(i \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{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)}}-\cos \left(d x +c \right)+1\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)^{4} \left(\frac{b}{\cos \left(d x +c \right)}\right)^{\frac{5}{2}}}"," ",0,"-2/3/d*(-1+cos(d*x+c))*(I*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*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)*(1+cos(d*x+c))^2/sin(d*x+c)^3/cos(d*x+c)^4/(b/cos(d*x+c))^(5/2)","C"
124,1,324,88,1.059000," ","int(sec(d*x+c)^4/(b*sec(d*x+c))^(5/2),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 \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) \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 \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{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)}}+i \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)}}-i \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)}}-\cos \left(d x +c \right)+1\right)}{d \cos \left(d x +c \right)^{3} \left(\frac{b}{\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \sin \left(d x +c \right)^{5}}"," ",0,"2/d*(1+cos(d*x+c))^2*(-1+cos(d*x+c))^2*(I*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)-I*cos(d*x+c)*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*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*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)-cos(d*x+c)+1)/cos(d*x+c)^3/(b/cos(d*x+c))^(5/2)/sin(d*x+c)^5","C"
125,1,98,63,0.765000," ","int(sec(d*x+c)^3/(b*sec(d*x+c))^(5/2),x)","-\frac{2 i \left(\frac{1}{1+\cos \left(d x +c \right)}\right)^{\frac{7}{2}} \left(-1+\cos \left(d x +c \right)\right) \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \left(1+\cos \left(d x +c \right)\right)^{2}}{d \left(\frac{b}{\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \left(\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \sin \left(d x +c \right)^{2}}"," ",0,"-2*I/d*(1/(1+cos(d*x+c)))^(7/2)*(-1+cos(d*x+c))*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*(1+cos(d*x+c))^2/(b/cos(d*x+c))^(5/2)/(cos(d*x+c)/(1+cos(d*x+c)))^(5/2)/sin(d*x+c)^2","C"
126,1,311,63,0.748000," ","int(sec(d*x+c)^2/(b*sec(d*x+c))^(5/2),x)","\frac{2 i \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{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)}}-2 i \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) \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 \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 \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 \left(\cos^{2}\left(d x +c \right)\right)+2 \cos \left(d x +c \right)}{d \cos \left(d x +c \right)^{3} \left(\frac{b}{\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \sin \left(d x +c \right)}"," ",0,"2/d*(I*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*(1/(1+cos(d*x+c)))^(1/2)-I*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)+I*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*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)-cos(d*x+c)^2+cos(d*x+c))/cos(d*x+c)^3/(b/cos(d*x+c))^(5/2)/sin(d*x+c)","C"
127,1,131,88,0.742000," ","int(sec(d*x+c)/(b*sec(d*x+c))^(5/2),x)","-\frac{2 \left(-1+\cos \left(d x +c \right)\right) \left(i \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)}}-\left(\cos^{2}\left(d x +c \right)\right)+\cos \left(d x +c \right)\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)^{3} \left(\frac{b}{\cos \left(d x +c \right)}\right)^{\frac{5}{2}}}"," ",0,"-2/3/d*(-1+cos(d*x+c))*(I*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)-cos(d*x+c)^2+cos(d*x+c))*(1+cos(d*x+c))^2/sin(d*x+c)^3/cos(d*x+c)^3/(b/cos(d*x+c))^(5/2)","C"
128,1,321,88,0.832000," ","int(1/(b*sec(d*x+c))^(5/2),x)","-\frac{2 \left(3 i \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) \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 i \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{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)}}+3 i \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)}}-3 i \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)}}+\cos^{4}\left(d x +c \right)+2 \left(\cos^{2}\left(d x +c \right)\right)-3 \cos \left(d x +c \right)\right)}{5 d \cos \left(d x +c \right)^{3} \sin \left(d x +c \right) \left(\frac{b}{\cos \left(d x +c \right)}\right)^{\frac{5}{2}}}"," ",0,"-2/5/d*(3*I*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)-3*I*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*(1/(1+cos(d*x+c)))^(1/2)+3*I*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)-3*I*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)+cos(d*x+c)^4+2*cos(d*x+c)^2-3*cos(d*x+c))/cos(d*x+c)^3/sin(d*x+c)/(b/cos(d*x+c))^(5/2)","C"
129,1,153,109,0.836000," ","int(cos(d*x+c)/(b*sec(d*x+c))^(5/2),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 \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 \left(\cos^{4}\left(d x +c \right)\right)+3 \left(\cos^{3}\left(d x +c \right)\right)-5 \left(\cos^{2}\left(d x +c \right)\right)+5 \cos \left(d x +c \right)\right)}{21 d \sin \left(d x +c \right)^{3} \cos \left(d x +c \right)^{3} \left(\frac{b}{\cos \left(d x +c \right)}\right)^{\frac{5}{2}}}"," ",0,"-2/21/d*(1+cos(d*x+c))^2*(-1+cos(d*x+c))*(5*I*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*cos(d*x+c)^4+3*cos(d*x+c)^3-5*cos(d*x+c)^2+5*cos(d*x+c))/sin(d*x+c)^3/cos(d*x+c)^3/(b/cos(d*x+c))^(5/2)","C"
130,1,333,110,0.938000," ","int(cos(d*x+c)^2/(b*sec(d*x+c))^(5/2),x)","-\frac{2 \left(5 \left(\cos^{6}\left(d x +c \right)\right)+21 i \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) \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)}}-21 i \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{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)}}+21 i \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)}}-21 i \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 \left(\cos^{4}\left(d x +c \right)\right)+14 \left(\cos^{2}\left(d x +c \right)\right)-21 \cos \left(d x +c \right)\right)}{45 d \cos \left(d x +c \right)^{3} \left(\frac{b}{\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \sin \left(d x +c \right)}"," ",0,"-2/45/d*(5*cos(d*x+c)^6+21*I*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)-21*I*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*(1/(1+cos(d*x+c)))^(1/2)+21*I*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)-21*I*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)+2*cos(d*x+c)^4+14*cos(d*x+c)^2-21*cos(d*x+c))/cos(d*x+c)^3/(b/cos(d*x+c))^(5/2)/sin(d*x+c)","C"
131,1,153,112,0.898000," ","int(1/(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 \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 \left(\cos^{4}\left(d x +c \right)\right)+3 \left(\cos^{3}\left(d x +c \right)\right)-5 \left(\cos^{2}\left(d x +c \right)\right)+5 \cos \left(d x +c \right)\right)}{21 d \left(\frac{b}{\cos \left(d x +c \right)}\right)^{\frac{7}{2}} \cos \left(d x +c \right)^{4} \sin \left(d x +c \right)^{3}}"," ",0,"-2/21/d*(1+cos(d*x+c))^2*(-1+cos(d*x+c))*(5*I*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*cos(d*x+c)^4+3*cos(d*x+c)^3-5*cos(d*x+c)^2+5*cos(d*x+c))/(b/cos(d*x+c))^(7/2)/cos(d*x+c)^4/sin(d*x+c)^3","C"
132,1,131,89,1.199000," ","int(sec(d*x+c)^(9/2)*(b*sec(d*x+c))^(1/2),x)","\frac{\left(3 \left(\cos^{4}\left(d x +c \right)\right) \ln \left(-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)-3 \left(\cos^{4}\left(d x +c \right)\right) \ln \left(-\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}\right)+3 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+2 \sin \left(d x +c \right)\right) \cos \left(d x +c \right) \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{9}{2}} \sqrt{\frac{b}{\cos \left(d x +c \right)}}}{8 d}"," ",0,"1/8/d*(3*cos(d*x+c)^4*ln(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))-3*cos(d*x+c)^4*ln(-(-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))+3*cos(d*x+c)^2*sin(d*x+c)+2*sin(d*x+c))*cos(d*x+c)*(1/cos(d*x+c))^(9/2)*(b/cos(d*x+c))^(1/2)","A"
133,1,52,60,1.069000," ","int(sec(d*x+c)^(7/2)*(b*sec(d*x+c))^(1/2),x)","\frac{\left(2 \left(\cos^{2}\left(d x +c \right)\right)+1\right) \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{7}{2}} \sqrt{\frac{b}{\cos \left(d x +c \right)}}\, \cos \left(d x +c \right) \sin \left(d x +c \right)}{3 d}"," ",0,"1/3/d*(2*cos(d*x+c)^2+1)*(1/cos(d*x+c))^(7/2)*(b/cos(d*x+c))^(1/2)*cos(d*x+c)*sin(d*x+c)","A"
134,1,114,60,1.068000," ","int(sec(d*x+c)^(5/2)*(b*sec(d*x+c))^(1/2),x)","-\frac{\left(\left(\cos^{2}\left(d x +c \right)\right) \ln \left(-\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}\right)-\left(\cos^{2}\left(d x +c \right)\right) \ln \left(-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)-\sin \left(d x +c \right)\right) \cos \left(d x +c \right) \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \sqrt{\frac{b}{\cos \left(d x +c \right)}}}{2 d}"," ",0,"-1/2/d*(cos(d*x+c)^2*ln(-(-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))-cos(d*x+c)^2*ln(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))-sin(d*x+c))*cos(d*x+c)*(1/cos(d*x+c))^(5/2)*(b/cos(d*x+c))^(1/2)","A"
135,1,39,28,1.076000," ","int(sec(d*x+c)^(3/2)*(b*sec(d*x+c))^(1/2),x)","\frac{\cos \left(d x +c \right) \sin \left(d x +c \right) \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sqrt{\frac{b}{\cos \left(d x +c \right)}}}{d}"," ",0,"1/d*cos(d*x+c)*sin(d*x+c)*(1/cos(d*x+c))^(3/2)*(b/cos(d*x+c))^(1/2)","A"
136,1,52,29,0.977000," ","int(sec(d*x+c)^(1/2)*(b*sec(d*x+c))^(1/2),x)","-\frac{2 \arctanh \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \sqrt{\frac{1}{\cos \left(d x +c \right)}}\, \sqrt{\frac{b}{\cos \left(d x +c \right)}}\, \cos \left(d x +c \right)}{d}"," ",0,"-2/d*arctanh((-1+cos(d*x+c))/sin(d*x+c))*(1/cos(d*x+c))^(1/2)*(b/cos(d*x+c))^(1/2)*cos(d*x+c)","A"
137,1,32,20,1.034000," ","int((b*sec(d*x+c))^(1/2)/sec(d*x+c)^(1/2),x)","\frac{\sqrt{\frac{b}{\cos \left(d x +c \right)}}\, \left(d x +c \right)}{d \sqrt{\frac{1}{\cos \left(d x +c \right)}}}"," ",0,"1/d*(b/cos(d*x+c))^(1/2)/(1/cos(d*x+c))^(1/2)*(d*x+c)","A"
138,1,41,28,1.157000," ","int((b*sec(d*x+c))^(1/2)/sec(d*x+c)^(3/2),x)","\frac{\sqrt{\frac{b}{\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)}{d \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \cos \left(d x +c \right)}"," ",0,"1/d*(b/cos(d*x+c))^(1/2)*sin(d*x+c)/(1/cos(d*x+c))^(3/2)/cos(d*x+c)","A"
139,1,54,51,1.297000," ","int((b*sec(d*x+c))^(1/2)/sec(d*x+c)^(5/2),x)","\frac{\left(\cos \left(d x +c \right) \sin \left(d x +c \right)+d x +c \right) \sqrt{\frac{b}{\cos \left(d x +c \right)}}}{2 d \cos \left(d x +c \right)^{2} \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{5}{2}}}"," ",0,"1/2/d*(cos(d*x+c)*sin(d*x+c)+d*x+c)*(b/cos(d*x+c))^(1/2)/cos(d*x+c)^2/(1/cos(d*x+c))^(5/2)","A"
140,1,52,60,1.387000," ","int((b*sec(d*x+c))^(1/2)/sec(d*x+c)^(7/2),x)","\frac{\left(2+\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{b}{\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)}{3 d \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{7}{2}} \cos \left(d x +c \right)^{3}}"," ",0,"1/3/d*(2+cos(d*x+c)^2)*(b/cos(d*x+c))^(1/2)*sin(d*x+c)/(1/cos(d*x+c))^(7/2)/cos(d*x+c)^3","A"
141,1,74,80,1.361000," ","int((b*sec(d*x+c))^(1/2)/sec(d*x+c)^(9/2),x)","\frac{\left(2 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)+3 \cos \left(d x +c \right) \sin \left(d x +c \right)+3 d x +3 c \right) \sqrt{\frac{b}{\cos \left(d x +c \right)}}}{8 d \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{9}{2}} \cos \left(d x +c \right)^{4}}"," ",0,"1/8/d*(2*cos(d*x+c)^3*sin(d*x+c)+3*cos(d*x+c)*sin(d*x+c)+3*d*x+3*c)*(b/cos(d*x+c))^(1/2)/(1/cos(d*x+c))^(9/2)/cos(d*x+c)^4","A"
142,1,131,92,0.940000," ","int(sec(d*x+c)^(7/2)*(b*sec(d*x+c))^(3/2),x)","\frac{\left(3 \left(\cos^{4}\left(d x +c \right)\right) \ln \left(-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)-3 \left(\cos^{4}\left(d x +c \right)\right) \ln \left(-\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}\right)+3 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+2 \sin \left(d x +c \right)\right) \cos \left(d x +c \right) \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{7}{2}} \left(\frac{b}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}}}{8 d}"," ",0,"1/8/d*(3*cos(d*x+c)^4*ln(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))-3*cos(d*x+c)^4*ln(-(-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))+3*cos(d*x+c)^2*sin(d*x+c)+2*sin(d*x+c))*cos(d*x+c)*(1/cos(d*x+c))^(7/2)*(b/cos(d*x+c))^(3/2)","A"
143,1,52,62,0.877000," ","int(sec(d*x+c)^(5/2)*(b*sec(d*x+c))^(3/2),x)","\frac{\left(2 \left(\cos^{2}\left(d x +c \right)\right)+1\right) \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \left(\frac{b}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \cos \left(d x +c \right) \sin \left(d x +c \right)}{3 d}"," ",0,"1/3/d*(2*cos(d*x+c)^2+1)*(1/cos(d*x+c))^(5/2)*(b/cos(d*x+c))^(3/2)*cos(d*x+c)*sin(d*x+c)","A"
144,1,114,62,0.904000," ","int(sec(d*x+c)^(3/2)*(b*sec(d*x+c))^(3/2),x)","-\frac{\left(\left(\cos^{2}\left(d x +c \right)\right) \ln \left(-\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}\right)-\left(\cos^{2}\left(d x +c \right)\right) \ln \left(-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)-\sin \left(d x +c \right)\right) \cos \left(d x +c \right) \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \left(\frac{b}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}}}{2 d}"," ",0,"-1/2/d*(cos(d*x+c)^2*ln(-(-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))-cos(d*x+c)^2*ln(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))-sin(d*x+c))*cos(d*x+c)*(1/cos(d*x+c))^(3/2)*(b/cos(d*x+c))^(3/2)","A"
145,1,39,29,1.011000," ","int(sec(d*x+c)^(1/2)*(b*sec(d*x+c))^(3/2),x)","\frac{\sqrt{\frac{1}{\cos \left(d x +c \right)}}\, \left(\frac{b}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \cos \left(d x +c \right) \sin \left(d x +c \right)}{d}"," ",0,"1/d*(1/cos(d*x+c))^(1/2)*(b/cos(d*x+c))^(3/2)*cos(d*x+c)*sin(d*x+c)","A"
146,1,52,30,1.277000," ","int((b*sec(d*x+c))^(3/2)/sec(d*x+c)^(1/2),x)","-\frac{2 \arctanh \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \cos \left(d x +c \right) \left(\frac{b}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}}}{d \sqrt{\frac{1}{\cos \left(d x +c \right)}}}"," ",0,"-2/d*arctanh((-1+cos(d*x+c))/sin(d*x+c))*cos(d*x+c)*(b/cos(d*x+c))^(3/2)/(1/cos(d*x+c))^(1/2)","A"
147,1,32,21,0.984000," ","int((b*sec(d*x+c))^(3/2)/sec(d*x+c)^(3/2),x)","\frac{\left(\frac{b}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \left(d x +c \right)}{d \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}}}"," ",0,"1/d*(b/cos(d*x+c))^(3/2)/(1/cos(d*x+c))^(3/2)*(d*x+c)","A"
148,1,41,29,1.105000," ","int((b*sec(d*x+c))^(3/2)/sec(d*x+c)^(5/2),x)","\frac{\sin \left(d x +c \right) \left(\frac{b}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}}}{d \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \cos \left(d x +c \right)}"," ",0,"1/d*sin(d*x+c)*(b/cos(d*x+c))^(3/2)/(1/cos(d*x+c))^(5/2)/cos(d*x+c)","A"
149,1,54,53,1.191000," ","int((b*sec(d*x+c))^(3/2)/sec(d*x+c)^(7/2),x)","\frac{\left(\cos \left(d x +c \right) \sin \left(d x +c \right)+d x +c \right) \left(\frac{b}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}}}{2 d \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{7}{2}} \cos \left(d x +c \right)^{2}}"," ",0,"1/2/d*(cos(d*x+c)*sin(d*x+c)+d*x+c)*(b/cos(d*x+c))^(3/2)/(1/cos(d*x+c))^(7/2)/cos(d*x+c)^2","A"
150,1,52,62,1.099000," ","int((b*sec(d*x+c))^(3/2)/sec(d*x+c)^(9/2),x)","\frac{\left(2+\cos^{2}\left(d x +c \right)\right) \left(\frac{b}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sin \left(d x +c \right)}{3 d \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{9}{2}} \cos \left(d x +c \right)^{3}}"," ",0,"1/3/d*(2+cos(d*x+c)^2)*(b/cos(d*x+c))^(3/2)*sin(d*x+c)/(1/cos(d*x+c))^(9/2)/cos(d*x+c)^3","A"
151,1,74,83,1.187000," ","int((b*sec(d*x+c))^(3/2)/sec(d*x+c)^(11/2),x)","\frac{\left(2 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)+3 \cos \left(d x +c \right) \sin \left(d x +c \right)+3 d x +3 c \right) \left(\frac{b}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}}}{8 d \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{11}{2}} \cos \left(d x +c \right)^{4}}"," ",0,"1/8/d*(2*cos(d*x+c)^3*sin(d*x+c)+3*cos(d*x+c)*sin(d*x+c)+3*d*x+3*c)*(b/cos(d*x+c))^(3/2)/(1/cos(d*x+c))^(11/2)/cos(d*x+c)^4","A"
152,1,62,100,0.942000," ","int(sec(d*x+c)^(7/2)*(b*sec(d*x+c))^(5/2),x)","\frac{\left(8 \left(\cos^{4}\left(d x +c \right)\right)+4 \left(\cos^{2}\left(d x +c \right)\right)+3\right) \sin \left(d x +c \right) \cos \left(d x +c \right) \left(\frac{b}{\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{7}{2}}}{15 d}"," ",0,"1/15/d*(8*cos(d*x+c)^4+4*cos(d*x+c)^2+3)*sin(d*x+c)*cos(d*x+c)*(b/cos(d*x+c))^(5/2)*(1/cos(d*x+c))^(7/2)","A"
153,1,52,66,0.947000," ","int(sec(d*x+c)^(3/2)*(b*sec(d*x+c))^(5/2),x)","\frac{\left(2 \left(\cos^{2}\left(d x +c \right)\right)+1\right) \cos \left(d x +c \right) \sin \left(d x +c \right) \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \left(\frac{b}{\cos \left(d x +c \right)}\right)^{\frac{5}{2}}}{3 d}"," ",0,"1/3/d*(2*cos(d*x+c)^2+1)*cos(d*x+c)*sin(d*x+c)*(1/cos(d*x+c))^(3/2)*(b/cos(d*x+c))^(5/2)","A"
154,1,114,66,0.957000," ","int(sec(d*x+c)^(1/2)*(b*sec(d*x+c))^(5/2),x)","-\frac{\left(\left(\cos^{2}\left(d x +c \right)\right) \ln \left(-\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}\right)-\left(\cos^{2}\left(d x +c \right)\right) \ln \left(-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)-\sin \left(d x +c \right)\right) \cos \left(d x +c \right) \sqrt{\frac{1}{\cos \left(d x +c \right)}}\, \left(\frac{b}{\cos \left(d x +c \right)}\right)^{\frac{5}{2}}}{2 d}"," ",0,"-1/2/d*(cos(d*x+c)^2*ln(-(-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))-cos(d*x+c)^2*ln(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))-sin(d*x+c))*cos(d*x+c)*(1/cos(d*x+c))^(1/2)*(b/cos(d*x+c))^(5/2)","A"
155,1,39,31,1.090000," ","int((b*sec(d*x+c))^(5/2)/sec(d*x+c)^(1/2),x)","\frac{\left(\frac{b}{\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \cos \left(d x +c \right) \sin \left(d x +c \right)}{d \sqrt{\frac{1}{\cos \left(d x +c \right)}}}"," ",0,"1/d*(b/cos(d*x+c))^(5/2)*cos(d*x+c)*sin(d*x+c)/(1/cos(d*x+c))^(1/2)","A"
156,1,52,32,0.961000," ","int((b*sec(d*x+c))^(5/2)/sec(d*x+c)^(3/2),x)","-\frac{2 \left(\frac{b}{\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \cos \left(d x +c \right) \arctanh \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)}{d \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}}}"," ",0,"-2/d*(b/cos(d*x+c))^(5/2)*cos(d*x+c)*arctanh((-1+cos(d*x+c))/sin(d*x+c))/(1/cos(d*x+c))^(3/2)","A"
157,1,32,23,1.015000," ","int((b*sec(d*x+c))^(5/2)/sec(d*x+c)^(5/2),x)","\frac{\left(\frac{b}{\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \left(d x +c \right)}{d \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{5}{2}}}"," ",0,"1/d*(b/cos(d*x+c))^(5/2)/(1/cos(d*x+c))^(5/2)*(d*x+c)","A"
158,1,41,31,1.126000," ","int((b*sec(d*x+c))^(5/2)/sec(d*x+c)^(7/2),x)","\frac{\left(\frac{b}{\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \sin \left(d x +c \right)}{d \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{7}{2}} \cos \left(d x +c \right)}"," ",0,"1/d*(b/cos(d*x+c))^(5/2)*sin(d*x+c)/(1/cos(d*x+c))^(7/2)/cos(d*x+c)","A"
159,1,54,57,0.980000," ","int((b*sec(d*x+c))^(5/2)/sec(d*x+c)^(9/2),x)","\frac{\left(\cos \left(d x +c \right) \sin \left(d x +c \right)+d x +c \right) \left(\frac{b}{\cos \left(d x +c \right)}\right)^{\frac{5}{2}}}{2 d \cos \left(d x +c \right)^{2} \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{9}{2}}}"," ",0,"1/2/d*(cos(d*x+c)*sin(d*x+c)+d*x+c)*(b/cos(d*x+c))^(5/2)/cos(d*x+c)^2/(1/cos(d*x+c))^(9/2)","A"
160,1,52,66,0.969000," ","int((b*sec(d*x+c))^(5/2)/sec(d*x+c)^(11/2),x)","\frac{\left(2+\cos^{2}\left(d x +c \right)\right) \left(\frac{b}{\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \sin \left(d x +c \right)}{3 d \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{11}{2}} \cos \left(d x +c \right)^{3}}"," ",0,"1/3/d*(2+cos(d*x+c)^2)*(b/cos(d*x+c))^(5/2)*sin(d*x+c)/(1/cos(d*x+c))^(11/2)/cos(d*x+c)^3","A"
161,1,114,60,0.867000," ","int(sec(d*x+c)^(7/2)/(b*sec(d*x+c))^(1/2),x)","-\frac{\left(\left(\cos^{2}\left(d x +c \right)\right) \ln \left(-\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}\right)-\left(\cos^{2}\left(d x +c \right)\right) \ln \left(-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)-\sin \left(d x +c \right)\right) \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{7}{2}} \cos \left(d x +c \right)}{2 d \sqrt{\frac{b}{\cos \left(d x +c \right)}}}"," ",0,"-1/2/d*(cos(d*x+c)^2*ln(-(-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))-cos(d*x+c)^2*ln(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))-sin(d*x+c))*(1/cos(d*x+c))^(7/2)*cos(d*x+c)/(b/cos(d*x+c))^(1/2)","A"
162,1,39,28,0.817000," ","int(sec(d*x+c)^(5/2)/(b*sec(d*x+c))^(1/2),x)","\frac{\left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \cos \left(d x +c \right) \sin \left(d x +c \right)}{d \sqrt{\frac{b}{\cos \left(d x +c \right)}}}"," ",0,"1/d*(1/cos(d*x+c))^(5/2)*cos(d*x+c)*sin(d*x+c)/(b/cos(d*x+c))^(1/2)","A"
163,1,52,29,0.832000," ","int(sec(d*x+c)^(3/2)/(b*sec(d*x+c))^(1/2),x)","-\frac{2 \cos \left(d x +c \right) \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \arctanh \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)}{d \sqrt{\frac{b}{\cos \left(d x +c \right)}}}"," ",0,"-2/d*cos(d*x+c)*(1/cos(d*x+c))^(3/2)*arctanh((-1+cos(d*x+c))/sin(d*x+c))/(b/cos(d*x+c))^(1/2)","A"
164,1,32,20,0.746000," ","int(sec(d*x+c)^(1/2)/(b*sec(d*x+c))^(1/2),x)","\frac{\sqrt{\frac{1}{\cos \left(d x +c \right)}}\, \left(d x +c \right)}{d \sqrt{\frac{b}{\cos \left(d x +c \right)}}}"," ",0,"1/d*(1/cos(d*x+c))^(1/2)/(b/cos(d*x+c))^(1/2)*(d*x+c)","A"
165,1,41,28,0.937000," ","int(1/sec(d*x+c)^(1/2)/(b*sec(d*x+c))^(1/2),x)","\frac{\sin \left(d x +c \right)}{d \sqrt{\frac{1}{\cos \left(d x +c \right)}}\, \sqrt{\frac{b}{\cos \left(d x +c \right)}}\, \cos \left(d x +c \right)}"," ",0,"1/d*sin(d*x+c)/(1/cos(d*x+c))^(1/2)/(b/cos(d*x+c))^(1/2)/cos(d*x+c)","A"
166,1,54,51,0.941000," ","int(1/sec(d*x+c)^(3/2)/(b*sec(d*x+c))^(1/2),x)","\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)+d x +c}{2 d \cos \left(d x +c \right)^{2} \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sqrt{\frac{b}{\cos \left(d x +c \right)}}}"," ",0,"1/2/d*(cos(d*x+c)*sin(d*x+c)+d*x+c)/cos(d*x+c)^2/(1/cos(d*x+c))^(3/2)/(b/cos(d*x+c))^(1/2)","A"
167,1,52,60,1.049000," ","int(1/sec(d*x+c)^(5/2)/(b*sec(d*x+c))^(1/2),x)","\frac{\sin \left(d x +c \right) \left(2+\cos^{2}\left(d x +c \right)\right)}{3 d \cos \left(d x +c \right)^{3} \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \sqrt{\frac{b}{\cos \left(d x +c \right)}}}"," ",0,"1/3/d*sin(d*x+c)*(2+cos(d*x+c)^2)/cos(d*x+c)^3/(1/cos(d*x+c))^(5/2)/(b/cos(d*x+c))^(1/2)","A"
168,1,114,66,0.821000," ","int(sec(d*x+c)^(9/2)/(b*sec(d*x+c))^(3/2),x)","-\frac{\left(\left(\cos^{2}\left(d x +c \right)\right) \ln \left(-\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}\right)-\left(\cos^{2}\left(d x +c \right)\right) \ln \left(-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)-\sin \left(d x +c \right)\right) \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{9}{2}} \cos \left(d x +c \right)}{2 d \left(\frac{b}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}}}"," ",0,"-1/2/d*(cos(d*x+c)^2*ln(-(-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))-cos(d*x+c)^2*ln(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))-sin(d*x+c))*(1/cos(d*x+c))^(9/2)*cos(d*x+c)/(b/cos(d*x+c))^(3/2)","A"
169,1,39,31,0.817000," ","int(sec(d*x+c)^(7/2)/(b*sec(d*x+c))^(3/2),x)","\frac{\left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{7}{2}} \cos \left(d x +c \right) \sin \left(d x +c \right)}{d \left(\frac{b}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}}}"," ",0,"1/d*(1/cos(d*x+c))^(7/2)*cos(d*x+c)*sin(d*x+c)/(b/cos(d*x+c))^(3/2)","A"
170,1,52,32,0.749000," ","int(sec(d*x+c)^(5/2)/(b*sec(d*x+c))^(3/2),x)","-\frac{2 \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \cos \left(d x +c \right) \arctanh \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)}{d \left(\frac{b}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}}}"," ",0,"-2/d*(1/cos(d*x+c))^(5/2)*cos(d*x+c)*arctanh((-1+cos(d*x+c))/sin(d*x+c))/(b/cos(d*x+c))^(3/2)","A"
171,1,32,23,0.759000," ","int(sec(d*x+c)^(3/2)/(b*sec(d*x+c))^(3/2),x)","\frac{\left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \left(d x +c \right)}{d \left(\frac{b}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}}}"," ",0,"1/d*(1/cos(d*x+c))^(3/2)/(b/cos(d*x+c))^(3/2)*(d*x+c)","A"
172,1,41,31,0.861000," ","int(sec(d*x+c)^(1/2)/(b*sec(d*x+c))^(3/2),x)","\frac{\sin \left(d x +c \right) \sqrt{\frac{1}{\cos \left(d x +c \right)}}}{d \left(\frac{b}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \cos \left(d x +c \right)}"," ",0,"1/d*sin(d*x+c)*(1/cos(d*x+c))^(1/2)/(b/cos(d*x+c))^(3/2)/cos(d*x+c)","A"
173,1,54,57,0.982000," ","int(1/sec(d*x+c)^(1/2)/(b*sec(d*x+c))^(3/2),x)","\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)+d x +c}{2 d \cos \left(d x +c \right)^{2} \sqrt{\frac{1}{\cos \left(d x +c \right)}}\, \left(\frac{b}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}}}"," ",0,"1/2/d*(cos(d*x+c)*sin(d*x+c)+d*x+c)/cos(d*x+c)^2/(1/cos(d*x+c))^(1/2)/(b/cos(d*x+c))^(3/2)","A"
174,1,52,66,1.024000," ","int(1/sec(d*x+c)^(3/2)/(b*sec(d*x+c))^(3/2),x)","\frac{\sin \left(d x +c \right) \left(2+\cos^{2}\left(d x +c \right)\right)}{3 d \cos \left(d x +c \right)^{3} \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \left(\frac{b}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}}}"," ",0,"1/3/d*sin(d*x+c)*(2+cos(d*x+c)^2)/cos(d*x+c)^3/(1/cos(d*x+c))^(3/2)/(b/cos(d*x+c))^(3/2)","A"
175,1,74,89,1.033000," ","int(1/sec(d*x+c)^(5/2)/(b*sec(d*x+c))^(3/2),x)","\frac{2 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)+3 \cos \left(d x +c \right) \sin \left(d x +c \right)+3 d x +3 c}{8 d \cos \left(d x +c \right)^{4} \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \left(\frac{b}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}}}"," ",0,"1/8/d*(2*cos(d*x+c)^3*sin(d*x+c)+3*cos(d*x+c)*sin(d*x+c)+3*d*x+3*c)/cos(d*x+c)^4/(1/cos(d*x+c))^(5/2)/(b/cos(d*x+c))^(3/2)","A"
176,1,114,66,0.816000," ","int(sec(d*x+c)^(11/2)/(b*sec(d*x+c))^(5/2),x)","-\frac{\left(\left(\cos^{2}\left(d x +c \right)\right) \ln \left(-\frac{-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)}{\sin \left(d x +c \right)}\right)-\left(\cos^{2}\left(d x +c \right)\right) \ln \left(-\frac{-\sin \left(d x +c \right)-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)-\sin \left(d x +c \right)\right) \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{11}{2}} \cos \left(d x +c \right)}{2 d \left(\frac{b}{\cos \left(d x +c \right)}\right)^{\frac{5}{2}}}"," ",0,"-1/2/d*(cos(d*x+c)^2*ln(-(-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))-cos(d*x+c)^2*ln(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))-sin(d*x+c))*(1/cos(d*x+c))^(11/2)*cos(d*x+c)/(b/cos(d*x+c))^(5/2)","A"
177,1,39,31,0.832000," ","int(sec(d*x+c)^(9/2)/(b*sec(d*x+c))^(5/2),x)","\frac{\left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{9}{2}} \cos \left(d x +c \right) \sin \left(d x +c \right)}{d \left(\frac{b}{\cos \left(d x +c \right)}\right)^{\frac{5}{2}}}"," ",0,"1/d*(1/cos(d*x+c))^(9/2)*cos(d*x+c)*sin(d*x+c)/(b/cos(d*x+c))^(5/2)","A"
178,1,52,32,0.783000," ","int(sec(d*x+c)^(7/2)/(b*sec(d*x+c))^(5/2),x)","-\frac{2 \cos \left(d x +c \right) \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{7}{2}} \arctanh \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)}{d \left(\frac{b}{\cos \left(d x +c \right)}\right)^{\frac{5}{2}}}"," ",0,"-2/d*cos(d*x+c)*(1/cos(d*x+c))^(7/2)*arctanh((-1+cos(d*x+c))/sin(d*x+c))/(b/cos(d*x+c))^(5/2)","A"
179,1,32,23,0.809000," ","int(sec(d*x+c)^(5/2)/(b*sec(d*x+c))^(5/2),x)","\frac{\left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \left(d x +c \right)}{d \left(\frac{b}{\cos \left(d x +c \right)}\right)^{\frac{5}{2}}}"," ",0,"1/d*(1/cos(d*x+c))^(5/2)/(b/cos(d*x+c))^(5/2)*(d*x+c)","A"
180,1,41,31,0.842000," ","int(sec(d*x+c)^(3/2)/(b*sec(d*x+c))^(5/2),x)","\frac{\sin \left(d x +c \right) \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}}}{d \left(\frac{b}{\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \cos \left(d x +c \right)}"," ",0,"1/d*sin(d*x+c)*(1/cos(d*x+c))^(3/2)/(b/cos(d*x+c))^(5/2)/cos(d*x+c)","A"
181,1,54,57,0.910000," ","int(sec(d*x+c)^(1/2)/(b*sec(d*x+c))^(5/2),x)","\frac{\left(\cos \left(d x +c \right) \sin \left(d x +c \right)+d x +c \right) \sqrt{\frac{1}{\cos \left(d x +c \right)}}}{2 d \cos \left(d x +c \right)^{2} \left(\frac{b}{\cos \left(d x +c \right)}\right)^{\frac{5}{2}}}"," ",0,"1/2/d*(cos(d*x+c)*sin(d*x+c)+d*x+c)*(1/cos(d*x+c))^(1/2)/cos(d*x+c)^2/(b/cos(d*x+c))^(5/2)","A"
182,1,52,66,1.131000," ","int(1/sec(d*x+c)^(1/2)/(b*sec(d*x+c))^(5/2),x)","\frac{\sin \left(d x +c \right) \left(2+\cos^{2}\left(d x +c \right)\right)}{3 d \cos \left(d x +c \right)^{3} \sqrt{\frac{1}{\cos \left(d x +c \right)}}\, \left(\frac{b}{\cos \left(d x +c \right)}\right)^{\frac{5}{2}}}"," ",0,"1/3/d*sin(d*x+c)*(2+cos(d*x+c)^2)/cos(d*x+c)^3/(1/cos(d*x+c))^(1/2)/(b/cos(d*x+c))^(5/2)","A"
183,1,74,89,1.120000," ","int(1/sec(d*x+c)^(3/2)/(b*sec(d*x+c))^(5/2),x)","\frac{2 \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)+3 \cos \left(d x +c \right) \sin \left(d x +c \right)+3 d x +3 c}{8 d \cos \left(d x +c \right)^{4} \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \left(\frac{b}{\cos \left(d x +c \right)}\right)^{\frac{5}{2}}}"," ",0,"1/8/d*(2*cos(d*x+c)^3*sin(d*x+c)+3*cos(d*x+c)*sin(d*x+c)+3*d*x+3*c)/cos(d*x+c)^4/(1/cos(d*x+c))^(3/2)/(b/cos(d*x+c))^(5/2)","A"
184,0,0,48,0.519000," ","int(sec(d*x+c)^2*(b*sec(d*x+c))^(1/3),x)","\int \left(\sec^{2}\left(d x +c \right)\right) \left(b \sec \left(d x +c \right)\right)^{\frac{1}{3}}\, dx"," ",0,"int(sec(d*x+c)^2*(b*sec(d*x+c))^(1/3),x)","F"
185,0,0,45,0.433000," ","int(sec(d*x+c)*(b*sec(d*x+c))^(1/3),x)","\int \sec \left(d x +c \right) \left(b \sec \left(d x +c \right)\right)^{\frac{1}{3}}\, dx"," ",0,"int(sec(d*x+c)*(b*sec(d*x+c))^(1/3),x)","F"
186,0,0,46,0.542000," ","int((b*sec(d*x+c))^(1/3),x)","\int \left(b \sec \left(d x +c \right)\right)^{\frac{1}{3}}\, dx"," ",0,"int((b*sec(d*x+c))^(1/3),x)","F"
187,0,0,48,0.585000," ","int(cos(d*x+c)*(b*sec(d*x+c))^(1/3),x)","\int \cos \left(d x +c \right) \left(b \sec \left(d x +c \right)\right)^{\frac{1}{3}}\, dx"," ",0,"int(cos(d*x+c)*(b*sec(d*x+c))^(1/3),x)","F"
188,0,0,48,1.059000," ","int(cos(d*x+c)^2*(b*sec(d*x+c))^(1/3),x)","\int \left(\cos^{2}\left(d x +c \right)\right) \left(b \sec \left(d x +c \right)\right)^{\frac{1}{3}}\, dx"," ",0,"int(cos(d*x+c)^2*(b*sec(d*x+c))^(1/3),x)","F"
189,0,0,48,0.435000," ","int(sec(d*x+c)^2*(b*sec(d*x+c))^(4/3),x)","\int \left(\sec^{2}\left(d x +c \right)\right) \left(b \sec \left(d x +c \right)\right)^{\frac{4}{3}}\, dx"," ",0,"int(sec(d*x+c)^2*(b*sec(d*x+c))^(4/3),x)","F"
190,0,0,45,0.432000," ","int(sec(d*x+c)*(b*sec(d*x+c))^(4/3),x)","\int \sec \left(d x +c \right) \left(b \sec \left(d x +c \right)\right)^{\frac{4}{3}}\, dx"," ",0,"int(sec(d*x+c)*(b*sec(d*x+c))^(4/3),x)","F"
191,0,0,46,0.441000," ","int((b*sec(d*x+c))^(4/3),x)","\int \left(b \sec \left(d x +c \right)\right)^{\frac{4}{3}}\, dx"," ",0,"int((b*sec(d*x+c))^(4/3),x)","F"
192,0,0,48,0.637000," ","int(cos(d*x+c)*(b*sec(d*x+c))^(4/3),x)","\int \cos \left(d x +c \right) \left(b \sec \left(d x +c \right)\right)^{\frac{4}{3}}\, dx"," ",0,"int(cos(d*x+c)*(b*sec(d*x+c))^(4/3),x)","F"
193,0,0,48,1.147000," ","int(cos(d*x+c)^2*(b*sec(d*x+c))^(4/3),x)","\int \left(\cos^{2}\left(d x +c \right)\right) \left(b \sec \left(d x +c \right)\right)^{\frac{4}{3}}\, dx"," ",0,"int(cos(d*x+c)^2*(b*sec(d*x+c))^(4/3),x)","F"
194,0,0,48,0.373000," ","int(sec(d*x+c)^2/(b*sec(d*x+c))^(1/3),x)","\int \frac{\sec^{2}\left(d x +c \right)}{\left(b \sec \left(d x +c \right)\right)^{\frac{1}{3}}}\, dx"," ",0,"int(sec(d*x+c)^2/(b*sec(d*x+c))^(1/3),x)","F"
195,0,0,45,0.444000," ","int(sec(d*x+c)/(b*sec(d*x+c))^(1/3),x)","\int \frac{\sec \left(d x +c \right)}{\left(b \sec \left(d x +c \right)\right)^{\frac{1}{3}}}\, dx"," ",0,"int(sec(d*x+c)/(b*sec(d*x+c))^(1/3),x)","F"
196,0,0,46,0.449000," ","int(1/(b*sec(d*x+c))^(1/3),x)","\int \frac{1}{\left(b \sec \left(d x +c \right)\right)^{\frac{1}{3}}}\, dx"," ",0,"int(1/(b*sec(d*x+c))^(1/3),x)","F"
197,0,0,48,0.451000," ","int(cos(d*x+c)/(b*sec(d*x+c))^(1/3),x)","\int \frac{\cos \left(d x +c \right)}{\left(b \sec \left(d x +c \right)\right)^{\frac{1}{3}}}\, dx"," ",0,"int(cos(d*x+c)/(b*sec(d*x+c))^(1/3),x)","F"
198,0,0,48,0.934000," ","int(cos(d*x+c)^2/(b*sec(d*x+c))^(1/3),x)","\int \frac{\cos^{2}\left(d x +c \right)}{\left(b \sec \left(d x +c \right)\right)^{\frac{1}{3}}}\, dx"," ",0,"int(cos(d*x+c)^2/(b*sec(d*x+c))^(1/3),x)","F"
199,0,0,48,0.439000," ","int(sec(d*x+c)^2/(b*sec(d*x+c))^(4/3),x)","\int \frac{\sec^{2}\left(d x +c \right)}{\left(b \sec \left(d x +c \right)\right)^{\frac{4}{3}}}\, dx"," ",0,"int(sec(d*x+c)^2/(b*sec(d*x+c))^(4/3),x)","F"
200,0,0,45,0.427000," ","int(sec(d*x+c)/(b*sec(d*x+c))^(4/3),x)","\int \frac{\sec \left(d x +c \right)}{\left(b \sec \left(d x +c \right)\right)^{\frac{4}{3}}}\, dx"," ",0,"int(sec(d*x+c)/(b*sec(d*x+c))^(4/3),x)","F"
201,0,0,46,0.380000," ","int(1/(b*sec(d*x+c))^(4/3),x)","\int \frac{1}{\left(b \sec \left(d x +c \right)\right)^{\frac{4}{3}}}\, dx"," ",0,"int(1/(b*sec(d*x+c))^(4/3),x)","F"
202,0,0,48,0.446000," ","int(cos(d*x+c)/(b*sec(d*x+c))^(4/3),x)","\int \frac{\cos \left(d x +c \right)}{\left(b \sec \left(d x +c \right)\right)^{\frac{4}{3}}}\, dx"," ",0,"int(cos(d*x+c)/(b*sec(d*x+c))^(4/3),x)","F"
203,0,0,48,1.027000," ","int(cos(d*x+c)^2/(b*sec(d*x+c))^(4/3),x)","\int \frac{\cos^{2}\left(d x +c \right)}{\left(b \sec \left(d x +c \right)\right)^{\frac{4}{3}}}\, dx"," ",0,"int(cos(d*x+c)^2/(b*sec(d*x+c))^(4/3),x)","F"
204,0,0,69,0.829000," ","int(sec(d*x+c)^m*(b*sec(d*x+c))^(4/3),x)","\int \left(\sec^{m}\left(d x +c \right)\right) \left(b \sec \left(d x +c \right)\right)^{\frac{4}{3}}\, dx"," ",0,"int(sec(d*x+c)^m*(b*sec(d*x+c))^(4/3),x)","F"
205,0,0,70,0.734000," ","int(sec(d*x+c)^m*(b*sec(d*x+c))^(2/3),x)","\int \left(\sec^{m}\left(d x +c \right)\right) \left(b \sec \left(d x +c \right)\right)^{\frac{2}{3}}\, dx"," ",0,"int(sec(d*x+c)^m*(b*sec(d*x+c))^(2/3),x)","F"
206,0,0,70,0.727000," ","int(sec(d*x+c)^m*(b*sec(d*x+c))^(1/3),x)","\int \left(\sec^{m}\left(d x +c \right)\right) \left(b \sec \left(d x +c \right)\right)^{\frac{1}{3}}\, dx"," ",0,"int(sec(d*x+c)^m*(b*sec(d*x+c))^(1/3),x)","F"
207,0,0,70,0.675000," ","int(sec(d*x+c)^m/(b*sec(d*x+c))^(1/3),x)","\int \frac{\sec^{m}\left(d x +c \right)}{\left(b \sec \left(d x +c \right)\right)^{\frac{1}{3}}}\, dx"," ",0,"int(sec(d*x+c)^m/(b*sec(d*x+c))^(1/3),x)","F"
208,0,0,70,0.582000," ","int(sec(d*x+c)^m/(b*sec(d*x+c))^(2/3),x)","\int \frac{\sec^{m}\left(d x +c \right)}{\left(b \sec \left(d x +c \right)\right)^{\frac{2}{3}}}\, dx"," ",0,"int(sec(d*x+c)^m/(b*sec(d*x+c))^(2/3),x)","F"
209,0,0,73,0.635000," ","int(sec(d*x+c)^m/(b*sec(d*x+c))^(4/3),x)","\int \frac{\sec^{m}\left(d x +c \right)}{\left(b \sec \left(d x +c \right)\right)^{\frac{4}{3}}}\, dx"," ",0,"int(sec(d*x+c)^m/(b*sec(d*x+c))^(4/3),x)","F"
210,0,0,79,2.425000," ","int(sec(d*x+c)^m*(b*sec(d*x+c))^n,x)","\int \left(\sec^{m}\left(d x +c \right)\right) \left(b \sec \left(d x +c \right)\right)^{n}\, dx"," ",0,"int(sec(d*x+c)^m*(b*sec(d*x+c))^n,x)","F"
211,0,0,62,1.469000," ","int(sec(d*x+c)^2*(b*sec(d*x+c))^n,x)","\int \left(\sec^{2}\left(d x +c \right)\right) \left(b \sec \left(d x +c \right)\right)^{n}\, dx"," ",0,"int(sec(d*x+c)^2*(b*sec(d*x+c))^n,x)","F"
212,0,0,53,1.692000," ","int(sec(d*x+c)*(b*sec(d*x+c))^n,x)","\int \sec \left(d x +c \right) \left(b \sec \left(d x +c \right)\right)^{n}\, dx"," ",0,"int(sec(d*x+c)*(b*sec(d*x+c))^n,x)","F"
213,0,0,63,1.069000," ","int((b*sec(d*x+c))^n,x)","\int \left(b \sec \left(d x +c \right)\right)^{n}\, dx"," ",0,"int((b*sec(d*x+c))^n,x)","F"
214,0,0,65,2.382000," ","int(cos(d*x+c)*(b*sec(d*x+c))^n,x)","\int \cos \left(d x +c \right) \left(b \sec \left(d x +c \right)\right)^{n}\, dx"," ",0,"int(cos(d*x+c)*(b*sec(d*x+c))^n,x)","F"
215,0,0,65,4.023000," ","int(cos(d*x+c)^2*(b*sec(d*x+c))^n,x)","\int \left(\cos^{2}\left(d x +c \right)\right) \left(b \sec \left(d x +c \right)\right)^{n}\, dx"," ",0,"int(cos(d*x+c)^2*(b*sec(d*x+c))^n,x)","F"
216,0,0,65,6.418000," ","int(cos(d*x+c)^3*(b*sec(d*x+c))^n,x)","\int \left(\cos^{3}\left(d x +c \right)\right) \left(b \sec \left(d x +c \right)\right)^{n}\, dx"," ",0,"int(cos(d*x+c)^3*(b*sec(d*x+c))^n,x)","F"
217,0,0,68,0.885000," ","int(sec(d*x+c)^(5/2)*(b*sec(d*x+c))^n,x)","\int \left(\sec^{\frac{5}{2}}\left(d x +c \right)\right) \left(b \sec \left(d x +c \right)\right)^{n}\, dx"," ",0,"int(sec(d*x+c)^(5/2)*(b*sec(d*x+c))^n,x)","F"
218,0,0,68,1.007000," ","int(sec(d*x+c)^(3/2)*(b*sec(d*x+c))^n,x)","\int \left(\sec^{\frac{3}{2}}\left(d x +c \right)\right) \left(b \sec \left(d x +c \right)\right)^{n}\, dx"," ",0,"int(sec(d*x+c)^(3/2)*(b*sec(d*x+c))^n,x)","F"
219,0,0,68,0.887000," ","int((b*sec(d*x+c))^n*sec(d*x+c)^(1/2),x)","\int \left(b \sec \left(d x +c \right)\right)^{n} \left(\sqrt{\sec}\left(d x +c \right)\right)\, dx"," ",0,"int((b*sec(d*x+c))^n*sec(d*x+c)^(1/2),x)","F"
220,0,0,68,0.880000," ","int((b*sec(d*x+c))^n/sec(d*x+c)^(1/2),x)","\int \frac{\left(b \sec \left(d x +c \right)\right)^{n}}{\sqrt{\sec \left(d x +c \right)}}\, dx"," ",0,"int((b*sec(d*x+c))^n/sec(d*x+c)^(1/2),x)","F"
221,0,0,68,0.969000," ","int((b*sec(d*x+c))^n/sec(d*x+c)^(3/2),x)","\int \frac{\left(b \sec \left(d x +c \right)\right)^{n}}{\sec \left(d x +c \right)^{\frac{3}{2}}}\, dx"," ",0,"int((b*sec(d*x+c))^n/sec(d*x+c)^(3/2),x)","F"
222,0,0,68,0.987000," ","int((b*sec(d*x+c))^n/sec(d*x+c)^(5/2),x)","\int \frac{\left(b \sec \left(d x +c \right)\right)^{n}}{\sec \left(d x +c \right)^{\frac{5}{2}}}\, dx"," ",0,"int((b*sec(d*x+c))^n/sec(d*x+c)^(5/2),x)","F"
223,1,17,16,0.137000," ","int((d*sec(b*x+a))^(7/2)*sin(b*x+a),x)","\frac{2 d \left(d \sec \left(b x +a \right)\right)^{\frac{5}{2}}}{5 b}"," ",0,"2/5*d*(d*sec(b*x+a))^(5/2)/b","A"
224,1,17,16,0.122000," ","int((d*sec(b*x+a))^(5/2)*sin(b*x+a),x)","\frac{2 d \left(d \sec \left(b x +a \right)\right)^{\frac{3}{2}}}{3 b}"," ",0,"2/3*d*(d*sec(b*x+a))^(3/2)/b","A"
225,1,17,16,0.122000," ","int((d*sec(b*x+a))^(3/2)*sin(b*x+a),x)","\frac{2 d \sqrt{d \sec \left(b x +a \right)}}{b}"," ",0,"2*d*(d*sec(b*x+a))^(1/2)/b","A"
226,1,17,16,0.187000," ","int((d*sec(b*x+a))^(1/2)*sin(b*x+a),x)","-\frac{2 d}{b \sqrt{d \sec \left(b x +a \right)}}"," ",0,"-2*d/b/(d*sec(b*x+a))^(1/2)","A"
227,1,17,16,0.150000," ","int(sin(b*x+a)/(d*sec(b*x+a))^(1/2),x)","-\frac{2 d}{3 b \left(d \sec \left(b x +a \right)\right)^{\frac{3}{2}}}"," ",0,"-2/3*d/b/(d*sec(b*x+a))^(3/2)","A"
228,1,357,35,0.909000," ","int((d*sec(b*x+a))^(5/2)*sin(b*x+a)^3,x)","-\frac{\left(-1+\cos \left(b x +a \right)\right) \left(12 \left(\cos^{3}\left(b x +a \right)\right) \sqrt{-\frac{\cos \left(b x +a \right)}{\left(\cos \left(b x +a \right)+1\right)^{2}}}+12 \left(\cos^{2}\left(b x +a \right)\right) \sqrt{-\frac{\cos \left(b x +a \right)}{\left(\cos \left(b x +a \right)+1\right)^{2}}}+3 \ln \left(-\frac{2 \left(2 \left(\cos^{2}\left(b x +a \right)\right) \sqrt{-\frac{\cos \left(b x +a \right)}{\left(\cos \left(b x +a \right)+1\right)^{2}}}-\left(\cos^{2}\left(b x +a \right)\right)+2 \cos \left(b x +a \right)-2 \sqrt{-\frac{\cos \left(b x +a \right)}{\left(\cos \left(b x +a \right)+1\right)^{2}}}-1\right)}{\sin \left(b x +a \right)^{2}}\right) \left(\cos^{2}\left(b x +a \right)\right)-3 \ln \left(-\frac{2 \left(\cos^{2}\left(b x +a \right)\right) \sqrt{-\frac{\cos \left(b x +a \right)}{\left(\cos \left(b x +a \right)+1\right)^{2}}}-\left(\cos^{2}\left(b x +a \right)\right)+2 \cos \left(b x +a \right)-2 \sqrt{-\frac{\cos \left(b x +a \right)}{\left(\cos \left(b x +a \right)+1\right)^{2}}}-1}{\sin \left(b x +a \right)^{2}}\right) \left(\cos^{2}\left(b x +a \right)\right)+4 \cos \left(b x +a \right) \sqrt{-\frac{\cos \left(b x +a \right)}{\left(\cos \left(b x +a \right)+1\right)^{2}}}+4 \sqrt{-\frac{\cos \left(b x +a \right)}{\left(\cos \left(b x +a \right)+1\right)^{2}}}\right) \cos \left(b x +a \right) \left(\frac{d}{\cos \left(b x +a \right)}\right)^{\frac{5}{2}}}{6 b \sqrt{-\frac{\cos \left(b x +a \right)}{\left(\cos \left(b x +a \right)+1\right)^{2}}}\, \sin \left(b x +a \right)^{2}}"," ",0,"-1/6/b*(-1+cos(b*x+a))*(12*cos(b*x+a)^3*(-cos(b*x+a)/(cos(b*x+a)+1)^2)^(1/2)+12*cos(b*x+a)^2*(-cos(b*x+a)/(cos(b*x+a)+1)^2)^(1/2)+3*ln(-2*(2*cos(b*x+a)^2*(-cos(b*x+a)/(cos(b*x+a)+1)^2)^(1/2)-cos(b*x+a)^2+2*cos(b*x+a)-2*(-cos(b*x+a)/(cos(b*x+a)+1)^2)^(1/2)-1)/sin(b*x+a)^2)*cos(b*x+a)^2-3*ln(-(2*cos(b*x+a)^2*(-cos(b*x+a)/(cos(b*x+a)+1)^2)^(1/2)-cos(b*x+a)^2+2*cos(b*x+a)-2*(-cos(b*x+a)/(cos(b*x+a)+1)^2)^(1/2)-1)/sin(b*x+a)^2)*cos(b*x+a)^2+4*cos(b*x+a)*(-cos(b*x+a)/(cos(b*x+a)+1)^2)^(1/2)+4*(-cos(b*x+a)/(cos(b*x+a)+1)^2)^(1/2))*cos(b*x+a)*(d/cos(b*x+a))^(5/2)/(-cos(b*x+a)/(cos(b*x+a)+1)^2)^(1/2)/sin(b*x+a)^2","B"
229,1,36,35,0.676000," ","int((d*sec(b*x+a))^(9/2)*sin(b*x+a)^3,x)","-\frac{2 \left(7 \left(\cos^{2}\left(b x +a \right)\right)-3\right) \cos \left(b x +a \right) \left(\frac{d}{\cos \left(b x +a \right)}\right)^{\frac{9}{2}}}{21 b}"," ",0,"-2/21/b*(7*cos(b*x+a)^2-3)*cos(b*x+a)*(d/cos(b*x+a))^(9/2)","A"
230,1,534,133,1.278000," ","int((d*csc(b*x+a))^(9/2)*(c*sec(b*x+a))^(1/2),x)","-\frac{\left(4 \sin \left(b x +a \right) \left(\cos^{3}\left(b x +a \right)\right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)+4 \sin \left(b x +a \right) \left(\cos^{2}\left(b x +a \right)\right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)-4 \sin \left(b x +a \right) \cos \left(b x +a \right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)-4 \sin \left(b x +a \right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)-2 \left(\cos^{3}\left(b x +a \right)\right) \sqrt{2}+3 \cos \left(b x +a \right) \sqrt{2}\right) \left(\frac{d}{\sin \left(b x +a \right)}\right)^{\frac{9}{2}} \sqrt{\frac{c}{\cos \left(b x +a \right)}}\, \sin \left(b x +a \right) \sqrt{2}}{7 b}"," ",0,"-1/7/b*(4*sin(b*x+a)*cos(b*x+a)^3*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))+4*sin(b*x+a)*cos(b*x+a)^2*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))-4*sin(b*x+a)*cos(b*x+a)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))-4*sin(b*x+a)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))-2*cos(b*x+a)^3*2^(1/2)+3*cos(b*x+a)*2^(1/2))*(d/sin(b*x+a))^(9/2)*(c/cos(b*x+a))^(1/2)*sin(b*x+a)*2^(1/2)","B"
231,1,54,57,1.194000," ","int((d*csc(b*x+a))^(7/2)*(c*sec(b*x+a))^(1/2),x)","\frac{2 \left(4 \left(\cos^{2}\left(b x +a \right)\right)-5\right) \cos \left(b x +a \right) \left(\frac{d}{\sin \left(b x +a \right)}\right)^{\frac{7}{2}} \sqrt{\frac{c}{\cos \left(b x +a \right)}}\, \sin \left(b x +a \right)}{5 b}"," ",0,"2/5/b*(4*cos(b*x+a)^2-5)*cos(b*x+a)*(d/sin(b*x+a))^(7/2)*(c/cos(b*x+a))^(1/2)*sin(b*x+a)","A"
232,1,281,104,1.229000," ","int((d*csc(b*x+a))^(5/2)*(c*sec(b*x+a))^(1/2),x)","\frac{\left(2 \sin \left(b x +a \right) \cos \left(b x +a \right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)+2 \sin \left(b x +a \right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)-\cos \left(b x +a \right) \sqrt{2}\right) \left(\frac{d}{\sin \left(b x +a \right)}\right)^{\frac{5}{2}} \sqrt{\frac{c}{\cos \left(b x +a \right)}}\, \sin \left(b x +a \right) \sqrt{2}}{3 b}"," ",0,"1/3/b*(2*sin(b*x+a)*cos(b*x+a)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))+2*sin(b*x+a)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))-cos(b*x+a)*2^(1/2))*(d/sin(b*x+a))^(5/2)*(c/cos(b*x+a))^(1/2)*sin(b*x+a)*2^(1/2)","B"
233,1,42,27,1.222000," ","int((d*csc(b*x+a))^(3/2)*(c*sec(b*x+a))^(1/2),x)","-\frac{2 \left(\frac{d}{\sin \left(b x +a \right)}\right)^{\frac{3}{2}} \sqrt{\frac{c}{\cos \left(b x +a \right)}}\, \cos \left(b x +a \right) \sin \left(b x +a \right)}{b}"," ",0,"-2/b*(d/sin(b*x+a))^(3/2)*(c/cos(b*x+a))^(1/2)*cos(b*x+a)*sin(b*x+a)","A"
234,1,155,73,1.415000," ","int((d*csc(b*x+a))^(1/2)*(c*sec(b*x+a))^(1/2),x)","-\frac{\sqrt{\frac{c}{\cos \left(b x +a \right)}}\, \sqrt{\frac{d}{\sin \left(b x +a \right)}}\, \left(\sin^{2}\left(b x +a \right)\right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{2}}{b \left(-1+\cos \left(b x +a \right)\right)}"," ",0,"-1/b*(c/cos(b*x+a))^(1/2)*(d/sin(b*x+a))^(1/2)*sin(b*x+a)^2*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))/(-1+cos(b*x+a))*2^(1/2)","B"
235,1,275,218,1.004000," ","int((c*sec(b*x+a))^(1/2)/(d*csc(b*x+a))^(1/2),x)","-\frac{\sqrt{\frac{c}{\cos \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \left(i \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-i \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-\EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-\EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)\right) \sin \left(b x +a \right) \sqrt{2}}{2 b \sqrt{\frac{d}{\sin \left(b x +a \right)}}\, \left(-1+\cos \left(b x +a \right)\right)}"," ",0,"-1/2/b*(c/cos(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*(I*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2-1/2*I,1/2*2^(1/2))-I*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2+1/2*I,1/2*2^(1/2))-EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2-1/2*I,1/2*2^(1/2))-EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2+1/2*I,1/2*2^(1/2)))*sin(b*x+a)/(d/sin(b*x+a))^(1/2)/(-1+cos(b*x+a))*2^(1/2)","C"
236,1,186,106,1.022000," ","int((c*sec(b*x+a))^(1/2)/(d*csc(b*x+a))^(3/2),x)","-\frac{\left(\sin \left(b x +a \right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)+\sqrt{2}\, \left(\cos^{2}\left(b x +a \right)\right)-\cos \left(b x +a \right) \sqrt{2}\right) \sqrt{\frac{c}{\cos \left(b x +a \right)}}\, \sqrt{2}}{2 b \left(-1+\cos \left(b x +a \right)\right) \left(\frac{d}{\sin \left(b x +a \right)}\right)^{\frac{3}{2}} \sin \left(b x +a \right)}"," ",0,"-1/2/b*(sin(b*x+a)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))+2^(1/2)*cos(b*x+a)^2-cos(b*x+a)*2^(1/2))*(c/cos(b*x+a))^(1/2)/(-1+cos(b*x+a))/(d/sin(b*x+a))^(3/2)/sin(b*x+a)*2^(1/2)","A"
237,1,514,259,1.104000," ","int((c*sec(b*x+a))^(1/2)/(d*csc(b*x+a))^(5/2),x)","\frac{\left(3 i \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-3 i \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+3 \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+3 \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-2 \sqrt{2}\, \left(\cos^{2}\left(b x +a \right)\right)+2 \cos \left(b x +a \right) \sqrt{2}\right) \sqrt{\frac{c}{\cos \left(b x +a \right)}}\, \sqrt{2}}{8 b \left(-1+\cos \left(b x +a \right)\right) \left(\frac{d}{\sin \left(b x +a \right)}\right)^{\frac{5}{2}} \sin \left(b x +a \right)}"," ",0,"1/8/b*(3*I*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2+1/2*I,1/2*2^(1/2))-3*I*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2-1/2*I,1/2*2^(1/2))+3*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2+1/2*I,1/2*2^(1/2))+3*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2-1/2*I,1/2*2^(1/2))-2*2^(1/2)*cos(b*x+a)^2+2*cos(b*x+a)*2^(1/2))*(c/cos(b*x+a))^(1/2)/(-1+cos(b*x+a))/(d/sin(b*x+a))^(5/2)/sin(b*x+a)*2^(1/2)","C"
238,1,64,86,1.079000," ","int((d*csc(b*x+a))^(9/2)*(c*sec(b*x+a))^(3/2),x)","\frac{2 \left(32 \left(\cos^{4}\left(b x +a \right)\right)-56 \left(\cos^{2}\left(b x +a \right)\right)+21\right) \cos \left(b x +a \right) \left(\frac{d}{\sin \left(b x +a \right)}\right)^{\frac{9}{2}} \left(\frac{c}{\cos \left(b x +a \right)}\right)^{\frac{3}{2}} \sin \left(b x +a \right)}{21 b}"," ",0,"2/21/b*(32*cos(b*x+a)^4-56*cos(b*x+a)^2+21)*cos(b*x+a)*(d/sin(b*x+a))^(9/2)*(c/cos(b*x+a))^(3/2)*sin(b*x+a)","A"
239,1,980,165,1.159000," ","int((d*csc(b*x+a))^(7/2)*(c*sec(b*x+a))^(3/2),x)","-\frac{\left(24 \left(\cos^{3}\left(b x +a \right)\right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticE \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)-12 \left(\cos^{3}\left(b x +a \right)\right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)+24 \left(\cos^{2}\left(b x +a \right)\right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticE \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)-12 \left(\cos^{2}\left(b x +a \right)\right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)-24 \cos \left(b x +a \right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticE \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)+12 \cos \left(b x +a \right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)-12 \left(\cos^{3}\left(b x +a \right)\right) \sqrt{2}-24 \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticE \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)+12 \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)+6 \sqrt{2}\, \left(\cos^{2}\left(b x +a \right)\right)+12 \cos \left(b x +a \right) \sqrt{2}-5 \sqrt{2}\right) \cos \left(b x +a \right) \left(\frac{d}{\sin \left(b x +a \right)}\right)^{\frac{7}{2}} \left(\frac{c}{\cos \left(b x +a \right)}\right)^{\frac{3}{2}} \sin \left(b x +a \right) \sqrt{2}}{5 b}"," ",0,"-1/5/b*(24*cos(b*x+a)^3*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticE(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))-12*cos(b*x+a)^3*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))+24*cos(b*x+a)^2*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticE(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))-12*cos(b*x+a)^2*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))-24*cos(b*x+a)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticE(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))+12*cos(b*x+a)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))-12*cos(b*x+a)^3*2^(1/2)-24*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticE(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))+12*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))+6*2^(1/2)*cos(b*x+a)^2+12*cos(b*x+a)*2^(1/2)-5*2^(1/2))*cos(b*x+a)*(d/sin(b*x+a))^(7/2)*(c/cos(b*x+a))^(3/2)*sin(b*x+a)*2^(1/2)","B"
240,1,54,57,1.036000," ","int((d*csc(b*x+a))^(5/2)*(c*sec(b*x+a))^(3/2),x)","-\frac{2 \left(4 \left(\cos^{2}\left(b x +a \right)\right)-3\right) \cos \left(b x +a \right) \left(\frac{d}{\sin \left(b x +a \right)}\right)^{\frac{5}{2}} \left(\frac{c}{\cos \left(b x +a \right)}\right)^{\frac{3}{2}} \sin \left(b x +a \right)}{3 b}"," ",0,"-2/3/b*(4*cos(b*x+a)^2-3)*cos(b*x+a)*(d/sin(b*x+a))^(5/2)*(c/cos(b*x+a))^(3/2)*sin(b*x+a)","A"
241,1,498,136,1.146000," ","int((d*csc(b*x+a))^(3/2)*(c*sec(b*x+a))^(3/2),x)","-\frac{\left(-4 \cos \left(b x +a \right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticE \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)+2 \cos \left(b x +a \right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)-4 \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticE \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)+2 \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)+2 \cos \left(b x +a \right) \sqrt{2}-\sqrt{2}\right) \cos \left(b x +a \right) \left(\frac{d}{\sin \left(b x +a \right)}\right)^{\frac{3}{2}} \left(\frac{c}{\cos \left(b x +a \right)}\right)^{\frac{3}{2}} \sin \left(b x +a \right) \sqrt{2}}{b}"," ",0,"-1/b*(-4*cos(b*x+a)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticE(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))+2*cos(b*x+a)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))-4*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticE(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))+2*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))+2*cos(b*x+a)*2^(1/2)-2^(1/2))*cos(b*x+a)*(d/sin(b*x+a))^(3/2)*(c/cos(b*x+a))^(3/2)*sin(b*x+a)*2^(1/2)","B"
242,1,42,27,1.148000," ","int((d*csc(b*x+a))^(1/2)*(c*sec(b*x+a))^(3/2),x)","\frac{2 \sqrt{\frac{d}{\sin \left(b x +a \right)}}\, \left(\frac{c}{\cos \left(b x +a \right)}\right)^{\frac{3}{2}} \cos \left(b x +a \right) \sin \left(b x +a \right)}{b}"," ",0,"2/b*(d/sin(b*x+a))^(1/2)*(c/cos(b*x+a))^(3/2)*cos(b*x+a)*sin(b*x+a)","A"
243,1,497,104,1.091000," ","int((c*sec(b*x+a))^(3/2)/(d*csc(b*x+a))^(1/2),x)","-\frac{\left(\cos \left(b x +a \right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)-2 \cos \left(b x +a \right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticE \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)+\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)-2 \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticE \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)+\cos \left(b x +a \right) \sqrt{2}-\sqrt{2}\right) \cos \left(b x +a \right) \left(\frac{c}{\cos \left(b x +a \right)}\right)^{\frac{3}{2}} \sqrt{2}}{b \sqrt{\frac{d}{\sin \left(b x +a \right)}}\, \sin \left(b x +a \right)}"," ",0,"-1/b*(cos(b*x+a)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))-2*cos(b*x+a)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticE(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))+((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))-2*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticE(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))+cos(b*x+a)*2^(1/2)-2^(1/2))*cos(b*x+a)*(c/cos(b*x+a))^(3/2)/(d/sin(b*x+a))^(1/2)/sin(b*x+a)*2^(1/2)","B"
244,1,646,271,1.062000," ","int((c*sec(b*x+a))^(3/2)/(d*csc(b*x+a))^(3/2),x)","\frac{\left(i \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sin \left(b x +a \right)-i \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sin \left(b x +a \right)+\EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sin \left(b x +a \right)+\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sin \left(b x +a \right)-2 \sin \left(b x +a \right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)+2 \cos \left(b x +a \right) \sqrt{2}-2 \sqrt{2}\right) \cos \left(b x +a \right) \left(\frac{c}{\cos \left(b x +a \right)}\right)^{\frac{3}{2}} \sqrt{2}}{2 b \left(-1+\cos \left(b x +a \right)\right) \left(\frac{d}{\sin \left(b x +a \right)}\right)^{\frac{3}{2}} \sin \left(b x +a \right)}"," ",0,"1/2/b*(I*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*sin(b*x+a)-I*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2+1/2*I,1/2*2^(1/2))*sin(b*x+a)+EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*sin(b*x+a)+((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2+1/2*I,1/2*2^(1/2))*sin(b*x+a)-2*sin(b*x+a)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))+2*cos(b*x+a)*2^(1/2)-2*2^(1/2))*cos(b*x+a)*(c/cos(b*x+a))^(3/2)/(-1+cos(b*x+a))/(d/sin(b*x+a))^(3/2)/sin(b*x+a)*2^(1/2)","C"
245,1,512,109,1.013000," ","int((c*sec(b*x+a))^(3/2)/(d*csc(b*x+a))^(5/2),x)","\frac{\left(6 \cos \left(b x +a \right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticE \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)-3 \cos \left(b x +a \right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)+6 \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticE \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)-3 \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)+\sqrt{2}\, \left(\cos^{2}\left(b x +a \right)\right)-3 \cos \left(b x +a \right) \sqrt{2}+2 \sqrt{2}\right) \cos \left(b x +a \right) \left(\frac{c}{\cos \left(b x +a \right)}\right)^{\frac{3}{2}} \sqrt{2}}{2 b \sin \left(b x +a \right)^{3} \left(\frac{d}{\sin \left(b x +a \right)}\right)^{\frac{5}{2}}}"," ",0,"1/2/b*(6*cos(b*x+a)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticE(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))-3*cos(b*x+a)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))+6*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticE(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))-3*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))+2^(1/2)*cos(b*x+a)^2-3*cos(b*x+a)*2^(1/2)+2*2^(1/2))*cos(b*x+a)*(c/cos(b*x+a))^(3/2)/sin(b*x+a)^3/(d/sin(b*x+a))^(5/2)*2^(1/2)","B"
246,1,555,165,1.194000," ","int((d*csc(b*x+a))^(9/2)*(c*sec(b*x+a))^(5/2),x)","-\frac{\left(40 \left(\cos^{4}\left(b x +a \right)\right) \sin \left(b x +a \right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)+40 \sin \left(b x +a \right) \left(\cos^{3}\left(b x +a \right)\right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)-40 \sin \left(b x +a \right) \left(\cos^{2}\left(b x +a \right)\right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)-40 \sin \left(b x +a \right) \cos \left(b x +a \right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)-20 \left(\cos^{4}\left(b x +a \right)\right) \sqrt{2}+30 \sqrt{2}\, \left(\cos^{2}\left(b x +a \right)\right)-7 \sqrt{2}\right) \cos \left(b x +a \right) \left(\frac{d}{\sin \left(b x +a \right)}\right)^{\frac{9}{2}} \left(\frac{c}{\cos \left(b x +a \right)}\right)^{\frac{5}{2}} \sin \left(b x +a \right) \sqrt{2}}{21 b}"," ",0,"-1/21/b*(40*cos(b*x+a)^4*sin(b*x+a)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))+40*sin(b*x+a)*cos(b*x+a)^3*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))-40*sin(b*x+a)*cos(b*x+a)^2*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))-40*sin(b*x+a)*cos(b*x+a)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))-20*cos(b*x+a)^4*2^(1/2)+30*2^(1/2)*cos(b*x+a)^2-7*2^(1/2))*cos(b*x+a)*(d/sin(b*x+a))^(9/2)*(c/cos(b*x+a))^(5/2)*sin(b*x+a)*2^(1/2)","B"
247,1,64,88,1.124000," ","int((d*csc(b*x+a))^(7/2)*(c*sec(b*x+a))^(5/2),x)","\frac{2 \left(32 \left(\cos^{4}\left(b x +a \right)\right)-40 \left(\cos^{2}\left(b x +a \right)\right)+5\right) \cos \left(b x +a \right) \left(\frac{d}{\sin \left(b x +a \right)}\right)^{\frac{7}{2}} \left(\frac{c}{\cos \left(b x +a \right)}\right)^{\frac{5}{2}} \sin \left(b x +a \right)}{15 b}"," ",0,"2/15/b*(32*cos(b*x+a)^4-40*cos(b*x+a)^2+5)*cos(b*x+a)*(d/sin(b*x+a))^(7/2)*(c/cos(b*x+a))^(5/2)*sin(b*x+a)","A"
248,1,300,136,1.164000," ","int((d*csc(b*x+a))^(5/2)*(c*sec(b*x+a))^(5/2),x)","\frac{\left(4 \sin \left(b x +a \right) \left(\cos^{2}\left(b x +a \right)\right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)+4 \sin \left(b x +a \right) \cos \left(b x +a \right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)-2 \sqrt{2}\, \left(\cos^{2}\left(b x +a \right)\right)+\sqrt{2}\right) \cos \left(b x +a \right) \left(\frac{d}{\sin \left(b x +a \right)}\right)^{\frac{5}{2}} \left(\frac{c}{\cos \left(b x +a \right)}\right)^{\frac{5}{2}} \sin \left(b x +a \right) \sqrt{2}}{3 b}"," ",0,"1/3/b*(4*sin(b*x+a)*cos(b*x+a)^2*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))+4*sin(b*x+a)*cos(b*x+a)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))-2*2^(1/2)*cos(b*x+a)^2+2^(1/2))*cos(b*x+a)*(d/sin(b*x+a))^(5/2)*(c/cos(b*x+a))^(5/2)*sin(b*x+a)*2^(1/2)","B"
249,1,54,57,1.042000," ","int((d*csc(b*x+a))^(3/2)*(c*sec(b*x+a))^(5/2),x)","-\frac{2 \left(4 \left(\cos^{2}\left(b x +a \right)\right)-1\right) \cos \left(b x +a \right) \left(\frac{d}{\sin \left(b x +a \right)}\right)^{\frac{3}{2}} \left(\frac{c}{\cos \left(b x +a \right)}\right)^{\frac{5}{2}} \sin \left(b x +a \right)}{3 b}"," ",0,"-2/3/b*(4*cos(b*x+a)^2-1)*cos(b*x+a)*(d/sin(b*x+a))^(3/2)*(c/cos(b*x+a))^(5/2)*sin(b*x+a)","A"
250,1,188,104,1.251000," ","int((d*csc(b*x+a))^(1/2)*(c*sec(b*x+a))^(5/2),x)","-\frac{\left(2 \sin \left(b x +a \right) \cos \left(b x +a \right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)-\cos \left(b x +a \right) \sqrt{2}+\sqrt{2}\right) \cos \left(b x +a \right) \sqrt{\frac{d}{\sin \left(b x +a \right)}}\, \left(\frac{c}{\cos \left(b x +a \right)}\right)^{\frac{5}{2}} \sin \left(b x +a \right) \sqrt{2}}{3 b \left(-1+\cos \left(b x +a \right)\right)}"," ",0,"-1/3/b*(2*sin(b*x+a)*cos(b*x+a)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))-cos(b*x+a)*2^(1/2)+2^(1/2))*cos(b*x+a)*(d/sin(b*x+a))^(1/2)*(c/cos(b*x+a))^(5/2)*sin(b*x+a)/(-1+cos(b*x+a))*2^(1/2)","A"
251,1,42,27,0.986000," ","int((c*sec(b*x+a))^(5/2)/(d*csc(b*x+a))^(1/2),x)","\frac{2 \left(\frac{c}{\cos \left(b x +a \right)}\right)^{\frac{5}{2}} \cos \left(b x +a \right) \sin \left(b x +a \right)}{3 b \sqrt{\frac{d}{\sin \left(b x +a \right)}}}"," ",0,"2/3/b*(c/cos(b*x+a))^(5/2)*cos(b*x+a)*sin(b*x+a)/(d/sin(b*x+a))^(1/2)","A"
252,1,190,109,1.072000," ","int((c*sec(b*x+a))^(5/2)/(d*csc(b*x+a))^(3/2),x)","\frac{\left(\sin \left(b x +a \right) \cos \left(b x +a \right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)+\cos \left(b x +a \right) \sqrt{2}-\sqrt{2}\right) \cos \left(b x +a \right) \left(\frac{c}{\cos \left(b x +a \right)}\right)^{\frac{5}{2}} \sqrt{2}}{3 b \left(-1+\cos \left(b x +a \right)\right) \left(\frac{d}{\sin \left(b x +a \right)}\right)^{\frac{3}{2}} \sin \left(b x +a \right)}"," ",0,"1/3/b*(sin(b*x+a)*cos(b*x+a)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))+cos(b*x+a)*2^(1/2)-2^(1/2))*cos(b*x+a)*(c/cos(b*x+a))^(5/2)/(-1+cos(b*x+a))/(d/sin(b*x+a))^(3/2)/sin(b*x+a)*2^(1/2)","A"
253,1,536,271,1.192000," ","int((c*sec(b*x+a))^(5/2)/(d*csc(b*x+a))^(5/2),x)","\frac{\left(3 i \cos \left(b x +a \right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-3 i \cos \left(b x +a \right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-3 \cos \left(b x +a \right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-3 \cos \left(b x +a \right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+2 \cos \left(b x +a \right) \sqrt{2}-2 \sqrt{2}\right) \cos \left(b x +a \right) \left(\frac{c}{\cos \left(b x +a \right)}\right)^{\frac{5}{2}} \sqrt{2}}{6 b \left(-1+\cos \left(b x +a \right)\right) \left(\frac{d}{\sin \left(b x +a \right)}\right)^{\frac{5}{2}} \sin \left(b x +a \right)}"," ",0,"1/6/b*(3*I*cos(b*x+a)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2-1/2*I,1/2*2^(1/2))-3*I*cos(b*x+a)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2+1/2*I,1/2*2^(1/2))-3*cos(b*x+a)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2-1/2*I,1/2*2^(1/2))-3*cos(b*x+a)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2+1/2*I,1/2*2^(1/2))+2*cos(b*x+a)*2^(1/2)-2*2^(1/2))*cos(b*x+a)*(c/cos(b*x+a))^(5/2)/(-1+cos(b*x+a))/(d/sin(b*x+a))^(5/2)/sin(b*x+a)*2^(1/2)","C"
254,1,54,57,1.207000," ","int((d*csc(b*x+a))^(9/2)/(c*sec(b*x+a))^(1/2),x)","\frac{2 \left(4 \left(\cos^{2}\left(b x +a \right)\right)-7\right) \left(\frac{d}{\sin \left(b x +a \right)}\right)^{\frac{9}{2}} \cos \left(b x +a \right) \sin \left(b x +a \right)}{21 b \sqrt{\frac{c}{\cos \left(b x +a \right)}}}"," ",0,"2/21/b*(4*cos(b*x+a)^2-7)*(d/sin(b*x+a))^(9/2)*cos(b*x+a)*sin(b*x+a)/(c/cos(b*x+a))^(1/2)","A"
255,1,976,133,1.228000," ","int((d*csc(b*x+a))^(7/2)/(c*sec(b*x+a))^(1/2),x)","-\frac{\left(4 \left(\cos^{3}\left(b x +a \right)\right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticE \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)-2 \left(\cos^{3}\left(b x +a \right)\right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)+4 \left(\cos^{2}\left(b x +a \right)\right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticE \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)-2 \left(\cos^{2}\left(b x +a \right)\right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)-4 \cos \left(b x +a \right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticE \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)+2 \cos \left(b x +a \right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)-2 \left(\cos^{3}\left(b x +a \right)\right) \sqrt{2}-4 \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticE \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)+2 \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)+\sqrt{2}\, \left(\cos^{2}\left(b x +a \right)\right)+2 \cos \left(b x +a \right) \sqrt{2}\right) \left(\frac{d}{\sin \left(b x +a \right)}\right)^{\frac{7}{2}} \sin \left(b x +a \right) \sqrt{2}}{5 b \sqrt{\frac{c}{\cos \left(b x +a \right)}}\, \cos \left(b x +a \right)}"," ",0,"-1/5/b*(4*cos(b*x+a)^3*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticE(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))-2*cos(b*x+a)^3*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))+4*cos(b*x+a)^2*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticE(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))-2*cos(b*x+a)^2*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))-4*cos(b*x+a)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticE(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))+2*cos(b*x+a)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))-2*cos(b*x+a)^3*2^(1/2)-4*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticE(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))+2*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))+2^(1/2)*cos(b*x+a)^2+2*cos(b*x+a)*2^(1/2))*(d/sin(b*x+a))^(7/2)*sin(b*x+a)/(c/cos(b*x+a))^(1/2)/cos(b*x+a)*2^(1/2)","B"
256,1,42,27,1.155000," ","int((d*csc(b*x+a))^(5/2)/(c*sec(b*x+a))^(1/2),x)","-\frac{2 \left(\frac{d}{\sin \left(b x +a \right)}\right)^{\frac{5}{2}} \cos \left(b x +a \right) \sin \left(b x +a \right)}{3 b \sqrt{\frac{c}{\cos \left(b x +a \right)}}}"," ",0,"-2/3/b*(d/sin(b*x+a))^(5/2)*cos(b*x+a)*sin(b*x+a)/(c/cos(b*x+a))^(1/2)","A"
257,1,494,104,1.199000," ","int((d*csc(b*x+a))^(3/2)/(c*sec(b*x+a))^(1/2),x)","\frac{\left(2 \cos \left(b x +a \right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticE \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)-\cos \left(b x +a \right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)+2 \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticE \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)-\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)-\cos \left(b x +a \right) \sqrt{2}\right) \left(\frac{d}{\sin \left(b x +a \right)}\right)^{\frac{3}{2}} \sin \left(b x +a \right) \sqrt{2}}{b \sqrt{\frac{c}{\cos \left(b x +a \right)}}\, \cos \left(b x +a \right)}"," ",0,"1/b*(2*cos(b*x+a)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticE(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))-cos(b*x+a)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))+2*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticE(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))-((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))-cos(b*x+a)*2^(1/2))*(d/sin(b*x+a))^(3/2)*sin(b*x+a)/(c/cos(b*x+a))^(1/2)/cos(b*x+a)*2^(1/2)","B"
258,1,316,218,1.242000," ","int((d*csc(b*x+a))^(1/2)/(c*sec(b*x+a))^(1/2),x)","-\frac{\sqrt{\frac{d}{\sin \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \left(i \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-i \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-2 \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)+\EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+\EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)\right) \left(\sin^{2}\left(b x +a \right)\right) \sqrt{2}}{2 b \sqrt{\frac{c}{\cos \left(b x +a \right)}}\, \cos \left(b x +a \right) \left(-1+\cos \left(b x +a \right)\right)}"," ",0,"-1/2/b*(d/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*(I*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2-1/2*I,1/2*2^(1/2))-I*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2+1/2*I,1/2*2^(1/2))-2*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))+EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2-1/2*I,1/2*2^(1/2))+EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2+1/2*I,1/2*2^(1/2)))*sin(b*x+a)^2/(c/cos(b*x+a))^(1/2)/cos(b*x+a)/(-1+cos(b*x+a))*2^(1/2)","C"
259,1,509,73,1.013000," ","int(1/(d*csc(b*x+a))^(1/2)/(c*sec(b*x+a))^(1/2),x)","-\frac{\left(2 \cos \left(b x +a \right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticE \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)-\cos \left(b x +a \right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)+2 \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticE \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)-\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)+\sqrt{2}\, \left(\cos^{2}\left(b x +a \right)\right)-\cos \left(b x +a \right) \sqrt{2}\right) \sqrt{2}}{2 b \cos \left(b x +a \right) \sin \left(b x +a \right) \sqrt{\frac{d}{\sin \left(b x +a \right)}}\, \sqrt{\frac{c}{\cos \left(b x +a \right)}}}"," ",0,"-1/2/b*(2*cos(b*x+a)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticE(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))-cos(b*x+a)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))+2*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticE(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))-((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))+2^(1/2)*cos(b*x+a)^2-cos(b*x+a)*2^(1/2))/cos(b*x+a)/sin(b*x+a)/(d/sin(b*x+a))^(1/2)/(c/cos(b*x+a))^(1/2)*2^(1/2)","B"
260,1,658,259,0.909000," ","int(1/(d*csc(b*x+a))^(3/2)/(c*sec(b*x+a))^(1/2),x)","-\frac{\left(i \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sin \left(b x +a \right)-i \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sin \left(b x +a \right)+\EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sin \left(b x +a \right)+\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sin \left(b x +a \right)-2 \sin \left(b x +a \right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)+2 \left(\cos^{3}\left(b x +a \right)\right) \sqrt{2}-2 \sqrt{2}\, \left(\cos^{2}\left(b x +a \right)\right)\right) \sqrt{2}}{8 b \left(-1+\cos \left(b x +a \right)\right) \left(\frac{d}{\sin \left(b x +a \right)}\right)^{\frac{3}{2}} \sqrt{\frac{c}{\cos \left(b x +a \right)}}\, \cos \left(b x +a \right) \sin \left(b x +a \right)}"," ",0,"-1/8/b*(I*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*sin(b*x+a)-I*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2+1/2*I,1/2*2^(1/2))*sin(b*x+a)+EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*sin(b*x+a)+((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2+1/2*I,1/2*2^(1/2))*sin(b*x+a)-2*sin(b*x+a)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))+2*cos(b*x+a)^3*2^(1/2)-2*2^(1/2)*cos(b*x+a)^2)/(-1+cos(b*x+a))/(d/sin(b*x+a))^(3/2)/(c/cos(b*x+a))^(1/2)/cos(b*x+a)/sin(b*x+a)*2^(1/2)","C"
261,1,523,106,1.008000," ","int(1/(d*csc(b*x+a))^(5/2)/(c*sec(b*x+a))^(1/2),x)","\frac{\left(2 \left(\cos^{4}\left(b x +a \right)\right) \sqrt{2}+3 \cos \left(b x +a \right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)-6 \cos \left(b x +a \right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticE \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)+3 \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)-6 \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticE \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)-5 \sqrt{2}\, \left(\cos^{2}\left(b x +a \right)\right)+3 \cos \left(b x +a \right) \sqrt{2}\right) \sqrt{2}}{12 b \cos \left(b x +a \right) \sin \left(b x +a \right)^{3} \left(\frac{d}{\sin \left(b x +a \right)}\right)^{\frac{5}{2}} \sqrt{\frac{c}{\cos \left(b x +a \right)}}}"," ",0,"1/12/b*(2*cos(b*x+a)^4*2^(1/2)+3*cos(b*x+a)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))-6*cos(b*x+a)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticE(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))+3*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))-6*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticE(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))-5*2^(1/2)*cos(b*x+a)^2+3*cos(b*x+a)*2^(1/2))/cos(b*x+a)/sin(b*x+a)^3/(d/sin(b*x+a))^(5/2)/(c/cos(b*x+a))^(1/2)*2^(1/2)","B"
262,1,54,92,1.097000," ","int((d*csc(b*x+a))^(11/2)/(c*sec(b*x+a))^(3/2),x)","\frac{2 \left(4 \left(\cos^{2}\left(b x +a \right)\right)-9\right) \left(\frac{d}{\sin \left(b x +a \right)}\right)^{\frac{11}{2}} \cos \left(b x +a \right) \sin \left(b x +a \right)}{45 b \left(\frac{c}{\cos \left(b x +a \right)}\right)^{\frac{3}{2}}}"," ",0,"2/45/b*(4*cos(b*x+a)^2-9)*(d/sin(b*x+a))^(11/2)*cos(b*x+a)*sin(b*x+a)/(c/cos(b*x+a))^(3/2)","A"
263,1,542,140,1.226000," ","int((d*csc(b*x+a))^(9/2)/(c*sec(b*x+a))^(3/2),x)","\frac{\left(2 \sin \left(b x +a \right) \left(\cos^{3}\left(b x +a \right)\right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)+2 \sin \left(b x +a \right) \left(\cos^{2}\left(b x +a \right)\right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)-2 \sin \left(b x +a \right) \cos \left(b x +a \right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)-2 \sin \left(b x +a \right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)-\left(\cos^{3}\left(b x +a \right)\right) \sqrt{2}-2 \cos \left(b x +a \right) \sqrt{2}\right) \left(\frac{d}{\sin \left(b x +a \right)}\right)^{\frac{9}{2}} \sin \left(b x +a \right) \sqrt{2}}{21 b \left(\frac{c}{\cos \left(b x +a \right)}\right)^{\frac{3}{2}} \cos \left(b x +a \right)^{2}}"," ",0,"1/21/b*(2*sin(b*x+a)*cos(b*x+a)^3*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))+2*sin(b*x+a)*cos(b*x+a)^2*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))-2*sin(b*x+a)*cos(b*x+a)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))-2*sin(b*x+a)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))-cos(b*x+a)^3*2^(1/2)-2*cos(b*x+a)*2^(1/2))*(d/sin(b*x+a))^(9/2)*sin(b*x+a)/(c/cos(b*x+a))^(3/2)/cos(b*x+a)^2*2^(1/2)","B"
264,1,42,27,1.097000," ","int((d*csc(b*x+a))^(7/2)/(c*sec(b*x+a))^(3/2),x)","-\frac{2 \left(\frac{d}{\sin \left(b x +a \right)}\right)^{\frac{7}{2}} \cos \left(b x +a \right) \sin \left(b x +a \right)}{5 b \left(\frac{c}{\cos \left(b x +a \right)}\right)^{\frac{3}{2}}}"," ",0,"-2/5/b*(d/sin(b*x+a))^(7/2)*cos(b*x+a)*sin(b*x+a)/(c/cos(b*x+a))^(3/2)","A"
265,1,286,109,1.193000," ","int((d*csc(b*x+a))^(5/2)/(c*sec(b*x+a))^(3/2),x)","-\frac{\left(\sin \left(b x +a \right) \cos \left(b x +a \right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)+\sin \left(b x +a \right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)+\cos \left(b x +a \right) \sqrt{2}\right) \left(\frac{d}{\sin \left(b x +a \right)}\right)^{\frac{5}{2}} \sin \left(b x +a \right) \sqrt{2}}{3 b \left(\frac{c}{\cos \left(b x +a \right)}\right)^{\frac{3}{2}} \cos \left(b x +a \right)^{2}}"," ",0,"-1/3/b*(sin(b*x+a)*cos(b*x+a)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))+sin(b*x+a)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))+cos(b*x+a)*2^(1/2))*(d/sin(b*x+a))^(5/2)*sin(b*x+a)/(c/cos(b*x+a))^(3/2)/cos(b*x+a)^2*2^(1/2)","B"
266,1,959,271,1.139000," ","int((d*csc(b*x+a))^(3/2)/(c*sec(b*x+a))^(3/2),x)","-\frac{\left(i \cos \left(b x +a \right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-i \cos \left(b x +a \right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-\cos \left(b x +a \right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-\cos \left(b x +a \right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+i \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-i \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+2 \cos \left(b x +a \right) \sqrt{2}\right) \left(\frac{d}{\sin \left(b x +a \right)}\right)^{\frac{3}{2}} \sin \left(b x +a \right) \sqrt{2}}{2 b \left(\frac{c}{\cos \left(b x +a \right)}\right)^{\frac{3}{2}} \cos \left(b x +a \right)^{2}}"," ",0,"-1/2/b*(I*cos(b*x+a)*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)-I*cos(b*x+a)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2+1/2*I,1/2*2^(1/2))-cos(b*x+a)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2-1/2*I,1/2*2^(1/2))-cos(b*x+a)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2+1/2*I,1/2*2^(1/2))+I*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)-I*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2+1/2*I,1/2*2^(1/2))-((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2-1/2*I,1/2*2^(1/2))-((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2+1/2*I,1/2*2^(1/2))+2*cos(b*x+a)*2^(1/2))*(d/sin(b*x+a))^(3/2)*sin(b*x+a)/(c/cos(b*x+a))^(3/2)/cos(b*x+a)^2*2^(1/2)","C"
267,1,193,105,1.225000," ","int((d*csc(b*x+a))^(1/2)/(c*sec(b*x+a))^(3/2),x)","\frac{\left(-\sin \left(b x +a \right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)+\sqrt{2}\, \left(\cos^{2}\left(b x +a \right)\right)-\cos \left(b x +a \right) \sqrt{2}\right) \sqrt{\frac{d}{\sin \left(b x +a \right)}}\, \sin \left(b x +a \right) \sqrt{2}}{2 b \left(-1+\cos \left(b x +a \right)\right) \left(\frac{c}{\cos \left(b x +a \right)}\right)^{\frac{3}{2}} \cos \left(b x +a \right)^{2}}"," ",0,"1/2/b*(-sin(b*x+a)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))+2^(1/2)*cos(b*x+a)^2-cos(b*x+a)*2^(1/2))*(d/sin(b*x+a))^(1/2)*sin(b*x+a)/(-1+cos(b*x+a))/(c/cos(b*x+a))^(3/2)/cos(b*x+a)^2*2^(1/2)","A"
268,1,520,259,0.988000," ","int(1/(d*csc(b*x+a))^(1/2)/(c*sec(b*x+a))^(3/2),x)","-\frac{\left(i \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-i \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-2 \sqrt{2}\, \left(\cos^{2}\left(b x +a \right)\right)+2 \cos \left(b x +a \right) \sqrt{2}\right) \sin \left(b x +a \right) \sqrt{2}}{8 b \left(-1+\cos \left(b x +a \right)\right) \cos \left(b x +a \right)^{2} \sqrt{\frac{d}{\sin \left(b x +a \right)}}\, \left(\frac{c}{\cos \left(b x +a \right)}\right)^{\frac{3}{2}}}"," ",0,"-1/8/b*(I*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)-I*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2+1/2*I,1/2*2^(1/2))-((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2-1/2*I,1/2*2^(1/2))-((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2+1/2*I,1/2*2^(1/2))-2*2^(1/2)*cos(b*x+a)^2+2*cos(b*x+a)*2^(1/2))*sin(b*x+a)/(-1+cos(b*x+a))/cos(b*x+a)^2/(d/sin(b*x+a))^(1/2)/(c/cos(b*x+a))^(3/2)*2^(1/2)","C"
269,1,220,140,0.882000," ","int(1/(d*csc(b*x+a))^(3/2)/(c*sec(b*x+a))^(3/2),x)","-\frac{\left(2 \left(\cos^{4}\left(b x +a \right)\right) \sqrt{2}+\sin \left(b x +a \right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)-2 \left(\cos^{3}\left(b x +a \right)\right) \sqrt{2}-\sqrt{2}\, \left(\cos^{2}\left(b x +a \right)\right)+\cos \left(b x +a \right) \sqrt{2}\right) \sqrt{2}}{12 b \left(-1+\cos \left(b x +a \right)\right) \left(\frac{d}{\sin \left(b x +a \right)}\right)^{\frac{3}{2}} \left(\frac{c}{\cos \left(b x +a \right)}\right)^{\frac{3}{2}} \cos \left(b x +a \right)^{2} \sin \left(b x +a \right)}"," ",0,"-1/12/b*(2*cos(b*x+a)^4*2^(1/2)+sin(b*x+a)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))-2*cos(b*x+a)^3*2^(1/2)-2^(1/2)*cos(b*x+a)^2+cos(b*x+a)*2^(1/2))/(-1+cos(b*x+a))/(d/sin(b*x+a))^(3/2)/(c/cos(b*x+a))^(3/2)/cos(b*x+a)^2/sin(b*x+a)*2^(1/2)","A"
270,1,548,302,0.848000," ","int(1/(d*csc(b*x+a))^(5/2)/(c*sec(b*x+a))^(3/2),x)","-\frac{\left(8 \left(\cos^{4}\left(b x +a \right)\right) \sqrt{2}+3 i \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-3 i \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-8 \left(\cos^{3}\left(b x +a \right)\right) \sqrt{2}-3 \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-3 \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-6 \sqrt{2}\, \left(\cos^{2}\left(b x +a \right)\right)+6 \cos \left(b x +a \right) \sqrt{2}\right) \sqrt{2}}{64 b \left(-1+\cos \left(b x +a \right)\right) \cos \left(b x +a \right)^{2} \sin \left(b x +a \right) \left(\frac{d}{\sin \left(b x +a \right)}\right)^{\frac{5}{2}} \left(\frac{c}{\cos \left(b x +a \right)}\right)^{\frac{3}{2}}}"," ",0,"-1/64/b*(8*cos(b*x+a)^4*2^(1/2)+3*I*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)-3*I*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2+1/2*I,1/2*2^(1/2))-8*cos(b*x+a)^3*2^(1/2)-3*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2-1/2*I,1/2*2^(1/2))-3*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2+1/2*I,1/2*2^(1/2))-6*2^(1/2)*cos(b*x+a)^2+6*cos(b*x+a)*2^(1/2))/(-1+cos(b*x+a))/cos(b*x+a)^2/sin(b*x+a)/(d/sin(b*x+a))^(5/2)/(c/cos(b*x+a))^(3/2)*2^(1/2)","C"
271,1,42,27,1.112000," ","int((d*csc(b*x+a))^(9/2)/(c*sec(b*x+a))^(5/2),x)","-\frac{2 \left(\frac{d}{\sin \left(b x +a \right)}\right)^{\frac{9}{2}} \cos \left(b x +a \right) \sin \left(b x +a \right)}{7 b \left(\frac{c}{\cos \left(b x +a \right)}\right)^{\frac{5}{2}}}"," ",0,"-2/7/b*(d/sin(b*x+a))^(9/2)*cos(b*x+a)*sin(b*x+a)/(c/cos(b*x+a))^(5/2)","A"
272,1,977,140,1.206000," ","int((d*csc(b*x+a))^(7/2)/(c*sec(b*x+a))^(5/2),x)","\frac{\left(6 \left(\cos^{3}\left(b x +a \right)\right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticE \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)-3 \left(\cos^{3}\left(b x +a \right)\right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)+6 \left(\cos^{2}\left(b x +a \right)\right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticE \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)-3 \left(\cos^{2}\left(b x +a \right)\right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)-6 \cos \left(b x +a \right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticE \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)+3 \cos \left(b x +a \right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)-6 \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticE \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)+3 \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)-3 \left(\cos^{3}\left(b x +a \right)\right) \sqrt{2}-\sqrt{2}\, \left(\cos^{2}\left(b x +a \right)\right)+3 \cos \left(b x +a \right) \sqrt{2}\right) \left(\frac{d}{\sin \left(b x +a \right)}\right)^{\frac{7}{2}} \sin \left(b x +a \right) \sqrt{2}}{5 b \left(\frac{c}{\cos \left(b x +a \right)}\right)^{\frac{5}{2}} \cos \left(b x +a \right)^{3}}"," ",0,"1/5/b*(6*cos(b*x+a)^3*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticE(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))-3*cos(b*x+a)^3*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))+6*cos(b*x+a)^2*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticE(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))-3*cos(b*x+a)^2*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))-6*cos(b*x+a)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticE(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))+3*cos(b*x+a)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))-6*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticE(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))+3*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))-3*cos(b*x+a)^3*2^(1/2)-2^(1/2)*cos(b*x+a)^2+3*cos(b*x+a)*2^(1/2))*(d/sin(b*x+a))^(7/2)*sin(b*x+a)/(c/cos(b*x+a))^(5/2)/cos(b*x+a)^3*2^(1/2)","B"
273,1,1239,271,1.226000," ","int((d*csc(b*x+a))^(5/2)/(c*sec(b*x+a))^(5/2),x)","-\frac{\left(3 i \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \cos \left(b x +a \right) \sin \left(b x +a \right)-3 i \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \cos \left(b x +a \right) \sin \left(b x +a \right)+3 \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \cos \left(b x +a \right) \sin \left(b x +a \right)+3 i \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sin \left(b x +a \right)+3 \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \cos \left(b x +a \right) \sin \left(b x +a \right)-3 i \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sin \left(b x +a \right)-6 \sin \left(b x +a \right) \cos \left(b x +a \right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)+3 \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sin \left(b x +a \right)+3 \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sin \left(b x +a \right)-6 \sin \left(b x +a \right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)+2 \sqrt{2}\, \left(\cos^{2}\left(b x +a \right)\right)\right) \left(\frac{d}{\sin \left(b x +a \right)}\right)^{\frac{5}{2}} \sin \left(b x +a \right) \sqrt{2}}{6 b \cos \left(b x +a \right)^{3} \left(\frac{c}{\cos \left(b x +a \right)}\right)^{\frac{5}{2}}}"," ",0,"-1/6/b*(3*I*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2-1/2*I,1/2*2^(1/2))*cos(b*x+a)*sin(b*x+a)-3*I*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2+1/2*I,1/2*2^(1/2))*cos(b*x+a)*sin(b*x+a)+3*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2-1/2*I,1/2*2^(1/2))*cos(b*x+a)*sin(b*x+a)+3*I*sin(b*x+a)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2-1/2*I,1/2*2^(1/2))+3*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2+1/2*I,1/2*2^(1/2))*cos(b*x+a)*sin(b*x+a)-3*I*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2+1/2*I,1/2*2^(1/2))*sin(b*x+a)-6*sin(b*x+a)*cos(b*x+a)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))+3*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*sin(b*x+a)+3*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2+1/2*I,1/2*2^(1/2))*sin(b*x+a)-6*sin(b*x+a)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))+2*2^(1/2)*cos(b*x+a)^2)*(d/sin(b*x+a))^(5/2)*sin(b*x+a)/cos(b*x+a)^3/(c/cos(b*x+a))^(5/2)*2^(1/2)","C"
274,1,507,109,1.171000," ","int((d*csc(b*x+a))^(3/2)/(c*sec(b*x+a))^(5/2),x)","\frac{\left(6 \cos \left(b x +a \right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticE \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)-3 \cos \left(b x +a \right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)+6 \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticE \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)-3 \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)+\sqrt{2}\, \left(\cos^{2}\left(b x +a \right)\right)-3 \cos \left(b x +a \right) \sqrt{2}\right) \left(\frac{d}{\sin \left(b x +a \right)}\right)^{\frac{3}{2}} \sin \left(b x +a \right) \sqrt{2}}{2 b \cos \left(b x +a \right)^{3} \left(\frac{c}{\cos \left(b x +a \right)}\right)^{\frac{5}{2}}}"," ",0,"1/2/b*(6*cos(b*x+a)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticE(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))-3*cos(b*x+a)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))+6*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticE(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))-3*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))+2^(1/2)*cos(b*x+a)^2-3*cos(b*x+a)*2^(1/2))*(d/sin(b*x+a))^(3/2)*sin(b*x+a)/cos(b*x+a)^3/(c/cos(b*x+a))^(5/2)*2^(1/2)","B"
275,1,658,259,1.197000," ","int((d*csc(b*x+a))^(1/2)/(c*sec(b*x+a))^(5/2),x)","-\frac{\left(3 i \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sin \left(b x +a \right)-3 i \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sin \left(b x +a \right)+3 \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sin \left(b x +a \right)-6 \sin \left(b x +a \right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)+3 \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sin \left(b x +a \right)-2 \left(\cos^{3}\left(b x +a \right)\right) \sqrt{2}+2 \sqrt{2}\, \left(\cos^{2}\left(b x +a \right)\right)\right) \sqrt{\frac{d}{\sin \left(b x +a \right)}}\, \sin \left(b x +a \right) \sqrt{2}}{8 b \left(-1+\cos \left(b x +a \right)\right) \cos \left(b x +a \right)^{3} \left(\frac{c}{\cos \left(b x +a \right)}\right)^{\frac{5}{2}}}"," ",0,"-1/8/b*(3*I*sin(b*x+a)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2-1/2*I,1/2*2^(1/2))-3*I*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2+1/2*I,1/2*2^(1/2))*sin(b*x+a)+3*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*sin(b*x+a)-6*sin(b*x+a)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))+3*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2+1/2*I,1/2*2^(1/2))*sin(b*x+a)-2*cos(b*x+a)^3*2^(1/2)+2*2^(1/2)*cos(b*x+a)^2)*(d/sin(b*x+a))^(1/2)*sin(b*x+a)/(-1+cos(b*x+a))/cos(b*x+a)^3/(c/cos(b*x+a))^(5/2)*2^(1/2)","C"
276,1,522,106,0.984000," ","int(1/(d*csc(b*x+a))^(1/2)/(c*sec(b*x+a))^(5/2),x)","-\frac{\left(2 \left(\cos^{4}\left(b x +a \right)\right) \sqrt{2}-3 \cos \left(b x +a \right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)+6 \cos \left(b x +a \right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticE \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)-3 \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)+6 \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticE \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)+\sqrt{2}\, \left(\cos^{2}\left(b x +a \right)\right)-3 \cos \left(b x +a \right) \sqrt{2}\right) \sqrt{2}}{12 b \sqrt{\frac{d}{\sin \left(b x +a \right)}}\, \left(\frac{c}{\cos \left(b x +a \right)}\right)^{\frac{5}{2}} \cos \left(b x +a \right)^{3} \sin \left(b x +a \right)}"," ",0,"-1/12/b*(2*cos(b*x+a)^4*2^(1/2)-3*cos(b*x+a)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))+6*cos(b*x+a)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticE(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))-3*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))+6*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticE(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))+2^(1/2)*cos(b*x+a)^2-3*cos(b*x+a)*2^(1/2))/(d/sin(b*x+a))^(1/2)/(c/cos(b*x+a))^(5/2)/cos(b*x+a)^3/sin(b*x+a)*2^(1/2)","B"
277,1,686,302,0.864000," ","int(1/(d*csc(b*x+a))^(3/2)/(c*sec(b*x+a))^(5/2),x)","-\frac{\left(3 i \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sin \left(b x +a \right)-3 i \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sin \left(b x +a \right)+8 \left(\cos^{5}\left(b x +a \right)\right) \sqrt{2}-8 \left(\cos^{4}\left(b x +a \right)\right) \sqrt{2}-6 \sin \left(b x +a \right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)+3 \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sin \left(b x +a \right)+3 \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sin \left(b x +a \right)-2 \left(\cos^{3}\left(b x +a \right)\right) \sqrt{2}+2 \sqrt{2}\, \left(\cos^{2}\left(b x +a \right)\right)\right) \sqrt{2}}{64 b \left(-1+\cos \left(b x +a \right)\right) \left(\frac{d}{\sin \left(b x +a \right)}\right)^{\frac{3}{2}} \left(\frac{c}{\cos \left(b x +a \right)}\right)^{\frac{5}{2}} \cos \left(b x +a \right)^{3} \sin \left(b x +a \right)}"," ",0,"-1/64/b*(3*I*sin(b*x+a)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2-1/2*I,1/2*2^(1/2))-3*I*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2+1/2*I,1/2*2^(1/2))*sin(b*x+a)+8*cos(b*x+a)^5*2^(1/2)-8*cos(b*x+a)^4*2^(1/2)-6*sin(b*x+a)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))+3*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*sin(b*x+a)+3*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2+1/2*I,1/2*2^(1/2))*sin(b*x+a)-2*cos(b*x+a)^3*2^(1/2)+2*2^(1/2)*cos(b*x+a)^2)/(-1+cos(b*x+a))/(d/sin(b*x+a))^(3/2)/(c/cos(b*x+a))^(5/2)/cos(b*x+a)^3/sin(b*x+a)*2^(1/2)","C"
278,1,536,140,0.870000," ","int(1/(d*csc(b*x+a))^(5/2)/(c*sec(b*x+a))^(5/2),x)","\frac{\left(4 \left(\cos^{6}\left(b x +a \right)\right) \sqrt{2}-6 \left(\cos^{4}\left(b x +a \right)\right) \sqrt{2}-6 \cos \left(b x +a \right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticE \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)+3 \cos \left(b x +a \right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)-6 \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticE \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)+3 \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)-\sqrt{2}\, \left(\cos^{2}\left(b x +a \right)\right)+3 \cos \left(b x +a \right) \sqrt{2}\right) \sqrt{2}}{40 b \cos \left(b x +a \right)^{3} \sin \left(b x +a \right)^{3} \left(\frac{d}{\sin \left(b x +a \right)}\right)^{\frac{5}{2}} \left(\frac{c}{\cos \left(b x +a \right)}\right)^{\frac{5}{2}}}"," ",0,"1/40/b*(4*cos(b*x+a)^6*2^(1/2)-6*cos(b*x+a)^4*2^(1/2)-6*cos(b*x+a)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticE(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))+3*cos(b*x+a)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))-6*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticE(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))+3*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))-2^(1/2)*cos(b*x+a)^2+3*cos(b*x+a)*2^(1/2))/cos(b*x+a)^3/sin(b*x+a)^3/(d/sin(b*x+a))^(5/2)/(c/cos(b*x+a))^(5/2)*2^(1/2)","B"
279,1,712,331,0.894000," ","int(1/(d*csc(b*x+a))^(7/2)/(c*sec(b*x+a))^(5/2),x)","\frac{\left(64 \sqrt{2}\, \left(\cos^{7}\left(b x +a \right)\right)-64 \left(\cos^{6}\left(b x +a \right)\right) \sqrt{2}+15 i \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sin \left(b x +a \right)-15 i \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sin \left(b x +a \right)-104 \left(\cos^{5}\left(b x +a \right)\right) \sqrt{2}+104 \left(\cos^{4}\left(b x +a \right)\right) \sqrt{2}-15 \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sin \left(b x +a \right)-15 \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sin \left(b x +a \right)+30 \sin \left(b x +a \right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)+10 \left(\cos^{3}\left(b x +a \right)\right) \sqrt{2}-10 \sqrt{2}\, \left(\cos^{2}\left(b x +a \right)\right)\right) \sqrt{2}}{768 b \left(-1+\cos \left(b x +a \right)\right) \cos \left(b x +a \right)^{3} \sin \left(b x +a \right)^{3} \left(\frac{d}{\sin \left(b x +a \right)}\right)^{\frac{7}{2}} \left(\frac{c}{\cos \left(b x +a \right)}\right)^{\frac{5}{2}}}"," ",0,"1/768/b*(64*2^(1/2)*cos(b*x+a)^7-64*cos(b*x+a)^6*2^(1/2)+15*I*sin(b*x+a)*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2+1/2*I,1/2*2^(1/2))*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)-15*I*sin(b*x+a)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2-1/2*I,1/2*2^(1/2))-104*cos(b*x+a)^5*2^(1/2)+104*cos(b*x+a)^4*2^(1/2)-15*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2+1/2*I,1/2*2^(1/2))*sin(b*x+a)-15*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*sin(b*x+a)+30*sin(b*x+a)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))+10*cos(b*x+a)^3*2^(1/2)-10*2^(1/2)*cos(b*x+a)^2)/(-1+cos(b*x+a))/cos(b*x+a)^3/sin(b*x+a)^3/(d/sin(b*x+a))^(7/2)/(c/cos(b*x+a))^(5/2)*2^(1/2)","C"
280,0,0,71,2.007000," ","int(csc(f*x+e)^n*sec(f*x+e)^m,x)","\int \left(\csc^{n}\left(f x +e \right)\right) \left(\sec^{m}\left(f x +e \right)\right)\, dx"," ",0,"int(csc(f*x+e)^n*sec(f*x+e)^m,x)","F"
281,0,0,76,1.840000," ","int(csc(f*x+e)^n*(a*sec(f*x+e))^m,x)","\int \left(\csc^{n}\left(f x +e \right)\right) \left(a \sec \left(f x +e \right)\right)^{m}\, dx"," ",0,"int(csc(f*x+e)^n*(a*sec(f*x+e))^m,x)","F"
282,0,0,74,1.885000," ","int((b*csc(f*x+e))^n*sec(f*x+e)^m,x)","\int \left(b \csc \left(f x +e \right)\right)^{n} \left(\sec^{m}\left(f x +e \right)\right)\, dx"," ",0,"int((b*csc(f*x+e))^n*sec(f*x+e)^m,x)","F"
283,0,0,79,1.867000," ","int((b*csc(f*x+e))^n*(a*sec(f*x+e))^m,x)","\int \left(b \csc \left(f x +e \right)\right)^{n} \left(a \sec \left(f x +e \right)\right)^{m}\, dx"," ",0,"int((b*csc(f*x+e))^n*(a*sec(f*x+e))^m,x)","F"
284,0,0,46,1.244000," ","int((b*csc(f*x+e))^n*sec(f*x+e)^5,x)","\int \left(b \csc \left(f x +e \right)\right)^{n} \left(\sec^{5}\left(f x +e \right)\right)\, dx"," ",0,"int((b*csc(f*x+e))^n*sec(f*x+e)^5,x)","F"
285,0,0,47,1.199000," ","int((b*csc(f*x+e))^n*sec(f*x+e)^3,x)","\int \left(b \csc \left(f x +e \right)\right)^{n} \left(\sec^{3}\left(f x +e \right)\right)\, dx"," ",0,"int((b*csc(f*x+e))^n*sec(f*x+e)^3,x)","F"
286,0,0,46,1.164000," ","int((b*csc(f*x+e))^n*sec(f*x+e),x)","\int \left(b \csc \left(f x +e \right)\right)^{n} \sec \left(f x +e \right)\, dx"," ",0,"int((b*csc(f*x+e))^n*sec(f*x+e),x)","F"
287,1,66,24,0.297000," ","int(cos(f*x+e)*(b*csc(f*x+e))^n,x)","-\frac{2 \tan \left(\frac{e}{2}+\frac{f x}{2}\right) {\mathrm e}^{n \ln \left(\frac{b \left(1+\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right)}{2 \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}\right)}}{f \left(-1+n \right) \left(1+\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right)}"," ",0,"-2/f/(-1+n)*tan(1/2*e+1/2*f*x)*exp(n*ln(1/2*b*(1+tan(1/2*e+1/2*f*x)^2)/tan(1/2*e+1/2*f*x)))/(1+tan(1/2*e+1/2*f*x)^2)","B"
288,0,0,52,3.865000," ","int(cos(f*x+e)^3*(b*csc(f*x+e))^n,x)","\int \left(\cos^{3}\left(f x +e \right)\right) \left(b \csc \left(f x +e \right)\right)^{n}\, dx"," ",0,"int(cos(f*x+e)^3*(b*csc(f*x+e))^n,x)","F"
289,0,0,78,4.433000," ","int(cos(f*x+e)^5*(b*csc(f*x+e))^n,x)","\int \left(\cos^{5}\left(f x +e \right)\right) \left(b \csc \left(f x +e \right)\right)^{n}\, dx"," ",0,"int(cos(f*x+e)^5*(b*csc(f*x+e))^n,x)","F"
290,0,0,62,1.283000," ","int((b*csc(f*x+e))^n*sec(f*x+e)^6,x)","\int \left(b \csc \left(f x +e \right)\right)^{n} \left(\sec^{6}\left(f x +e \right)\right)\, dx"," ",0,"int((b*csc(f*x+e))^n*sec(f*x+e)^6,x)","F"
291,0,0,62,1.221000," ","int((b*csc(f*x+e))^n*sec(f*x+e)^4,x)","\int \left(b \csc \left(f x +e \right)\right)^{n} \left(\sec^{4}\left(f x +e \right)\right)\, dx"," ",0,"int((b*csc(f*x+e))^n*sec(f*x+e)^4,x)","F"
292,0,0,62,1.124000," ","int((b*csc(f*x+e))^n*sec(f*x+e)^2,x)","\int \left(b \csc \left(f x +e \right)\right)^{n} \left(\sec^{2}\left(f x +e \right)\right)\, dx"," ",0,"int((b*csc(f*x+e))^n*sec(f*x+e)^2,x)","F"
293,0,0,62,1.510000," ","int((b*csc(f*x+e))^n,x)","\int \left(b \csc \left(f x +e \right)\right)^{n}\, dx"," ",0,"int((b*csc(f*x+e))^n,x)","F"
294,0,0,62,2.680000," ","int(cos(f*x+e)^2*(b*csc(f*x+e))^n,x)","\int \left(\cos^{2}\left(f x +e \right)\right) \left(b \csc \left(f x +e \right)\right)^{n}\, dx"," ",0,"int(cos(f*x+e)^2*(b*csc(f*x+e))^n,x)","F"
295,0,0,62,3.063000," ","int(cos(f*x+e)^4*(b*csc(f*x+e))^n,x)","\int \left(\cos^{4}\left(f x +e \right)\right) \left(b \csc \left(f x +e \right)\right)^{n}\, dx"," ",0,"int(cos(f*x+e)^4*(b*csc(f*x+e))^n,x)","F"
296,0,0,69,0.886000," ","int((b*csc(f*x+e))^n*(c*sec(f*x+e))^(3/2),x)","\int \left(b \csc \left(f x +e \right)\right)^{n} \left(c \sec \left(f x +e \right)\right)^{\frac{3}{2}}\, dx"," ",0,"int((b*csc(f*x+e))^n*(c*sec(f*x+e))^(3/2),x)","F"
297,0,0,69,0.922000," ","int((b*csc(f*x+e))^n*(c*sec(f*x+e))^(1/2),x)","\int \left(b \csc \left(f x +e \right)\right)^{n} \sqrt{c \sec \left(f x +e \right)}\, dx"," ",0,"int((b*csc(f*x+e))^n*(c*sec(f*x+e))^(1/2),x)","F"
298,0,0,69,0.793000," ","int((b*csc(f*x+e))^n/(c*sec(f*x+e))^(1/2),x)","\int \frac{\left(b \csc \left(f x +e \right)\right)^{n}}{\sqrt{c \sec \left(f x +e \right)}}\, dx"," ",0,"int((b*csc(f*x+e))^n/(c*sec(f*x+e))^(1/2),x)","F"
299,0,0,69,0.730000," ","int((b*csc(f*x+e))^n/(c*sec(f*x+e))^(3/2),x)","\int \frac{\left(b \csc \left(f x +e \right)\right)^{n}}{\left(c \sec \left(f x +e \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int((b*csc(f*x+e))^n/(c*sec(f*x+e))^(3/2),x)","F"