1,1,87,0,0.0559017,"\int \sec ^6(c+d x) \left(A+C \sec ^2(c+d x)\right) \, dx","Int[Sec[c + d*x]^6*(A + C*Sec[c + d*x]^2),x]","\frac{(7 A+6 C) \tan ^5(c+d x)}{35 d}+\frac{2 (7 A+6 C) \tan ^3(c+d x)}{21 d}+\frac{(7 A+6 C) \tan (c+d x)}{7 d}+\frac{C \tan (c+d x) \sec ^6(c+d x)}{7 d}","\frac{(7 A+6 C) \tan ^5(c+d x)}{35 d}+\frac{2 (7 A+6 C) \tan ^3(c+d x)}{21 d}+\frac{(7 A+6 C) \tan (c+d x)}{7 d}+\frac{C \tan (c+d x) \sec ^6(c+d x)}{7 d}",1,"((7*A + 6*C)*Tan[c + d*x])/(7*d) + (C*Sec[c + d*x]^6*Tan[c + d*x])/(7*d) + (2*(7*A + 6*C)*Tan[c + d*x]^3)/(21*d) + ((7*A + 6*C)*Tan[c + d*x]^5)/(35*d)","A",3,2,21,0.09524,1,"{4046, 3767}"
2,1,98,0,0.0631755,"\int \sec ^5(c+d x) \left(A+C \sec ^2(c+d x)\right) \, dx","Int[Sec[c + d*x]^5*(A + C*Sec[c + d*x]^2),x]","\frac{(6 A+5 C) \tanh ^{-1}(\sin (c+d x))}{16 d}+\frac{(6 A+5 C) \tan (c+d x) \sec ^3(c+d x)}{24 d}+\frac{(6 A+5 C) \tan (c+d x) \sec (c+d x)}{16 d}+\frac{C \tan (c+d x) \sec ^5(c+d x)}{6 d}","\frac{(6 A+5 C) \tanh ^{-1}(\sin (c+d x))}{16 d}+\frac{(6 A+5 C) \tan (c+d x) \sec ^3(c+d x)}{24 d}+\frac{(6 A+5 C) \tan (c+d x) \sec (c+d x)}{16 d}+\frac{C \tan (c+d x) \sec ^5(c+d x)}{6 d}",1,"((6*A + 5*C)*ArcTanh[Sin[c + d*x]])/(16*d) + ((6*A + 5*C)*Sec[c + d*x]*Tan[c + d*x])/(16*d) + ((6*A + 5*C)*Sec[c + d*x]^3*Tan[c + d*x])/(24*d) + (C*Sec[c + d*x]^5*Tan[c + d*x])/(6*d)","A",4,3,21,0.1429,1,"{4046, 3768, 3770}"
3,1,65,0,0.0439876,"\int \sec ^4(c+d x) \left(A+C \sec ^2(c+d x)\right) \, dx","Int[Sec[c + d*x]^4*(A + C*Sec[c + d*x]^2),x]","\frac{(5 A+4 C) \tan ^3(c+d x)}{15 d}+\frac{(5 A+4 C) \tan (c+d x)}{5 d}+\frac{C \tan (c+d x) \sec ^4(c+d x)}{5 d}","\frac{(5 A+4 C) \tan ^3(c+d x)}{15 d}+\frac{(5 A+4 C) \tan (c+d x)}{5 d}+\frac{C \tan (c+d x) \sec ^4(c+d x)}{5 d}",1,"((5*A + 4*C)*Tan[c + d*x])/(5*d) + (C*Sec[c + d*x]^4*Tan[c + d*x])/(5*d) + ((5*A + 4*C)*Tan[c + d*x]^3)/(15*d)","A",3,2,21,0.09524,1,"{4046, 3767}"
4,1,70,0,0.0467736,"\int \sec ^3(c+d x) \left(A+C \sec ^2(c+d x)\right) \, dx","Int[Sec[c + d*x]^3*(A + C*Sec[c + d*x]^2),x]","\frac{(4 A+3 C) \tanh ^{-1}(\sin (c+d x))}{8 d}+\frac{(4 A+3 C) \tan (c+d x) \sec (c+d x)}{8 d}+\frac{C \tan (c+d x) \sec ^3(c+d x)}{4 d}","\frac{(4 A+3 C) \tanh ^{-1}(\sin (c+d x))}{8 d}+\frac{(4 A+3 C) \tan (c+d x) \sec (c+d x)}{8 d}+\frac{C \tan (c+d x) \sec ^3(c+d x)}{4 d}",1,"((4*A + 3*C)*ArcTanh[Sin[c + d*x]])/(8*d) + ((4*A + 3*C)*Sec[c + d*x]*Tan[c + d*x])/(8*d) + (C*Sec[c + d*x]^3*Tan[c + d*x])/(4*d)","A",3,3,21,0.1429,1,"{4046, 3768, 3770}"
5,1,43,0,0.0404934,"\int \sec ^2(c+d x) \left(A+C \sec ^2(c+d x)\right) \, dx","Int[Sec[c + d*x]^2*(A + C*Sec[c + d*x]^2),x]","\frac{(3 A+2 C) \tan (c+d x)}{3 d}+\frac{C \tan (c+d x) \sec ^2(c+d x)}{3 d}","\frac{(3 A+2 C) \tan (c+d x)}{3 d}+\frac{C \tan (c+d x) \sec ^2(c+d x)}{3 d}",1,"((3*A + 2*C)*Tan[c + d*x])/(3*d) + (C*Sec[c + d*x]^2*Tan[c + d*x])/(3*d)","A",3,3,21,0.1429,1,"{4046, 3767, 8}"
6,1,40,0,0.0254462,"\int \sec (c+d x) \left(A+C \sec ^2(c+d x)\right) \, dx","Int[Sec[c + d*x]*(A + C*Sec[c + d*x]^2),x]","\frac{(2 A+C) \tanh ^{-1}(\sin (c+d x))}{2 d}+\frac{C \tan (c+d x) \sec (c+d x)}{2 d}","\frac{(2 A+C) \tanh ^{-1}(\sin (c+d x))}{2 d}+\frac{C \tan (c+d x) \sec (c+d x)}{2 d}",1,"((2*A + C)*ArcTanh[Sin[c + d*x]])/(2*d) + (C*Sec[c + d*x]*Tan[c + d*x])/(2*d)","A",2,2,19,0.1053,1,"{4046, 3770}"
7,1,15,0,0.0130266,"\int \left(A+C \sec ^2(c+d x)\right) \, dx","Int[A + C*Sec[c + d*x]^2,x]","A x+\frac{C \tan (c+d x)}{d}","A x+\frac{C \tan (c+d x)}{d}",1,"A*x + (C*Tan[c + d*x])/d","A",3,2,12,0.1667,1,"{3767, 8}"
8,1,24,0,0.0265544,"\int \cos (c+d x) \left(A+C \sec ^2(c+d x)\right) \, dx","Int[Cos[c + d*x]*(A + C*Sec[c + d*x]^2),x]","\frac{A \sin (c+d x)}{d}+\frac{C \tanh ^{-1}(\sin (c+d x))}{d}","\frac{A \sin (c+d x)}{d}+\frac{C \tanh ^{-1}(\sin (c+d x))}{d}",1,"(C*ArcTanh[Sin[c + d*x]])/d + (A*Sin[c + d*x])/d","A",2,2,19,0.1053,1,"{4045, 3770}"
9,1,31,0,0.0302677,"\int \cos ^2(c+d x) \left(A+C \sec ^2(c+d x)\right) \, dx","Int[Cos[c + d*x]^2*(A + C*Sec[c + d*x]^2),x]","\frac{A \sin (c+d x) \cos (c+d x)}{2 d}+\frac{1}{2} x (A+2 C)","\frac{A \sin (c+d x) \cos (c+d x)}{2 d}+\frac{1}{2} x (A+2 C)",1,"((A + 2*C)*x)/2 + (A*Cos[c + d*x]*Sin[c + d*x])/(2*d)","A",2,2,21,0.09524,1,"{4045, 8}"
10,1,30,0,0.0473099,"\int \cos ^3(c+d x) \left(A+C \sec ^2(c+d x)\right) \, dx","Int[Cos[c + d*x]^3*(A + C*Sec[c + d*x]^2),x]","\frac{(A+C) \sin (c+d x)}{d}-\frac{A \sin ^3(c+d x)}{3 d}","\frac{(A+C) \sin (c+d x)}{d}-\frac{A \sin ^3(c+d x)}{3 d}",1,"((A + C)*Sin[c + d*x])/d - (A*Sin[c + d*x]^3)/(3*d)","A",3,2,21,0.09524,1,"{4044, 3013}"
11,1,61,0,0.0435039,"\int \cos ^4(c+d x) \left(A+C \sec ^2(c+d x)\right) \, dx","Int[Cos[c + d*x]^4*(A + C*Sec[c + d*x]^2),x]","\frac{(3 A+4 C) \sin (c+d x) \cos (c+d x)}{8 d}+\frac{A \sin (c+d x) \cos ^3(c+d x)}{4 d}+\frac{1}{8} x (3 A+4 C)","\frac{(3 A+4 C) \sin (c+d x) \cos (c+d x)}{8 d}+\frac{A \sin (c+d x) \cos ^3(c+d x)}{4 d}+\frac{1}{8} x (3 A+4 C)",1,"((3*A + 4*C)*x)/8 + ((3*A + 4*C)*Cos[c + d*x]*Sin[c + d*x])/(8*d) + (A*Cos[c + d*x]^3*Sin[c + d*x])/(4*d)","A",3,3,21,0.1429,1,"{4045, 2635, 8}"
12,1,50,0,0.0676302,"\int \cos ^5(c+d x) \left(A+C \sec ^2(c+d x)\right) \, dx","Int[Cos[c + d*x]^5*(A + C*Sec[c + d*x]^2),x]","-\frac{(2 A+C) \sin ^3(c+d x)}{3 d}+\frac{(A+C) \sin (c+d x)}{d}+\frac{A \sin ^5(c+d x)}{5 d}","-\frac{(2 A+C) \sin ^3(c+d x)}{3 d}+\frac{(A+C) \sin (c+d x)}{d}+\frac{A \sin ^5(c+d x)}{5 d}",1,"((A + C)*Sin[c + d*x])/d - ((2*A + C)*Sin[c + d*x]^3)/(3*d) + (A*Sin[c + d*x]^5)/(5*d)","A",4,3,21,0.1429,1,"{4044, 3013, 373}"
13,1,89,0,0.0586294,"\int \cos ^6(c+d x) \left(A+C \sec ^2(c+d x)\right) \, dx","Int[Cos[c + d*x]^6*(A + C*Sec[c + d*x]^2),x]","\frac{(5 A+6 C) \sin (c+d x) \cos ^3(c+d x)}{24 d}+\frac{(5 A+6 C) \sin (c+d x) \cos (c+d x)}{16 d}+\frac{A \sin (c+d x) \cos ^5(c+d x)}{6 d}+\frac{1}{16} x (5 A+6 C)","\frac{(5 A+6 C) \sin (c+d x) \cos ^3(c+d x)}{24 d}+\frac{(5 A+6 C) \sin (c+d x) \cos (c+d x)}{16 d}+\frac{A \sin (c+d x) \cos ^5(c+d x)}{6 d}+\frac{1}{16} x (5 A+6 C)",1,"((5*A + 6*C)*x)/16 + ((5*A + 6*C)*Cos[c + d*x]*Sin[c + d*x])/(16*d) + ((5*A + 6*C)*Cos[c + d*x]^3*Sin[c + d*x])/(24*d) + (A*Cos[c + d*x]^5*Sin[c + d*x])/(6*d)","A",4,3,21,0.1429,1,"{4045, 2635, 8}"
14,1,26,0,0.0395476,"\int \sec ^m(c+d x) \left(-\frac{C m}{1+m}+C \sec ^2(c+d x)\right) \, dx","Int[Sec[c + d*x]^m*(-((C*m)/(1 + m)) + C*Sec[c + d*x]^2),x]","\frac{C \sin (c+d x) \sec ^{m+1}(c+d x)}{d (m+1)}","\frac{C \sin (c+d x) \sec ^{m+1}(c+d x)}{d (m+1)}",1,"(C*Sec[c + d*x]^(1 + m)*Sin[c + d*x])/(d*(1 + m))","A",1,1,29,0.03448,1,"{4043}"
15,1,25,0,0.0406406,"\int \sec ^m(c+d x) \left(A-\frac{A (1+m) \sec ^2(c+d x)}{m}\right) \, dx","Int[Sec[c + d*x]^m*(A - (A*(1 + m)*Sec[c + d*x]^2)/m),x]","-\frac{A \sin (c+d x) \sec ^{m+1}(c+d x)}{d m}","-\frac{A \sin (c+d x) \sec ^{m+1}(c+d x)}{d m}",1,"-((A*Sec[c + d*x]^(1 + m)*Sin[c + d*x])/(d*m))","A",1,1,28,0.03571,1,"{4043}"
16,1,110,0,0.0812271,"\int (b \sec (c+d x))^{5/2} \left(A+C \sec ^2(c+d x)\right) \, dx","Int[(b*Sec[c + d*x])^(5/2)*(A + C*Sec[c + d*x]^2),x]","\frac{2 b^2 (7 A+5 C) \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \sec (c+d x)}}{21 d}+\frac{2 b (7 A+5 C) \sin (c+d x) (b \sec (c+d x))^{3/2}}{21 d}+\frac{2 C \tan (c+d x) (b \sec (c+d x))^{5/2}}{7 d}","\frac{2 b^2 (7 A+5 C) \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \sec (c+d x)}}{21 d}+\frac{2 b (7 A+5 C) \sin (c+d x) (b \sec (c+d x))^{3/2}}{21 d}+\frac{2 C \tan (c+d x) (b \sec (c+d x))^{5/2}}{7 d}",1,"(2*b^2*(7*A + 5*C)*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2]*Sqrt[b*Sec[c + d*x]])/(21*d) + (2*b*(7*A + 5*C)*(b*Sec[c + d*x])^(3/2)*Sin[c + d*x])/(21*d) + (2*C*(b*Sec[c + d*x])^(5/2)*Tan[c + d*x])/(7*d)","A",4,4,25,0.1600,1,"{4046, 3768, 3771, 2641}"
17,1,110,0,0.0825354,"\int (b \sec (c+d x))^{3/2} \left(A+C \sec ^2(c+d x)\right) \, dx","Int[(b*Sec[c + d*x])^(3/2)*(A + C*Sec[c + d*x]^2),x]","-\frac{2 b^2 (5 A+3 C) E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{5 d \sqrt{\cos (c+d x)} \sqrt{b \sec (c+d x)}}+\frac{2 b (5 A+3 C) \sin (c+d x) \sqrt{b \sec (c+d x)}}{5 d}+\frac{2 C \tan (c+d x) (b \sec (c+d x))^{3/2}}{5 d}","-\frac{2 b^2 (5 A+3 C) E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{5 d \sqrt{\cos (c+d x)} \sqrt{b \sec (c+d x)}}+\frac{2 b (5 A+3 C) \sin (c+d x) \sqrt{b \sec (c+d x)}}{5 d}+\frac{2 C \tan (c+d x) (b \sec (c+d x))^{3/2}}{5 d}",1,"(-2*b^2*(5*A + 3*C)*EllipticE[(c + d*x)/2, 2])/(5*d*Sqrt[Cos[c + d*x]]*Sqrt[b*Sec[c + d*x]]) + (2*b*(5*A + 3*C)*Sqrt[b*Sec[c + d*x]]*Sin[c + d*x])/(5*d) + (2*C*(b*Sec[c + d*x])^(3/2)*Tan[c + d*x])/(5*d)","A",4,4,25,0.1600,1,"{4046, 3768, 3771, 2639}"
18,1,72,0,0.0539407,"\int \sqrt{b \sec (c+d x)} \left(A+C \sec ^2(c+d x)\right) \, dx","Int[Sqrt[b*Sec[c + d*x]]*(A + C*Sec[c + d*x]^2),x]","\frac{2 (3 A+C) \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \sec (c+d x)}}{3 d}+\frac{2 C \tan (c+d x) \sqrt{b \sec (c+d x)}}{3 d}","\frac{2 (3 A+C) \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \sec (c+d x)}}{3 d}+\frac{2 C \tan (c+d x) \sqrt{b \sec (c+d x)}}{3 d}",1,"(2*(3*A + C)*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2]*Sqrt[b*Sec[c + d*x]])/(3*d) + (2*C*Sqrt[b*Sec[c + d*x]]*Tan[c + d*x])/(3*d)","A",3,3,25,0.1200,1,"{4046, 3771, 2641}"
19,1,68,0,0.056838,"\int \frac{A+C \sec ^2(c+d x)}{\sqrt{b \sec (c+d x)}} \, dx","Int[(A + C*Sec[c + d*x]^2)/Sqrt[b*Sec[c + d*x]],x]","\frac{2 (A-C) E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{d \sqrt{\cos (c+d x)} \sqrt{b \sec (c+d x)}}+\frac{2 C \tan (c+d x)}{d \sqrt{b \sec (c+d x)}}","\frac{2 (A-C) E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{d \sqrt{\cos (c+d x)} \sqrt{b \sec (c+d x)}}+\frac{2 C \tan (c+d x)}{d \sqrt{b \sec (c+d x)}}",1,"(2*(A - C)*EllipticE[(c + d*x)/2, 2])/(d*Sqrt[Cos[c + d*x]]*Sqrt[b*Sec[c + d*x]]) + (2*C*Tan[c + d*x])/(d*Sqrt[b*Sec[c + d*x]])","A",3,3,25,0.1200,1,"{4046, 3771, 2639}"
20,1,75,0,0.0640951,"\int \frac{A+C \sec ^2(c+d x)}{(b \sec (c+d x))^{3/2}} \, dx","Int[(A + C*Sec[c + d*x]^2)/(b*Sec[c + d*x])^(3/2),x]","\frac{2 (A+3 C) \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \sec (c+d x)}}{3 b^2 d}+\frac{2 A \tan (c+d x)}{3 d (b \sec (c+d x))^{3/2}}","\frac{2 (A+3 C) \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \sec (c+d x)}}{3 b^2 d}+\frac{2 A \tan (c+d x)}{3 d (b \sec (c+d x))^{3/2}}",1,"(2*(A + 3*C)*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2]*Sqrt[b*Sec[c + d*x]])/(3*b^2*d) + (2*A*Tan[c + d*x])/(3*d*(b*Sec[c + d*x])^(3/2))","A",3,3,25,0.1200,1,"{4045, 3771, 2641}"
21,1,77,0,0.0636336,"\int \frac{A+C \sec ^2(c+d x)}{(b \sec (c+d x))^{5/2}} \, dx","Int[(A + C*Sec[c + d*x]^2)/(b*Sec[c + d*x])^(5/2),x]","\frac{2 (3 A+5 C) E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{5 b^2 d \sqrt{\cos (c+d x)} \sqrt{b \sec (c+d x)}}+\frac{2 A \tan (c+d x)}{5 d (b \sec (c+d x))^{5/2}}","\frac{2 (3 A+5 C) E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{5 b^2 d \sqrt{\cos (c+d x)} \sqrt{b \sec (c+d x)}}+\frac{2 A \tan (c+d x)}{5 d (b \sec (c+d x))^{5/2}}",1,"(2*(3*A + 5*C)*EllipticE[(c + d*x)/2, 2])/(5*b^2*d*Sqrt[Cos[c + d*x]]*Sqrt[b*Sec[c + d*x]]) + (2*A*Tan[c + d*x])/(5*d*(b*Sec[c + d*x])^(5/2))","A",3,3,25,0.1200,1,"{4045, 3771, 2639}"
22,1,112,0,0.0896406,"\int \frac{A+C \sec ^2(c+d x)}{(b \sec (c+d x))^{7/2}} \, dx","Int[(A + C*Sec[c + d*x]^2)/(b*Sec[c + d*x])^(7/2),x]","\frac{2 (5 A+7 C) \sin (c+d x)}{21 b^3 d \sqrt{b \sec (c+d x)}}+\frac{2 (5 A+7 C) \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \sec (c+d x)}}{21 b^4 d}+\frac{2 A \tan (c+d x)}{7 d (b \sec (c+d x))^{7/2}}","\frac{2 (5 A+7 C) \sin (c+d x)}{21 b^3 d \sqrt{b \sec (c+d x)}}+\frac{2 (5 A+7 C) \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \sec (c+d x)}}{21 b^4 d}+\frac{2 A \tan (c+d x)}{7 d (b \sec (c+d x))^{7/2}}",1,"(2*(5*A + 7*C)*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2]*Sqrt[b*Sec[c + d*x]])/(21*b^4*d) + (2*(5*A + 7*C)*Sin[c + d*x])/(21*b^3*d*Sqrt[b*Sec[c + d*x]]) + (2*A*Tan[c + d*x])/(7*d*(b*Sec[c + d*x])^(7/2))","A",4,4,25,0.1600,1,"{4045, 3769, 3771, 2641}"
23,1,112,0,0.0864181,"\int \frac{A+C \sec ^2(c+d x)}{(b \sec (c+d x))^{9/2}} \, dx","Int[(A + C*Sec[c + d*x]^2)/(b*Sec[c + d*x])^(9/2),x]","\frac{2 (7 A+9 C) \sin (c+d x)}{45 b^3 d (b \sec (c+d x))^{3/2}}+\frac{2 (7 A+9 C) E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{15 b^4 d \sqrt{\cos (c+d x)} \sqrt{b \sec (c+d x)}}+\frac{2 A \tan (c+d x)}{9 d (b \sec (c+d x))^{9/2}}","\frac{2 (7 A+9 C) \sin (c+d x)}{45 b^3 d (b \sec (c+d x))^{3/2}}+\frac{2 (7 A+9 C) E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{15 b^4 d \sqrt{\cos (c+d x)} \sqrt{b \sec (c+d x)}}+\frac{2 A \tan (c+d x)}{9 d (b \sec (c+d x))^{9/2}}",1,"(2*(7*A + 9*C)*EllipticE[(c + d*x)/2, 2])/(15*b^4*d*Sqrt[Cos[c + d*x]]*Sqrt[b*Sec[c + d*x]]) + (2*(7*A + 9*C)*Sin[c + d*x])/(45*b^3*d*(b*Sec[c + d*x])^(3/2)) + (2*A*Tan[c + d*x])/(9*d*(b*Sec[c + d*x])^(9/2))","A",4,4,25,0.1600,1,"{4045, 3769, 3771, 2639}"
24,1,21,0,0.02323,"\int \frac{3+3 \sec ^2(c+d x)}{\sqrt{\sec (c+d x)}} \, dx","Int[(3 + 3*Sec[c + d*x]^2)/Sqrt[Sec[c + d*x]],x]","\frac{6 \sin (c+d x) \sqrt{\sec (c+d x)}}{d}","\frac{6 \sin (c+d x) \sqrt{\sec (c+d x)}}{d}",1,"(6*Sqrt[Sec[c + d*x]]*Sin[c + d*x])/d","A",1,1,23,0.04348,1,"{4043}"
25,1,21,0,0.0294609,"\int \sec ^m(e+f x) \left(m-(1+m) \sec ^2(e+f x)\right) \, dx","Int[Sec[e + f*x]^m*(m - (1 + m)*Sec[e + f*x]^2),x]","-\frac{\sin (e+f x) \sec ^{m+1}(e+f x)}{f}","-\frac{\sin (e+f x) \sec ^{m+1}(e+f x)}{f}",1,"-((Sec[e + f*x]^(1 + m)*Sin[e + f*x])/f)","A",1,1,24,0.04167,1,"{4043}"
26,1,19,0,0.0239556,"\int \sec ^5(e+f x) \left(5-6 \sec ^2(e+f x)\right) \, dx","Int[Sec[e + f*x]^5*(5 - 6*Sec[e + f*x]^2),x]","-\frac{\tan (e+f x) \sec ^5(e+f x)}{f}","-\frac{\tan (e+f x) \sec ^5(e+f x)}{f}",1,"-((Sec[e + f*x]^5*Tan[e + f*x])/f)","A",1,1,21,0.04762,1,"{4043}"
27,1,19,0,0.0234097,"\int \sec ^4(e+f x) \left(4-5 \sec ^2(e+f x)\right) \, dx","Int[Sec[e + f*x]^4*(4 - 5*Sec[e + f*x]^2),x]","-\frac{\tan (e+f x) \sec ^4(e+f x)}{f}","-\frac{\tan (e+f x) \sec ^4(e+f x)}{f}",1,"-((Sec[e + f*x]^4*Tan[e + f*x])/f)","A",1,1,21,0.04762,1,"{4043}"
28,1,19,0,0.0232353,"\int \sec ^3(e+f x) \left(3-4 \sec ^2(e+f x)\right) \, dx","Int[Sec[e + f*x]^3*(3 - 4*Sec[e + f*x]^2),x]","-\frac{\tan (e+f x) \sec ^3(e+f x)}{f}","-\frac{\tan (e+f x) \sec ^3(e+f x)}{f}",1,"-((Sec[e + f*x]^3*Tan[e + f*x])/f)","A",1,1,21,0.04762,1,"{4043}"
29,1,19,0,0.0233235,"\int \sec ^2(e+f x) \left(2-3 \sec ^2(e+f x)\right) \, dx","Int[Sec[e + f*x]^2*(2 - 3*Sec[e + f*x]^2),x]","-\frac{\tan (e+f x) \sec ^2(e+f x)}{f}","-\frac{\tan (e+f x) \sec ^2(e+f x)}{f}",1,"-((Sec[e + f*x]^2*Tan[e + f*x])/f)","A",1,1,21,0.04762,1,"{4043}"
30,1,17,0,0.015395,"\int \sec (e+f x) \left(1-2 \sec ^2(e+f x)\right) \, dx","Int[Sec[e + f*x]*(1 - 2*Sec[e + f*x]^2),x]","-\frac{\tan (e+f x) \sec (e+f x)}{f}","-\frac{\tan (e+f x) \sec (e+f x)}{f}",1,"-((Sec[e + f*x]*Tan[e + f*x])/f)","A",1,1,19,0.05263,1,"{4043}"
31,1,11,0,0.0126015,"\int -\sec ^2(e+f x) \, dx","Int[-Sec[e + f*x]^2,x]","-\frac{\tan (e+f x)}{f}","-\frac{\tan (e+f x)}{f}",1,"-(Tan[e + f*x]/f)","A",2,2,10,0.2000,1,"{3767, 8}"
32,1,11,0,0.0045571,"\int -\cos (e+f x) \, dx","Int[-Cos[e + f*x],x]","-\frac{\sin (e+f x)}{f}","-\frac{\sin (e+f x)}{f}",1,"-(Sin[e + f*x]/f)","A",1,1,8,0.1250,1,"{2637}"
33,1,17,0,0.0226518,"\int \cos ^2(e+f x) \left(-2+\sec ^2(e+f x)\right) \, dx","Int[Cos[e + f*x]^2*(-2 + Sec[e + f*x]^2),x]","-\frac{\sin (e+f x) \cos (e+f x)}{f}","-\frac{\sin (e+f x) \cos (e+f x)}{f}",1,"-((Cos[e + f*x]*Sin[e + f*x])/f)","A",1,1,19,0.05263,1,"{4043}"
34,1,19,0,0.0242992,"\int \cos ^3(e+f x) \left(-3+2 \sec ^2(e+f x)\right) \, dx","Int[Cos[e + f*x]^3*(-3 + 2*Sec[e + f*x]^2),x]","-\frac{\sin (e+f x) \cos ^2(e+f x)}{f}","-\frac{\sin (e+f x) \cos ^2(e+f x)}{f}",1,"-((Cos[e + f*x]^2*Sin[e + f*x])/f)","A",1,1,21,0.04762,1,"{4043}"
35,1,19,0,0.0238439,"\int \cos ^4(e+f x) \left(-4+3 \sec ^2(e+f x)\right) \, dx","Int[Cos[e + f*x]^4*(-4 + 3*Sec[e + f*x]^2),x]","-\frac{\sin (e+f x) \cos ^3(e+f x)}{f}","-\frac{\sin (e+f x) \cos ^3(e+f x)}{f}",1,"-((Cos[e + f*x]^3*Sin[e + f*x])/f)","A",1,1,21,0.04762,1,"{4043}"
36,1,19,0,0.0251379,"\int \cos ^5(e+f x) \left(-5+4 \sec ^2(e+f x)\right) \, dx","Int[Cos[e + f*x]^5*(-5 + 4*Sec[e + f*x]^2),x]","-\frac{\sin (e+f x) \cos ^4(e+f x)}{f}","-\frac{\sin (e+f x) \cos ^4(e+f x)}{f}",1,"-((Cos[e + f*x]^4*Sin[e + f*x])/f)","A",1,1,21,0.04762,1,"{4043}"
37,1,85,0,0.0716354,"\int \sec ^3(c+d x) \left(B \sec (c+d x)+C \sec ^2(c+d x)\right) \, dx","Int[Sec[c + d*x]^3*(B*Sec[c + d*x] + C*Sec[c + d*x]^2),x]","\frac{B \tan ^3(c+d x)}{3 d}+\frac{B \tan (c+d x)}{d}+\frac{3 C \tanh ^{-1}(\sin (c+d x))}{8 d}+\frac{C \tan (c+d x) \sec ^3(c+d x)}{4 d}+\frac{3 C \tan (c+d x) \sec (c+d x)}{8 d}","\frac{B \tan ^3(c+d x)}{3 d}+\frac{B \tan (c+d x)}{d}+\frac{3 C \tanh ^{-1}(\sin (c+d x))}{8 d}+\frac{C \tan (c+d x) \sec ^3(c+d x)}{4 d}+\frac{3 C \tan (c+d x) \sec (c+d x)}{8 d}",1,"(3*C*ArcTanh[Sin[c + d*x]])/(8*d) + (B*Tan[c + d*x])/d + (3*C*Sec[c + d*x]*Tan[c + d*x])/(8*d) + (C*Sec[c + d*x]^3*Tan[c + d*x])/(4*d) + (B*Tan[c + d*x]^3)/(3*d)","A",7,5,28,0.1786,1,"{4047, 3767, 12, 3768, 3770}"
38,1,63,0,0.0575337,"\int \sec ^2(c+d x) \left(B \sec (c+d x)+C \sec ^2(c+d x)\right) \, dx","Int[Sec[c + d*x]^2*(B*Sec[c + d*x] + C*Sec[c + d*x]^2),x]","\frac{B \tanh ^{-1}(\sin (c+d x))}{2 d}+\frac{B \tan (c+d x) \sec (c+d x)}{2 d}+\frac{C \tan ^3(c+d x)}{3 d}+\frac{C \tan (c+d x)}{d}","\frac{B \tanh ^{-1}(\sin (c+d x))}{2 d}+\frac{B \tan (c+d x) \sec (c+d x)}{2 d}+\frac{C \tan ^3(c+d x)}{3 d}+\frac{C \tan (c+d x)}{d}",1,"(B*ArcTanh[Sin[c + d*x]])/(2*d) + (C*Tan[c + d*x])/d + (B*Sec[c + d*x]*Tan[c + d*x])/(2*d) + (C*Tan[c + d*x]^3)/(3*d)","A",6,5,28,0.1786,1,"{4047, 3768, 3770, 12, 3767}"
39,1,47,0,0.0428867,"\int \sec (c+d x) \left(B \sec (c+d x)+C \sec ^2(c+d x)\right) \, dx","Int[Sec[c + d*x]*(B*Sec[c + d*x] + C*Sec[c + d*x]^2),x]","\frac{B \tan (c+d x)}{d}+\frac{C \tanh ^{-1}(\sin (c+d x))}{2 d}+\frac{C \tan (c+d x) \sec (c+d x)}{2 d}","\frac{B \tan (c+d x)}{d}+\frac{C \tanh ^{-1}(\sin (c+d x))}{2 d}+\frac{C \tan (c+d x) \sec (c+d x)}{2 d}",1,"(C*ArcTanh[Sin[c + d*x]])/(2*d) + (B*Tan[c + d*x])/d + (C*Sec[c + d*x]*Tan[c + d*x])/(2*d)","A",6,6,26,0.2308,1,"{4047, 3767, 8, 12, 3768, 3770}"
40,1,24,0,0.0180718,"\int \left(B \sec (c+d x)+C \sec ^2(c+d x)\right) \, dx","Int[B*Sec[c + d*x] + C*Sec[c + d*x]^2,x]","\frac{B \tanh ^{-1}(\sin (c+d x))}{d}+\frac{C \tan (c+d x)}{d}","\frac{B \tanh ^{-1}(\sin (c+d x))}{d}+\frac{C \tan (c+d x)}{d}",1,"(B*ArcTanh[Sin[c + d*x]])/d + (C*Tan[c + d*x])/d","A",4,3,19,0.1579,1,"{3770, 3767, 8}"
41,1,16,0,0.0294041,"\int \cos (c+d x) \left(B \sec (c+d x)+C \sec ^2(c+d x)\right) \, dx","Int[Cos[c + d*x]*(B*Sec[c + d*x] + C*Sec[c + d*x]^2),x]","B x+\frac{C \tanh ^{-1}(\sin (c+d x))}{d}","B x+\frac{C \tanh ^{-1}(\sin (c+d x))}{d}",1,"B*x + (C*ArcTanh[Sin[c + d*x]])/d","A",4,4,26,0.1538,1,"{4047, 8, 12, 3770}"
42,1,15,0,0.0319256,"\int \cos ^2(c+d x) \left(B \sec (c+d x)+C \sec ^2(c+d x)\right) \, dx","Int[Cos[c + d*x]^2*(B*Sec[c + d*x] + C*Sec[c + d*x]^2),x]","\frac{B \sin (c+d x)}{d}+C x","\frac{B \sin (c+d x)}{d}+C x",1,"C*x + (B*Sin[c + d*x])/d","A",3,3,28,0.1071,1,"{4047, 2637, 8}"
43,1,38,0,0.0422158,"\int \cos ^3(c+d x) \left(B \sec (c+d x)+C \sec ^2(c+d x)\right) \, dx","Int[Cos[c + d*x]^3*(B*Sec[c + d*x] + C*Sec[c + d*x]^2),x]","\frac{B \sin (c+d x) \cos (c+d x)}{2 d}+\frac{B x}{2}+\frac{C \sin (c+d x)}{d}","\frac{B \sin (c+d x) \cos (c+d x)}{2 d}+\frac{B x}{2}+\frac{C \sin (c+d x)}{d}",1,"(B*x)/2 + (C*Sin[c + d*x])/d + (B*Cos[c + d*x]*Sin[c + d*x])/(2*d)","A",5,5,28,0.1786,1,"{4047, 2635, 8, 12, 2637}"
44,1,54,0,0.051129,"\int \cos ^4(c+d x) \left(B \sec (c+d x)+C \sec ^2(c+d x)\right) \, dx","Int[Cos[c + d*x]^4*(B*Sec[c + d*x] + C*Sec[c + d*x]^2),x]","-\frac{B \sin ^3(c+d x)}{3 d}+\frac{B \sin (c+d x)}{d}+\frac{C \sin (c+d x) \cos (c+d x)}{2 d}+\frac{C x}{2}","-\frac{B \sin ^3(c+d x)}{3 d}+\frac{B \sin (c+d x)}{d}+\frac{C \sin (c+d x) \cos (c+d x)}{2 d}+\frac{C x}{2}",1,"(C*x)/2 + (B*Sin[c + d*x])/d + (C*Cos[c + d*x]*Sin[c + d*x])/(2*d) - (B*Sin[c + d*x]^3)/(3*d)","A",6,5,28,0.1786,1,"{4047, 2633, 12, 2635, 8}"
45,1,76,0,0.0646908,"\int \cos ^5(c+d x) \left(B \sec (c+d x)+C \sec ^2(c+d x)\right) \, dx","Int[Cos[c + d*x]^5*(B*Sec[c + d*x] + C*Sec[c + d*x]^2),x]","\frac{B \sin (c+d x) \cos ^3(c+d x)}{4 d}+\frac{3 B \sin (c+d x) \cos (c+d x)}{8 d}+\frac{3 B x}{8}-\frac{C \sin ^3(c+d x)}{3 d}+\frac{C \sin (c+d x)}{d}","\frac{B \sin (c+d x) \cos ^3(c+d x)}{4 d}+\frac{3 B \sin (c+d x) \cos (c+d x)}{8 d}+\frac{3 B x}{8}-\frac{C \sin ^3(c+d x)}{3 d}+\frac{C \sin (c+d x)}{d}",1,"(3*B*x)/8 + (C*Sin[c + d*x])/d + (3*B*Cos[c + d*x]*Sin[c + d*x])/(8*d) + (B*Cos[c + d*x]^3*Sin[c + d*x])/(4*d) - (C*Sin[c + d*x]^3)/(3*d)","A",7,5,28,0.1786,1,"{4047, 2635, 8, 12, 2633}"
46,1,92,0,0.0756441,"\int \cos ^6(c+d x) \left(B \sec (c+d x)+C \sec ^2(c+d x)\right) \, dx","Int[Cos[c + d*x]^6*(B*Sec[c + d*x] + C*Sec[c + d*x]^2),x]","\frac{B \sin ^5(c+d x)}{5 d}-\frac{2 B \sin ^3(c+d x)}{3 d}+\frac{B \sin (c+d x)}{d}+\frac{C \sin (c+d x) \cos ^3(c+d x)}{4 d}+\frac{3 C \sin (c+d x) \cos (c+d x)}{8 d}+\frac{3 C x}{8}","\frac{B \sin ^5(c+d x)}{5 d}-\frac{2 B \sin ^3(c+d x)}{3 d}+\frac{B \sin (c+d x)}{d}+\frac{C \sin (c+d x) \cos ^3(c+d x)}{4 d}+\frac{3 C \sin (c+d x) \cos (c+d x)}{8 d}+\frac{3 C x}{8}",1,"(3*C*x)/8 + (B*Sin[c + d*x])/d + (3*C*Cos[c + d*x]*Sin[c + d*x])/(8*d) + (C*Cos[c + d*x]^3*Sin[c + d*x])/(4*d) - (2*B*Sin[c + d*x]^3)/(3*d) + (B*Sin[c + d*x]^5)/(5*d)","A",7,5,28,0.1786,1,"{4047, 2633, 12, 2635, 8}"
47,1,169,0,0.1435182,"\int (b \sec (c+d x))^{3/2} \left(B \sec (c+d x)+C \sec ^2(c+d x)\right) \, dx","Int[(b*Sec[c + d*x])^(3/2)*(B*Sec[c + d*x] + C*Sec[c + d*x]^2),x]","-\frac{6 b^2 C E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{5 d \sqrt{\cos (c+d x)} \sqrt{b \sec (c+d x)}}+\frac{2 B \sin (c+d x) (b \sec (c+d x))^{3/2}}{3 d}+\frac{2 b B \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \sec (c+d x)}}{3 d}+\frac{2 C \sin (c+d x) (b \sec (c+d x))^{5/2}}{5 b d}+\frac{6 b C \sin (c+d x) \sqrt{b \sec (c+d x)}}{5 d}","-\frac{6 b^2 C E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{5 d \sqrt{\cos (c+d x)} \sqrt{b \sec (c+d x)}}+\frac{2 B \sin (c+d x) (b \sec (c+d x))^{3/2}}{3 d}+\frac{2 b B \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \sec (c+d x)}}{3 d}+\frac{2 C \sin (c+d x) (b \sec (c+d x))^{5/2}}{5 b d}+\frac{6 b C \sin (c+d x) \sqrt{b \sec (c+d x)}}{5 d}",1,"(-6*b^2*C*EllipticE[(c + d*x)/2, 2])/(5*d*Sqrt[Cos[c + d*x]]*Sqrt[b*Sec[c + d*x]]) + (2*b*B*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2]*Sqrt[b*Sec[c + d*x]])/(3*d) + (6*b*C*Sqrt[b*Sec[c + d*x]]*Sin[c + d*x])/(5*d) + (2*B*(b*Sec[c + d*x])^(3/2)*Sin[c + d*x])/(3*d) + (2*C*(b*Sec[c + d*x])^(5/2)*Sin[c + d*x])/(5*b*d)","A",10,7,32,0.2188,1,"{4047, 3768, 3771, 2641, 12, 16, 2639}"
48,1,135,0,0.1224622,"\int \sqrt{b \sec (c+d x)} \left(B \sec (c+d x)+C \sec ^2(c+d x)\right) \, dx","Int[Sqrt[b*Sec[c + d*x]]*(B*Sec[c + d*x] + C*Sec[c + d*x]^2),x]","\frac{2 B \sin (c+d x) \sqrt{b \sec (c+d x)}}{d}-\frac{2 b B E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{d \sqrt{\cos (c+d x)} \sqrt{b \sec (c+d x)}}+\frac{2 C \sin (c+d x) (b \sec (c+d x))^{3/2}}{3 b d}+\frac{2 C \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \sec (c+d x)}}{3 d}","\frac{2 B \sin (c+d x) \sqrt{b \sec (c+d x)}}{d}-\frac{2 b B E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{d \sqrt{\cos (c+d x)} \sqrt{b \sec (c+d x)}}+\frac{2 C \sin (c+d x) (b \sec (c+d x))^{3/2}}{3 b d}+\frac{2 C \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \sec (c+d x)}}{3 d}",1,"(-2*b*B*EllipticE[(c + d*x)/2, 2])/(d*Sqrt[Cos[c + d*x]]*Sqrt[b*Sec[c + d*x]]) + (2*C*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2]*Sqrt[b*Sec[c + d*x]])/(3*d) + (2*B*Sqrt[b*Sec[c + d*x]]*Sin[c + d*x])/d + (2*C*(b*Sec[c + d*x])^(3/2)*Sin[c + d*x])/(3*b*d)","A",9,7,32,0.2188,1,"{4047, 3768, 3771, 2639, 12, 16, 2641}"
49,1,109,0,0.1006717,"\int \frac{B \sec (c+d x)+C \sec ^2(c+d x)}{\sqrt{b \sec (c+d x)}} \, dx","Int[(B*Sec[c + d*x] + C*Sec[c + d*x]^2)/Sqrt[b*Sec[c + d*x]],x]","\frac{2 B \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \sec (c+d x)}}{b d}+\frac{2 C \sin (c+d x) \sqrt{b \sec (c+d x)}}{b d}-\frac{2 C E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{d \sqrt{\cos (c+d x)} \sqrt{b \sec (c+d x)}}","\frac{2 B \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \sec (c+d x)}}{b d}+\frac{2 C \sin (c+d x) \sqrt{b \sec (c+d x)}}{b d}-\frac{2 C E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{d \sqrt{\cos (c+d x)} \sqrt{b \sec (c+d x)}}",1,"(-2*C*EllipticE[(c + d*x)/2, 2])/(d*Sqrt[Cos[c + d*x]]*Sqrt[b*Sec[c + d*x]]) + (2*B*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2]*Sqrt[b*Sec[c + d*x]])/(b*d) + (2*C*Sqrt[b*Sec[c + d*x]]*Sin[c + d*x])/(b*d)","A",8,7,32,0.2188,1,"{4047, 3771, 2641, 12, 16, 3768, 2639}"
50,1,85,0,0.0916077,"\int \frac{B \sec (c+d x)+C \sec ^2(c+d x)}{(b \sec (c+d x))^{3/2}} \, dx","Int[(B*Sec[c + d*x] + C*Sec[c + d*x]^2)/(b*Sec[c + d*x])^(3/2),x]","\frac{2 C \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \sec (c+d x)}}{b^2 d}+\frac{2 B E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{b d \sqrt{\cos (c+d x)} \sqrt{b \sec (c+d x)}}","\frac{2 C \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \sec (c+d x)}}{b^2 d}+\frac{2 B E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{b d \sqrt{\cos (c+d x)} \sqrt{b \sec (c+d x)}}",1,"(2*B*EllipticE[(c + d*x)/2, 2])/(b*d*Sqrt[Cos[c + d*x]]*Sqrt[b*Sec[c + d*x]]) + (2*C*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2]*Sqrt[b*Sec[c + d*x]])/(b^2*d)","A",7,6,32,0.1875,1,"{4047, 3771, 2639, 12, 16, 2641}"
51,1,116,0,0.1067096,"\int \frac{B \sec (c+d x)+C \sec ^2(c+d x)}{(b \sec (c+d x))^{5/2}} \, dx","Int[(B*Sec[c + d*x] + C*Sec[c + d*x]^2)/(b*Sec[c + d*x])^(5/2),x]","\frac{2 B \sin (c+d x)}{3 b^2 d \sqrt{b \sec (c+d x)}}+\frac{2 B \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \sec (c+d x)}}{3 b^3 d}+\frac{2 C E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{b^2 d \sqrt{\cos (c+d x)} \sqrt{b \sec (c+d x)}}","\frac{2 B \sin (c+d x)}{3 b^2 d \sqrt{b \sec (c+d x)}}+\frac{2 B \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \sec (c+d x)}}{3 b^3 d}+\frac{2 C E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{b^2 d \sqrt{\cos (c+d x)} \sqrt{b \sec (c+d x)}}",1,"(2*C*EllipticE[(c + d*x)/2, 2])/(b^2*d*Sqrt[Cos[c + d*x]]*Sqrt[b*Sec[c + d*x]]) + (2*B*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2]*Sqrt[b*Sec[c + d*x]])/(3*b^3*d) + (2*B*Sin[c + d*x])/(3*b^2*d*Sqrt[b*Sec[c + d*x]])","A",8,7,32,0.2188,1,"{4047, 3769, 3771, 2641, 12, 16, 2639}"
52,1,147,0,0.1346841,"\int \frac{B \sec (c+d x)+C \sec ^2(c+d x)}{(b \sec (c+d x))^{7/2}} \, dx","Int[(B*Sec[c + d*x] + C*Sec[c + d*x]^2)/(b*Sec[c + d*x])^(7/2),x]","\frac{2 B \sin (c+d x)}{5 b^2 d (b \sec (c+d x))^{3/2}}+\frac{6 B E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{5 b^3 d \sqrt{\cos (c+d x)} \sqrt{b \sec (c+d x)}}+\frac{2 C \sin (c+d x)}{3 b^3 d \sqrt{b \sec (c+d x)}}+\frac{2 C \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \sec (c+d x)}}{3 b^4 d}","\frac{2 B \sin (c+d x)}{5 b^2 d (b \sec (c+d x))^{3/2}}+\frac{6 B E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{5 b^3 d \sqrt{\cos (c+d x)} \sqrt{b \sec (c+d x)}}+\frac{2 C \sin (c+d x)}{3 b^3 d \sqrt{b \sec (c+d x)}}+\frac{2 C \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \sec (c+d x)}}{3 b^4 d}",1,"(6*B*EllipticE[(c + d*x)/2, 2])/(5*b^3*d*Sqrt[Cos[c + d*x]]*Sqrt[b*Sec[c + d*x]]) + (2*C*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2]*Sqrt[b*Sec[c + d*x]])/(3*b^4*d) + (2*B*Sin[c + d*x])/(5*b^2*d*(b*Sec[c + d*x])^(3/2)) + (2*C*Sin[c + d*x])/(3*b^3*d*Sqrt[b*Sec[c + d*x]])","A",9,7,32,0.2188,1,"{4047, 3769, 3771, 2639, 12, 16, 2641}"
53,1,176,0,0.143917,"\int \frac{B \sec (c+d x)+C \sec ^2(c+d x)}{(b \sec (c+d x))^{9/2}} \, dx","Int[(B*Sec[c + d*x] + C*Sec[c + d*x]^2)/(b*Sec[c + d*x])^(9/2),x]","\frac{10 B \sin (c+d x)}{21 b^4 d \sqrt{b \sec (c+d x)}}+\frac{2 B \sin (c+d x)}{7 b^2 d (b \sec (c+d x))^{5/2}}+\frac{10 B \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \sec (c+d x)}}{21 b^5 d}+\frac{2 C \sin (c+d x)}{5 b^3 d (b \sec (c+d x))^{3/2}}+\frac{6 C E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{5 b^4 d \sqrt{\cos (c+d x)} \sqrt{b \sec (c+d x)}}","\frac{10 B \sin (c+d x)}{21 b^4 d \sqrt{b \sec (c+d x)}}+\frac{2 B \sin (c+d x)}{7 b^2 d (b \sec (c+d x))^{5/2}}+\frac{10 B \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \sec (c+d x)}}{21 b^5 d}+\frac{2 C \sin (c+d x)}{5 b^3 d (b \sec (c+d x))^{3/2}}+\frac{6 C E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{5 b^4 d \sqrt{\cos (c+d x)} \sqrt{b \sec (c+d x)}}",1,"(6*C*EllipticE[(c + d*x)/2, 2])/(5*b^4*d*Sqrt[Cos[c + d*x]]*Sqrt[b*Sec[c + d*x]]) + (10*B*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2]*Sqrt[b*Sec[c + d*x]])/(21*b^5*d) + (2*B*Sin[c + d*x])/(7*b^2*d*(b*Sec[c + d*x])^(5/2)) + (2*C*Sin[c + d*x])/(5*b^3*d*(b*Sec[c + d*x])^(3/2)) + (10*B*Sin[c + d*x])/(21*b^4*d*Sqrt[b*Sec[c + d*x]])","A",10,7,32,0.2188,1,"{4047, 3769, 3771, 2641, 12, 16, 2639}"
54,1,122,0,0.0985237,"\int \sec ^4(c+d x) \left(A+B \sec (c+d x)+C \sec ^2(c+d x)\right) \, dx","Int[Sec[c + d*x]^4*(A + B*Sec[c + d*x] + C*Sec[c + d*x]^2),x]","\frac{(5 A+4 C) \tan ^3(c+d x)}{15 d}+\frac{(5 A+4 C) \tan (c+d x)}{5 d}+\frac{3 B \tanh ^{-1}(\sin (c+d x))}{8 d}+\frac{B \tan (c+d x) \sec ^3(c+d x)}{4 d}+\frac{3 B \tan (c+d x) \sec (c+d x)}{8 d}+\frac{C \tan (c+d x) \sec ^4(c+d x)}{5 d}","\frac{(5 A+4 C) \tan ^3(c+d x)}{15 d}+\frac{(5 A+4 C) \tan (c+d x)}{5 d}+\frac{3 B \tanh ^{-1}(\sin (c+d x))}{8 d}+\frac{B \tan (c+d x) \sec ^3(c+d x)}{4 d}+\frac{3 B \tan (c+d x) \sec (c+d x)}{8 d}+\frac{C \tan (c+d x) \sec ^4(c+d x)}{5 d}",1,"(3*B*ArcTanh[Sin[c + d*x]])/(8*d) + ((5*A + 4*C)*Tan[c + d*x])/(5*d) + (3*B*Sec[c + d*x]*Tan[c + d*x])/(8*d) + (B*Sec[c + d*x]^3*Tan[c + d*x])/(4*d) + (C*Sec[c + d*x]^4*Tan[c + d*x])/(5*d) + ((5*A + 4*C)*Tan[c + d*x]^3)/(15*d)","A",7,5,29,0.1724,1,"{4047, 3768, 3770, 4046, 3767}"
55,1,97,0,0.0843856,"\int \sec ^3(c+d x) \left(A+B \sec (c+d x)+C \sec ^2(c+d x)\right) \, dx","Int[Sec[c + d*x]^3*(A + B*Sec[c + d*x] + C*Sec[c + d*x]^2),x]","\frac{(4 A+3 C) \tanh ^{-1}(\sin (c+d x))}{8 d}+\frac{(4 A+3 C) \tan (c+d x) \sec (c+d x)}{8 d}+\frac{B \tan ^3(c+d x)}{3 d}+\frac{B \tan (c+d x)}{d}+\frac{C \tan (c+d x) \sec ^3(c+d x)}{4 d}","\frac{(4 A+3 C) \tanh ^{-1}(\sin (c+d x))}{8 d}+\frac{(4 A+3 C) \tan (c+d x) \sec (c+d x)}{8 d}+\frac{B \tan ^3(c+d x)}{3 d}+\frac{B \tan (c+d x)}{d}+\frac{C \tan (c+d x) \sec ^3(c+d x)}{4 d}",1,"((4*A + 3*C)*ArcTanh[Sin[c + d*x]])/(8*d) + (B*Tan[c + d*x])/d + ((4*A + 3*C)*Sec[c + d*x]*Tan[c + d*x])/(8*d) + (C*Sec[c + d*x]^3*Tan[c + d*x])/(4*d) + (B*Tan[c + d*x]^3)/(3*d)","A",6,5,29,0.1724,1,"{4047, 3767, 4046, 3768, 3770}"
56,1,78,0,0.0805421,"\int \sec ^2(c+d x) \left(A+B \sec (c+d x)+C \sec ^2(c+d x)\right) \, dx","Int[Sec[c + d*x]^2*(A + B*Sec[c + d*x] + C*Sec[c + d*x]^2),x]","\frac{(3 A+2 C) \tan (c+d x)}{3 d}+\frac{B \tanh ^{-1}(\sin (c+d x))}{2 d}+\frac{B \tan (c+d x) \sec (c+d x)}{2 d}+\frac{C \tan (c+d x) \sec ^2(c+d x)}{3 d}","\frac{(3 A+2 C) \tan (c+d x)}{3 d}+\frac{B \tanh ^{-1}(\sin (c+d x))}{2 d}+\frac{B \tan (c+d x) \sec (c+d x)}{2 d}+\frac{C \tan (c+d x) \sec ^2(c+d x)}{3 d}",1,"(B*ArcTanh[Sin[c + d*x]])/(2*d) + ((3*A + 2*C)*Tan[c + d*x])/(3*d) + (B*Sec[c + d*x]*Tan[c + d*x])/(2*d) + (C*Sec[c + d*x]^2*Tan[c + d*x])/(3*d)","A",6,6,29,0.2069,1,"{4047, 3768, 3770, 4046, 3767, 8}"
57,1,51,0,0.0510769,"\int \sec (c+d x) \left(A+B \sec (c+d x)+C \sec ^2(c+d x)\right) \, dx","Int[Sec[c + d*x]*(A + B*Sec[c + d*x] + C*Sec[c + d*x]^2),x]","\frac{(2 A+C) \tanh ^{-1}(\sin (c+d x))}{2 d}+\frac{B \tan (c+d x)}{d}+\frac{C \tan (c+d x) \sec (c+d x)}{2 d}","\frac{(2 A+C) \tanh ^{-1}(\sin (c+d x))}{2 d}+\frac{B \tan (c+d x)}{d}+\frac{C \tan (c+d x) \sec (c+d x)}{2 d}",1,"((2*A + C)*ArcTanh[Sin[c + d*x]])/(2*d) + (B*Tan[c + d*x])/d + (C*Sec[c + d*x]*Tan[c + d*x])/(2*d)","A",5,5,27,0.1852,1,"{4047, 3767, 8, 4046, 3770}"
58,1,27,0,0.0192748,"\int \left(A+B \sec (c+d x)+C \sec ^2(c+d x)\right) \, dx","Int[A + B*Sec[c + d*x] + C*Sec[c + d*x]^2,x]","A x+\frac{B \tanh ^{-1}(\sin (c+d x))}{d}+\frac{C \tan (c+d x)}{d}","A x+\frac{B \tanh ^{-1}(\sin (c+d x))}{d}+\frac{C \tan (c+d x)}{d}",1,"A*x + (B*ArcTanh[Sin[c + d*x]])/d + (C*Tan[c + d*x])/d","A",4,3,20,0.1500,1,"{3770, 3767, 8}"
59,1,27,0,0.049924,"\int \cos (c+d x) \left(A+B \sec (c+d x)+C \sec ^2(c+d x)\right) \, dx","Int[Cos[c + d*x]*(A + B*Sec[c + d*x] + C*Sec[c + d*x]^2),x]","\frac{A \sin (c+d x)}{d}+B x+\frac{C \tanh ^{-1}(\sin (c+d x))}{d}","\frac{A \sin (c+d x)}{d}+B x+\frac{C \tanh ^{-1}(\sin (c+d x))}{d}",1,"B*x + (C*ArcTanh[Sin[c + d*x]])/d + (A*Sin[c + d*x])/d","A",4,4,27,0.1481,1,"{4047, 8, 4045, 3770}"
60,1,42,0,0.0592603,"\int \cos ^2(c+d x) \left(A+B \sec (c+d x)+C \sec ^2(c+d x)\right) \, dx","Int[Cos[c + d*x]^2*(A + B*Sec[c + d*x] + C*Sec[c + d*x]^2),x]","\frac{A \sin (c+d x) \cos (c+d x)}{2 d}+\frac{1}{2} x (A+2 C)+\frac{B \sin (c+d x)}{d}","\frac{A \sin (c+d x) \cos (c+d x)}{2 d}+\frac{1}{2} x (A+2 C)+\frac{B \sin (c+d x)}{d}",1,"((A + 2*C)*x)/2 + (B*Sin[c + d*x])/d + (A*Cos[c + d*x]*Sin[c + d*x])/(2*d)","A",4,4,29,0.1379,1,"{4047, 2637, 4045, 8}"
61,1,56,0,0.0837534,"\int \cos ^3(c+d x) \left(A+B \sec (c+d x)+C \sec ^2(c+d x)\right) \, dx","Int[Cos[c + d*x]^3*(A + B*Sec[c + d*x] + C*Sec[c + d*x]^2),x]","\frac{(A+C) \sin (c+d x)}{d}-\frac{A \sin ^3(c+d x)}{3 d}+\frac{B \sin (c+d x) \cos (c+d x)}{2 d}+\frac{B x}{2}","\frac{(A+C) \sin (c+d x)}{d}-\frac{A \sin ^3(c+d x)}{3 d}+\frac{B \sin (c+d x) \cos (c+d x)}{2 d}+\frac{B x}{2}",1,"(B*x)/2 + ((A + C)*Sin[c + d*x])/d + (B*Cos[c + d*x]*Sin[c + d*x])/(2*d) - (A*Sin[c + d*x]^3)/(3*d)","A",6,5,29,0.1724,1,"{4047, 2635, 8, 4044, 3013}"
62,1,88,0,0.0825976,"\int \cos ^4(c+d x) \left(A+B \sec (c+d x)+C \sec ^2(c+d x)\right) \, dx","Int[Cos[c + d*x]^4*(A + B*Sec[c + d*x] + C*Sec[c + d*x]^2),x]","\frac{(3 A+4 C) \sin (c+d x) \cos (c+d x)}{8 d}+\frac{A \sin (c+d x) \cos ^3(c+d x)}{4 d}+\frac{1}{8} x (3 A+4 C)-\frac{B \sin ^3(c+d x)}{3 d}+\frac{B \sin (c+d x)}{d}","\frac{(3 A+4 C) \sin (c+d x) \cos (c+d x)}{8 d}+\frac{A \sin (c+d x) \cos ^3(c+d x)}{4 d}+\frac{1}{8} x (3 A+4 C)-\frac{B \sin ^3(c+d x)}{3 d}+\frac{B \sin (c+d x)}{d}",1,"((3*A + 4*C)*x)/8 + (B*Sin[c + d*x])/d + ((3*A + 4*C)*Cos[c + d*x]*Sin[c + d*x])/(8*d) + (A*Cos[c + d*x]^3*Sin[c + d*x])/(4*d) - (B*Sin[c + d*x]^3)/(3*d)","A",6,5,29,0.1724,1,"{4047, 2633, 4045, 2635, 8}"
63,1,98,0,0.1152021,"\int \cos ^5(c+d x) \left(A+B \sec (c+d x)+C \sec ^2(c+d x)\right) \, dx","Int[Cos[c + d*x]^5*(A + B*Sec[c + d*x] + C*Sec[c + d*x]^2),x]","-\frac{(2 A+C) \sin ^3(c+d x)}{3 d}+\frac{(A+C) \sin (c+d x)}{d}+\frac{A \sin ^5(c+d x)}{5 d}+\frac{B \sin (c+d x) \cos ^3(c+d x)}{4 d}+\frac{3 B \sin (c+d x) \cos (c+d x)}{8 d}+\frac{3 B x}{8}","-\frac{(2 A+C) \sin ^3(c+d x)}{3 d}+\frac{(A+C) \sin (c+d x)}{d}+\frac{A \sin ^5(c+d x)}{5 d}+\frac{B \sin (c+d x) \cos ^3(c+d x)}{4 d}+\frac{3 B \sin (c+d x) \cos (c+d x)}{8 d}+\frac{3 B x}{8}",1,"(3*B*x)/8 + ((A + C)*Sin[c + d*x])/d + (3*B*Cos[c + d*x]*Sin[c + d*x])/(8*d) + (B*Cos[c + d*x]^3*Sin[c + d*x])/(4*d) - ((2*A + C)*Sin[c + d*x]^3)/(3*d) + (A*Sin[c + d*x]^5)/(5*d)","A",8,6,29,0.2069,1,"{4047, 2635, 8, 4044, 3013, 373}"
64,1,132,0,0.0991188,"\int \cos ^6(c+d x) \left(A+B \sec (c+d x)+C \sec ^2(c+d x)\right) \, dx","Int[Cos[c + d*x]^6*(A + B*Sec[c + d*x] + C*Sec[c + d*x]^2),x]","\frac{(5 A+6 C) \sin (c+d x) \cos ^3(c+d x)}{24 d}+\frac{(5 A+6 C) \sin (c+d x) \cos (c+d x)}{16 d}+\frac{A \sin (c+d x) \cos ^5(c+d x)}{6 d}+\frac{1}{16} x (5 A+6 C)+\frac{B \sin ^5(c+d x)}{5 d}-\frac{2 B \sin ^3(c+d x)}{3 d}+\frac{B \sin (c+d x)}{d}","\frac{(5 A+6 C) \sin (c+d x) \cos ^3(c+d x)}{24 d}+\frac{(5 A+6 C) \sin (c+d x) \cos (c+d x)}{16 d}+\frac{A \sin (c+d x) \cos ^5(c+d x)}{6 d}+\frac{1}{16} x (5 A+6 C)+\frac{B \sin ^5(c+d x)}{5 d}-\frac{2 B \sin ^3(c+d x)}{3 d}+\frac{B \sin (c+d x)}{d}",1,"((5*A + 6*C)*x)/16 + (B*Sin[c + d*x])/d + ((5*A + 6*C)*Cos[c + d*x]*Sin[c + d*x])/(16*d) + ((5*A + 6*C)*Cos[c + d*x]^3*Sin[c + d*x])/(24*d) + (A*Cos[c + d*x]^5*Sin[c + d*x])/(6*d) - (2*B*Sin[c + d*x]^3)/(3*d) + (B*Sin[c + d*x]^5)/(5*d)","A",7,5,29,0.1724,1,"{4047, 2633, 4045, 2635, 8}"
65,1,178,0,0.1610573,"\int (b \sec (c+d x))^{3/2} \left(A+B \sec (c+d x)+C \sec ^2(c+d x)\right) \, dx","Int[(b*Sec[c + d*x])^(3/2)*(A + B*Sec[c + d*x] + C*Sec[c + d*x]^2),x]","-\frac{2 b^2 (5 A+3 C) E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{5 d \sqrt{\cos (c+d x)} \sqrt{b \sec (c+d x)}}+\frac{2 b (5 A+3 C) \sin (c+d x) \sqrt{b \sec (c+d x)}}{5 d}+\frac{2 B \sin (c+d x) (b \sec (c+d x))^{3/2}}{3 d}+\frac{2 b B \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \sec (c+d x)}}{3 d}+\frac{2 C \tan (c+d x) (b \sec (c+d x))^{3/2}}{5 d}","-\frac{2 b^2 (5 A+3 C) E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{5 d \sqrt{\cos (c+d x)} \sqrt{b \sec (c+d x)}}+\frac{2 b (5 A+3 C) \sin (c+d x) \sqrt{b \sec (c+d x)}}{5 d}+\frac{2 B \sin (c+d x) (b \sec (c+d x))^{3/2}}{3 d}+\frac{2 b B \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \sec (c+d x)}}{3 d}+\frac{2 C \tan (c+d x) (b \sec (c+d x))^{3/2}}{5 d}",1,"(-2*b^2*(5*A + 3*C)*EllipticE[(c + d*x)/2, 2])/(5*d*Sqrt[Cos[c + d*x]]*Sqrt[b*Sec[c + d*x]]) + (2*b*B*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2]*Sqrt[b*Sec[c + d*x]])/(3*d) + (2*b*(5*A + 3*C)*Sqrt[b*Sec[c + d*x]]*Sin[c + d*x])/(5*d) + (2*B*(b*Sec[c + d*x])^(3/2)*Sin[c + d*x])/(3*d) + (2*C*(b*Sec[c + d*x])^(3/2)*Tan[c + d*x])/(5*d)","A",8,6,33,0.1818,1,"{4047, 3768, 3771, 2641, 4046, 2639}"
66,1,136,0,0.1276503,"\int \sqrt{b \sec (c+d x)} \left(A+B \sec (c+d x)+C \sec ^2(c+d x)\right) \, dx","Int[Sqrt[b*Sec[c + d*x]]*(A + B*Sec[c + d*x] + C*Sec[c + d*x]^2),x]","\frac{2 (3 A+C) \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \sec (c+d x)}}{3 d}+\frac{2 B \sin (c+d x) \sqrt{b \sec (c+d x)}}{d}-\frac{2 b B E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{d \sqrt{\cos (c+d x)} \sqrt{b \sec (c+d x)}}+\frac{2 C \tan (c+d x) \sqrt{b \sec (c+d x)}}{3 d}","\frac{2 (3 A+C) \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \sec (c+d x)}}{3 d}+\frac{2 B \sin (c+d x) \sqrt{b \sec (c+d x)}}{d}-\frac{2 b B E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{d \sqrt{\cos (c+d x)} \sqrt{b \sec (c+d x)}}+\frac{2 C \tan (c+d x) \sqrt{b \sec (c+d x)}}{3 d}",1,"(-2*b*B*EllipticE[(c + d*x)/2, 2])/(d*Sqrt[Cos[c + d*x]]*Sqrt[b*Sec[c + d*x]]) + (2*(3*A + C)*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2]*Sqrt[b*Sec[c + d*x]])/(3*d) + (2*B*Sqrt[b*Sec[c + d*x]]*Sin[c + d*x])/d + (2*C*Sqrt[b*Sec[c + d*x]]*Tan[c + d*x])/(3*d)","A",7,6,33,0.1818,1,"{4047, 3768, 3771, 2639, 4046, 2641}"
67,1,110,0,0.1111772,"\int \frac{A+B \sec (c+d x)+C \sec ^2(c+d x)}{\sqrt{b \sec (c+d x)}} \, dx","Int[(A + B*Sec[c + d*x] + C*Sec[c + d*x]^2)/Sqrt[b*Sec[c + d*x]],x]","\frac{2 (A-C) E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{d \sqrt{\cos (c+d x)} \sqrt{b \sec (c+d x)}}+\frac{2 B \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \sec (c+d x)}}{b d}+\frac{2 C \tan (c+d x)}{d \sqrt{b \sec (c+d x)}}","\frac{2 (A-C) E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{d \sqrt{\cos (c+d x)} \sqrt{b \sec (c+d x)}}+\frac{2 B \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \sec (c+d x)}}{b d}+\frac{2 C \tan (c+d x)}{d \sqrt{b \sec (c+d x)}}",1,"(2*(A - C)*EllipticE[(c + d*x)/2, 2])/(d*Sqrt[Cos[c + d*x]]*Sqrt[b*Sec[c + d*x]]) + (2*B*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2]*Sqrt[b*Sec[c + d*x]])/(b*d) + (2*C*Tan[c + d*x])/(d*Sqrt[b*Sec[c + d*x]])","A",6,5,33,0.1515,1,"{4047, 3771, 2641, 4046, 2639}"
68,1,117,0,0.1338696,"\int \frac{A+B \sec (c+d x)+C \sec ^2(c+d x)}{(b \sec (c+d x))^{3/2}} \, dx","Int[(A + B*Sec[c + d*x] + C*Sec[c + d*x]^2)/(b*Sec[c + d*x])^(3/2),x]","\frac{2 (A+3 C) \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \sec (c+d x)}}{3 b^2 d}+\frac{2 A \tan (c+d x)}{3 d (b \sec (c+d x))^{3/2}}+\frac{2 B E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{b d \sqrt{\cos (c+d x)} \sqrt{b \sec (c+d x)}}","\frac{2 (A+3 C) \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \sec (c+d x)}}{3 b^2 d}+\frac{2 A \tan (c+d x)}{3 d (b \sec (c+d x))^{3/2}}+\frac{2 B E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{b d \sqrt{\cos (c+d x)} \sqrt{b \sec (c+d x)}}",1,"(2*B*EllipticE[(c + d*x)/2, 2])/(b*d*Sqrt[Cos[c + d*x]]*Sqrt[b*Sec[c + d*x]]) + (2*(A + 3*C)*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2]*Sqrt[b*Sec[c + d*x]])/(3*b^2*d) + (2*A*Tan[c + d*x])/(3*d*(b*Sec[c + d*x])^(3/2))","A",6,5,33,0.1515,1,"{4047, 3771, 2639, 4045, 2641}"
69,1,150,0,0.1542785,"\int \frac{A+B \sec (c+d x)+C \sec ^2(c+d x)}{(b \sec (c+d x))^{5/2}} \, dx","Int[(A + B*Sec[c + d*x] + C*Sec[c + d*x]^2)/(b*Sec[c + d*x])^(5/2),x]","\frac{2 (3 A+5 C) E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{5 b^2 d \sqrt{\cos (c+d x)} \sqrt{b \sec (c+d x)}}+\frac{2 A \tan (c+d x)}{5 d (b \sec (c+d x))^{5/2}}+\frac{2 B \sin (c+d x)}{3 b^2 d \sqrt{b \sec (c+d x)}}+\frac{2 B \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \sec (c+d x)}}{3 b^3 d}","\frac{2 (3 A+5 C) E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{5 b^2 d \sqrt{\cos (c+d x)} \sqrt{b \sec (c+d x)}}+\frac{2 A \tan (c+d x)}{5 d (b \sec (c+d x))^{5/2}}+\frac{2 B \sin (c+d x)}{3 b^2 d \sqrt{b \sec (c+d x)}}+\frac{2 B \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \sec (c+d x)}}{3 b^3 d}",1,"(2*(3*A + 5*C)*EllipticE[(c + d*x)/2, 2])/(5*b^2*d*Sqrt[Cos[c + d*x]]*Sqrt[b*Sec[c + d*x]]) + (2*B*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2]*Sqrt[b*Sec[c + d*x]])/(3*b^3*d) + (2*B*Sin[c + d*x])/(3*b^2*d*Sqrt[b*Sec[c + d*x]]) + (2*A*Tan[c + d*x])/(5*d*(b*Sec[c + d*x])^(5/2))","A",7,6,33,0.1818,1,"{4047, 3769, 3771, 2641, 4045, 2639}"
70,1,185,0,0.1586531,"\int \frac{A+B \sec (c+d x)+C \sec ^2(c+d x)}{(b \sec (c+d x))^{7/2}} \, dx","Int[(A + B*Sec[c + d*x] + C*Sec[c + d*x]^2)/(b*Sec[c + d*x])^(7/2),x]","\frac{2 (5 A+7 C) \sin (c+d x)}{21 b^3 d \sqrt{b \sec (c+d x)}}+\frac{2 (5 A+7 C) \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \sec (c+d x)}}{21 b^4 d}+\frac{2 A \tan (c+d x)}{7 d (b \sec (c+d x))^{7/2}}+\frac{2 B \sin (c+d x)}{5 b^2 d (b \sec (c+d x))^{3/2}}+\frac{6 B E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{5 b^3 d \sqrt{\cos (c+d x)} \sqrt{b \sec (c+d x)}}","\frac{2 (5 A+7 C) \sin (c+d x)}{21 b^3 d \sqrt{b \sec (c+d x)}}+\frac{2 (5 A+7 C) \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \sec (c+d x)}}{21 b^4 d}+\frac{2 A \tan (c+d x)}{7 d (b \sec (c+d x))^{7/2}}+\frac{2 B \sin (c+d x)}{5 b^2 d (b \sec (c+d x))^{3/2}}+\frac{6 B E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{5 b^3 d \sqrt{\cos (c+d x)} \sqrt{b \sec (c+d x)}}",1,"(6*B*EllipticE[(c + d*x)/2, 2])/(5*b^3*d*Sqrt[Cos[c + d*x]]*Sqrt[b*Sec[c + d*x]]) + (2*(5*A + 7*C)*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2]*Sqrt[b*Sec[c + d*x]])/(21*b^4*d) + (2*B*Sin[c + d*x])/(5*b^2*d*(b*Sec[c + d*x])^(3/2)) + (2*(5*A + 7*C)*Sin[c + d*x])/(21*b^3*d*Sqrt[b*Sec[c + d*x]]) + (2*A*Tan[c + d*x])/(7*d*(b*Sec[c + d*x])^(7/2))","A",8,6,33,0.1818,1,"{4047, 3769, 3771, 2639, 4045, 2641}"