1,1,11,10,0.053000," ","int(cos(b*x+a),x)","\frac{\sin \left(b x +a \right)}{b}"," ",0,"sin(b*x+a)/b","A"
2,1,27,21,0.047000," ","int(cos(b*x+a)^2,x)","\frac{\frac{\cos \left(b x +a \right) \sin \left(b x +a \right)}{2}+\frac{b x}{2}+\frac{a}{2}}{b}"," ",0,"1/b*(1/2*cos(b*x+a)*sin(b*x+a)+1/2*b*x+1/2*a)","A"
3,1,22,24,0.117000," ","int(cos(b*x+a)^3,x)","\frac{\left(2+\cos^{2}\left(b x +a \right)\right) \sin \left(b x +a \right)}{3 b}"," ",0,"1/3/b*(2+cos(b*x+a)^2)*sin(b*x+a)","A"
4,1,38,40,0.080000," ","int(cos(b*x+a)^4,x)","\frac{\frac{\left(\cos^{3}\left(b x +a \right)+\frac{3 \cos \left(b x +a \right)}{2}\right) \sin \left(b x +a \right)}{4}+\frac{3 b x}{8}+\frac{3 a}{8}}{b}"," ",0,"1/b*(1/4*(cos(b*x+a)^3+3/2*cos(b*x+a))*sin(b*x+a)+3/8*b*x+3/8*a)","A"
5,1,32,37,0.099000," ","int(cos(b*x+a)^5,x)","\frac{\left(\frac{8}{3}+\cos^{4}\left(b x +a \right)+\frac{4 \left(\cos^{2}\left(b x +a \right)\right)}{3}\right) \sin \left(b x +a \right)}{5 b}"," ",0,"1/5/b*(8/3+cos(b*x+a)^4+4/3*cos(b*x+a)^2)*sin(b*x+a)","A"
6,1,48,59,0.095000," ","int(cos(b*x+a)^6,x)","\frac{\frac{\left(\cos^{5}\left(b x +a \right)+\frac{5 \left(\cos^{3}\left(b x +a \right)\right)}{4}+\frac{15 \cos \left(b x +a \right)}{8}\right) \sin \left(b x +a \right)}{6}+\frac{5 b x}{16}+\frac{5 a}{16}}{b}"," ",0,"1/b*(1/6*(cos(b*x+a)^5+5/4*cos(b*x+a)^3+15/8*cos(b*x+a))*sin(b*x+a)+5/16*b*x+5/16*a)","A"
7,1,42,50,0.096000," ","int(cos(b*x+a)^7,x)","\frac{\left(\frac{16}{5}+\cos^{6}\left(b x +a \right)+\frac{6 \left(\cos^{4}\left(b x +a \right)\right)}{5}+\frac{8 \left(\cos^{2}\left(b x +a \right)\right)}{5}\right) \sin \left(b x +a \right)}{7 b}"," ",0,"1/7/b*(16/5+cos(b*x+a)^6+6/5*cos(b*x+a)^4+8/5*cos(b*x+a)^2)*sin(b*x+a)","A"
8,1,58,78,0.102000," ","int(cos(b*x+a)^8,x)","\frac{\frac{\left(\cos^{7}\left(b x +a \right)+\frac{7 \left(\cos^{5}\left(b x +a \right)\right)}{6}+\frac{35 \left(\cos^{3}\left(b x +a \right)\right)}{24}+\frac{35 \cos \left(b x +a \right)}{16}\right) \sin \left(b x +a \right)}{8}+\frac{35 b x}{128}+\frac{35 a}{128}}{b}"," ",0,"1/b*(1/8*(cos(b*x+a)^7+7/6*cos(b*x+a)^5+35/24*cos(b*x+a)^3+35/16*cos(b*x+a))*sin(b*x+a)+35/128*b*x+35/128*a)","A"
9,1,199,81,0.195000," ","int(cos(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"
10,1,202,62,0.076000," ","int(cos(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"
11,1,179,62,0.107000," ","int(cos(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"
12,1,133,42,0.060000," ","int(cos(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"
13,1,18,42,0.127000," ","int(1/cos(b*x+a)^(1/2),x)","\frac{2 \,\mathrm{am}^{-1}\left(\frac{b x}{2}+\frac{a}{2}| \sqrt{2}\right)}{b}"," ",0,"2/b*InverseJacobiAM(1/2*b*x+1/2*a,2^(1/2))","C"
14,1,101,62,0.085000," ","int(1/cos(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"
15,1,213,62,0.116000," ","int(1/cos(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"
16,1,358,81,0.134000," ","int(1/cos(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"
17,1,210,110,0.127000," ","int((c*cos(b*x+a))^(7/2),x)","-\frac{2 \sqrt{c \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)}\, c^{4} \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{-c \left(2 \left(\sin^{4}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-\left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)\right)}\, \sin \left(\frac{b x}{2}+\frac{a}{2}\right) \sqrt{c \left(2 \left(\cos^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1\right)}\, b}"," ",0,"-2/21*(c*(2*cos(1/2*b*x+1/2*a)^2-1)*sin(1/2*b*x+1/2*a)^2)^(1/2)*c^4*(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))/(-c*(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)/(c*(2*cos(1/2*b*x+1/2*a)^2-1))^(1/2)/b","A"
18,1,213,86,0.072000," ","int((c*cos(b*x+a))^(5/2),x)","-\frac{2 \sqrt{c \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)}\, c^{3} \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{-c \left(2 \left(\sin^{4}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-\left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)\right)}\, \sin \left(\frac{b x}{2}+\frac{a}{2}\right) \sqrt{c \left(2 \left(\cos^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1\right)}\, b}"," ",0,"-2/5*(c*(2*cos(1/2*b*x+1/2*a)^2-1)*sin(1/2*b*x+1/2*a)^2)^(1/2)*c^3*(-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))/(-c*(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)/(c*(2*cos(1/2*b*x+1/2*a)^2-1))^(1/2)/b","B"
19,1,190,86,0.075000," ","int((c*cos(b*x+a))^(3/2),x)","-\frac{2 \sqrt{c \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)}\, c^{2} \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{-c \left(2 \left(\sin^{4}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-\left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)\right)}\, \sin \left(\frac{b x}{2}+\frac{a}{2}\right) \sqrt{c \left(2 \left(\cos^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1\right)}\, b}"," ",0,"-2/3*(c*(2*cos(1/2*b*x+1/2*a)^2-1)*sin(1/2*b*x+1/2*a)^2)^(1/2)*c^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))/(-c*(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)/(c*(2*cos(1/2*b*x+1/2*a)^2-1))^(1/2)/b","B"
20,1,142,60,0.069000," ","int((c*cos(b*x+a))^(1/2),x)","\frac{2 \sqrt{c \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)}\, c \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{-c \left(2 \left(\sin^{4}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-\left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)\right)}\, \sin \left(\frac{b x}{2}+\frac{a}{2}\right) \sqrt{c \left(2 \left(\cos^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1\right)}\, b}"," ",0,"2*(c*(2*cos(1/2*b*x+1/2*a)^2-1)*sin(1/2*b*x+1/2*a)^2)^(1/2)*c*(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))/(-c*(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)/(c*(2*cos(1/2*b*x+1/2*a)^2-1))^(1/2)/b","B"
21,1,54,60,0.054000," ","int(1/(c*cos(b*x+a))^(1/2),x)","\frac{2 \sqrt{2 \left(\cos^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1}\, \mathrm{am}^{-1}\left(\frac{b x}{2}+\frac{a}{2}| \sqrt{2}\right)}{b \sqrt{c \left(2 \left(\cos^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1\right)}}"," ",0,"2/b/(c*(2*cos(1/2*b*x+1/2*a)^2-1))^(1/2)*(2*cos(1/2*b*x+1/2*a)^2-1)^(1/2)*InverseJacobiAM(1/2*b*x+1/2*a,2^(1/2))","C"
22,1,168,88,0.111000," ","int(1/(c*cos(b*x+a))^(3/2),x)","-\frac{2 \sqrt{-2 \left(\sin^{4}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) c +c \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)}\, \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)}{c \sqrt{-c \left(2 \left(\sin^{4}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-\left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)\right)}\, \sin \left(\frac{b x}{2}+\frac{a}{2}\right) \sqrt{c \left(2 \left(\cos^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1\right)}\, b}"," ",0,"-2/c*(-2*sin(1/2*b*x+1/2*a)^4*c+c*sin(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)*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))/(-c*(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)/(c*(2*cos(1/2*b*x+1/2*a)^2-1))^(1/2)/b","A"
23,1,241,88,0.208000," ","int(1/(c*cos(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{c \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 c^{2} \sqrt{-c \left(2 \left(\sin^{4}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-\left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)\right)}\, \left(2 \left(\cos^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1\right) \sin \left(\frac{b x}{2}+\frac{a}{2}\right) \sqrt{c \left(2 \left(\cos^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1\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))/c^2*(c*(2*cos(1/2*b*x+1/2*a)^2-1)*sin(1/2*b*x+1/2*a)^2)^(1/2)/(-c*(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)/sin(1/2*b*x+1/2*a)/(c*(2*cos(1/2*b*x+1/2*a)^2-1))^(1/2)/b","B"
24,1,366,112,0.195000," ","int(1/(c*cos(b*x+a))^(7/2),x)","\frac{2 \sqrt{c \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) c +c \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)}}{5 c^{4} \sin \left(\frac{b x}{2}+\frac{a}{2}\right)^{3} \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) \sqrt{c \left(2 \left(\cos^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1\right)}\, b}"," ",0,"2/5*(c*(2*cos(1/2*b*x+1/2*a)^2-1)*sin(1/2*b*x+1/2*a)^2)^(1/2)/c^4/sin(1/2*b*x+1/2*a)^3/(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)*(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*c+c*sin(1/2*b*x+1/2*a)^2)^(1/2)/(c*(2*cos(1/2*b*x+1/2*a)^2-1))^(1/2)/b","B"
25,0,0,43,0.184000," ","int(cos(b*x+a)^(4/3),x)","\int \cos^{\frac{4}{3}}\left(b x +a \right)\, dx"," ",0,"int(cos(b*x+a)^(4/3),x)","F"
26,0,0,43,0.227000," ","int(cos(b*x+a)^(2/3),x)","\int \cos^{\frac{2}{3}}\left(b x +a \right)\, dx"," ",0,"int(cos(b*x+a)^(2/3),x)","F"
27,0,0,43,0.120000," ","int(cos(b*x+a)^(1/3),x)","\int \cos^{\frac{1}{3}}\left(b x +a \right)\, dx"," ",0,"int(cos(b*x+a)^(1/3),x)","F"
28,0,0,43,0.088000," ","int(1/cos(b*x+a)^(1/3),x)","\int \frac{1}{\cos \left(b x +a \right)^{\frac{1}{3}}}\, dx"," ",0,"int(1/cos(b*x+a)^(1/3),x)","F"
29,0,0,43,0.091000," ","int(1/cos(b*x+a)^(2/3),x)","\int \frac{1}{\cos \left(b x +a \right)^{\frac{2}{3}}}\, dx"," ",0,"int(1/cos(b*x+a)^(2/3),x)","F"
30,0,0,43,0.050000," ","int(1/cos(b*x+a)^(4/3),x)","\int \frac{1}{\cos \left(b x +a \right)^{\frac{4}{3}}}\, dx"," ",0,"int(1/cos(b*x+a)^(4/3),x)","F"
31,0,0,48,0.059000," ","int((c*cos(b*x+a))^(4/3),x)","\int \left(c \cos \left(b x +a \right)\right)^{\frac{4}{3}}\, dx"," ",0,"int((c*cos(b*x+a))^(4/3),x)","F"
32,0,0,48,0.139000," ","int((c*cos(b*x+a))^(2/3),x)","\int \left(c \cos \left(b x +a \right)\right)^{\frac{2}{3}}\, dx"," ",0,"int((c*cos(b*x+a))^(2/3),x)","F"
33,0,0,48,0.128000," ","int((c*cos(b*x+a))^(1/3),x)","\int \left(c \cos \left(b x +a \right)\right)^{\frac{1}{3}}\, dx"," ",0,"int((c*cos(b*x+a))^(1/3),x)","F"
34,0,0,48,0.105000," ","int(1/(c*cos(b*x+a))^(1/3),x)","\int \frac{1}{\left(c \cos \left(b x +a \right)\right)^{\frac{1}{3}}}\, dx"," ",0,"int(1/(c*cos(b*x+a))^(1/3),x)","F"
35,0,0,48,0.088000," ","int(1/(c*cos(b*x+a))^(2/3),x)","\int \frac{1}{\left(c \cos \left(b x +a \right)\right)^{\frac{2}{3}}}\, dx"," ",0,"int(1/(c*cos(b*x+a))^(2/3),x)","F"
36,0,0,48,0.058000," ","int(1/(c*cos(b*x+a))^(4/3),x)","\int \frac{1}{\left(c \cos \left(b x +a \right)\right)^{\frac{4}{3}}}\, dx"," ",0,"int(1/(c*cos(b*x+a))^(4/3),x)","F"
37,0,0,58,0.388000," ","int(cos(b*x+a)^n,x)","\int \cos^{n}\left(b x +a \right)\, dx"," ",0,"int(cos(b*x+a)^n,x)","F"
38,0,0,63,0.313000," ","int((c*cos(b*x+a))^n,x)","\int \left(c \cos \left(b x +a \right)\right)^{n}\, dx"," ",0,"int((c*cos(b*x+a))^n,x)","F"
39,1,32,41,0.090000," ","int((a*cos(x)^2)^(5/2),x)","\frac{a^{3} \cos \left(x \right) \sin \left(x \right) \left(3 \left(\cos^{4}\left(x \right)\right)+4 \left(\cos^{2}\left(x \right)\right)+8\right)}{15 \sqrt{a \left(\cos^{2}\left(x \right)\right)}}"," ",0,"1/15*a^3*cos(x)*sin(x)*(3*cos(x)^4+4*cos(x)^2+8)/(a*cos(x)^2)^(1/2)","A"
40,1,24,26,0.082000," ","int((a*cos(x)^2)^(3/2),x)","\frac{a^{2} \cos \left(x \right) \sin \left(x \right) \left(2+\cos^{2}\left(x \right)\right)}{3 \sqrt{a \left(\cos^{2}\left(x \right)\right)}}"," ",0,"1/3*a^2*cos(x)*sin(x)*(2+cos(x)^2)/(a*cos(x)^2)^(1/2)","A"
41,1,15,11,0.055000," ","int((a*cos(x)^2)^(1/2),x)","\frac{a \cos \left(x \right) \sin \left(x \right)}{\sqrt{a \left(\cos^{2}\left(x \right)\right)}}"," ",0,"1/(a*cos(x)^2)^(1/2)*a*cos(x)*sin(x)","A"
42,1,48,14,0.082000," ","int(1/(a*cos(x)^2)^(1/2),x)","\frac{\cos \left(x \right) \sqrt{a \left(\sin^{2}\left(x \right)\right)}\, \ln \left(\frac{2 \sqrt{a}\, \sqrt{a \left(\sin^{2}\left(x \right)\right)}+2 a}{\cos \left(x \right)}\right)}{\sqrt{a}\, \sin \left(x \right) \sqrt{a \left(\cos^{2}\left(x \right)\right)}}"," ",0,"cos(x)*(a*sin(x)^2)^(1/2)/a^(1/2)*ln(2*(a^(1/2)*(a*sin(x)^2)^(1/2)+a)/cos(x))/sin(x)/(a*cos(x)^2)^(1/2)","B"
43,1,70,34,0.088000," ","int(1/(a*cos(x)^2)^(3/2),x)","\frac{\sqrt{a \left(\sin^{2}\left(x \right)\right)}\, \left(\ln \left(\frac{2 \sqrt{a}\, \sqrt{a \left(\sin^{2}\left(x \right)\right)}+2 a}{\cos \left(x \right)}\right) a \left(\cos^{2}\left(x \right)\right)+\sqrt{a}\, \sqrt{a \left(\sin^{2}\left(x \right)\right)}\right)}{2 a^{\frac{5}{2}} \cos \left(x \right) \sin \left(x \right) \sqrt{a \left(\cos^{2}\left(x \right)\right)}}"," ",0,"1/2/a^(5/2)/cos(x)*(a*sin(x)^2)^(1/2)*(ln(2*(a^(1/2)*(a*sin(x)^2)^(1/2)+a)/cos(x))*a*cos(x)^2+a^(1/2)*(a*sin(x)^2)^(1/2))/sin(x)/(a*cos(x)^2)^(1/2)","B"
44,1,89,49,0.095000," ","int(1/(a*cos(x)^2)^(5/2),x)","\frac{\sqrt{a \left(\sin^{2}\left(x \right)\right)}\, \left(3 \ln \left(\frac{2 \sqrt{a}\, \sqrt{a \left(\sin^{2}\left(x \right)\right)}+2 a}{\cos \left(x \right)}\right) a \left(\cos^{4}\left(x \right)\right)+3 \sqrt{a \left(\sin^{2}\left(x \right)\right)}\, \left(\cos^{2}\left(x \right)\right) \sqrt{a}+2 \sqrt{a}\, \sqrt{a \left(\sin^{2}\left(x \right)\right)}\right)}{8 a^{\frac{7}{2}} \cos \left(x \right)^{3} \sin \left(x \right) \sqrt{a \left(\cos^{2}\left(x \right)\right)}}"," ",0,"1/8/a^(7/2)/cos(x)^3*(a*sin(x)^2)^(1/2)*(3*ln(2*(a^(1/2)*(a*sin(x)^2)^(1/2)+a)/cos(x))*a*cos(x)^4+3*(a*sin(x)^2)^(1/2)*cos(x)^2*a^(1/2)+2*a^(1/2)*(a*sin(x)^2)^(1/2))/sin(x)/(a*cos(x)^2)^(1/2)","A"
45,1,114,110,0.387000," ","int((a*cos(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)+195 i \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) \sin \left(x \right)+91 \left(\cos^{5}\left(x \right)\right)-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} \left(a \left(\cos^{3}\left(x \right)\right)\right)^{\frac{5}{2}}}{1155 \sin \left(x \right)^{3} \cos \left(x \right)^{8}}"," ",0,"-2/1155*(-1+cos(x))*(-77*cos(x)^8+77*cos(x)^7-91*cos(x)^6+195*I*(1/(cos(x)+1))^(1/2)*(cos(x)/(cos(x)+1))^(1/2)*EllipticF(I*(-1+cos(x))/sin(x),I)*sin(x)+91*cos(x)^5-117*cos(x)^4+117*cos(x)^3-195*cos(x)^2+195*cos(x))*(cos(x)+1)^2*(a*cos(x)^3)^(5/2)/sin(x)^3/cos(x)^8","C"
46,1,198,68,0.159000," ","int((a*cos(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 \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) \sin \left(x \right)+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) \left(a \left(\cos^{3}\left(x \right)\right)\right)^{\frac{3}{2}}}{45 \cos \left(x \right)^{5} \sin \left(x \right)}"," ",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))*(a*cos(x)^3)^(3/2)/cos(x)^5/sin(x)","C"
47,1,76,49,0.180000," ","int((a*cos(x)^3)^(1/2),x)","-\frac{2 \left(-1+\cos \left(x \right)\right) \left(i \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) \sin \left(x \right)-\left(\cos^{2}\left(x \right)\right)+\cos \left(x \right)\right) \left(\cos \left(x \right)+1\right)^{2} \sqrt{a \left(\cos^{3}\left(x \right)\right)}}{3 \cos \left(x \right)^{2} \sin \left(x \right)^{3}}"," ",0,"-2/3*(-1+cos(x))*(I*(1/(cos(x)+1))^(1/2)*(cos(x)/(cos(x)+1))^(1/2)*EllipticF(I*(-1+cos(x))/sin(x),I)*sin(x)-cos(x)^2+cos(x))*(cos(x)+1)^2*(a*cos(x)^3)^(1/2)/cos(x)^2/sin(x)^3","C"
48,1,191,51,0.306000," ","int(1/(a*cos(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 \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) \sin \left(x \right)-\cos \left(x \right)+1\right) \cos \left(x \right)}{\sqrt{a \left(\cos^{3}\left(x \right)\right)}\, \sin \left(x \right)^{5}}"," ",0,"2*(cos(x)+1)^2*(-1+cos(x))^2*(I*cos(x)*sin(x)*(1/(cos(x)+1))^(1/2)*(cos(x)/(cos(x)+1))^(1/2)*EllipticE(I*(-1+cos(x))/sin(x),I)-I*cos(x)*sin(x)*(1/(cos(x)+1))^(1/2)*(cos(x)/(cos(x)+1))^(1/2)*EllipticF(I*(-1+cos(x))/sin(x),I)+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*(1/(cos(x)+1))^(1/2)*(cos(x)/(cos(x)+1))^(1/2)*EllipticF(I*(-1+cos(x))/sin(x),I)*sin(x)-cos(x)+1)*cos(x)/(a*cos(x)^3)^(1/2)/sin(x)^5","C"
49,1,87,72,0.309000," ","int(1/(a*cos(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)}{21 \sin \left(x \right)^{3} \left(a \left(\cos^{3}\left(x \right)\right)\right)^{\frac{3}{2}}}"," ",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)/sin(x)^3/(a*cos(x)^3)^(3/2)","C"
50,1,223,110,0.379000," ","int(1/(a*cos(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}}\, \EllipticF \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}}\, \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 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 \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)}{585 \sin \left(x \right)^{5} \left(a \left(\cos^{3}\left(x \right)\right)\right)^{\frac{5}{2}}}"," ",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)*EllipticF(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)*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*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*cos(x)^7-154*cos(x)^6-22*cos(x)^4-10*cos(x)^2-45)*cos(x)/sin(x)^5/(a*cos(x)^3)^(5/2)","C"
51,1,57,108,0.412000," ","int((a*cos(x)^4)^(5/2),x)","\frac{\left(a \left(\cos^{4}\left(x \right)\right)\right)^{\frac{5}{2}} \left(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 \right)}{1280 \cos \left(x \right)^{10}}"," ",0,"1/1280*(a*cos(x)^4)^(5/2)*(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"
52,1,41,62,0.171000," ","int((a*cos(x)^4)^(3/2),x)","\frac{\left(a \left(\cos^{4}\left(x \right)\right)\right)^{\frac{3}{2}} \left(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 \right)}{48 \cos \left(x \right)^{6}}"," ",0,"1/48*(a*cos(x)^4)^(3/2)*(8*sin(x)*cos(x)^5+10*cos(x)^3*sin(x)+15*cos(x)*sin(x)+15*x)/cos(x)^6","A"
53,1,22,28,0.091000," ","int((a*cos(x)^4)^(1/2),x)","\frac{\sqrt{a \left(\cos^{4}\left(x \right)\right)}\, \left(\cos \left(x \right) \sin \left(x \right)+x \right)}{2 \cos \left(x \right)^{2}}"," ",0,"1/2*(a*cos(x)^4)^(1/2)*(cos(x)*sin(x)+x)/cos(x)^2","A"
54,1,14,13,0.082000," ","int(1/(a*cos(x)^4)^(1/2),x)","\frac{\cos \left(x \right) \sin \left(x \right)}{\sqrt{a \left(\cos^{4}\left(x \right)\right)}}"," ",0,"cos(x)*sin(x)/(a*cos(x)^4)^(1/2)","A"
55,1,29,57,0.097000," ","int(1/(a*cos(x)^4)^(3/2),x)","\frac{\sin \left(x \right) \left(8 \left(\cos^{4}\left(x \right)\right)+4 \left(\cos^{2}\left(x \right)\right)+3\right) \cos \left(x \right)}{15 \left(a \left(\cos^{4}\left(x \right)\right)\right)^{\frac{3}{2}}}"," ",0,"1/15*sin(x)*(8*cos(x)^4+4*cos(x)^2+3)*cos(x)/(a*cos(x)^4)^(3/2)","A"
56,1,41,99,0.149000," ","int(1/(a*cos(x)^4)^(5/2),x)","\frac{\sin \left(x \right) \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)}{315 \left(a \left(\cos^{4}\left(x \right)\right)\right)^{\frac{5}{2}}}"," ",0,"1/315*sin(x)*(128*cos(x)^8+64*cos(x)^6+48*cos(x)^4+40*cos(x)^2+35)*cos(x)/(a*cos(x)^4)^(5/2)","A"
57,0,0,70,0.191000," ","int((b*cos(d*x+c)^m)^n,x)","\int \left(b \left(\cos^{m}\left(d x +c \right)\right)\right)^{n}\, dx"," ",0,"int((b*cos(d*x+c)^m)^n,x)","F"
58,0,0,77,0.413000," ","int((c*cos(b*x+a)^m)^(5/2),x)","\int \left(c \left(\cos^{m}\left(b x +a \right)\right)\right)^{\frac{5}{2}}\, dx"," ",0,"int((c*cos(b*x+a)^m)^(5/2),x)","F"
59,0,0,73,0.096000," ","int((c*cos(b*x+a)^m)^(3/2),x)","\int \left(c \left(\cos^{m}\left(b x +a \right)\right)\right)^{\frac{3}{2}}\, dx"," ",0,"int((c*cos(b*x+a)^m)^(3/2),x)","F"
60,0,0,66,0.081000," ","int((c*cos(b*x+a)^m)^(1/2),x)","\int \sqrt{c \left(\cos^{m}\left(b x +a \right)\right)}\, dx"," ",0,"int((c*cos(b*x+a)^m)^(1/2),x)","F"
61,0,0,68,0.085000," ","int(1/(c*cos(b*x+a)^m)^(1/2),x)","\int \frac{1}{\sqrt{c \left(\cos^{m}\left(b x +a \right)\right)}}\, dx"," ",0,"int(1/(c*cos(b*x+a)^m)^(1/2),x)","F"
62,0,0,77,0.068000," ","int(1/(c*cos(b*x+a)^m)^(3/2),x)","\int \frac{1}{\left(c \left(\cos^{m}\left(b x +a \right)\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int(1/(c*cos(b*x+a)^m)^(3/2),x)","F"
63,0,0,77,0.073000," ","int(1/(c*cos(b*x+a)^m)^(5/2),x)","\int \frac{1}{\left(c \left(\cos^{m}\left(b x +a \right)\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"int(1/(c*cos(b*x+a)^m)^(5/2),x)","F"
64,0,0,24,0.143000," ","int((c*cos(b*x+a)^m)^(1/m),x)","\int \left(c \left(\cos^{m}\left(b x +a \right)\right)\right)^{\frac{1}{m}}\, dx"," ",0,"int((c*cos(b*x+a)^m)^(1/m),x)","F"
65,0,0,72,0.202000," ","int((a*(b*cos(d*x+c))^p)^n,x)","\int \left(a \left(b \cos \left(d x +c \right)\right)^{p}\right)^{n}\, dx"," ",0,"int((a*(b*cos(d*x+c))^p)^n,x)","F"
66,1,234,131,0.156000," ","int(cos(d*x+c)^5*(b*cos(d*x+c))^(1/2),x)","-\frac{2 \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, b \left(448 \left(\cos^{13}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1568 \left(\cos^{11}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+2384 \left(\cos^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-2040 \left(\cos^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1084 \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-370 \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+15 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+62 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{77 \sqrt{-b \left(2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}\, d}"," ",0,"-2/77*(b*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*b*(448*cos(1/2*d*x+1/2*c)^13-1568*cos(1/2*d*x+1/2*c)^11+2384*cos(1/2*d*x+1/2*c)^9-2040*cos(1/2*d*x+1/2*c)^7+1084*cos(1/2*d*x+1/2*c)^5-370*cos(1/2*d*x+1/2*c)^3+15*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+62*cos(1/2*d*x+1/2*c))/(-b*(2*sin(1/2*d*x+1/2*c)^4-sin(1/2*d*x+1/2*c)^2))^(1/2)/sin(1/2*d*x+1/2*c)/(b*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/d","A"
67,1,221,109,0.129000," ","int(cos(d*x+c)^4*(b*cos(d*x+c))^(1/2),x)","-\frac{2 \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, b \left(160 \left(\cos^{11}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-480 \left(\cos^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+616 \left(\cos^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-432 \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+160 \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-21 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-24 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{45 \sqrt{-b \left(2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}\, d}"," ",0,"-2/45*(b*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*b*(160*cos(1/2*d*x+1/2*c)^11-480*cos(1/2*d*x+1/2*c)^9+616*cos(1/2*d*x+1/2*c)^7-432*cos(1/2*d*x+1/2*c)^5+160*cos(1/2*d*x+1/2*c)^3-21*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-24*cos(1/2*d*x+1/2*c))/(-b*(2*sin(1/2*d*x+1/2*c)^4-sin(1/2*d*x+1/2*c)^2))^(1/2)/sin(1/2*d*x+1/2*c)/(b*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/d","B"
68,1,208,107,0.124000," ","int(cos(d*x+c)^3*(b*cos(d*x+c))^(1/2),x)","-\frac{2 \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, b \left(48 \left(\cos^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-120 \left(\cos^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+128 \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-72 \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+5 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+16 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{21 \sqrt{-b \left(2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}\, d}"," ",0,"-2/21*(b*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*b*(48*cos(1/2*d*x+1/2*c)^9-120*cos(1/2*d*x+1/2*c)^7+128*cos(1/2*d*x+1/2*c)^5-72*cos(1/2*d*x+1/2*c)^3+5*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+16*cos(1/2*d*x+1/2*c))/(-b*(2*sin(1/2*d*x+1/2*c)^4-sin(1/2*d*x+1/2*c)^2))^(1/2)/sin(1/2*d*x+1/2*c)/(b*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/d","A"
69,1,211,85,0.113000," ","int(cos(d*x+c)^2*(b*cos(d*x+c))^(1/2),x)","-\frac{2 \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, b \left(-8 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+8 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-3 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{5 \sqrt{-b \left(2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}\, d}"," ",0,"-2/5*(b*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*b*(-8*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6+8*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)-3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-2*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c))/(-b*(2*sin(1/2*d*x+1/2*c)^4-sin(1/2*d*x+1/2*c)^2))^(1/2)/sin(1/2*d*x+1/2*c)/(b*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/d","B"
70,1,188,83,0.108000," ","int(cos(d*x+c)*(b*cos(d*x+c))^(1/2),x)","-\frac{2 \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, b \left(4 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 \sqrt{-b \left(2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}\, d}"," ",0,"-2/3*(b*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*b*(4*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-2*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c))/(-b*(2*sin(1/2*d*x+1/2*c)^4-sin(1/2*d*x+1/2*c)^2))^(1/2)/sin(1/2*d*x+1/2*c)/(b*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/d","B"
71,1,142,60,0.089000," ","int((b*cos(d*x+c))^(1/2),x)","\frac{2 \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, b \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{\sqrt{-b \left(2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}\, d}"," ",0,"2*(b*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*b*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))/(-b*(2*sin(1/2*d*x+1/2*c)^4-sin(1/2*d*x+1/2*c)^2))^(1/2)/sin(1/2*d*x+1/2*c)/(b*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/d","B"
72,1,142,61,0.105000," ","int(sec(d*x+c)*(b*cos(d*x+c))^(1/2),x)","-\frac{2 \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, b \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{\sqrt{-b \left(2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}\, d}"," ",0,"-2*(b*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*b*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-b*(2*sin(1/2*d*x+1/2*c)^4-sin(1/2*d*x+1/2*c)^2))^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))/sin(1/2*d*x+1/2*c)/(b*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/d","B"
73,1,166,83,0.145000," ","int(sec(d*x+c)^2*(b*cos(d*x+c))^(1/2),x)","-\frac{2 b \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b}\, \left(\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{\sqrt{-b \left(2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}\, d}"," ",0,"-2*b*(-2*sin(1/2*d*x+1/2*c)^4*b+sin(1/2*d*x+1/2*c)^2*b)^(1/2)*((sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-2*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c))/(-b*(2*sin(1/2*d*x+1/2*c)^4-sin(1/2*d*x+1/2*c)^2))^(1/2)/sin(1/2*d*x+1/2*c)/(b*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/d","A"
74,1,239,86,0.138000," ","int(sec(d*x+c)^3*(b*cos(d*x+c))^(1/2),x)","-\frac{2 \left(-2 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right) b \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}}{3 \sqrt{-b \left(2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}\, \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}\, d}"," ",0,"-2/3*(-2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*sin(1/2*d*x+1/2*c)^2+(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-2*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c))*b*(b*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)/(-b*(2*sin(1/2*d*x+1/2*c)^4-sin(1/2*d*x+1/2*c)^2))^(1/2)/(2*cos(1/2*d*x+1/2*c)^2-1)/sin(1/2*d*x+1/2*c)/(b*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/d","B"
75,1,363,107,0.197000," ","int(sec(d*x+c)^4*(b*cos(d*x+c))^(1/2),x)","\frac{2 \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(12 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-24 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-12 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+24 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+3 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-8 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b}}{5 \sin \left(\frac{d x}{2}+\frac{c}{2}\right)^{3} \left(8 \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-12 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+6 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}\, d}"," ",0,"2/5*(b*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)^3/(8*sin(1/2*d*x+1/2*c)^6-12*sin(1/2*d*x+1/2*c)^4+6*sin(1/2*d*x+1/2*c)^2-1)*(12*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^4-24*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6-12*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^2+24*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-8*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c))*(-2*sin(1/2*d*x+1/2*c)^4*b+sin(1/2*d*x+1/2*c)^2*b)^(1/2)/(b*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/d","B"
76,1,396,110,0.162000," ","int(sec(d*x+c)^5*(b*cos(d*x+c))^(1/2),x)","-\frac{2 \left(-40 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+60 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-40 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-30 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+40 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+5 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-16 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right) b \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}}{21 \sqrt{-b \left(2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}\, \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)^{3} \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}\, d}"," ",0,"-2/21*(-40*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*sin(1/2*d*x+1/2*c)^6+60*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*sin(1/2*d*x+1/2*c)^4-40*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6-30*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*sin(1/2*d*x+1/2*c)^2+40*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+5*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-16*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c))*b*(b*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)/(-b*(2*sin(1/2*d*x+1/2*c)^4-sin(1/2*d*x+1/2*c)^2))^(1/2)/(2*cos(1/2*d*x+1/2*c)^2-1)^3/sin(1/2*d*x+1/2*c)/(b*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/d","B"
77,1,412,131,0.196000," ","int(sec(d*x+c)^6*(b*cos(d*x+c))^(1/2),x)","-\frac{2 \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, b \left(-\frac{\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-b \left(2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}}{144 b \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}-\frac{7 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-b \left(2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}}{180 b \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}-\frac{14 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)}{15 \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}}+\frac{7 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{15 \sqrt{-b \left(2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}}-\frac{7 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \left(\EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-\EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)\right)}{15 \sqrt{-b \left(2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}}\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}\, d}"," ",0,"-2*(b*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*b*(-1/144*cos(1/2*d*x+1/2*c)/b*(-b*(2*sin(1/2*d*x+1/2*c)^4-sin(1/2*d*x+1/2*c)^2))^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^5-7/180*cos(1/2*d*x+1/2*c)/b*(-b*(2*sin(1/2*d*x+1/2*c)^4-sin(1/2*d*x+1/2*c)^2))^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^3-14/15*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)/(b*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)+7/15*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-b*(2*sin(1/2*d*x+1/2*c)^4-sin(1/2*d*x+1/2*c)^2))^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-7/15*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-b*(2*sin(1/2*d*x+1/2*c)^4-sin(1/2*d*x+1/2*c)^2))^(1/2)*(EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))))/sin(1/2*d*x+1/2*c)/(b*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/d","B"
78,1,236,134,0.125000," ","int(cos(d*x+c)^4*(b*cos(d*x+c))^(3/2),x)","-\frac{2 \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, b^{2} \left(448 \left(\cos^{13}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1568 \left(\cos^{11}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+2384 \left(\cos^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-2040 \left(\cos^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1084 \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-370 \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+15 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+62 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{77 \sqrt{-b \left(2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}\, d}"," ",0,"-2/77*(b*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*b^2*(448*cos(1/2*d*x+1/2*c)^13-1568*cos(1/2*d*x+1/2*c)^11+2384*cos(1/2*d*x+1/2*c)^9-2040*cos(1/2*d*x+1/2*c)^7+1084*cos(1/2*d*x+1/2*c)^5-370*cos(1/2*d*x+1/2*c)^3+15*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+62*cos(1/2*d*x+1/2*c))/(-b*(2*sin(1/2*d*x+1/2*c)^4-sin(1/2*d*x+1/2*c)^2))^(1/2)/sin(1/2*d*x+1/2*c)/(b*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/d","A"
79,1,223,107,0.119000," ","int(cos(d*x+c)^3*(b*cos(d*x+c))^(3/2),x)","-\frac{2 \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, b^{2} \left(160 \left(\cos^{11}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-480 \left(\cos^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+616 \left(\cos^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-432 \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+160 \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-21 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-24 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{45 \sqrt{-b \left(2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}\, d}"," ",0,"-2/45*(b*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*b^2*(160*cos(1/2*d*x+1/2*c)^11-480*cos(1/2*d*x+1/2*c)^9+616*cos(1/2*d*x+1/2*c)^7-432*cos(1/2*d*x+1/2*c)^5+160*cos(1/2*d*x+1/2*c)^3-21*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-24*cos(1/2*d*x+1/2*c))/(-b*(2*sin(1/2*d*x+1/2*c)^4-sin(1/2*d*x+1/2*c)^2))^(1/2)/sin(1/2*d*x+1/2*c)/(b*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/d","B"
80,1,210,110,0.125000," ","int(cos(d*x+c)^2*(b*cos(d*x+c))^(3/2),x)","-\frac{2 \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, b^{2} \left(48 \left(\cos^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-120 \left(\cos^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+128 \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-72 \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+5 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+16 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{21 \sqrt{-b \left(2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}\, d}"," ",0,"-2/21*(b*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*b^2*(48*cos(1/2*d*x+1/2*c)^9-120*cos(1/2*d*x+1/2*c)^7+128*cos(1/2*d*x+1/2*c)^5-72*cos(1/2*d*x+1/2*c)^3+5*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+16*cos(1/2*d*x+1/2*c))/(-b*(2*sin(1/2*d*x+1/2*c)^4-sin(1/2*d*x+1/2*c)^2))^(1/2)/sin(1/2*d*x+1/2*c)/(b*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/d","A"
81,1,213,83,0.122000," ","int(cos(d*x+c)*(b*cos(d*x+c))^(3/2),x)","-\frac{2 \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, b^{2} \left(-8 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+8 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-3 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{5 \sqrt{-b \left(2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}\, d}"," ",0,"-2/5*(b*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*b^2*(-8*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6+8*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)-3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-2*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c))/(-b*(2*sin(1/2*d*x+1/2*c)^4-sin(1/2*d*x+1/2*c)^2))^(1/2)/sin(1/2*d*x+1/2*c)/(b*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/d","B"
82,1,190,86,0.119000," ","int((b*cos(d*x+c))^(3/2),x)","-\frac{2 \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, b^{2} \left(4 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 \sqrt{-b \left(2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}\, d}"," ",0,"-2/3*(b*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*b^2*(4*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-2*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c))/(-b*(2*sin(1/2*d*x+1/2*c)^4-sin(1/2*d*x+1/2*c)^2))^(1/2)/sin(1/2*d*x+1/2*c)/(b*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/d","B"
83,1,144,61,0.104000," ","int((b*cos(d*x+c))^(3/2)*sec(d*x+c),x)","\frac{2 \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, b^{2} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{\sqrt{-b \left(2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}\, d}"," ",0,"2*(b*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*b^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))/(-b*(2*sin(1/2*d*x+1/2*c)^4-sin(1/2*d*x+1/2*c)^2))^(1/2)/sin(1/2*d*x+1/2*c)/(b*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/d","B"
84,1,144,63,0.115000," ","int((b*cos(d*x+c))^(3/2)*sec(d*x+c)^2,x)","-\frac{2 \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, b^{2} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{\sqrt{-b \left(2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}\, d}"," ",0,"-2*(b*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*b^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-b*(2*sin(1/2*d*x+1/2*c)^4-sin(1/2*d*x+1/2*c)^2))^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))/sin(1/2*d*x+1/2*c)/(b*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/d","B"
85,1,168,86,0.132000," ","int((b*cos(d*x+c))^(3/2)*sec(d*x+c)^3,x)","-\frac{2 b^{2} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b}\, \left(\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{\sqrt{-b \left(2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}\, d}"," ",0,"-2*b^2*(-2*sin(1/2*d*x+1/2*c)^4*b+sin(1/2*d*x+1/2*c)^2*b)^(1/2)*((sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-2*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c))/(-b*(2*sin(1/2*d*x+1/2*c)^4-sin(1/2*d*x+1/2*c)^2))^(1/2)/sin(1/2*d*x+1/2*c)/(b*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/d","A"
86,1,241,88,0.131000," ","int((b*cos(d*x+c))^(3/2)*sec(d*x+c)^4,x)","-\frac{2 \left(-2 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{2} \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}}{3 \sqrt{-b \left(2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}\, \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}\, d}"," ",0,"-2/3*(-2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*sin(1/2*d*x+1/2*c)^2+(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-2*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c))*b^2*(b*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)/(-b*(2*sin(1/2*d*x+1/2*c)^4-sin(1/2*d*x+1/2*c)^2))^(1/2)/(2*cos(1/2*d*x+1/2*c)^2-1)/sin(1/2*d*x+1/2*c)/(b*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/d","B"
87,1,364,110,0.182000," ","int((b*cos(d*x+c))^(3/2)*sec(d*x+c)^5,x)","\frac{2 \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, b \left(12 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-24 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-12 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+24 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+3 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-8 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b}}{5 \sin \left(\frac{d x}{2}+\frac{c}{2}\right)^{3} \left(8 \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-12 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+6 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}\, d}"," ",0,"2/5*(b*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*b/sin(1/2*d*x+1/2*c)^3/(8*sin(1/2*d*x+1/2*c)^6-12*sin(1/2*d*x+1/2*c)^4+6*sin(1/2*d*x+1/2*c)^2-1)*(12*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^4-24*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6-12*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^2+24*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-8*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c))*(-2*sin(1/2*d*x+1/2*c)^4*b+sin(1/2*d*x+1/2*c)^2*b)^(1/2)/(b*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/d","B"
88,1,398,112,0.151000," ","int((b*cos(d*x+c))^(3/2)*sec(d*x+c)^6,x)","-\frac{2 \left(-40 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+60 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-40 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-30 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+40 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+5 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-16 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{2} \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}}{21 \sqrt{-b \left(2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}\, \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)^{3} \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}\, d}"," ",0,"-2/21*(-40*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*sin(1/2*d*x+1/2*c)^6+60*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*sin(1/2*d*x+1/2*c)^4-40*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6-30*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*sin(1/2*d*x+1/2*c)^2+40*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+5*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-16*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c))*b^2*(b*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)/(-b*(2*sin(1/2*d*x+1/2*c)^4-sin(1/2*d*x+1/2*c)^2))^(1/2)/(2*cos(1/2*d*x+1/2*c)^2-1)^3/sin(1/2*d*x+1/2*c)/(b*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/d","B"
89,1,414,134,0.196000," ","int((b*cos(d*x+c))^(3/2)*sec(d*x+c)^7,x)","-\frac{2 \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, b^{2} \left(-\frac{\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-b \left(2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}}{144 b \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}-\frac{7 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-b \left(2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}}{180 b \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}-\frac{14 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)}{15 \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}}+\frac{7 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{15 \sqrt{-b \left(2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}}-\frac{7 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \left(\EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-\EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)\right)}{15 \sqrt{-b \left(2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}}\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}\, d}"," ",0,"-2*(b*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*b^2*(-1/144*cos(1/2*d*x+1/2*c)/b*(-b*(2*sin(1/2*d*x+1/2*c)^4-sin(1/2*d*x+1/2*c)^2))^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^5-7/180*cos(1/2*d*x+1/2*c)/b*(-b*(2*sin(1/2*d*x+1/2*c)^4-sin(1/2*d*x+1/2*c)^2))^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^3-14/15*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)/(b*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)+7/15*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-b*(2*sin(1/2*d*x+1/2*c)^4-sin(1/2*d*x+1/2*c)^2))^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-7/15*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-b*(2*sin(1/2*d*x+1/2*c)^4-sin(1/2*d*x+1/2*c)^2))^(1/2)*(EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))))/sin(1/2*d*x+1/2*c)/(b*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/d","B"
90,1,236,133,0.143000," ","int(cos(d*x+c)^3*(b*cos(d*x+c))^(5/2),x)","-\frac{2 \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, b^{3} \left(448 \left(\cos^{13}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1568 \left(\cos^{11}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+2384 \left(\cos^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-2040 \left(\cos^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1084 \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-370 \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+15 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+62 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{77 \sqrt{-b \left(2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}\, d}"," ",0,"-2/77*(b*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*b^3*(448*cos(1/2*d*x+1/2*c)^13-1568*cos(1/2*d*x+1/2*c)^11+2384*cos(1/2*d*x+1/2*c)^9-2040*cos(1/2*d*x+1/2*c)^7+1084*cos(1/2*d*x+1/2*c)^5-370*cos(1/2*d*x+1/2*c)^3+15*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+62*cos(1/2*d*x+1/2*c))/(-b*(2*sin(1/2*d*x+1/2*c)^4-sin(1/2*d*x+1/2*c)^2))^(1/2)/sin(1/2*d*x+1/2*c)/(b*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/d","A"
91,1,223,110,0.128000," ","int(cos(d*x+c)^2*(b*cos(d*x+c))^(5/2),x)","-\frac{2 \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, b^{3} \left(160 \left(\cos^{11}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-480 \left(\cos^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+616 \left(\cos^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-432 \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+160 \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-21 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-24 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{45 \sqrt{-b \left(2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}\, d}"," ",0,"-2/45*(b*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*b^3*(160*cos(1/2*d*x+1/2*c)^11-480*cos(1/2*d*x+1/2*c)^9+616*cos(1/2*d*x+1/2*c)^7-432*cos(1/2*d*x+1/2*c)^5+160*cos(1/2*d*x+1/2*c)^3-21*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-24*cos(1/2*d*x+1/2*c))/(-b*(2*sin(1/2*d*x+1/2*c)^4-sin(1/2*d*x+1/2*c)^2))^(1/2)/sin(1/2*d*x+1/2*c)/(b*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/d","B"
92,1,210,109,0.104000," ","int(cos(d*x+c)*(b*cos(d*x+c))^(5/2),x)","-\frac{2 \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, b^{3} \left(48 \left(\cos^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-120 \left(\cos^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+128 \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-72 \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+5 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+16 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{21 \sqrt{-b \left(2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}\, d}"," ",0,"-2/21*(b*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*b^3*(48*cos(1/2*d*x+1/2*c)^9-120*cos(1/2*d*x+1/2*c)^7+128*cos(1/2*d*x+1/2*c)^5-72*cos(1/2*d*x+1/2*c)^3+5*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+16*cos(1/2*d*x+1/2*c))/(-b*(2*sin(1/2*d*x+1/2*c)^4-sin(1/2*d*x+1/2*c)^2))^(1/2)/sin(1/2*d*x+1/2*c)/(b*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/d","A"
93,1,213,86,0.126000," ","int((b*cos(d*x+c))^(5/2),x)","-\frac{2 \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, b^{3} \left(-8 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+8 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-3 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{5 \sqrt{-b \left(2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}\, d}"," ",0,"-2/5*(b*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*b^3*(-8*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6+8*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)-3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-2*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c))/(-b*(2*sin(1/2*d*x+1/2*c)^4-sin(1/2*d*x+1/2*c)^2))^(1/2)/sin(1/2*d*x+1/2*c)/(b*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/d","B"
94,1,190,88,0.135000," ","int((b*cos(d*x+c))^(5/2)*sec(d*x+c),x)","-\frac{2 \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, b^{3} \left(4 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 \sqrt{-b \left(2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}\, d}"," ",0,"-2/3*(b*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*b^3*(4*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-2*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c))/(-b*(2*sin(1/2*d*x+1/2*c)^4-sin(1/2*d*x+1/2*c)^2))^(1/2)/sin(1/2*d*x+1/2*c)/(b*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/d","B"
95,1,144,63,0.096000," ","int((b*cos(d*x+c))^(5/2)*sec(d*x+c)^2,x)","\frac{2 \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, b^{3} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{\sqrt{-b \left(2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}\, d}"," ",0,"2*(b*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*b^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))/(-b*(2*sin(1/2*d*x+1/2*c)^4-sin(1/2*d*x+1/2*c)^2))^(1/2)/sin(1/2*d*x+1/2*c)/(b*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/d","B"
96,1,144,63,0.132000," ","int((b*cos(d*x+c))^(5/2)*sec(d*x+c)^3,x)","-\frac{2 \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, b^{3} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{\sqrt{-b \left(2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}\, d}"," ",0,"-2*(b*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*b^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-b*(2*sin(1/2*d*x+1/2*c)^4-sin(1/2*d*x+1/2*c)^2))^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))/sin(1/2*d*x+1/2*c)/(b*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/d","B"
97,1,168,88,0.128000," ","int((b*cos(d*x+c))^(5/2)*sec(d*x+c)^4,x)","-\frac{2 b^{3} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b}\, \left(\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{\sqrt{-b \left(2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}\, d}"," ",0,"-2*b^3*(-2*sin(1/2*d*x+1/2*c)^4*b+sin(1/2*d*x+1/2*c)^2*b)^(1/2)*((sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-2*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c))/(-b*(2*sin(1/2*d*x+1/2*c)^4-sin(1/2*d*x+1/2*c)^2))^(1/2)/sin(1/2*d*x+1/2*c)/(b*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/d","A"
98,1,241,88,0.139000," ","int((b*cos(d*x+c))^(5/2)*sec(d*x+c)^5,x)","-\frac{2 \left(-2 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{3} \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}}{3 \sqrt{-b \left(2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}\, \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}\, d}"," ",0,"-2/3*(-2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*sin(1/2*d*x+1/2*c)^2+(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-2*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c))*b^3*(b*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)/(-b*(2*sin(1/2*d*x+1/2*c)^4-sin(1/2*d*x+1/2*c)^2))^(1/2)/(2*cos(1/2*d*x+1/2*c)^2-1)/sin(1/2*d*x+1/2*c)/(b*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/d","B"
99,1,366,112,0.205000," ","int((b*cos(d*x+c))^(5/2)*sec(d*x+c)^6,x)","\frac{2 \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, b^{2} \left(12 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-24 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-12 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+24 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+3 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-8 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b}}{5 \sin \left(\frac{d x}{2}+\frac{c}{2}\right)^{3} \left(8 \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-12 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+6 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}\, d}"," ",0,"2/5*(b*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*b^2/sin(1/2*d*x+1/2*c)^3/(8*sin(1/2*d*x+1/2*c)^6-12*sin(1/2*d*x+1/2*c)^4+6*sin(1/2*d*x+1/2*c)^2-1)*(12*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^4-24*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6-12*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^2+24*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-8*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c))*(-2*sin(1/2*d*x+1/2*c)^4*b+sin(1/2*d*x+1/2*c)^2*b)^(1/2)/(b*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/d","B"
100,1,398,112,0.150000," ","int((b*cos(d*x+c))^(5/2)*sec(d*x+c)^7,x)","-\frac{2 \left(-40 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+60 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-40 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-30 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+40 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+5 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-16 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{3} \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}}{21 \sqrt{-b \left(2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}\, \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)^{3} \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}\, d}"," ",0,"-2/21*(-40*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*sin(1/2*d*x+1/2*c)^6+60*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*sin(1/2*d*x+1/2*c)^4-40*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6-30*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*sin(1/2*d*x+1/2*c)^2+40*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+5*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-16*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c))*b^3*(b*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)/(-b*(2*sin(1/2*d*x+1/2*c)^4-sin(1/2*d*x+1/2*c)^2))^(1/2)/(2*cos(1/2*d*x+1/2*c)^2-1)^3/sin(1/2*d*x+1/2*c)/(b*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/d","B"
101,1,414,136,0.231000," ","int((b*cos(d*x+c))^(5/2)*sec(d*x+c)^8,x)","-\frac{2 \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, b^{3} \left(-\frac{\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-b \left(2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}}{144 b \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}-\frac{7 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-b \left(2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}}{180 b \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}-\frac{14 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)}{15 \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}}+\frac{7 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{15 \sqrt{-b \left(2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}}-\frac{7 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \left(\EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-\EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)\right)}{15 \sqrt{-b \left(2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}}\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}\, d}"," ",0,"-2*(b*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*b^3*(-1/144*cos(1/2*d*x+1/2*c)/b*(-b*(2*sin(1/2*d*x+1/2*c)^4-sin(1/2*d*x+1/2*c)^2))^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^5-7/180*cos(1/2*d*x+1/2*c)/b*(-b*(2*sin(1/2*d*x+1/2*c)^4-sin(1/2*d*x+1/2*c)^2))^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^3-14/15*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)/(b*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)+7/15*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-b*(2*sin(1/2*d*x+1/2*c)^4-sin(1/2*d*x+1/2*c)^2))^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-7/15*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-b*(2*sin(1/2*d*x+1/2*c)^4-sin(1/2*d*x+1/2*c)^2))^(1/2)*(EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))))/sin(1/2*d*x+1/2*c)/(b*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/d","B"
102,1,210,110,0.136000," ","int((b*cos(d*x+c))^(7/2),x)","-\frac{2 \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, b^{4} \left(48 \left(\cos^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-120 \left(\cos^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+128 \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-72 \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+5 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+16 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{21 \sqrt{-b \left(2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}\, d}"," ",0,"-2/21*(b*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*b^4*(48*cos(1/2*d*x+1/2*c)^9-120*cos(1/2*d*x+1/2*c)^7+128*cos(1/2*d*x+1/2*c)^5-72*cos(1/2*d*x+1/2*c)^3+5*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+16*cos(1/2*d*x+1/2*c))/(-b*(2*sin(1/2*d*x+1/2*c)^4-sin(1/2*d*x+1/2*c)^2))^(1/2)/sin(1/2*d*x+1/2*c)/(b*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/d","A"
103,1,233,133,0.150000," ","int(cos(d*x+c)^6/(b*cos(d*x+c))^(1/2),x)","-\frac{2 \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(448 \left(\cos^{13}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1568 \left(\cos^{11}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+2384 \left(\cos^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-2040 \left(\cos^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1084 \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-370 \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+15 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+62 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{77 \sqrt{-b \left(2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}\, d}"," ",0,"-2/77*(b*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(448*cos(1/2*d*x+1/2*c)^13-1568*cos(1/2*d*x+1/2*c)^11+2384*cos(1/2*d*x+1/2*c)^9-2040*cos(1/2*d*x+1/2*c)^7+1084*cos(1/2*d*x+1/2*c)^5-370*cos(1/2*d*x+1/2*c)^3+15*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+62*cos(1/2*d*x+1/2*c))/(-b*(2*sin(1/2*d*x+1/2*c)^4-sin(1/2*d*x+1/2*c)^2))^(1/2)/sin(1/2*d*x+1/2*c)/(b*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/d","A"
104,1,220,112,0.143000," ","int(cos(d*x+c)^5/(b*cos(d*x+c))^(1/2),x)","-\frac{2 \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(160 \left(\cos^{11}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-480 \left(\cos^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+616 \left(\cos^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-432 \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+160 \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-21 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-24 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{45 \sqrt{-b \left(2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}\, d}"," ",0,"-2/45*(b*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(160*cos(1/2*d*x+1/2*c)^11-480*cos(1/2*d*x+1/2*c)^9+616*cos(1/2*d*x+1/2*c)^7-432*cos(1/2*d*x+1/2*c)^5+160*cos(1/2*d*x+1/2*c)^3-21*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-24*cos(1/2*d*x+1/2*c))/(-b*(2*sin(1/2*d*x+1/2*c)^4-sin(1/2*d*x+1/2*c)^2))^(1/2)/sin(1/2*d*x+1/2*c)/(b*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/d","A"
105,1,207,109,0.152000," ","int(cos(d*x+c)^4/(b*cos(d*x+c))^(1/2),x)","-\frac{2 \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(48 \left(\cos^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-120 \left(\cos^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+128 \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-72 \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+5 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+16 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{21 \sqrt{-b \left(2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}\, d}"," ",0,"-2/21*(b*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(48*cos(1/2*d*x+1/2*c)^9-120*cos(1/2*d*x+1/2*c)^7+128*cos(1/2*d*x+1/2*c)^5-72*cos(1/2*d*x+1/2*c)^3+5*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+16*cos(1/2*d*x+1/2*c))/(-b*(2*sin(1/2*d*x+1/2*c)^4-sin(1/2*d*x+1/2*c)^2))^(1/2)/sin(1/2*d*x+1/2*c)/(b*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/d","A"
106,1,210,88,0.146000," ","int(cos(d*x+c)^3/(b*cos(d*x+c))^(1/2),x)","-\frac{2 \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(-8 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+8 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-3 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{5 \sqrt{-b \left(2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}\, d}"," ",0,"-2/5*(b*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(-8*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6+8*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)-3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-2*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c))/(-b*(2*sin(1/2*d*x+1/2*c)^4-sin(1/2*d*x+1/2*c)^2))^(1/2)/sin(1/2*d*x+1/2*c)/(b*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/d","B"
107,1,187,85,0.169000," ","int(cos(d*x+c)^2/(b*cos(d*x+c))^(1/2),x)","-\frac{2 \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(4 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 \sqrt{-b \left(2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}\, d}"," ",0,"-2/3*(b*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(4*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-2*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c))/(-b*(2*sin(1/2*d*x+1/2*c)^4-sin(1/2*d*x+1/2*c)^2))^(1/2)/sin(1/2*d*x+1/2*c)/(b*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/d","B"
108,1,141,63,0.127000," ","int(cos(d*x+c)/(b*cos(d*x+c))^(1/2),x)","\frac{2 \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{\sqrt{-b \left(2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}\, d}"," ",0,"2*(b*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))/(-b*(2*sin(1/2*d*x+1/2*c)^4-sin(1/2*d*x+1/2*c)^2))^(1/2)/sin(1/2*d*x+1/2*c)/(b*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/d","B"
109,1,54,60,0.053000," ","int(1/(b*cos(d*x+c))^(1/2),x)","\frac{2 \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \mathrm{am}^{-1}\left(\frac{d x}{2}+\frac{c}{2}| \sqrt{2}\right)}{d \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}}"," ",0,"2/d/(b*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)*(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)*InverseJacobiAM(1/2*d*x+1/2*c,2^(1/2))","C"
110,1,165,85,0.161000," ","int(sec(d*x+c)/(b*cos(d*x+c))^(1/2),x)","-\frac{2 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b}\, \left(\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{\sqrt{-b \left(2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}\, d}"," ",0,"-2*(-2*sin(1/2*d*x+1/2*c)^4*b+sin(1/2*d*x+1/2*c)^2*b)^(1/2)*((sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-2*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c))/(-b*(2*sin(1/2*d*x+1/2*c)^4-sin(1/2*d*x+1/2*c)^2))^(1/2)/sin(1/2*d*x+1/2*c)/(b*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/d","A"
111,1,238,83,0.159000," ","int(sec(d*x+c)^2/(b*cos(d*x+c))^(1/2),x)","-\frac{2 \left(-2 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right) \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}}{3 \sqrt{-b \left(2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}\, \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}\, d}"," ",0,"-2/3*(-2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*sin(1/2*d*x+1/2*c)^2+(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-2*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c))*(b*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)/(-b*(2*sin(1/2*d*x+1/2*c)^4-sin(1/2*d*x+1/2*c)^2))^(1/2)/(2*cos(1/2*d*x+1/2*c)^2-1)/sin(1/2*d*x+1/2*c)/(b*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/d","B"
112,1,366,109,0.247000," ","int(sec(d*x+c)^3/(b*cos(d*x+c))^(1/2),x)","\frac{2 \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(12 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-24 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-12 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+24 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+3 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-8 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b}}{5 b \sin \left(\frac{d x}{2}+\frac{c}{2}\right)^{3} \left(8 \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-12 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+6 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}\, d}"," ",0,"2/5*(b*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)/b/sin(1/2*d*x+1/2*c)^3/(8*sin(1/2*d*x+1/2*c)^6-12*sin(1/2*d*x+1/2*c)^4+6*sin(1/2*d*x+1/2*c)^2-1)*(12*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^4-24*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6-12*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^2+24*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-8*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c))*(-2*sin(1/2*d*x+1/2*c)^4*b+sin(1/2*d*x+1/2*c)^2*b)^(1/2)/(b*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/d","B"
113,1,395,107,0.185000," ","int(sec(d*x+c)^4/(b*cos(d*x+c))^(1/2),x)","-\frac{2 \left(-40 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+60 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-40 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-30 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+40 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+5 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-16 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right) \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}}{21 \sqrt{-b \left(2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}\, \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)^{3} \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}\, d}"," ",0,"-2/21*(-40*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*sin(1/2*d*x+1/2*c)^6+60*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*sin(1/2*d*x+1/2*c)^4-40*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6-30*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*sin(1/2*d*x+1/2*c)^2+40*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+5*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-16*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c))*(b*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)/(-b*(2*sin(1/2*d*x+1/2*c)^4-sin(1/2*d*x+1/2*c)^2))^(1/2)/(2*cos(1/2*d*x+1/2*c)^2-1)^3/sin(1/2*d*x+1/2*c)/(b*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/d","B"
114,1,411,133,0.250000," ","int(sec(d*x+c)^5/(b*cos(d*x+c))^(1/2),x)","-\frac{\sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(-\frac{\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-b \left(2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}}{72 b \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}-\frac{7 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-b \left(2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}}{90 b \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}-\frac{28 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)}{15 \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}}+\frac{14 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{15 \sqrt{-b \left(2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}}-\frac{14 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \left(\EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-\EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)\right)}{15 \sqrt{-b \left(2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}}\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}\, d}"," ",0,"-(b*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(-1/72*cos(1/2*d*x+1/2*c)/b*(-b*(2*sin(1/2*d*x+1/2*c)^4-sin(1/2*d*x+1/2*c)^2))^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^5-7/90*cos(1/2*d*x+1/2*c)/b*(-b*(2*sin(1/2*d*x+1/2*c)^4-sin(1/2*d*x+1/2*c)^2))^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^3-28/15*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)/(b*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)+14/15*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-b*(2*sin(1/2*d*x+1/2*c)^4-sin(1/2*d*x+1/2*c)^2))^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-14/15*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-b*(2*sin(1/2*d*x+1/2*c)^4-sin(1/2*d*x+1/2*c)^2))^(1/2)*(EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))))/sin(1/2*d*x+1/2*c)/(b*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/d","B"
115,1,236,136,0.154000," ","int(cos(d*x+c)^7/(b*cos(d*x+c))^(3/2),x)","-\frac{2 \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(448 \left(\cos^{13}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1568 \left(\cos^{11}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+2384 \left(\cos^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-2040 \left(\cos^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1084 \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-370 \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+15 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+62 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{77 b \sqrt{-b \left(2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}\, d}"," ",0,"-2/77*(b*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)/b*(448*cos(1/2*d*x+1/2*c)^13-1568*cos(1/2*d*x+1/2*c)^11+2384*cos(1/2*d*x+1/2*c)^9-2040*cos(1/2*d*x+1/2*c)^7+1084*cos(1/2*d*x+1/2*c)^5-370*cos(1/2*d*x+1/2*c)^3+15*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+62*cos(1/2*d*x+1/2*c))/(-b*(2*sin(1/2*d*x+1/2*c)^4-sin(1/2*d*x+1/2*c)^2))^(1/2)/sin(1/2*d*x+1/2*c)/(b*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/d","A"
116,1,223,112,0.155000," ","int(cos(d*x+c)^6/(b*cos(d*x+c))^(3/2),x)","-\frac{2 \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(160 \left(\cos^{11}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-480 \left(\cos^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+616 \left(\cos^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-432 \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+160 \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-21 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-24 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{45 b \sqrt{-b \left(2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}\, d}"," ",0,"-2/45*(b*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)/b*(160*cos(1/2*d*x+1/2*c)^11-480*cos(1/2*d*x+1/2*c)^9+616*cos(1/2*d*x+1/2*c)^7-432*cos(1/2*d*x+1/2*c)^5+160*cos(1/2*d*x+1/2*c)^3-21*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-24*cos(1/2*d*x+1/2*c))/(-b*(2*sin(1/2*d*x+1/2*c)^4-sin(1/2*d*x+1/2*c)^2))^(1/2)/sin(1/2*d*x+1/2*c)/(b*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/d","A"
117,1,210,112,0.203000," ","int(cos(d*x+c)^5/(b*cos(d*x+c))^(3/2),x)","-\frac{2 \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(48 \left(\cos^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-120 \left(\cos^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+128 \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-72 \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+5 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+16 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{21 b \sqrt{-b \left(2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}\, d}"," ",0,"-2/21*(b*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)/b*(48*cos(1/2*d*x+1/2*c)^9-120*cos(1/2*d*x+1/2*c)^7+128*cos(1/2*d*x+1/2*c)^5-72*cos(1/2*d*x+1/2*c)^3+5*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+16*cos(1/2*d*x+1/2*c))/(-b*(2*sin(1/2*d*x+1/2*c)^4-sin(1/2*d*x+1/2*c)^2))^(1/2)/sin(1/2*d*x+1/2*c)/(b*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/d","A"
118,1,213,88,0.158000," ","int(cos(d*x+c)^4/(b*cos(d*x+c))^(3/2),x)","-\frac{2 \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(-8 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+8 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-3 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{5 b \sqrt{-b \left(2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}\, d}"," ",0,"-2/5*(b*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)/b*(-8*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6+8*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)-3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-2*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c))/(-b*(2*sin(1/2*d*x+1/2*c)^4-sin(1/2*d*x+1/2*c)^2))^(1/2)/sin(1/2*d*x+1/2*c)/(b*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/d","B"
119,1,190,88,0.238000," ","int(cos(d*x+c)^3/(b*cos(d*x+c))^(3/2),x)","-\frac{2 \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(4 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 b \sqrt{-b \left(2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}\, d}"," ",0,"-2/3*(b*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)/b*(4*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-2*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c))/(-b*(2*sin(1/2*d*x+1/2*c)^4-sin(1/2*d*x+1/2*c)^2))^(1/2)/sin(1/2*d*x+1/2*c)/(b*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/d","B"
120,1,144,63,0.190000," ","int(cos(d*x+c)^2/(b*cos(d*x+c))^(3/2),x)","\frac{2 \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{b \sqrt{-b \left(2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}\, d}"," ",0,"2*(b*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))/b/(-b*(2*sin(1/2*d*x+1/2*c)^4-sin(1/2*d*x+1/2*c)^2))^(1/2)/sin(1/2*d*x+1/2*c)/(b*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/d","B"
121,1,144,63,0.132000," ","int(cos(d*x+c)/(b*cos(d*x+c))^(3/2),x)","-\frac{2 \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{b \sqrt{-b \left(2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}\, d}"," ",0,"-2*(b*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)/b*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-b*(2*sin(1/2*d*x+1/2*c)^4-sin(1/2*d*x+1/2*c)^2))^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))/sin(1/2*d*x+1/2*c)/(b*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/d","B"
122,1,168,88,0.158000," ","int(1/(b*cos(d*x+c))^(3/2),x)","-\frac{2 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b}\, \left(\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{b \sqrt{-b \left(2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}\, d}"," ",0,"-2/b*(-2*sin(1/2*d*x+1/2*c)^4*b+sin(1/2*d*x+1/2*c)^2*b)^(1/2)*((sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-2*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c))/(-b*(2*sin(1/2*d*x+1/2*c)^4-sin(1/2*d*x+1/2*c)^2))^(1/2)/sin(1/2*d*x+1/2*c)/(b*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/d","A"
123,1,241,85,0.165000," ","int(sec(d*x+c)/(b*cos(d*x+c))^(3/2),x)","-\frac{2 \left(-2 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right) \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}}{3 b \sqrt{-b \left(2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}\, \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}\, d}"," ",0,"-2/3*(-2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*sin(1/2*d*x+1/2*c)^2+(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-2*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c))/b*(b*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)/(-b*(2*sin(1/2*d*x+1/2*c)^4-sin(1/2*d*x+1/2*c)^2))^(1/2)/(2*cos(1/2*d*x+1/2*c)^2-1)/sin(1/2*d*x+1/2*c)/(b*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/d","B"
124,1,366,110,0.256000," ","int(sec(d*x+c)^2/(b*cos(d*x+c))^(3/2),x)","\frac{2 \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(12 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-24 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-12 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+24 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+3 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-8 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b}}{5 b^{2} \sin \left(\frac{d x}{2}+\frac{c}{2}\right)^{3} \left(8 \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-12 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+6 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}\, d}"," ",0,"2/5*(b*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)/b^2/sin(1/2*d*x+1/2*c)^3/(8*sin(1/2*d*x+1/2*c)^6-12*sin(1/2*d*x+1/2*c)^4+6*sin(1/2*d*x+1/2*c)^2-1)*(12*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^4-24*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6-12*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^2+24*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-8*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c))*(-2*sin(1/2*d*x+1/2*c)^4*b+sin(1/2*d*x+1/2*c)^2*b)^(1/2)/(b*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/d","B"
125,1,398,109,0.182000," ","int(sec(d*x+c)^3/(b*cos(d*x+c))^(3/2),x)","-\frac{2 \left(-40 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+60 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-40 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-30 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+40 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+5 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-16 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right) \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}}{21 b \sqrt{-b \left(2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}\, \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)^{3} \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}\, d}"," ",0,"-2/21*(-40*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*sin(1/2*d*x+1/2*c)^6+60*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*sin(1/2*d*x+1/2*c)^4-40*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6-30*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*sin(1/2*d*x+1/2*c)^2+40*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+5*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-16*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c))/b*(b*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)/(-b*(2*sin(1/2*d*x+1/2*c)^4-sin(1/2*d*x+1/2*c)^2))^(1/2)/(2*cos(1/2*d*x+1/2*c)^2-1)^3/sin(1/2*d*x+1/2*c)/(b*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/d","B"
126,1,414,134,0.263000," ","int(sec(d*x+c)^4/(b*cos(d*x+c))^(3/2),x)","-\frac{2 \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(-\frac{\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-b \left(2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}}{144 b \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}-\frac{7 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-b \left(2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}}{180 b \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}-\frac{14 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)}{15 \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}}+\frac{7 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{15 \sqrt{-b \left(2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}}-\frac{7 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \left(\EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-\EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)\right)}{15 \sqrt{-b \left(2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}}\right)}{b \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}\, d}"," ",0,"-2*(b*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)/b*(-1/144*cos(1/2*d*x+1/2*c)/b*(-b*(2*sin(1/2*d*x+1/2*c)^4-sin(1/2*d*x+1/2*c)^2))^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^5-7/180*cos(1/2*d*x+1/2*c)/b*(-b*(2*sin(1/2*d*x+1/2*c)^4-sin(1/2*d*x+1/2*c)^2))^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^3-14/15*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)/(b*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)+7/15*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-b*(2*sin(1/2*d*x+1/2*c)^4-sin(1/2*d*x+1/2*c)^2))^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-7/15*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-b*(2*sin(1/2*d*x+1/2*c)^4-sin(1/2*d*x+1/2*c)^2))^(1/2)*(EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))))/sin(1/2*d*x+1/2*c)/(b*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/d","B"
127,1,236,136,0.194000," ","int(cos(d*x+c)^8/(b*cos(d*x+c))^(5/2),x)","-\frac{2 \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(448 \left(\cos^{13}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1568 \left(\cos^{11}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+2384 \left(\cos^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-2040 \left(\cos^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1084 \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-370 \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+15 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+62 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{77 b^{2} \sqrt{-b \left(2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}\, d}"," ",0,"-2/77*(b*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)/b^2*(448*cos(1/2*d*x+1/2*c)^13-1568*cos(1/2*d*x+1/2*c)^11+2384*cos(1/2*d*x+1/2*c)^9-2040*cos(1/2*d*x+1/2*c)^7+1084*cos(1/2*d*x+1/2*c)^5-370*cos(1/2*d*x+1/2*c)^3+15*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+62*cos(1/2*d*x+1/2*c))/(-b*(2*sin(1/2*d*x+1/2*c)^4-sin(1/2*d*x+1/2*c)^2))^(1/2)/sin(1/2*d*x+1/2*c)/(b*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/d","A"
128,1,223,112,0.181000," ","int(cos(d*x+c)^7/(b*cos(d*x+c))^(5/2),x)","-\frac{2 \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(160 \left(\cos^{11}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-480 \left(\cos^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+616 \left(\cos^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-432 \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+160 \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-21 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-24 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{45 b^{2} \sqrt{-b \left(2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}\, d}"," ",0,"-2/45*(b*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)/b^2*(160*cos(1/2*d*x+1/2*c)^11-480*cos(1/2*d*x+1/2*c)^9+616*cos(1/2*d*x+1/2*c)^7-432*cos(1/2*d*x+1/2*c)^5+160*cos(1/2*d*x+1/2*c)^3-21*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-24*cos(1/2*d*x+1/2*c))/(-b*(2*sin(1/2*d*x+1/2*c)^4-sin(1/2*d*x+1/2*c)^2))^(1/2)/sin(1/2*d*x+1/2*c)/(b*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/d","A"
129,1,210,112,0.185000," ","int(cos(d*x+c)^6/(b*cos(d*x+c))^(5/2),x)","-\frac{2 \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(48 \left(\cos^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-120 \left(\cos^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+128 \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-72 \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+5 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+16 \cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{21 b^{2} \sqrt{-b \left(2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}\, d}"," ",0,"-2/21*(b*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)/b^2*(48*cos(1/2*d*x+1/2*c)^9-120*cos(1/2*d*x+1/2*c)^7+128*cos(1/2*d*x+1/2*c)^5-72*cos(1/2*d*x+1/2*c)^3+5*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+16*cos(1/2*d*x+1/2*c))/(-b*(2*sin(1/2*d*x+1/2*c)^4-sin(1/2*d*x+1/2*c)^2))^(1/2)/sin(1/2*d*x+1/2*c)/(b*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/d","A"
130,1,213,88,0.162000," ","int(cos(d*x+c)^5/(b*cos(d*x+c))^(5/2),x)","-\frac{2 \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(-8 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+8 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-3 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{5 b^{2} \sqrt{-b \left(2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}\, d}"," ",0,"-2/5*(b*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)/b^2*(-8*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6+8*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)-3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-2*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c))/(-b*(2*sin(1/2*d*x+1/2*c)^4-sin(1/2*d*x+1/2*c)^2))^(1/2)/sin(1/2*d*x+1/2*c)/(b*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/d","B"
131,1,190,88,0.159000," ","int(cos(d*x+c)^4/(b*cos(d*x+c))^(5/2),x)","-\frac{2 \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(4 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 b^{2} \sqrt{-b \left(2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}\, d}"," ",0,"-2/3*(b*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)/b^2*(4*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-2*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c))/(-b*(2*sin(1/2*d*x+1/2*c)^4-sin(1/2*d*x+1/2*c)^2))^(1/2)/sin(1/2*d*x+1/2*c)/(b*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/d","B"
132,1,144,63,0.147000," ","int(cos(d*x+c)^3/(b*cos(d*x+c))^(5/2),x)","\frac{2 \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{b^{2} \sqrt{-b \left(2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}\, d}"," ",0,"2*(b*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))/b^2/(-b*(2*sin(1/2*d*x+1/2*c)^4-sin(1/2*d*x+1/2*c)^2))^(1/2)/sin(1/2*d*x+1/2*c)/(b*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/d","B"
133,1,144,63,0.135000," ","int(cos(d*x+c)^2/(b*cos(d*x+c))^(5/2),x)","-\frac{2 \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{b^{2} \sqrt{-b \left(2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}\, d}"," ",0,"-2*(b*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)/b^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-b*(2*sin(1/2*d*x+1/2*c)^4-sin(1/2*d*x+1/2*c)^2))^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))/sin(1/2*d*x+1/2*c)/(b*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/d","B"
134,1,168,88,0.185000," ","int(cos(d*x+c)/(b*cos(d*x+c))^(5/2),x)","-\frac{2 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b}\, \left(\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{b^{2} \sqrt{-b \left(2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}\, d}"," ",0,"-2/b^2*(-2*sin(1/2*d*x+1/2*c)^4*b+sin(1/2*d*x+1/2*c)^2*b)^(1/2)*((sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-2*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c))/(-b*(2*sin(1/2*d*x+1/2*c)^4-sin(1/2*d*x+1/2*c)^2))^(1/2)/sin(1/2*d*x+1/2*c)/(b*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/d","A"
135,1,241,88,0.166000," ","int(1/(b*cos(d*x+c))^(5/2),x)","-\frac{2 \left(-2 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right) \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}}{3 b^{2} \sqrt{-b \left(2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}\, \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}\, d}"," ",0,"-2/3*(-2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*sin(1/2*d*x+1/2*c)^2+(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-2*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c))/b^2*(b*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)/(-b*(2*sin(1/2*d*x+1/2*c)^4-sin(1/2*d*x+1/2*c)^2))^(1/2)/(2*cos(1/2*d*x+1/2*c)^2-1)/sin(1/2*d*x+1/2*c)/(b*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/d","B"
136,1,366,109,0.266000," ","int(sec(d*x+c)/(b*cos(d*x+c))^(5/2),x)","\frac{2 \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(12 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-24 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-12 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+24 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+3 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-8 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b}}{5 b^{3} \sin \left(\frac{d x}{2}+\frac{c}{2}\right)^{3} \left(8 \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-12 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+6 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}\, d}"," ",0,"2/5*(b*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)/b^3/sin(1/2*d*x+1/2*c)^3/(8*sin(1/2*d*x+1/2*c)^6-12*sin(1/2*d*x+1/2*c)^4+6*sin(1/2*d*x+1/2*c)^2-1)*(12*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^4-24*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6-12*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^2+24*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-8*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c))*(-2*sin(1/2*d*x+1/2*c)^4*b+sin(1/2*d*x+1/2*c)^2*b)^(1/2)/(b*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/d","B"
137,1,398,110,0.193000," ","int(sec(d*x+c)^2/(b*cos(d*x+c))^(5/2),x)","-\frac{2 \left(-40 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+60 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-40 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-30 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+40 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+5 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-16 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right) \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}}{21 b^{2} \sqrt{-b \left(2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}\, \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)^{3} \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}\, d}"," ",0,"-2/21*(-40*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*sin(1/2*d*x+1/2*c)^6+60*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*sin(1/2*d*x+1/2*c)^4-40*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6-30*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*sin(1/2*d*x+1/2*c)^2+40*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+5*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-16*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c))/b^2*(b*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)/(-b*(2*sin(1/2*d*x+1/2*c)^4-sin(1/2*d*x+1/2*c)^2))^(1/2)/(2*cos(1/2*d*x+1/2*c)^2-1)^3/sin(1/2*d*x+1/2*c)/(b*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/d","B"
138,1,414,133,0.286000," ","int(sec(d*x+c)^3/(b*cos(d*x+c))^(5/2),x)","-\frac{2 \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(-\frac{\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-b \left(2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}}{144 b \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}-\frac{7 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-b \left(2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}}{180 b \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}-\frac{14 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)}{15 \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}}+\frac{7 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{15 \sqrt{-b \left(2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}}-\frac{7 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \left(\EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-\EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)\right)}{15 \sqrt{-b \left(2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}}\right)}{b^{2} \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}\, d}"," ",0,"-2*(b*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)/b^2*(-1/144*cos(1/2*d*x+1/2*c)/b*(-b*(2*sin(1/2*d*x+1/2*c)^4-sin(1/2*d*x+1/2*c)^2))^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^5-7/180*cos(1/2*d*x+1/2*c)/b*(-b*(2*sin(1/2*d*x+1/2*c)^4-sin(1/2*d*x+1/2*c)^2))^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^3-14/15*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)/(b*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)+7/15*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-b*(2*sin(1/2*d*x+1/2*c)^4-sin(1/2*d*x+1/2*c)^2))^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-7/15*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-b*(2*sin(1/2*d*x+1/2*c)^4-sin(1/2*d*x+1/2*c)^2))^(1/2)*(EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))))/sin(1/2*d*x+1/2*c)/(b*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/d","B"
139,1,366,112,0.260000," ","int(1/(b*cos(d*x+c))^(7/2),x)","\frac{2 \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(12 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-24 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-12 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+24 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+3 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-8 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b}}{5 b^{4} \sin \left(\frac{d x}{2}+\frac{c}{2}\right)^{3} \left(8 \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-12 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+6 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \sqrt{b \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}\, d}"," ",0,"2/5*(b*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)/b^4/sin(1/2*d*x+1/2*c)^3/(8*sin(1/2*d*x+1/2*c)^6-12*sin(1/2*d*x+1/2*c)^4+6*sin(1/2*d*x+1/2*c)^2-1)*(12*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^4-24*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6-12*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^2+24*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-8*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c))*(-2*sin(1/2*d*x+1/2*c)^4*b+sin(1/2*d*x+1/2*c)^2*b)^(1/2)/(b*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/d","B"
140,1,62,80,0.180000," ","int(cos(d*x+c)^(7/2)*(b*cos(d*x+c))^(1/2),x)","\frac{\sqrt{b \cos \left(d x +c \right)}\, \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)}{8 d \sqrt{\cos \left(d x +c \right)}}"," ",0,"1/8/d*(b*cos(d*x+c))^(1/2)*(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)^(1/2)","A"
141,1,40,60,0.112000," ","int(cos(d*x+c)^(5/2)*(b*cos(d*x+c))^(1/2),x)","\frac{\left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{b \cos \left(d x +c \right)}}{3 d \sqrt{\cos \left(d x +c \right)}}"," ",0,"1/3/d*(2+cos(d*x+c)^2)*sin(d*x+c)*(b*cos(d*x+c))^(1/2)/cos(d*x+c)^(1/2)","A"
142,1,42,51,0.118000," ","int(cos(d*x+c)^(3/2)*(b*cos(d*x+c))^(1/2),x)","\frac{\sqrt{b \cos \left(d x +c \right)}\, \left(\cos \left(d x +c \right) \sin \left(d x +c \right)+d x +c \right)}{2 d \sqrt{\cos \left(d x +c \right)}}"," ",0,"1/2/d*(b*cos(d*x+c))^(1/2)*(cos(d*x+c)*sin(d*x+c)+d*x+c)/cos(d*x+c)^(1/2)","A"
143,1,29,28,0.112000," ","int(cos(d*x+c)^(1/2)*(b*cos(d*x+c))^(1/2),x)","\frac{\sin \left(d x +c \right) \sqrt{b \cos \left(d x +c \right)}}{d \sqrt{\cos \left(d x +c \right)}}"," ",0,"sin(d*x+c)*(b*cos(d*x+c))^(1/2)/d/cos(d*x+c)^(1/2)","A"
144,1,28,20,0.083000," ","int((b*cos(d*x+c))^(1/2)/cos(d*x+c)^(1/2),x)","\frac{\sqrt{b \cos \left(d x +c \right)}\, \left(d x +c \right)}{d \sqrt{\cos \left(d x +c \right)}}"," ",0,"1/d*(b*cos(d*x+c))^(1/2)/cos(d*x+c)^(1/2)*(d*x+c)","A"
145,1,42,29,0.107000," ","int((b*cos(d*x+c))^(1/2)/cos(d*x+c)^(3/2),x)","-\frac{2 \arctanh \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \sqrt{b \cos \left(d x +c \right)}}{d \sqrt{\cos \left(d x +c \right)}}"," ",0,"-2/d*arctanh((-1+cos(d*x+c))/sin(d*x+c))*(b*cos(d*x+c))^(1/2)/cos(d*x+c)^(1/2)","A"
146,1,29,28,0.115000," ","int((b*cos(d*x+c))^(1/2)/cos(d*x+c)^(5/2),x)","\frac{\sin \left(d x +c \right) \sqrt{b \cos \left(d x +c \right)}}{d \cos \left(d x +c \right)^{\frac{3}{2}}}"," ",0,"sin(d*x+c)*(b*cos(d*x+c))^(1/2)/d/cos(d*x+c)^(3/2)","A"
147,1,104,60,0.141000," ","int((b*cos(d*x+c))^(1/2)/cos(d*x+c)^(7/2),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) \sqrt{b \cos \left(d x +c \right)}}{2 d \cos \left(d x +c \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))*(b*cos(d*x+c))^(1/2)/cos(d*x+c)^(5/2)","A"
148,1,42,60,0.124000," ","int((b*cos(d*x+c))^(1/2)/cos(d*x+c)^(9/2),x)","\frac{\left(2 \left(\cos^{2}\left(d x +c \right)\right)+1\right) \sqrt{b \cos \left(d x +c \right)}\, \sin \left(d x +c \right)}{3 d \cos \left(d x +c \right)^{\frac{7}{2}}}"," ",0,"1/3/d*(2*cos(d*x+c)^2+1)*(b*cos(d*x+c))^(1/2)*sin(d*x+c)/cos(d*x+c)^(7/2)","A"
149,1,121,89,0.197000," ","int((b*cos(d*x+c))^(1/2)/cos(d*x+c)^(11/2),x)","-\frac{\left(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^{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^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)-2 \sin \left(d x +c \right)\right) \sqrt{b \cos \left(d x +c \right)}}{8 d \cos \left(d x +c \right)^{\frac{9}{2}}}"," ",0,"-1/8/d*(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)^4*ln(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))-3*cos(d*x+c)^2*sin(d*x+c)-2*sin(d*x+c))*(b*cos(d*x+c))^(1/2)/cos(d*x+c)^(9/2)","A"
150,1,62,83,0.138000," ","int(cos(d*x+c)^(5/2)*(b*cos(d*x+c))^(3/2),x)","\frac{\left(b \cos \left(d x +c \right)\right)^{\frac{3}{2}} \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)}{8 d \cos \left(d x +c \right)^{\frac{3}{2}}}"," ",0,"1/8/d*(b*cos(d*x+c))^(3/2)*(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)^(3/2)","A"
151,1,40,62,0.084000," ","int(cos(d*x+c)^(3/2)*(b*cos(d*x+c))^(3/2),x)","\frac{\left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \left(b \cos \left(d x +c \right)\right)^{\frac{3}{2}}}{3 d \cos \left(d x +c \right)^{\frac{3}{2}}}"," ",0,"1/3/d*(2+cos(d*x+c)^2)*sin(d*x+c)*(b*cos(d*x+c))^(3/2)/cos(d*x+c)^(3/2)","A"
152,1,42,53,0.096000," ","int(cos(d*x+c)^(1/2)*(b*cos(d*x+c))^(3/2),x)","\frac{\left(b \cos \left(d x +c \right)\right)^{\frac{3}{2}} \left(\cos \left(d x +c \right) \sin \left(d x +c \right)+d x +c \right)}{2 d \cos \left(d x +c \right)^{\frac{3}{2}}}"," ",0,"1/2/d*(b*cos(d*x+c))^(3/2)*(cos(d*x+c)*sin(d*x+c)+d*x+c)/cos(d*x+c)^(3/2)","A"
153,1,29,29,0.097000," ","int((b*cos(d*x+c))^(3/2)/cos(d*x+c)^(1/2),x)","\frac{\left(b \cos \left(d x +c \right)\right)^{\frac{3}{2}} \sin \left(d x +c \right)}{d \cos \left(d x +c \right)^{\frac{3}{2}}}"," ",0,"1/d*(b*cos(d*x+c))^(3/2)*sin(d*x+c)/cos(d*x+c)^(3/2)","A"
154,1,28,21,0.058000," ","int((b*cos(d*x+c))^(3/2)/cos(d*x+c)^(3/2),x)","\frac{\left(b \cos \left(d x +c \right)\right)^{\frac{3}{2}} \left(d x +c \right)}{d \cos \left(d x +c \right)^{\frac{3}{2}}}"," ",0,"1/d*(b*cos(d*x+c))^(3/2)/cos(d*x+c)^(3/2)*(d*x+c)","A"
155,1,42,30,0.081000," ","int((b*cos(d*x+c))^(3/2)/cos(d*x+c)^(5/2),x)","-\frac{2 \arctanh \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \left(b \cos \left(d x +c \right)\right)^{\frac{3}{2}}}{d \cos \left(d x +c \right)^{\frac{3}{2}}}"," ",0,"-2/d*arctanh((-1+cos(d*x+c))/sin(d*x+c))*(b*cos(d*x+c))^(3/2)/cos(d*x+c)^(3/2)","A"
156,1,29,29,0.096000," ","int((b*cos(d*x+c))^(3/2)/cos(d*x+c)^(7/2),x)","\frac{\left(b \cos \left(d x +c \right)\right)^{\frac{3}{2}} \sin \left(d x +c \right)}{d \cos \left(d x +c \right)^{\frac{5}{2}}}"," ",0,"1/d*(b*cos(d*x+c))^(3/2)*sin(d*x+c)/cos(d*x+c)^(5/2)","A"
157,1,104,62,0.111000," ","int((b*cos(d*x+c))^(3/2)/cos(d*x+c)^(9/2),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(b \cos \left(d x +c \right)\right)^{\frac{3}{2}}}{2 d \cos \left(d x +c \right)^{\frac{7}{2}}}"," ",0,"-1/2/d*(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))*(b*cos(d*x+c))^(3/2)/cos(d*x+c)^(7/2)","A"
158,1,42,62,0.086000," ","int((b*cos(d*x+c))^(3/2)/cos(d*x+c)^(11/2),x)","\frac{\left(2 \left(\cos^{2}\left(d x +c \right)\right)+1\right) \left(b \cos \left(d x +c \right)\right)^{\frac{3}{2}} \sin \left(d x +c \right)}{3 d \cos \left(d x +c \right)^{\frac{9}{2}}}"," ",0,"1/3/d*(2*cos(d*x+c)^2+1)*(b*cos(d*x+c))^(3/2)*sin(d*x+c)/cos(d*x+c)^(9/2)","A"
159,1,121,92,0.140000," ","int((b*cos(d*x+c))^(3/2)/cos(d*x+c)^(13/2),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) \left(b \cos \left(d x +c \right)\right)^{\frac{3}{2}}}{8 d \cos \left(d x +c \right)^{\frac{11}{2}}}"," ",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))*(b*cos(d*x+c))^(3/2)/cos(d*x+c)^(11/2)","A"
160,1,52,100,0.121000," ","int(cos(d*x+c)^(5/2)*(b*cos(d*x+c))^(5/2),x)","\frac{\left(3 \left(\cos^{4}\left(d x +c \right)\right)+4 \left(\cos^{2}\left(d x +c \right)\right)+8\right) \sin \left(d x +c \right) \left(b \cos \left(d x +c \right)\right)^{\frac{5}{2}}}{15 d \cos \left(d x +c \right)^{\frac{5}{2}}}"," ",0,"1/15/d*(3*cos(d*x+c)^4+4*cos(d*x+c)^2+8)*sin(d*x+c)*(b*cos(d*x+c))^(5/2)/cos(d*x+c)^(5/2)","A"
161,1,62,89,0.121000," ","int(cos(d*x+c)^(3/2)*(b*cos(d*x+c))^(5/2),x)","\frac{\left(b \cos \left(d x +c \right)\right)^{\frac{5}{2}} \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)}{8 d \cos \left(d x +c \right)^{\frac{5}{2}}}"," ",0,"1/8/d*(b*cos(d*x+c))^(5/2)*(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)^(5/2)","A"
162,1,40,66,0.106000," ","int(cos(d*x+c)^(1/2)*(b*cos(d*x+c))^(5/2),x)","\frac{\left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \left(b \cos \left(d x +c \right)\right)^{\frac{5}{2}}}{3 d \cos \left(d x +c \right)^{\frac{5}{2}}}"," ",0,"1/3/d*(2+cos(d*x+c)^2)*sin(d*x+c)*(b*cos(d*x+c))^(5/2)/cos(d*x+c)^(5/2)","A"
163,1,42,57,0.116000," ","int((b*cos(d*x+c))^(5/2)/cos(d*x+c)^(1/2),x)","\frac{\left(\cos \left(d x +c \right) \sin \left(d x +c \right)+d x +c \right) \left(b \cos \left(d x +c \right)\right)^{\frac{5}{2}}}{2 d \cos \left(d x +c \right)^{\frac{5}{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)^(5/2)","A"
164,1,29,31,0.079000," ","int((b*cos(d*x+c))^(5/2)/cos(d*x+c)^(3/2),x)","\frac{\left(b \cos \left(d x +c \right)\right)^{\frac{5}{2}} \sin \left(d x +c \right)}{d \cos \left(d x +c \right)^{\frac{5}{2}}}"," ",0,"1/d*(b*cos(d*x+c))^(5/2)*sin(d*x+c)/cos(d*x+c)^(5/2)","A"
165,1,28,23,0.063000," ","int((b*cos(d*x+c))^(5/2)/cos(d*x+c)^(5/2),x)","\frac{\left(b \cos \left(d x +c \right)\right)^{\frac{5}{2}} \left(d x +c \right)}{d \cos \left(d x +c \right)^{\frac{5}{2}}}"," ",0,"1/d*(b*cos(d*x+c))^(5/2)/cos(d*x+c)^(5/2)*(d*x+c)","A"
166,1,42,32,0.082000," ","int((b*cos(d*x+c))^(5/2)/cos(d*x+c)^(7/2),x)","-\frac{2 \arctanh \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \left(b \cos \left(d x +c \right)\right)^{\frac{5}{2}}}{d \cos \left(d x +c \right)^{\frac{5}{2}}}"," ",0,"-2/d*arctanh((-1+cos(d*x+c))/sin(d*x+c))*(b*cos(d*x+c))^(5/2)/cos(d*x+c)^(5/2)","A"
167,1,29,31,0.084000," ","int((b*cos(d*x+c))^(5/2)/cos(d*x+c)^(9/2),x)","\frac{\left(b \cos \left(d x +c \right)\right)^{\frac{5}{2}} \sin \left(d x +c \right)}{d \cos \left(d x +c \right)^{\frac{7}{2}}}"," ",0,"1/d*(b*cos(d*x+c))^(5/2)*sin(d*x+c)/cos(d*x+c)^(7/2)","A"
168,1,104,66,0.110000," ","int((b*cos(d*x+c))^(5/2)/cos(d*x+c)^(11/2),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(b \cos \left(d x +c \right)\right)^{\frac{5}{2}}}{2 d \cos \left(d x +c \right)^{\frac{9}{2}}}"," ",0,"-1/2/d*(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))*(b*cos(d*x+c))^(5/2)/cos(d*x+c)^(9/2)","A"
169,1,42,66,0.104000," ","int((b*cos(d*x+c))^(5/2)/cos(d*x+c)^(13/2),x)","\frac{\left(2 \left(\cos^{2}\left(d x +c \right)\right)+1\right) \left(b \cos \left(d x +c \right)\right)^{\frac{5}{2}} \sin \left(d x +c \right)}{3 d \cos \left(d x +c \right)^{\frac{11}{2}}}"," ",0,"1/3/d*(2*cos(d*x+c)^2+1)*(b*cos(d*x+c))^(5/2)*sin(d*x+c)/cos(d*x+c)^(11/2)","A"
170,1,121,98,0.161000," ","int((b*cos(d*x+c))^(5/2)/cos(d*x+c)^(15/2),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) \left(b \cos \left(d x +c \right)\right)^{\frac{5}{2}}}{8 d \cos \left(d x +c \right)^{\frac{13}{2}}}"," ",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))*(b*cos(d*x+c))^(5/2)/cos(d*x+c)^(13/2)","A"
171,1,52,91,0.120000," ","int(cos(d*x+c)^(11/2)/(b*cos(d*x+c))^(1/2),x)","\frac{\left(3 \left(\cos^{4}\left(d x +c \right)\right)+4 \left(\cos^{2}\left(d x +c \right)\right)+8\right) \sin \left(d x +c \right) \left(\sqrt{\cos}\left(d x +c \right)\right)}{15 d \sqrt{b \cos \left(d x +c \right)}}"," ",0,"1/15/d*(3*cos(d*x+c)^4+4*cos(d*x+c)^2+8)*sin(d*x+c)*cos(d*x+c)^(1/2)/(b*cos(d*x+c))^(1/2)","A"
172,1,62,80,0.150000," ","int(cos(d*x+c)^(9/2)/(b*cos(d*x+c))^(1/2),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(\sqrt{\cos}\left(d x +c \right)\right)}{8 d \sqrt{b \cos \left(d x +c \right)}}"," ",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)^(1/2)/(b*cos(d*x+c))^(1/2)","A"
173,1,40,60,0.104000," ","int(cos(d*x+c)^(7/2)/(b*cos(d*x+c))^(1/2),x)","\frac{\left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \left(\sqrt{\cos}\left(d x +c \right)\right)}{3 d \sqrt{b \cos \left(d x +c \right)}}"," ",0,"1/3/d*(2+cos(d*x+c)^2)*sin(d*x+c)*cos(d*x+c)^(1/2)/(b*cos(d*x+c))^(1/2)","A"
174,1,42,51,0.130000," ","int(cos(d*x+c)^(5/2)/(b*cos(d*x+c))^(1/2),x)","\frac{\left(\cos \left(d x +c \right) \sin \left(d x +c \right)+d x +c \right) \left(\sqrt{\cos}\left(d x +c \right)\right)}{2 d \sqrt{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)^(1/2)/(b*cos(d*x+c))^(1/2)","A"
175,1,29,28,0.113000," ","int(cos(d*x+c)^(3/2)/(b*cos(d*x+c))^(1/2),x)","\frac{\sin \left(d x +c \right) \left(\sqrt{\cos}\left(d x +c \right)\right)}{d \sqrt{b \cos \left(d x +c \right)}}"," ",0,"sin(d*x+c)*cos(d*x+c)^(1/2)/d/(b*cos(d*x+c))^(1/2)","A"
176,1,28,20,0.078000," ","int(cos(d*x+c)^(1/2)/(b*cos(d*x+c))^(1/2),x)","\frac{\left(\sqrt{\cos}\left(d x +c \right)\right) \left(d x +c \right)}{d \sqrt{b \cos \left(d x +c \right)}}"," ",0,"1/d*cos(d*x+c)^(1/2)/(b*cos(d*x+c))^(1/2)*(d*x+c)","A"
177,1,42,29,0.101000," ","int(1/cos(d*x+c)^(1/2)/(b*cos(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) \left(\sqrt{\cos}\left(d x +c \right)\right)}{d \sqrt{b \cos \left(d x +c \right)}}"," ",0,"-2/d*arctanh((-1+cos(d*x+c))/sin(d*x+c))*cos(d*x+c)^(1/2)/(b*cos(d*x+c))^(1/2)","A"
178,1,29,28,0.115000," ","int(1/cos(d*x+c)^(3/2)/(b*cos(d*x+c))^(1/2),x)","\frac{\sin \left(d x +c \right)}{d \sqrt{\cos \left(d x +c \right)}\, \sqrt{b \cos \left(d x +c \right)}}"," ",0,"sin(d*x+c)/d/cos(d*x+c)^(1/2)/(b*cos(d*x+c))^(1/2)","A"
179,1,104,60,0.136000," ","int(1/cos(d*x+c)^(5/2)/(b*cos(d*x+c))^(1/2),x)","-\frac{\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)}{2 d \sqrt{b \cos \left(d x +c \right)}\, \cos \left(d x +c \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))/(b*cos(d*x+c))^(1/2)/cos(d*x+c)^(3/2)","A"
180,1,42,60,0.097000," ","int(1/cos(d*x+c)^(7/2)/(b*cos(d*x+c))^(1/2),x)","\frac{\sin \left(d x +c \right) \left(2 \left(\cos^{2}\left(d x +c \right)\right)+1\right)}{3 d \sqrt{b \cos \left(d x +c \right)}\, \cos \left(d x +c \right)^{\frac{5}{2}}}"," ",0,"1/3/d*sin(d*x+c)*(2*cos(d*x+c)^2+1)/(b*cos(d*x+c))^(1/2)/cos(d*x+c)^(5/2)","A"
181,1,121,89,0.151000," ","int(1/cos(d*x+c)^(9/2)/(b*cos(d*x+c))^(1/2),x)","\frac{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)}{8 d \sqrt{b \cos \left(d x +c \right)}\, \cos \left(d x +c \right)^{\frac{7}{2}}}"," ",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))/(b*cos(d*x+c))^(1/2)/cos(d*x+c)^(7/2)","A"
182,1,62,89,0.137000," ","int(cos(d*x+c)^(11/2)/(b*cos(d*x+c))^(3/2),x)","\frac{\left(\cos^{\frac{3}{2}}\left(d x +c \right)\right) \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)}{8 d \left(b \cos \left(d x +c \right)\right)^{\frac{3}{2}}}"," ",0,"1/8/d*cos(d*x+c)^(3/2)*(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)","A"
183,1,40,66,0.086000," ","int(cos(d*x+c)^(9/2)/(b*cos(d*x+c))^(3/2),x)","\frac{\left(2+\cos^{2}\left(d x +c \right)\right) \left(\cos^{\frac{3}{2}}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3 d \left(b \cos \left(d x +c \right)\right)^{\frac{3}{2}}}"," ",0,"1/3/d*(2+cos(d*x+c)^2)*cos(d*x+c)^(3/2)*sin(d*x+c)/(b*cos(d*x+c))^(3/2)","A"
184,1,42,57,0.107000," ","int(cos(d*x+c)^(7/2)/(b*cos(d*x+c))^(3/2),x)","\frac{\left(\cos^{\frac{3}{2}}\left(d x +c \right)\right) \left(\cos \left(d x +c \right) \sin \left(d x +c \right)+d x +c \right)}{2 d \left(b \cos \left(d x +c \right)\right)^{\frac{3}{2}}}"," ",0,"1/2/d*cos(d*x+c)^(3/2)*(cos(d*x+c)*sin(d*x+c)+d*x+c)/(b*cos(d*x+c))^(3/2)","A"
185,1,29,31,0.080000," ","int(cos(d*x+c)^(5/2)/(b*cos(d*x+c))^(3/2),x)","\frac{\sin \left(d x +c \right) \left(\cos^{\frac{3}{2}}\left(d x +c \right)\right)}{d \left(b \cos \left(d x +c \right)\right)^{\frac{3}{2}}}"," ",0,"1/d*sin(d*x+c)*cos(d*x+c)^(3/2)/(b*cos(d*x+c))^(3/2)","A"
186,1,28,23,0.080000," ","int(cos(d*x+c)^(3/2)/(b*cos(d*x+c))^(3/2),x)","\frac{\left(\cos^{\frac{3}{2}}\left(d x +c \right)\right) \left(d x +c \right)}{d \left(b \cos \left(d x +c \right)\right)^{\frac{3}{2}}}"," ",0,"1/d*cos(d*x+c)^(3/2)/(b*cos(d*x+c))^(3/2)*(d*x+c)","A"
187,1,42,32,0.110000," ","int(cos(d*x+c)^(1/2)/(b*cos(d*x+c))^(3/2),x)","-\frac{2 \arctanh \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right) \left(\cos^{\frac{3}{2}}\left(d x +c \right)\right)}{d \left(b \cos \left(d x +c \right)\right)^{\frac{3}{2}}}"," ",0,"-2/d*arctanh((-1+cos(d*x+c))/sin(d*x+c))*cos(d*x+c)^(3/2)/(b*cos(d*x+c))^(3/2)","A"
188,1,29,31,0.116000," ","int(1/cos(d*x+c)^(1/2)/(b*cos(d*x+c))^(3/2),x)","\frac{\left(\sqrt{\cos}\left(d x +c \right)\right) \sin \left(d x +c \right)}{d \left(b \cos \left(d x +c \right)\right)^{\frac{3}{2}}}"," ",0,"1/d*cos(d*x+c)^(1/2)*sin(d*x+c)/(b*cos(d*x+c))^(3/2)","A"
189,1,102,66,0.105000," ","int(1/cos(d*x+c)^(3/2)/(b*cos(d*x+c))^(3/2),x)","\frac{\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)-\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)+\sin \left(d x +c \right)}{2 d \left(b \cos \left(d x +c \right)\right)^{\frac{3}{2}} \sqrt{\cos \left(d x +c \right)}}"," ",0,"1/2/d*(cos(d*x+c)^2*ln(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))-cos(d*x+c)^2*ln(-(-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c))+sin(d*x+c))/(b*cos(d*x+c))^(3/2)/cos(d*x+c)^(1/2)","A"
190,1,42,66,0.107000," ","int(1/cos(d*x+c)^(5/2)/(b*cos(d*x+c))^(3/2),x)","\frac{\sin \left(d x +c \right) \left(2 \left(\cos^{2}\left(d x +c \right)\right)+1\right)}{3 d \left(b \cos \left(d x +c \right)\right)^{\frac{3}{2}} \cos \left(d x +c \right)^{\frac{3}{2}}}"," ",0,"1/3/d*sin(d*x+c)*(2*cos(d*x+c)^2+1)/(b*cos(d*x+c))^(3/2)/cos(d*x+c)^(3/2)","A"
191,1,121,98,0.167000," ","int(1/cos(d*x+c)^(7/2)/(b*cos(d*x+c))^(3/2),x)","\frac{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)}{8 d \left(b \cos \left(d x +c \right)\right)^{\frac{3}{2}} \cos \left(d x +c \right)^{\frac{5}{2}}}"," ",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))/(b*cos(d*x+c))^(3/2)/cos(d*x+c)^(5/2)","A"
192,1,62,89,0.151000," ","int(cos(d*x+c)^(13/2)/(b*cos(d*x+c))^(5/2),x)","\frac{\left(\cos^{\frac{5}{2}}\left(d x +c \right)\right) \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)}{8 d \left(b \cos \left(d x +c \right)\right)^{\frac{5}{2}}}"," ",0,"1/8/d*cos(d*x+c)^(5/2)*(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))^(5/2)","A"
193,1,40,66,0.097000," ","int(cos(d*x+c)^(11/2)/(b*cos(d*x+c))^(5/2),x)","\frac{\left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \left(\cos^{\frac{5}{2}}\left(d x +c \right)\right)}{3 d \left(b \cos \left(d x +c \right)\right)^{\frac{5}{2}}}"," ",0,"1/3/d*(2+cos(d*x+c)^2)*sin(d*x+c)*cos(d*x+c)^(5/2)/(b*cos(d*x+c))^(5/2)","A"
194,1,42,57,0.109000," ","int(cos(d*x+c)^(9/2)/(b*cos(d*x+c))^(5/2),x)","\frac{\left(\cos^{\frac{5}{2}}\left(d x +c \right)\right) \left(\cos \left(d x +c \right) \sin \left(d x +c \right)+d x +c \right)}{2 d \left(b \cos \left(d x +c \right)\right)^{\frac{5}{2}}}"," ",0,"1/2/d*cos(d*x+c)^(5/2)*(cos(d*x+c)*sin(d*x+c)+d*x+c)/(b*cos(d*x+c))^(5/2)","A"
195,1,29,31,0.097000," ","int(cos(d*x+c)^(7/2)/(b*cos(d*x+c))^(5/2),x)","\frac{\sin \left(d x +c \right) \left(\cos^{\frac{5}{2}}\left(d x +c \right)\right)}{d \left(b \cos \left(d x +c \right)\right)^{\frac{5}{2}}}"," ",0,"1/d*sin(d*x+c)*cos(d*x+c)^(5/2)/(b*cos(d*x+c))^(5/2)","A"
196,1,28,23,0.077000," ","int(cos(d*x+c)^(5/2)/(b*cos(d*x+c))^(5/2),x)","\frac{\left(\cos^{\frac{5}{2}}\left(d x +c \right)\right) \left(d x +c \right)}{d \left(b \cos \left(d x +c \right)\right)^{\frac{5}{2}}}"," ",0,"1/d*cos(d*x+c)^(5/2)/(b*cos(d*x+c))^(5/2)*(d*x+c)","A"
197,1,42,32,0.084000," ","int(cos(d*x+c)^(3/2)/(b*cos(d*x+c))^(5/2),x)","-\frac{2 \left(\cos^{\frac{5}{2}}\left(d x +c \right)\right) \arctanh \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}\right)}{d \left(b \cos \left(d x +c \right)\right)^{\frac{5}{2}}}"," ",0,"-2/d*cos(d*x+c)^(5/2)*arctanh((-1+cos(d*x+c))/sin(d*x+c))/(b*cos(d*x+c))^(5/2)","A"
198,1,29,31,0.119000," ","int(cos(d*x+c)^(1/2)/(b*cos(d*x+c))^(5/2),x)","\frac{\left(\cos^{\frac{3}{2}}\left(d x +c \right)\right) \sin \left(d x +c \right)}{d \left(b \cos \left(d x +c \right)\right)^{\frac{5}{2}}}"," ",0,"1/d*cos(d*x+c)^(3/2)*sin(d*x+c)/(b*cos(d*x+c))^(5/2)","A"
199,1,104,66,0.115000," ","int(1/cos(d*x+c)^(1/2)/(b*cos(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(\sqrt{\cos}\left(d x +c \right)\right)}{2 d \left(b \cos \left(d x +c \right)\right)^{\frac{5}{2}}}"," ",0,"-1/2/d*(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)^(1/2)/(b*cos(d*x+c))^(5/2)","A"
200,1,42,66,0.111000," ","int(1/cos(d*x+c)^(3/2)/(b*cos(d*x+c))^(5/2),x)","\frac{\sin \left(d x +c \right) \left(2 \left(\cos^{2}\left(d x +c \right)\right)+1\right)}{3 d \left(b \cos \left(d x +c \right)\right)^{\frac{5}{2}} \sqrt{\cos \left(d x +c \right)}}"," ",0,"1/3/d*sin(d*x+c)*(2*cos(d*x+c)^2+1)/(b*cos(d*x+c))^(5/2)/cos(d*x+c)^(1/2)","A"
201,1,121,98,0.155000," ","int(1/cos(d*x+c)^(5/2)/(b*cos(d*x+c))^(5/2),x)","-\frac{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^{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^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)-2 \sin \left(d x +c \right)}{8 d \left(b \cos \left(d x +c \right)\right)^{\frac{5}{2}} \cos \left(d x +c \right)^{\frac{3}{2}}}"," ",0,"-1/8/d*(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)^4*ln(-(-sin(d*x+c)-1+cos(d*x+c))/sin(d*x+c))-3*cos(d*x+c)^2*sin(d*x+c)-2*sin(d*x+c))/(b*cos(d*x+c))^(5/2)/cos(d*x+c)^(3/2)","A"
202,0,0,70,0.134000," ","int(cos(d*x+c)^m*(b*cos(d*x+c))^(1/3),x)","\int \left(\cos^{m}\left(d x +c \right)\right) \left(b \cos \left(d x +c \right)\right)^{\frac{1}{3}}\, dx"," ",0,"int(cos(d*x+c)^m*(b*cos(d*x+c))^(1/3),x)","F"
203,0,0,48,0.187000," ","int(cos(d*x+c)^2*(b*cos(d*x+c))^(1/3),x)","\int \left(\cos^{2}\left(d x +c \right)\right) \left(b \cos \left(d x +c \right)\right)^{\frac{1}{3}}\, dx"," ",0,"int(cos(d*x+c)^2*(b*cos(d*x+c))^(1/3),x)","F"
204,0,0,48,0.078000," ","int(cos(d*x+c)*(b*cos(d*x+c))^(1/3),x)","\int \cos \left(d x +c \right) \left(b \cos \left(d x +c \right)\right)^{\frac{1}{3}}\, dx"," ",0,"int(cos(d*x+c)*(b*cos(d*x+c))^(1/3),x)","F"
205,0,0,48,0.131000," ","int((b*cos(d*x+c))^(1/3),x)","\int \left(b \cos \left(d x +c \right)\right)^{\frac{1}{3}}\, dx"," ",0,"int((b*cos(d*x+c))^(1/3),x)","F"
206,0,0,45,0.129000," ","int((b*cos(d*x+c))^(1/3)*sec(d*x+c),x)","\int \left(b \cos \left(d x +c \right)\right)^{\frac{1}{3}} \sec \left(d x +c \right)\, dx"," ",0,"int((b*cos(d*x+c))^(1/3)*sec(d*x+c),x)","F"
207,0,0,46,0.108000," ","int((b*cos(d*x+c))^(1/3)*sec(d*x+c)^2,x)","\int \left(b \cos \left(d x +c \right)\right)^{\frac{1}{3}} \left(\sec^{2}\left(d x +c \right)\right)\, dx"," ",0,"int((b*cos(d*x+c))^(1/3)*sec(d*x+c)^2,x)","F"
208,0,0,48,0.118000," ","int((b*cos(d*x+c))^(1/3)*sec(d*x+c)^3,x)","\int \left(b \cos \left(d x +c \right)\right)^{\frac{1}{3}} \left(\sec^{3}\left(d x +c \right)\right)\, dx"," ",0,"int((b*cos(d*x+c))^(1/3)*sec(d*x+c)^3,x)","F"
209,0,0,70,0.090000," ","int(cos(d*x+c)^m*(b*cos(d*x+c))^(2/3),x)","\int \left(\cos^{m}\left(d x +c \right)\right) \left(b \cos \left(d x +c \right)\right)^{\frac{2}{3}}\, dx"," ",0,"int(cos(d*x+c)^m*(b*cos(d*x+c))^(2/3),x)","F"
210,0,0,48,0.157000," ","int(cos(d*x+c)^2*(b*cos(d*x+c))^(2/3),x)","\int \left(\cos^{2}\left(d x +c \right)\right) \left(b \cos \left(d x +c \right)\right)^{\frac{2}{3}}\, dx"," ",0,"int(cos(d*x+c)^2*(b*cos(d*x+c))^(2/3),x)","F"
211,0,0,48,0.071000," ","int(cos(d*x+c)*(b*cos(d*x+c))^(2/3),x)","\int \cos \left(d x +c \right) \left(b \cos \left(d x +c \right)\right)^{\frac{2}{3}}\, dx"," ",0,"int(cos(d*x+c)*(b*cos(d*x+c))^(2/3),x)","F"
212,0,0,48,0.091000," ","int((b*cos(d*x+c))^(2/3),x)","\int \left(b \cos \left(d x +c \right)\right)^{\frac{2}{3}}\, dx"," ",0,"int((b*cos(d*x+c))^(2/3),x)","F"
213,0,0,45,0.131000," ","int((b*cos(d*x+c))^(2/3)*sec(d*x+c),x)","\int \left(b \cos \left(d x +c \right)\right)^{\frac{2}{3}} \sec \left(d x +c \right)\, dx"," ",0,"int((b*cos(d*x+c))^(2/3)*sec(d*x+c),x)","F"
214,0,0,46,0.111000," ","int((b*cos(d*x+c))^(2/3)*sec(d*x+c)^2,x)","\int \left(b \cos \left(d x +c \right)\right)^{\frac{2}{3}} \left(\sec^{2}\left(d x +c \right)\right)\, dx"," ",0,"int((b*cos(d*x+c))^(2/3)*sec(d*x+c)^2,x)","F"
215,0,0,48,0.121000," ","int((b*cos(d*x+c))^(2/3)*sec(d*x+c)^3,x)","\int \left(b \cos \left(d x +c \right)\right)^{\frac{2}{3}} \left(\sec^{3}\left(d x +c \right)\right)\, dx"," ",0,"int((b*cos(d*x+c))^(2/3)*sec(d*x+c)^3,x)","F"
216,0,0,71,0.101000," ","int(cos(d*x+c)^m*(b*cos(d*x+c))^(4/3),x)","\int \left(\cos^{m}\left(d x +c \right)\right) \left(b \cos \left(d x +c \right)\right)^{\frac{4}{3}}\, dx"," ",0,"int(cos(d*x+c)^m*(b*cos(d*x+c))^(4/3),x)","F"
217,0,0,48,0.163000," ","int(cos(d*x+c)^2*(b*cos(d*x+c))^(4/3),x)","\int \left(\cos^{2}\left(d x +c \right)\right) \left(b \cos \left(d x +c \right)\right)^{\frac{4}{3}}\, dx"," ",0,"int(cos(d*x+c)^2*(b*cos(d*x+c))^(4/3),x)","F"
218,0,0,48,0.076000," ","int(cos(d*x+c)*(b*cos(d*x+c))^(4/3),x)","\int \cos \left(d x +c \right) \left(b \cos \left(d x +c \right)\right)^{\frac{4}{3}}\, dx"," ",0,"int(cos(d*x+c)*(b*cos(d*x+c))^(4/3),x)","F"
219,0,0,48,0.022000," ","int((b*cos(d*x+c))^(4/3),x)","\int \left(b \cos \left(d x +c \right)\right)^{\frac{4}{3}}\, dx"," ",0,"int((b*cos(d*x+c))^(4/3),x)","F"
220,0,0,45,0.103000," ","int((b*cos(d*x+c))^(4/3)*sec(d*x+c),x)","\int \left(b \cos \left(d x +c \right)\right)^{\frac{4}{3}} \sec \left(d x +c \right)\, dx"," ",0,"int((b*cos(d*x+c))^(4/3)*sec(d*x+c),x)","F"
221,0,0,46,0.123000," ","int((b*cos(d*x+c))^(4/3)*sec(d*x+c)^2,x)","\int \left(b \cos \left(d x +c \right)\right)^{\frac{4}{3}} \left(\sec^{2}\left(d x +c \right)\right)\, dx"," ",0,"int((b*cos(d*x+c))^(4/3)*sec(d*x+c)^2,x)","F"
222,0,0,48,0.102000," ","int((b*cos(d*x+c))^(4/3)*sec(d*x+c)^3,x)","\int \left(b \cos \left(d x +c \right)\right)^{\frac{4}{3}} \left(\sec^{3}\left(d x +c \right)\right)\, dx"," ",0,"int((b*cos(d*x+c))^(4/3)*sec(d*x+c)^3,x)","F"
223,0,0,70,0.069000," ","int(cos(d*x+c)^m/(b*cos(d*x+c))^(1/3),x)","\int \frac{\cos^{m}\left(d x +c \right)}{\left(b \cos \left(d x +c \right)\right)^{\frac{1}{3}}}\, dx"," ",0,"int(cos(d*x+c)^m/(b*cos(d*x+c))^(1/3),x)","F"
224,0,0,48,0.128000," ","int(cos(d*x+c)^2/(b*cos(d*x+c))^(1/3),x)","\int \frac{\cos^{2}\left(d x +c \right)}{\left(b \cos \left(d x +c \right)\right)^{\frac{1}{3}}}\, dx"," ",0,"int(cos(d*x+c)^2/(b*cos(d*x+c))^(1/3),x)","F"
225,0,0,48,0.092000," ","int(cos(d*x+c)/(b*cos(d*x+c))^(1/3),x)","\int \frac{\cos \left(d x +c \right)}{\left(b \cos \left(d x +c \right)\right)^{\frac{1}{3}}}\, dx"," ",0,"int(cos(d*x+c)/(b*cos(d*x+c))^(1/3),x)","F"
226,0,0,48,0.043000," ","int(1/(b*cos(d*x+c))^(1/3),x)","\int \frac{1}{\left(b \cos \left(d x +c \right)\right)^{\frac{1}{3}}}\, dx"," ",0,"int(1/(b*cos(d*x+c))^(1/3),x)","F"
227,0,0,45,0.084000," ","int(sec(d*x+c)/(b*cos(d*x+c))^(1/3),x)","\int \frac{\sec \left(d x +c \right)}{\left(b \cos \left(d x +c \right)\right)^{\frac{1}{3}}}\, dx"," ",0,"int(sec(d*x+c)/(b*cos(d*x+c))^(1/3),x)","F"
228,0,0,46,0.087000," ","int(sec(d*x+c)^2/(b*cos(d*x+c))^(1/3),x)","\int \frac{\sec^{2}\left(d x +c \right)}{\left(b \cos \left(d x +c \right)\right)^{\frac{1}{3}}}\, dx"," ",0,"int(sec(d*x+c)^2/(b*cos(d*x+c))^(1/3),x)","F"
229,0,0,48,0.128000," ","int(sec(d*x+c)^3/(b*cos(d*x+c))^(1/3),x)","\int \frac{\sec^{3}\left(d x +c \right)}{\left(b \cos \left(d x +c \right)\right)^{\frac{1}{3}}}\, dx"," ",0,"int(sec(d*x+c)^3/(b*cos(d*x+c))^(1/3),x)","F"
230,0,0,70,0.066000," ","int(cos(d*x+c)^m/(b*cos(d*x+c))^(2/3),x)","\int \frac{\cos^{m}\left(d x +c \right)}{\left(b \cos \left(d x +c \right)\right)^{\frac{2}{3}}}\, dx"," ",0,"int(cos(d*x+c)^m/(b*cos(d*x+c))^(2/3),x)","F"
231,0,0,48,0.135000," ","int(cos(d*x+c)^2/(b*cos(d*x+c))^(2/3),x)","\int \frac{\cos^{2}\left(d x +c \right)}{\left(b \cos \left(d x +c \right)\right)^{\frac{2}{3}}}\, dx"," ",0,"int(cos(d*x+c)^2/(b*cos(d*x+c))^(2/3),x)","F"
232,0,0,48,0.072000," ","int(cos(d*x+c)/(b*cos(d*x+c))^(2/3),x)","\int \frac{\cos \left(d x +c \right)}{\left(b \cos \left(d x +c \right)\right)^{\frac{2}{3}}}\, dx"," ",0,"int(cos(d*x+c)/(b*cos(d*x+c))^(2/3),x)","F"
233,0,0,48,0.033000," ","int(1/(b*cos(d*x+c))^(2/3),x)","\int \frac{1}{\left(b \cos \left(d x +c \right)\right)^{\frac{2}{3}}}\, dx"," ",0,"int(1/(b*cos(d*x+c))^(2/3),x)","F"
234,0,0,45,0.078000," ","int(sec(d*x+c)/(b*cos(d*x+c))^(2/3),x)","\int \frac{\sec \left(d x +c \right)}{\left(b \cos \left(d x +c \right)\right)^{\frac{2}{3}}}\, dx"," ",0,"int(sec(d*x+c)/(b*cos(d*x+c))^(2/3),x)","F"
235,0,0,46,0.086000," ","int(sec(d*x+c)^2/(b*cos(d*x+c))^(2/3),x)","\int \frac{\sec^{2}\left(d x +c \right)}{\left(b \cos \left(d x +c \right)\right)^{\frac{2}{3}}}\, dx"," ",0,"int(sec(d*x+c)^2/(b*cos(d*x+c))^(2/3),x)","F"
236,0,0,48,0.123000," ","int(sec(d*x+c)^3/(b*cos(d*x+c))^(2/3),x)","\int \frac{\sec^{3}\left(d x +c \right)}{\left(b \cos \left(d x +c \right)\right)^{\frac{2}{3}}}\, dx"," ",0,"int(sec(d*x+c)^3/(b*cos(d*x+c))^(2/3),x)","F"
237,0,0,71,0.072000," ","int(cos(d*x+c)^m/(b*cos(d*x+c))^(4/3),x)","\int \frac{\cos^{m}\left(d x +c \right)}{\left(b \cos \left(d x +c \right)\right)^{\frac{4}{3}}}\, dx"," ",0,"int(cos(d*x+c)^m/(b*cos(d*x+c))^(4/3),x)","F"
238,0,0,48,0.130000," ","int(cos(d*x+c)^2/(b*cos(d*x+c))^(4/3),x)","\int \frac{\cos^{2}\left(d x +c \right)}{\left(b \cos \left(d x +c \right)\right)^{\frac{4}{3}}}\, dx"," ",0,"int(cos(d*x+c)^2/(b*cos(d*x+c))^(4/3),x)","F"
239,0,0,48,0.092000," ","int(cos(d*x+c)/(b*cos(d*x+c))^(4/3),x)","\int \frac{\cos \left(d x +c \right)}{\left(b \cos \left(d x +c \right)\right)^{\frac{4}{3}}}\, dx"," ",0,"int(cos(d*x+c)/(b*cos(d*x+c))^(4/3),x)","F"
240,0,0,48,0.023000," ","int(1/(b*cos(d*x+c))^(4/3),x)","\int \frac{1}{\left(b \cos \left(d x +c \right)\right)^{\frac{4}{3}}}\, dx"," ",0,"int(1/(b*cos(d*x+c))^(4/3),x)","F"
241,0,0,45,0.082000," ","int(sec(d*x+c)/(b*cos(d*x+c))^(4/3),x)","\int \frac{\sec \left(d x +c \right)}{\left(b \cos \left(d x +c \right)\right)^{\frac{4}{3}}}\, dx"," ",0,"int(sec(d*x+c)/(b*cos(d*x+c))^(4/3),x)","F"
242,0,0,46,0.099000," ","int(sec(d*x+c)^2/(b*cos(d*x+c))^(4/3),x)","\int \frac{\sec^{2}\left(d x +c \right)}{\left(b \cos \left(d x +c \right)\right)^{\frac{4}{3}}}\, dx"," ",0,"int(sec(d*x+c)^2/(b*cos(d*x+c))^(4/3),x)","F"
243,0,0,48,0.110000," ","int(sec(d*x+c)^3/(b*cos(d*x+c))^(4/3),x)","\int \frac{\sec^{3}\left(d x +c \right)}{\left(b \cos \left(d x +c \right)\right)^{\frac{4}{3}}}\, dx"," ",0,"int(sec(d*x+c)^3/(b*cos(d*x+c))^(4/3),x)","F"
244,0,0,80,0.891000," ","int((a*cos(f*x+e))^m*(b*cos(f*x+e))^n,x)","\int \left(a \cos \left(f x +e \right)\right)^{m} \left(b \cos \left(f x +e \right)\right)^{n}\, dx"," ",0,"int((a*cos(f*x+e))^m*(b*cos(f*x+e))^n,x)","F"
245,0,0,63,1.330000," ","int(cos(d*x+c)^2*(b*cos(d*x+c))^n,x)","\int \left(\cos^{2}\left(d x +c \right)\right) \left(b \cos \left(d x +c \right)\right)^{n}\, dx"," ",0,"int(cos(d*x+c)^2*(b*cos(d*x+c))^n,x)","F"
246,0,0,63,1.147000," ","int(cos(d*x+c)*(b*cos(d*x+c))^n,x)","\int \cos \left(d x +c \right) \left(b \cos \left(d x +c \right)\right)^{n}\, dx"," ",0,"int(cos(d*x+c)*(b*cos(d*x+c))^n,x)","F"
247,0,0,63,0.231000," ","int((b*cos(d*x+c))^n,x)","\int \left(b \cos \left(d x +c \right)\right)^{n}\, dx"," ",0,"int((b*cos(d*x+c))^n,x)","F"
248,0,0,54,0.479000," ","int((b*cos(d*x+c))^n*sec(d*x+c),x)","\int \left(b \cos \left(d x +c \right)\right)^{n} \sec \left(d x +c \right)\, dx"," ",0,"int((b*cos(d*x+c))^n*sec(d*x+c),x)","F"
249,0,0,62,0.402000," ","int((b*cos(d*x+c))^n*sec(d*x+c)^2,x)","\int \left(b \cos \left(d x +c \right)\right)^{n} \left(\sec^{2}\left(d x +c \right)\right)\, dx"," ",0,"int((b*cos(d*x+c))^n*sec(d*x+c)^2,x)","F"
250,0,0,62,0.568000," ","int((b*cos(d*x+c))^n*sec(d*x+c)^3,x)","\int \left(b \cos \left(d x +c \right)\right)^{n} \left(\sec^{3}\left(d x +c \right)\right)\, dx"," ",0,"int((b*cos(d*x+c))^n*sec(d*x+c)^3,x)","F"
251,0,0,64,0.341000," ","int((b*cos(d*x+c))^n*sec(d*x+c)^4,x)","\int \left(b \cos \left(d x +c \right)\right)^{n} \left(\sec^{4}\left(d x +c \right)\right)\, dx"," ",0,"int((b*cos(d*x+c))^n*sec(d*x+c)^4,x)","F"
252,0,0,68,0.132000," ","int(cos(d*x+c)^(5/2)*(b*cos(d*x+c))^n,x)","\int \left(\cos^{\frac{5}{2}}\left(d x +c \right)\right) \left(b \cos \left(d x +c \right)\right)^{n}\, dx"," ",0,"int(cos(d*x+c)^(5/2)*(b*cos(d*x+c))^n,x)","F"
253,0,0,68,0.104000," ","int(cos(d*x+c)^(3/2)*(b*cos(d*x+c))^n,x)","\int \left(\cos^{\frac{3}{2}}\left(d x +c \right)\right) \left(b \cos \left(d x +c \right)\right)^{n}\, dx"," ",0,"int(cos(d*x+c)^(3/2)*(b*cos(d*x+c))^n,x)","F"
254,0,0,68,0.124000," ","int(cos(d*x+c)^(1/2)*(b*cos(d*x+c))^n,x)","\int \left(\sqrt{\cos}\left(d x +c \right)\right) \left(b \cos \left(d x +c \right)\right)^{n}\, dx"," ",0,"int(cos(d*x+c)^(1/2)*(b*cos(d*x+c))^n,x)","F"
255,0,0,68,0.099000," ","int((b*cos(d*x+c))^n/cos(d*x+c)^(1/2),x)","\int \frac{\left(b \cos \left(d x +c \right)\right)^{n}}{\sqrt{\cos \left(d x +c \right)}}\, dx"," ",0,"int((b*cos(d*x+c))^n/cos(d*x+c)^(1/2),x)","F"
256,0,0,68,0.096000," ","int((b*cos(d*x+c))^n/cos(d*x+c)^(3/2),x)","\int \frac{\left(b \cos \left(d x +c \right)\right)^{n}}{\cos \left(d x +c \right)^{\frac{3}{2}}}\, dx"," ",0,"int((b*cos(d*x+c))^n/cos(d*x+c)^(3/2),x)","F"
257,0,0,68,0.096000," ","int((b*cos(d*x+c))^n/cos(d*x+c)^(5/2),x)","\int \frac{\left(b \cos \left(d x +c \right)\right)^{n}}{\cos \left(d x +c \right)^{\frac{5}{2}}}\, dx"," ",0,"int((b*cos(d*x+c))^n/cos(d*x+c)^(5/2),x)","F"
258,0,0,68,0.092000," ","int((b*cos(d*x+c))^n/cos(d*x+c)^(7/2),x)","\int \frac{\left(b \cos \left(d x +c \right)\right)^{n}}{\cos \left(d x +c \right)^{\frac{7}{2}}}\, dx"," ",0,"int((b*cos(d*x+c))^n/cos(d*x+c)^(7/2),x)","F"
259,0,0,68,0.085000," ","int((b*cos(d*x+c))^n/cos(d*x+c)^(9/2),x)","\int \frac{\left(b \cos \left(d x +c \right)\right)^{n}}{\cos \left(d x +c \right)^{\frac{9}{2}}}\, dx"," ",0,"int((b*cos(d*x+c))^n/cos(d*x+c)^(9/2),x)","F"
260,0,0,82,0.842000," ","int((a*cos(f*x+e))^m*(b*sec(f*x+e))^n,x)","\int \left(a \cos \left(f x +e \right)\right)^{m} \left(b \sec \left(f x +e \right)\right)^{n}\, dx"," ",0,"int((a*cos(f*x+e))^m*(b*sec(f*x+e))^n,x)","F"
261,1,14,13,0.038000," ","int(cos(b*x+a)*csc(b*x+a)^(1/2),x)","\frac{2}{b \sqrt{\csc \left(b x +a \right)}}"," ",0,"2/b/csc(b*x+a)^(1/2)","A"
262,1,14,13,0.023000," ","int(cos(b*x+a)/csc(b*x+a)^(1/2),x)","\frac{2}{3 b \csc \left(b x +a \right)^{\frac{3}{2}}}"," ",0,"2/3/b/csc(b*x+a)^(3/2)","A"
263,1,88,87,0.160000," ","int(cos(b*x+a)^2*csc(b*x+a)^(1/2),x)","\frac{\frac{2 \sqrt{\sin \left(b x +a \right)+1}\, \sqrt{-2 \sin \left(b x +a \right)+2}\, \sqrt{-\sin \left(b x +a \right)}\, \EllipticF \left(\sqrt{\sin \left(b x +a \right)+1}, \frac{\sqrt{2}}{2}\right)}{3}+\frac{2 \left(\cos^{2}\left(b x +a \right)\right) \sin \left(b x +a \right)}{3}}{\cos \left(b x +a \right) \sqrt{\sin \left(b x +a \right)}\, b}"," ",0,"(2/3*(sin(b*x+a)+1)^(1/2)*(-2*sin(b*x+a)+2)^(1/2)*(-sin(b*x+a))^(1/2)*EllipticF((sin(b*x+a)+1)^(1/2),1/2*2^(1/2))+2/3*cos(b*x+a)^2*sin(b*x+a))/cos(b*x+a)/sin(b*x+a)^(1/2)/b","A"
264,1,142,87,0.140000," ","int(cos(b*x+a)^2/csc(b*x+a)^(1/2),x)","\frac{-\frac{2 \left(\sin^{4}\left(b x +a \right)\right)}{5}+\frac{2 \left(\sin^{2}\left(b x +a \right)\right)}{5}-\frac{4 \sqrt{\sin \left(b x +a \right)+1}\, \sqrt{-2 \sin \left(b x +a \right)+2}\, \sqrt{-\sin \left(b x +a \right)}\, \EllipticE \left(\sqrt{\sin \left(b x +a \right)+1}, \frac{\sqrt{2}}{2}\right)}{5}+\frac{2 \sqrt{\sin \left(b x +a \right)+1}\, \sqrt{-2 \sin \left(b x +a \right)+2}\, \sqrt{-\sin \left(b x +a \right)}\, \EllipticF \left(\sqrt{\sin \left(b x +a \right)+1}, \frac{\sqrt{2}}{2}\right)}{5}}{\cos \left(b x +a \right) \sqrt{\sin \left(b x +a \right)}\, b}"," ",0,"(-2/5*sin(b*x+a)^4+2/5*sin(b*x+a)^2-4/5*(sin(b*x+a)+1)^(1/2)*(-2*sin(b*x+a)+2)^(1/2)*(-sin(b*x+a))^(1/2)*EllipticE((sin(b*x+a)+1)^(1/2),1/2*2^(1/2))+2/5*(sin(b*x+a)+1)^(1/2)*(-2*sin(b*x+a)+2)^(1/2)*(-sin(b*x+a))^(1/2)*EllipticF((sin(b*x+a)+1)^(1/2),1/2*2^(1/2)))/cos(b*x+a)/sin(b*x+a)^(1/2)/b","A"
265,1,14,13,0.096000," ","int(cos(x)^3*csc(x)^(9/2),x)","-\frac{2}{7 \sin \left(x \right)^{\frac{7}{2}}}+\frac{2}{3 \sin \left(x \right)^{\frac{3}{2}}}"," ",0,"-2/7/sin(x)^(7/2)+2/3/sin(x)^(3/2)","A"
266,1,26,27,0.093000," ","int(cos(b*x+a)^3*csc(b*x+a)^(1/2),x)","\frac{-\frac{2 \left(\sin^{\frac{5}{2}}\left(b x +a \right)\right)}{5}+2 \left(\sqrt{\sin}\left(b x +a \right)\right)}{b}"," ",0,"(-2/5*sin(b*x+a)^(5/2)+2*sin(b*x+a)^(1/2))/b","A"
267,1,26,27,0.076000," ","int(cos(b*x+a)^3/csc(b*x+a)^(1/2),x)","\frac{-\frac{2 \left(\sin^{\frac{7}{2}}\left(b x +a \right)\right)}{7}+\frac{2 \left(\sin^{\frac{3}{2}}\left(b x +a \right)\right)}{3}}{b}"," ",0,"(-2/7*sin(b*x+a)^(7/2)+2/3*sin(b*x+a)^(3/2))/b","A"
268,1,100,108,0.159000," ","int(cos(b*x+a)^4*csc(b*x+a)^(1/2),x)","\frac{\frac{2 \left(\sin^{5}\left(b x +a \right)\right)}{7}-\frac{8 \left(\sin^{3}\left(b x +a \right)\right)}{7}+\frac{6 \sin \left(b x +a \right)}{7}+\frac{4 \sqrt{\sin \left(b x +a \right)+1}\, \sqrt{-2 \sin \left(b x +a \right)+2}\, \sqrt{-\sin \left(b x +a \right)}\, \EllipticF \left(\sqrt{\sin \left(b x +a \right)+1}, \frac{\sqrt{2}}{2}\right)}{7}}{\cos \left(b x +a \right) \sqrt{\sin \left(b x +a \right)}\, b}"," ",0,"(2/7*sin(b*x+a)^5-8/7*sin(b*x+a)^3+6/7*sin(b*x+a)+4/7*(sin(b*x+a)+1)^(1/2)*(-2*sin(b*x+a)+2)^(1/2)*(-sin(b*x+a))^(1/2)*EllipticF((sin(b*x+a)+1)^(1/2),1/2*2^(1/2)))/cos(b*x+a)/sin(b*x+a)^(1/2)/b","A"
269,1,152,108,0.140000," ","int(cos(b*x+a)^4/csc(b*x+a)^(1/2),x)","\frac{-\frac{2 \left(\cos^{6}\left(b x +a \right)\right)}{9}-\frac{8 \sqrt{\sin \left(b x +a \right)+1}\, \sqrt{-2 \sin \left(b x +a \right)+2}\, \sqrt{-\sin \left(b x +a \right)}\, \EllipticE \left(\sqrt{\sin \left(b x +a \right)+1}, \frac{\sqrt{2}}{2}\right)}{15}+\frac{4 \sqrt{\sin \left(b x +a \right)+1}\, \sqrt{-2 \sin \left(b x +a \right)+2}\, \sqrt{-\sin \left(b x +a \right)}\, \EllipticF \left(\sqrt{\sin \left(b x +a \right)+1}, \frac{\sqrt{2}}{2}\right)}{15}-\frac{2 \left(\cos^{4}\left(b x +a \right)\right)}{45}+\frac{4 \left(\cos^{2}\left(b x +a \right)\right)}{15}}{\cos \left(b x +a \right) \sqrt{\sin \left(b x +a \right)}\, b}"," ",0,"(-2/9*cos(b*x+a)^6-8/15*(sin(b*x+a)+1)^(1/2)*(-2*sin(b*x+a)+2)^(1/2)*(-sin(b*x+a))^(1/2)*EllipticE((sin(b*x+a)+1)^(1/2),1/2*2^(1/2))+4/15*(sin(b*x+a)+1)^(1/2)*(-2*sin(b*x+a)+2)^(1/2)*(-sin(b*x+a))^(1/2)*EllipticF((sin(b*x+a)+1)^(1/2),1/2*2^(1/2))-2/45*cos(b*x+a)^4+4/15*cos(b*x+a)^2)/cos(b*x+a)/sin(b*x+a)^(1/2)/b","A"
270,1,7,6,0.020000," ","int(cos(x)*csc(x)^(7/3),x)","-\frac{3 \left(\csc^{\frac{4}{3}}\left(x \right)\right)}{4}"," ",0,"-3/4*csc(x)^(4/3)","A"
271,1,28,28,0.175000," ","int(csc(b*x+a)^(1/2)*sec(b*x+a),x)","\frac{\arctanh \left(\sqrt{\sin}\left(b x +a \right)\right)}{b}+\frac{\arctan \left(\sqrt{\sin}\left(b x +a \right)\right)}{b}"," ",0,"1/b*arctanh(sin(b*x+a)^(1/2))+1/b*arctan(sin(b*x+a)^(1/2))","A"
272,1,48,27,0.188000," ","int(sec(b*x+a)/csc(b*x+a)^(1/2),x)","-\frac{\ln \left(\sqrt{\sin}\left(b x +a \right)-1\right)}{2 b}+\frac{\ln \left(\sqrt{\sin}\left(b x +a \right)+1\right)}{2 b}-\frac{\arctan \left(\sqrt{\sin}\left(b x +a \right)\right)}{b}"," ",0,"-1/2/b*ln(sin(b*x+a)^(1/2)-1)+1/2/b*ln(sin(b*x+a)^(1/2)+1)-1/b*arctan(sin(b*x+a)^(1/2))","A"
273,1,123,86,0.188000," ","int(csc(b*x+a)^(1/2)*sec(b*x+a)^2,x)","\frac{\sqrt{\left(\cos^{2}\left(b x +a \right)\right) \sin \left(b x +a \right)}\, \left(\sqrt{\sin \left(b x +a \right)+1}\, \sqrt{-2 \sin \left(b x +a \right)+2}\, \sqrt{-\sin \left(b x +a \right)}\, \EllipticF \left(\sqrt{\sin \left(b x +a \right)+1}, \frac{\sqrt{2}}{2}\right)+2 \sin \left(b x +a \right)\right)}{2 \sqrt{-\sin \left(b x +a \right) \left(\sin \left(b x +a \right)-1\right) \left(\sin \left(b x +a \right)+1\right)}\, \cos \left(b x +a \right) \sqrt{\sin \left(b x +a \right)}\, b}"," ",0,"1/2*(cos(b*x+a)^2*sin(b*x+a))^(1/2)*((sin(b*x+a)+1)^(1/2)*(-2*sin(b*x+a)+2)^(1/2)*(-sin(b*x+a))^(1/2)*EllipticF((sin(b*x+a)+1)^(1/2),1/2*2^(1/2))+2*sin(b*x+a))/(-sin(b*x+a)*(sin(b*x+a)-1)*(sin(b*x+a)+1))^(1/2)/cos(b*x+a)/sin(b*x+a)^(1/2)/b","A"
274,1,177,85,0.192000," ","int(sec(b*x+a)^2/csc(b*x+a)^(1/2),x)","\frac{\sqrt{\left(\cos^{2}\left(b x +a \right)\right) \sin \left(b x +a \right)}\, \left(2 \sqrt{\sin \left(b x +a \right)+1}\, \sqrt{-2 \sin \left(b x +a \right)+2}\, \sqrt{-\sin \left(b x +a \right)}\, \EllipticE \left(\sqrt{\sin \left(b x +a \right)+1}, \frac{\sqrt{2}}{2}\right)-\sqrt{\sin \left(b x +a \right)+1}\, \sqrt{-2 \sin \left(b x +a \right)+2}\, \sqrt{-\sin \left(b x +a \right)}\, \EllipticF \left(\sqrt{\sin \left(b x +a \right)+1}, \frac{\sqrt{2}}{2}\right)-2 \left(\cos^{2}\left(b x +a \right)\right)+2\right)}{2 \sqrt{-\sin \left(b x +a \right) \left(\sin \left(b x +a \right)-1\right) \left(\sin \left(b x +a \right)+1\right)}\, \cos \left(b x +a \right) \sqrt{\sin \left(b x +a \right)}\, b}"," ",0,"1/2*(cos(b*x+a)^2*sin(b*x+a))^(1/2)*(2*(sin(b*x+a)+1)^(1/2)*(-2*sin(b*x+a)+2)^(1/2)*(-sin(b*x+a))^(1/2)*EllipticE((sin(b*x+a)+1)^(1/2),1/2*2^(1/2))-(sin(b*x+a)+1)^(1/2)*(-2*sin(b*x+a)+2)^(1/2)*(-sin(b*x+a))^(1/2)*EllipticF((sin(b*x+a)+1)^(1/2),1/2*2^(1/2))-2*cos(b*x+a)^2+2)/(-sin(b*x+a)*(sin(b*x+a)-1)*(sin(b*x+a)+1))^(1/2)/cos(b*x+a)/sin(b*x+a)^(1/2)/b","B"
275,1,73,50,0.189000," ","int(csc(b*x+a)^(1/2)*sec(b*x+a)^3,x)","\frac{-\left(3 \ln \left(\sqrt{\sin}\left(b x +a \right)-1\right)-3 \ln \left(\sqrt{\sin}\left(b x +a \right)+1\right)-6 \arctan \left(\sqrt{\sin}\left(b x +a \right)\right)\right) \left(\cos^{2}\left(b x +a \right)\right)+4 \left(\sqrt{\sin}\left(b x +a \right)\right)}{8 \cos \left(b x +a \right)^{2} b}"," ",0,"1/8*(-(3*ln(sin(b*x+a)^(1/2)-1)-3*ln(sin(b*x+a)^(1/2)+1)-6*arctan(sin(b*x+a)^(1/2)))*cos(b*x+a)^2+4*sin(b*x+a)^(1/2))/cos(b*x+a)^2/b","A"
276,1,71,50,0.173000," ","int(sec(b*x+a)^3/csc(b*x+a)^(1/2),x)","\frac{-\left(\ln \left(\sqrt{\sin}\left(b x +a \right)-1\right)-\ln \left(\sqrt{\sin}\left(b x +a \right)+1\right)+2 \arctan \left(\sqrt{\sin}\left(b x +a \right)\right)\right) \left(\cos^{2}\left(b x +a \right)\right)+4 \left(\sin^{\frac{3}{2}}\left(b x +a \right)\right)}{8 \cos \left(b x +a \right)^{2} b}"," ",0,"1/8*(-(ln(sin(b*x+a)^(1/2)-1)-ln(sin(b*x+a)^(1/2)+1)+2*arctan(sin(b*x+a)^(1/2)))*cos(b*x+a)^2+4*sin(b*x+a)^(3/2))/cos(b*x+a)^2/b","A"
277,1,168,108,0.201000," ","int(csc(b*x+a)^(1/2)*sec(b*x+a)^4,x)","-\frac{\sqrt{\left(\cos^{2}\left(b x +a \right)\right) \sin \left(b x +a \right)}\, \left(5 \sqrt{\sin \left(b x +a \right)+1}\, \sqrt{-2 \sin \left(b x +a \right)+2}\, \sqrt{-\sin \left(b x +a \right)}\, \EllipticF \left(\sqrt{\sin \left(b x +a \right)+1}, \frac{\sqrt{2}}{2}\right) \left(\cos^{2}\left(b x +a \right)\right)+10 \left(\cos^{2}\left(b x +a \right)\right) \sin \left(b x +a \right)+4 \sin \left(b x +a \right)\right)}{12 \left(\sin \left(b x +a \right)+1\right) \sqrt{-\sin \left(b x +a \right) \left(\sin \left(b x +a \right)-1\right) \left(\sin \left(b x +a \right)+1\right)}\, \left(\sin \left(b x +a \right)-1\right) \cos \left(b x +a \right) \sqrt{\sin \left(b x +a \right)}\, b}"," ",0,"-1/12*(cos(b*x+a)^2*sin(b*x+a))^(1/2)*(5*(sin(b*x+a)+1)^(1/2)*(-2*sin(b*x+a)+2)^(1/2)*(-sin(b*x+a))^(1/2)*EllipticF((sin(b*x+a)+1)^(1/2),1/2*2^(1/2))*cos(b*x+a)^2+10*cos(b*x+a)^2*sin(b*x+a)+4*sin(b*x+a))/(sin(b*x+a)+1)/(-sin(b*x+a)*(sin(b*x+a)-1)*(sin(b*x+a)+1))^(1/2)/(sin(b*x+a)-1)/cos(b*x+a)/sin(b*x+a)^(1/2)/b","A"
278,1,160,108,0.323000," ","int(sec(b*x+a)^4/csc(b*x+a)^(1/2),x)","\frac{6 \sqrt{\sin \left(b x +a \right)+1}\, \sqrt{-2 \sin \left(b x +a \right)+2}\, \sqrt{-\sin \left(b x +a \right)}\, \EllipticE \left(\sqrt{\sin \left(b x +a \right)+1}, \frac{\sqrt{2}}{2}\right) \left(\cos^{2}\left(b x +a \right)\right)-3 \sqrt{\sin \left(b x +a \right)+1}\, \sqrt{-2 \sin \left(b x +a \right)+2}\, \sqrt{-\sin \left(b x +a \right)}\, \EllipticF \left(\sqrt{\sin \left(b x +a \right)+1}, \frac{\sqrt{2}}{2}\right) \left(\cos^{2}\left(b x +a \right)\right)-6 \left(\cos^{4}\left(b x +a \right)\right)+2 \left(\cos^{2}\left(b x +a \right)\right)+4}{12 \sqrt{\sin \left(b x +a \right)}\, \cos \left(b x +a \right)^{3} b}"," ",0,"1/12/sin(b*x+a)^(1/2)/cos(b*x+a)^3*(6*(sin(b*x+a)+1)^(1/2)*(-2*sin(b*x+a)+2)^(1/2)*(-sin(b*x+a))^(1/2)*EllipticE((sin(b*x+a)+1)^(1/2),1/2*2^(1/2))*cos(b*x+a)^2-3*(sin(b*x+a)+1)^(1/2)*(-2*sin(b*x+a)+2)^(1/2)*(-sin(b*x+a))^(1/2)*EllipticF((sin(b*x+a)+1)^(1/2),1/2*2^(1/2))*cos(b*x+a)^2-6*cos(b*x+a)^4+2*cos(b*x+a)^2+4)/b","A"
279,0,0,64,0.219000," ","int((d*cos(b*x+a))^(3/2)*csc(b*x+a)^p,x)","\int \left(d \cos \left(b x +a \right)\right)^{\frac{3}{2}} \left(\csc^{p}\left(b x +a \right)\right)\, dx"," ",0,"int((d*cos(b*x+a))^(3/2)*csc(b*x+a)^p,x)","F"
280,0,0,64,0.141000," ","int((d*cos(b*x+a))^(1/2)*csc(b*x+a)^p,x)","\int \sqrt{d \cos \left(b x +a \right)}\, \left(\csc^{p}\left(b x +a \right)\right)\, dx"," ",0,"int((d*cos(b*x+a))^(1/2)*csc(b*x+a)^p,x)","F"
281,0,0,64,0.132000," ","int(csc(b*x+a)^p/(d*cos(b*x+a))^(1/2),x)","\int \frac{\csc^{p}\left(b x +a \right)}{\sqrt{d \cos \left(b x +a \right)}}\, dx"," ",0,"int(csc(b*x+a)^p/(d*cos(b*x+a))^(1/2),x)","F"
282,0,0,66,0.128000," ","int(csc(b*x+a)^p/(d*cos(b*x+a))^(3/2),x)","\int \frac{\csc^{p}\left(b x +a \right)}{\left(d \cos \left(b x +a \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int(csc(b*x+a)^p/(d*cos(b*x+a))^(3/2),x)","F"
283,0,0,66,0.148000," ","int(csc(b*x+a)^p/(d*cos(b*x+a))^(5/2),x)","\int \frac{\csc^{p}\left(b x +a \right)}{\left(d \cos \left(b x +a \right)\right)^{\frac{5}{2}}}\, dx"," ",0,"int(csc(b*x+a)^p/(d*cos(b*x+a))^(5/2),x)","F"
284,0,0,71,0.653000," ","int(cos(f*x+e)^m*csc(f*x+e)^n,x)","\int \left(\cos^{m}\left(f x +e \right)\right) \left(\csc^{n}\left(f x +e \right)\right)\, dx"," ",0,"int(cos(f*x+e)^m*csc(f*x+e)^n,x)","F"
285,0,0,74,0.555000," ","int((a*cos(f*x+e))^m*csc(f*x+e)^n,x)","\int \left(a \cos \left(f x +e \right)\right)^{m} \left(\csc^{n}\left(f x +e \right)\right)\, dx"," ",0,"int((a*cos(f*x+e))^m*csc(f*x+e)^n,x)","F"
286,0,0,74,0.627000," ","int(cos(f*x+e)^m*(b*csc(f*x+e))^n,x)","\int \left(\cos^{m}\left(f x +e \right)\right) \left(b \csc \left(f x +e \right)\right)^{n}\, dx"," ",0,"int(cos(f*x+e)^m*(b*csc(f*x+e))^n,x)","F"
287,0,0,77,0.661000," ","int((a*cos(f*x+e))^m*(b*csc(f*x+e))^n,x)","\int \left(a \cos \left(f x +e \right)\right)^{m} \left(b \csc \left(f x +e \right)\right)^{n}\, dx"," ",0,"int((a*cos(f*x+e))^m*(b*csc(f*x+e))^n,x)","F"
288,0,0,70,0.171000," ","int((a*cos(f*x+e))^m*(b*csc(f*x+e))^(7/2),x)","\int \left(a \cos \left(f x +e \right)\right)^{m} \left(b \csc \left(f x +e \right)\right)^{\frac{7}{2}}\, dx"," ",0,"int((a*cos(f*x+e))^m*(b*csc(f*x+e))^(7/2),x)","F"
289,0,0,68,0.170000," ","int((a*cos(f*x+e))^m*(b*csc(f*x+e))^(5/2),x)","\int \left(a \cos \left(f x +e \right)\right)^{m} \left(b \csc \left(f x +e \right)\right)^{\frac{5}{2}}\, dx"," ",0,"int((a*cos(f*x+e))^m*(b*csc(f*x+e))^(5/2),x)","F"
290,0,0,68,0.156000," ","int((a*cos(f*x+e))^m*(b*csc(f*x+e))^(3/2),x)","\int \left(a \cos \left(f x +e \right)\right)^{m} \left(b \csc \left(f x +e \right)\right)^{\frac{3}{2}}\, dx"," ",0,"int((a*cos(f*x+e))^m*(b*csc(f*x+e))^(3/2),x)","F"
291,0,0,70,0.157000," ","int((a*cos(f*x+e))^m*(b*csc(f*x+e))^(1/2),x)","\int \left(a \cos \left(f x +e \right)\right)^{m} \sqrt{b \csc \left(f x +e \right)}\, dx"," ",0,"int((a*cos(f*x+e))^m*(b*csc(f*x+e))^(1/2),x)","F"
292,0,0,70,0.140000," ","int((a*cos(f*x+e))^m/(b*csc(f*x+e))^(1/2),x)","\int \frac{\left(a \cos \left(f x +e \right)\right)^{m}}{\sqrt{b \csc \left(f x +e \right)}}\, dx"," ",0,"int((a*cos(f*x+e))^m/(b*csc(f*x+e))^(1/2),x)","F"
293,0,0,70,0.136000," ","int((a*cos(f*x+e))^m/(b*csc(f*x+e))^(3/2),x)","\int \frac{\left(a \cos \left(f x +e \right)\right)^{m}}{\left(b \csc \left(f x +e \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int((a*cos(f*x+e))^m/(b*csc(f*x+e))^(3/2),x)","F"
294,0,0,70,0.132000," ","int((a*cos(f*x+e))^m/(b*csc(f*x+e))^(5/2),x)","\int \frac{\left(a \cos \left(f x +e \right)\right)^{m}}{\left(b \csc \left(f x +e \right)\right)^{\frac{5}{2}}}\, dx"," ",0,"int((a*cos(f*x+e))^m/(b*csc(f*x+e))^(5/2),x)","F"