1,1,11,0,0.0042149,"\int \sec (a+b x) \, dx","Int[Sec[a + b*x],x]","\frac{\tanh ^{-1}(\sin (a+b x))}{b}","\frac{\tanh ^{-1}(\sin (a+b x))}{b}",1,"ArcTanh[Sin[a + b*x]]/b","A",1,1,6,0.1667,1,"{3770}"
2,1,10,0,0.0087791,"\int \sec ^2(a+b x) \, dx","Int[Sec[a + b*x]^2,x]","\frac{\tan (a+b x)}{b}","\frac{\tan (a+b x)}{b}",1,"Tan[a + b*x]/b","A",2,2,8,0.2500,1,"{3767, 8}"
3,1,34,0,0.0143485,"\int \sec ^3(a+b x) \, dx","Int[Sec[a + b*x]^3,x]","\frac{\tanh ^{-1}(\sin (a+b x))}{2 b}+\frac{\tan (a+b x) \sec (a+b x)}{2 b}","\frac{\tanh ^{-1}(\sin (a+b x))}{2 b}+\frac{\tan (a+b x) \sec (a+b x)}{2 b}",1,"ArcTanh[Sin[a + b*x]]/(2*b) + (Sec[a + b*x]*Tan[a + b*x])/(2*b)","A",2,2,8,0.2500,1,"{3768, 3770}"
4,1,26,0,0.0112607,"\int \sec ^4(a+b x) \, dx","Int[Sec[a + b*x]^4,x]","\frac{\tan ^3(a+b x)}{3 b}+\frac{\tan (a+b x)}{b}","\frac{\tan ^3(a+b x)}{3 b}+\frac{\tan (a+b x)}{b}",1,"Tan[a + b*x]/b + Tan[a + b*x]^3/(3*b)","A",2,1,8,0.1250,1,"{3767}"
5,1,55,0,0.0250803,"\int \sec ^5(a+b x) \, dx","Int[Sec[a + b*x]^5,x]","\frac{3 \tanh ^{-1}(\sin (a+b x))}{8 b}+\frac{\tan (a+b x) \sec ^3(a+b x)}{4 b}+\frac{3 \tan (a+b x) \sec (a+b x)}{8 b}","\frac{3 \tanh ^{-1}(\sin (a+b x))}{8 b}+\frac{\tan (a+b x) \sec ^3(a+b x)}{4 b}+\frac{3 \tan (a+b x) \sec (a+b x)}{8 b}",1,"(3*ArcTanh[Sin[a + b*x]])/(8*b) + (3*Sec[a + b*x]*Tan[a + b*x])/(8*b) + (Sec[a + b*x]^3*Tan[a + b*x])/(4*b)","A",3,2,8,0.2500,1,"{3768, 3770}"
6,1,41,0,0.0148022,"\int \sec ^6(a+b x) \, dx","Int[Sec[a + b*x]^6,x]","\frac{\tan ^5(a+b x)}{5 b}+\frac{2 \tan ^3(a+b x)}{3 b}+\frac{\tan (a+b x)}{b}","\frac{\tan ^5(a+b x)}{5 b}+\frac{2 \tan ^3(a+b x)}{3 b}+\frac{\tan (a+b x)}{b}",1,"Tan[a + b*x]/b + (2*Tan[a + b*x]^3)/(3*b) + Tan[a + b*x]^5/(5*b)","A",2,1,8,0.1250,1,"{3767}"
7,1,76,0,0.0386378,"\int \sec ^7(a+b x) \, dx","Int[Sec[a + b*x]^7,x]","\frac{5 \tanh ^{-1}(\sin (a+b x))}{16 b}+\frac{\tan (a+b x) \sec ^5(a+b x)}{6 b}+\frac{5 \tan (a+b x) \sec ^3(a+b x)}{24 b}+\frac{5 \tan (a+b x) \sec (a+b x)}{16 b}","\frac{5 \tanh ^{-1}(\sin (a+b x))}{16 b}+\frac{\tan (a+b x) \sec ^5(a+b x)}{6 b}+\frac{5 \tan (a+b x) \sec ^3(a+b x)}{24 b}+\frac{5 \tan (a+b x) \sec (a+b x)}{16 b}",1,"(5*ArcTanh[Sin[a + b*x]])/(16*b) + (5*Sec[a + b*x]*Tan[a + b*x])/(16*b) + (5*Sec[a + b*x]^3*Tan[a + b*x])/(24*b) + (Sec[a + b*x]^5*Tan[a + b*x])/(6*b)","A",4,2,8,0.2500,1,"{3768, 3770}"
8,1,53,0,0.0167995,"\int \sec ^8(a+b x) \, dx","Int[Sec[a + b*x]^8,x]","\frac{\tan ^7(a+b x)}{7 b}+\frac{3 \tan ^5(a+b x)}{5 b}+\frac{\tan ^3(a+b x)}{b}+\frac{\tan (a+b x)}{b}","\frac{\tan ^7(a+b x)}{7 b}+\frac{3 \tan ^5(a+b x)}{5 b}+\frac{\tan ^3(a+b x)}{b}+\frac{\tan (a+b x)}{b}",1,"Tan[a + b*x]/b + Tan[a + b*x]^3/b + (3*Tan[a + b*x]^5)/(5*b) + Tan[a + b*x]^7/(7*b)","A",2,1,8,0.1250,1,"{3767}"
9,1,85,0,0.0370816,"\int \sec ^{\frac{7}{2}}(a+b x) \, dx","Int[Sec[a + b*x]^(7/2),x]","\frac{2 \sin (a+b x) \sec ^{\frac{5}{2}}(a+b x)}{5 b}+\frac{6 \sin (a+b x) \sqrt{\sec (a+b x)}}{5 b}-\frac{6 \sqrt{\cos (a+b x)} \sqrt{\sec (a+b x)} E\left(\left.\frac{1}{2} (a+b x)\right|2\right)}{5 b}","\frac{2 \sin (a+b x) \sec ^{\frac{5}{2}}(a+b x)}{5 b}+\frac{6 \sin (a+b x) \sqrt{\sec (a+b x)}}{5 b}-\frac{6 \sqrt{\cos (a+b x)} \sqrt{\sec (a+b x)} E\left(\left.\frac{1}{2} (a+b x)\right|2\right)}{5 b}",1,"(-6*Sqrt[Cos[a + b*x]]*EllipticE[(a + b*x)/2, 2]*Sqrt[Sec[a + b*x]])/(5*b) + (6*Sqrt[Sec[a + b*x]]*Sin[a + b*x])/(5*b) + (2*Sec[a + b*x]^(5/2)*Sin[a + b*x])/(5*b)","A",4,3,10,0.3000,1,"{3768, 3771, 2639}"
10,1,62,0,0.0269803,"\int \sec ^{\frac{5}{2}}(a+b x) \, dx","Int[Sec[a + b*x]^(5/2),x]","\frac{2 \sin (a+b x) \sec ^{\frac{3}{2}}(a+b x)}{3 b}+\frac{2 \sqrt{\cos (a+b x)} \sqrt{\sec (a+b x)} F\left(\left.\frac{1}{2} (a+b x)\right|2\right)}{3 b}","\frac{2 \sin (a+b x) \sec ^{\frac{3}{2}}(a+b x)}{3 b}+\frac{2 \sqrt{\cos (a+b x)} \sqrt{\sec (a+b x)} F\left(\left.\frac{1}{2} (a+b x)\right|2\right)}{3 b}",1,"(2*Sqrt[Cos[a + b*x]]*EllipticF[(a + b*x)/2, 2]*Sqrt[Sec[a + b*x]])/(3*b) + (2*Sec[a + b*x]^(3/2)*Sin[a + b*x])/(3*b)","A",3,3,10,0.3000,1,"{3768, 3771, 2641}"
11,1,58,0,0.0255371,"\int \sec ^{\frac{3}{2}}(a+b x) \, dx","Int[Sec[a + b*x]^(3/2),x]","\frac{2 \sin (a+b x) \sqrt{\sec (a+b x)}}{b}-\frac{2 \sqrt{\cos (a+b x)} \sqrt{\sec (a+b x)} E\left(\left.\frac{1}{2} (a+b x)\right|2\right)}{b}","\frac{2 \sin (a+b x) \sqrt{\sec (a+b x)}}{b}-\frac{2 \sqrt{\cos (a+b x)} \sqrt{\sec (a+b x)} E\left(\left.\frac{1}{2} (a+b x)\right|2\right)}{b}",1,"(-2*Sqrt[Cos[a + b*x]]*EllipticE[(a + b*x)/2, 2]*Sqrt[Sec[a + b*x]])/b + (2*Sqrt[Sec[a + b*x]]*Sin[a + b*x])/b","A",3,3,10,0.3000,1,"{3768, 3771, 2639}"
12,1,36,0,0.0167242,"\int \sqrt{\sec (a+b x)} \, dx","Int[Sqrt[Sec[a + b*x]],x]","\frac{2 \sqrt{\cos (a+b x)} \sqrt{\sec (a+b x)} F\left(\left.\frac{1}{2} (a+b x)\right|2\right)}{b}","\frac{2 \sqrt{\cos (a+b x)} \sqrt{\sec (a+b x)} F\left(\left.\frac{1}{2} (a+b x)\right|2\right)}{b}",1,"(2*Sqrt[Cos[a + b*x]]*EllipticF[(a + b*x)/2, 2]*Sqrt[Sec[a + b*x]])/b","A",2,2,10,0.2000,1,"{3771, 2641}"
13,1,36,0,0.0171722,"\int \frac{1}{\sqrt{\sec (a+b x)}} \, dx","Int[1/Sqrt[Sec[a + b*x]],x]","\frac{2 \sqrt{\cos (a+b x)} \sqrt{\sec (a+b x)} E\left(\left.\frac{1}{2} (a+b x)\right|2\right)}{b}","\frac{2 \sqrt{\cos (a+b x)} \sqrt{\sec (a+b x)} E\left(\left.\frac{1}{2} (a+b x)\right|2\right)}{b}",1,"(2*Sqrt[Cos[a + b*x]]*EllipticE[(a + b*x)/2, 2]*Sqrt[Sec[a + b*x]])/b","A",2,2,10,0.2000,1,"{3771, 2639}"
14,1,62,0,0.0280829,"\int \frac{1}{\sec ^{\frac{3}{2}}(a+b x)} \, dx","Int[Sec[a + b*x]^(-3/2),x]","\frac{2 \sin (a+b x)}{3 b \sqrt{\sec (a+b x)}}+\frac{2 \sqrt{\cos (a+b x)} \sqrt{\sec (a+b x)} F\left(\left.\frac{1}{2} (a+b x)\right|2\right)}{3 b}","\frac{2 \sin (a+b x)}{3 b \sqrt{\sec (a+b x)}}+\frac{2 \sqrt{\cos (a+b x)} \sqrt{\sec (a+b x)} F\left(\left.\frac{1}{2} (a+b x)\right|2\right)}{3 b}",1,"(2*Sqrt[Cos[a + b*x]]*EllipticF[(a + b*x)/2, 2]*Sqrt[Sec[a + b*x]])/(3*b) + (2*Sin[a + b*x])/(3*b*Sqrt[Sec[a + b*x]])","A",3,3,10,0.3000,1,"{3769, 3771, 2641}"
15,1,62,0,0.0286673,"\int \frac{1}{\sec ^{\frac{5}{2}}(a+b x)} \, dx","Int[Sec[a + b*x]^(-5/2),x]","\frac{2 \sin (a+b x)}{5 b \sec ^{\frac{3}{2}}(a+b x)}+\frac{6 \sqrt{\cos (a+b x)} \sqrt{\sec (a+b x)} E\left(\left.\frac{1}{2} (a+b x)\right|2\right)}{5 b}","\frac{2 \sin (a+b x)}{5 b \sec ^{\frac{3}{2}}(a+b x)}+\frac{6 \sqrt{\cos (a+b x)} \sqrt{\sec (a+b x)} E\left(\left.\frac{1}{2} (a+b x)\right|2\right)}{5 b}",1,"(6*Sqrt[Cos[a + b*x]]*EllipticE[(a + b*x)/2, 2]*Sqrt[Sec[a + b*x]])/(5*b) + (2*Sin[a + b*x])/(5*b*Sec[a + b*x]^(3/2))","A",3,3,10,0.3000,1,"{3769, 3771, 2639}"
16,1,85,0,0.0403677,"\int \frac{1}{\sec ^{\frac{7}{2}}(a+b x)} \, dx","Int[Sec[a + b*x]^(-7/2),x]","\frac{2 \sin (a+b x)}{7 b \sec ^{\frac{5}{2}}(a+b x)}+\frac{10 \sin (a+b x)}{21 b \sqrt{\sec (a+b x)}}+\frac{10 \sqrt{\cos (a+b x)} \sqrt{\sec (a+b x)} F\left(\left.\frac{1}{2} (a+b x)\right|2\right)}{21 b}","\frac{2 \sin (a+b x)}{7 b \sec ^{\frac{5}{2}}(a+b x)}+\frac{10 \sin (a+b x)}{21 b \sqrt{\sec (a+b x)}}+\frac{10 \sqrt{\cos (a+b x)} \sqrt{\sec (a+b x)} F\left(\left.\frac{1}{2} (a+b x)\right|2\right)}{21 b}",1,"(10*Sqrt[Cos[a + b*x]]*EllipticF[(a + b*x)/2, 2]*Sqrt[Sec[a + b*x]])/(21*b) + (2*Sin[a + b*x])/(7*b*Sec[a + b*x]^(5/2)) + (10*Sin[a + b*x])/(21*b*Sqrt[Sec[a + b*x]])","A",4,3,10,0.3000,1,"{3769, 3771, 2641}"
17,1,98,0,0.0558185,"\int (c \sec (a+b x))^{7/2} \, dx","Int[(c*Sec[a + b*x])^(7/2),x]","\frac{6 c^3 \sin (a+b x) \sqrt{c \sec (a+b x)}}{5 b}-\frac{6 c^4 E\left(\left.\frac{1}{2} (a+b x)\right|2\right)}{5 b \sqrt{\cos (a+b x)} \sqrt{c \sec (a+b x)}}+\frac{2 c \sin (a+b x) (c \sec (a+b x))^{5/2}}{5 b}","\frac{6 c^3 \sin (a+b x) \sqrt{c \sec (a+b x)}}{5 b}-\frac{6 c^4 E\left(\left.\frac{1}{2} (a+b x)\right|2\right)}{5 b \sqrt{\cos (a+b x)} \sqrt{c \sec (a+b x)}}+\frac{2 c \sin (a+b x) (c \sec (a+b x))^{5/2}}{5 b}",1,"(-6*c^4*EllipticE[(a + b*x)/2, 2])/(5*b*Sqrt[Cos[a + b*x]]*Sqrt[c*Sec[a + b*x]]) + (6*c^3*Sqrt[c*Sec[a + b*x]]*Sin[a + b*x])/(5*b) + (2*c*(c*Sec[a + b*x])^(5/2)*Sin[a + b*x])/(5*b)","A",4,3,12,0.2500,1,"{3768, 3771, 2639}"
18,1,70,0,0.0336493,"\int (c \sec (a+b x))^{5/2} \, dx","Int[(c*Sec[a + b*x])^(5/2),x]","\frac{2 c^2 \sqrt{\cos (a+b x)} F\left(\left.\frac{1}{2} (a+b x)\right|2\right) \sqrt{c \sec (a+b x)}}{3 b}+\frac{2 c \sin (a+b x) (c \sec (a+b x))^{3/2}}{3 b}","\frac{2 c^2 \sqrt{\cos (a+b x)} F\left(\left.\frac{1}{2} (a+b x)\right|2\right) \sqrt{c \sec (a+b x)}}{3 b}+\frac{2 c \sin (a+b x) (c \sec (a+b x))^{3/2}}{3 b}",1,"(2*c^2*Sqrt[Cos[a + b*x]]*EllipticF[(a + b*x)/2, 2]*Sqrt[c*Sec[a + b*x]])/(3*b) + (2*c*(c*Sec[a + b*x])^(3/2)*Sin[a + b*x])/(3*b)","A",3,3,12,0.2500,1,"{3768, 3771, 2641}"
19,1,66,0,0.0395353,"\int (c \sec (a+b x))^{3/2} \, dx","Int[(c*Sec[a + b*x])^(3/2),x]","\frac{2 c \sin (a+b x) \sqrt{c \sec (a+b x)}}{b}-\frac{2 c^2 E\left(\left.\frac{1}{2} (a+b x)\right|2\right)}{b \sqrt{\cos (a+b x)} \sqrt{c \sec (a+b x)}}","\frac{2 c \sin (a+b x) \sqrt{c \sec (a+b x)}}{b}-\frac{2 c^2 E\left(\left.\frac{1}{2} (a+b x)\right|2\right)}{b \sqrt{\cos (a+b x)} \sqrt{c \sec (a+b x)}}",1,"(-2*c^2*EllipticE[(a + b*x)/2, 2])/(b*Sqrt[Cos[a + b*x]]*Sqrt[c*Sec[a + b*x]]) + (2*c*Sqrt[c*Sec[a + b*x]]*Sin[a + b*x])/b","A",3,3,12,0.2500,1,"{3768, 3771, 2639}"
20,1,38,0,0.0192504,"\int \sqrt{c \sec (a+b x)} \, dx","Int[Sqrt[c*Sec[a + b*x]],x]","\frac{2 \sqrt{\cos (a+b x)} F\left(\left.\frac{1}{2} (a+b x)\right|2\right) \sqrt{c \sec (a+b x)}}{b}","\frac{2 \sqrt{\cos (a+b x)} F\left(\left.\frac{1}{2} (a+b x)\right|2\right) \sqrt{c \sec (a+b x)}}{b}",1,"(2*Sqrt[Cos[a + b*x]]*EllipticF[(a + b*x)/2, 2]*Sqrt[c*Sec[a + b*x]])/b","A",2,2,12,0.1667,1,"{3771, 2641}"
21,1,38,0,0.0272559,"\int \frac{1}{\sqrt{c \sec (a+b x)}} \, dx","Int[1/Sqrt[c*Sec[a + b*x]],x]","\frac{2 E\left(\left.\frac{1}{2} (a+b x)\right|2\right)}{b \sqrt{\cos (a+b x)} \sqrt{c \sec (a+b x)}}","\frac{2 E\left(\left.\frac{1}{2} (a+b x)\right|2\right)}{b \sqrt{\cos (a+b x)} \sqrt{c \sec (a+b x)}}",1,"(2*EllipticE[(a + b*x)/2, 2])/(b*Sqrt[Cos[a + b*x]]*Sqrt[c*Sec[a + b*x]])","A",2,2,12,0.1667,1,"{3771, 2639}"
22,1,72,0,0.0461409,"\int \frac{1}{(c \sec (a+b x))^{3/2}} \, dx","Int[(c*Sec[a + b*x])^(-3/2),x]","\frac{2 \sqrt{\cos (a+b x)} F\left(\left.\frac{1}{2} (a+b x)\right|2\right) \sqrt{c \sec (a+b x)}}{3 b c^2}+\frac{2 \sin (a+b x)}{3 b c \sqrt{c \sec (a+b x)}}","\frac{2 \sqrt{\cos (a+b x)} F\left(\left.\frac{1}{2} (a+b x)\right|2\right) \sqrt{c \sec (a+b x)}}{3 b c^2}+\frac{2 \sin (a+b x)}{3 b c \sqrt{c \sec (a+b x)}}",1,"(2*Sqrt[Cos[a + b*x]]*EllipticF[(a + b*x)/2, 2]*Sqrt[c*Sec[a + b*x]])/(3*b*c^2) + (2*Sin[a + b*x])/(3*b*c*Sqrt[c*Sec[a + b*x]])","A",3,3,12,0.2500,1,"{3769, 3771, 2641}"
23,1,72,0,0.0378077,"\int \frac{1}{(c \sec (a+b x))^{5/2}} \, dx","Int[(c*Sec[a + b*x])^(-5/2),x]","\frac{6 E\left(\left.\frac{1}{2} (a+b x)\right|2\right)}{5 b c^2 \sqrt{\cos (a+b x)} \sqrt{c \sec (a+b x)}}+\frac{2 \sin (a+b x)}{5 b c (c \sec (a+b x))^{3/2}}","\frac{6 E\left(\left.\frac{1}{2} (a+b x)\right|2\right)}{5 b c^2 \sqrt{\cos (a+b x)} \sqrt{c \sec (a+b x)}}+\frac{2 \sin (a+b x)}{5 b c (c \sec (a+b x))^{3/2}}",1,"(6*EllipticE[(a + b*x)/2, 2])/(5*b*c^2*Sqrt[Cos[a + b*x]]*Sqrt[c*Sec[a + b*x]]) + (2*Sin[a + b*x])/(5*b*c*(c*Sec[a + b*x])^(3/2))","A",3,3,12,0.2500,1,"{3769, 3771, 2639}"
24,1,100,0,0.059252,"\int \frac{1}{(c \sec (a+b x))^{7/2}} \, dx","Int[(c*Sec[a + b*x])^(-7/2),x]","\frac{10 \sin (a+b x)}{21 b c^3 \sqrt{c \sec (a+b x)}}+\frac{10 \sqrt{\cos (a+b x)} F\left(\left.\frac{1}{2} (a+b x)\right|2\right) \sqrt{c \sec (a+b x)}}{21 b c^4}+\frac{2 \sin (a+b x)}{7 b c (c \sec (a+b x))^{5/2}}","\frac{10 \sin (a+b x)}{21 b c^3 \sqrt{c \sec (a+b x)}}+\frac{10 \sqrt{\cos (a+b x)} F\left(\left.\frac{1}{2} (a+b x)\right|2\right) \sqrt{c \sec (a+b x)}}{21 b c^4}+\frac{2 \sin (a+b x)}{7 b c (c \sec (a+b x))^{5/2}}",1,"(10*Sqrt[Cos[a + b*x]]*EllipticF[(a + b*x)/2, 2]*Sqrt[c*Sec[a + b*x]])/(21*b*c^4) + (2*Sin[a + b*x])/(7*b*c*(c*Sec[a + b*x])^(5/2)) + (10*Sin[a + b*x])/(21*b*c^3*Sqrt[c*Sec[a + b*x]])","A",4,3,12,0.2500,1,"{3769, 3771, 2641}"
25,1,51,0,0.023147,"\int \sec ^{\frac{4}{3}}(a+b x) \, dx","Int[Sec[a + b*x]^(4/3),x]","\frac{3 \sin (a+b x) \sqrt[3]{\sec (a+b x)} \, _2F_1\left(-\frac{1}{6},\frac{1}{2};\frac{5}{6};\cos ^2(a+b x)\right)}{b \sqrt{\sin ^2(a+b x)}}","\frac{3 \sin (a+b x) \sqrt[3]{\sec (a+b x)} \, _2F_1\left(-\frac{1}{6},\frac{1}{2};\frac{5}{6};\cos ^2(a+b x)\right)}{b \sqrt{\sin ^2(a+b x)}}",1,"(3*Hypergeometric2F1[-1/6, 1/2, 5/6, Cos[a + b*x]^2]*Sec[a + b*x]^(1/3)*Sin[a + b*x])/(b*Sqrt[Sin[a + b*x]^2])","A",2,2,10,0.2000,1,"{3772, 2643}"
26,1,51,0,0.0276046,"\int \sec ^{\frac{2}{3}}(a+b x) \, dx","Int[Sec[a + b*x]^(2/3),x]","-\frac{3 \sin (a+b x) \, _2F_1\left(\frac{1}{6},\frac{1}{2};\frac{7}{6};\cos ^2(a+b x)\right)}{b \sqrt{\sin ^2(a+b x)} \sqrt[3]{\sec (a+b x)}}","-\frac{3 \sin (a+b x) \, _2F_1\left(\frac{1}{6},\frac{1}{2};\frac{7}{6};\cos ^2(a+b x)\right)}{b \sqrt{\sin ^2(a+b x)} \sqrt[3]{\sec (a+b x)}}",1,"(-3*Hypergeometric2F1[1/6, 1/2, 7/6, Cos[a + b*x]^2]*Sin[a + b*x])/(b*Sec[a + b*x]^(1/3)*Sqrt[Sin[a + b*x]^2])","A",2,2,10,0.2000,1,"{3772, 2643}"
27,1,53,0,0.0332359,"\int \sqrt[3]{\sec (a+b x)} \, dx","Int[Sec[a + b*x]^(1/3),x]","-\frac{3 \sin (a+b x) \, _2F_1\left(\frac{1}{3},\frac{1}{2};\frac{4}{3};\cos ^2(a+b x)\right)}{2 b \sqrt{\sin ^2(a+b x)} \sec ^{\frac{2}{3}}(a+b x)}","-\frac{3 \sin (a+b x) \, _2F_1\left(\frac{1}{3},\frac{1}{2};\frac{4}{3};\cos ^2(a+b x)\right)}{2 b \sqrt{\sin ^2(a+b x)} \sec ^{\frac{2}{3}}(a+b x)}",1,"(-3*Hypergeometric2F1[1/3, 1/2, 4/3, Cos[a + b*x]^2]*Sin[a + b*x])/(2*b*Sec[a + b*x]^(2/3)*Sqrt[Sin[a + b*x]^2])","A",2,2,10,0.2000,1,"{3772, 2643}"
28,1,53,0,0.0254906,"\int \frac{1}{\sqrt[3]{\sec (a+b x)}} \, dx","Int[Sec[a + b*x]^(-1/3),x]","-\frac{3 \sin (a+b x) \, _2F_1\left(\frac{1}{2},\frac{2}{3};\frac{5}{3};\cos ^2(a+b x)\right)}{4 b \sqrt{\sin ^2(a+b x)} \sec ^{\frac{4}{3}}(a+b x)}","-\frac{3 \sin (a+b x) \, _2F_1\left(\frac{1}{2},\frac{2}{3};\frac{5}{3};\cos ^2(a+b x)\right)}{4 b \sqrt{\sin ^2(a+b x)} \sec ^{\frac{4}{3}}(a+b x)}",1,"(-3*Hypergeometric2F1[1/2, 2/3, 5/3, Cos[a + b*x]^2]*Sin[a + b*x])/(4*b*Sec[a + b*x]^(4/3)*Sqrt[Sin[a + b*x]^2])","A",2,2,10,0.2000,1,"{3772, 2643}"
29,1,53,0,0.0254632,"\int \frac{1}{\sec ^{\frac{2}{3}}(a+b x)} \, dx","Int[Sec[a + b*x]^(-2/3),x]","-\frac{3 \sin (a+b x) \, _2F_1\left(\frac{1}{2},\frac{5}{6};\frac{11}{6};\cos ^2(a+b x)\right)}{5 b \sqrt{\sin ^2(a+b x)} \sec ^{\frac{5}{3}}(a+b x)}","-\frac{3 \sin (a+b x) \, _2F_1\left(\frac{1}{2},\frac{5}{6};\frac{11}{6};\cos ^2(a+b x)\right)}{5 b \sqrt{\sin ^2(a+b x)} \sec ^{\frac{5}{3}}(a+b x)}",1,"(-3*Hypergeometric2F1[1/2, 5/6, 11/6, Cos[a + b*x]^2]*Sin[a + b*x])/(5*b*Sec[a + b*x]^(5/3)*Sqrt[Sin[a + b*x]^2])","A",2,2,10,0.2000,1,"{3772, 2643}"
30,1,53,0,0.0247945,"\int \frac{1}{\sec ^{\frac{4}{3}}(a+b x)} \, dx","Int[Sec[a + b*x]^(-4/3),x]","-\frac{3 \sin (a+b x) \, _2F_1\left(\frac{1}{2},\frac{7}{6};\frac{13}{6};\cos ^2(a+b x)\right)}{7 b \sqrt{\sin ^2(a+b x)} \sec ^{\frac{7}{3}}(a+b x)}","-\frac{3 \sin (a+b x) \, _2F_1\left(\frac{1}{2},\frac{7}{6};\frac{13}{6};\cos ^2(a+b x)\right)}{7 b \sqrt{\sin ^2(a+b x)} \sec ^{\frac{7}{3}}(a+b x)}",1,"(-3*Hypergeometric2F1[1/2, 7/6, 13/6, Cos[a + b*x]^2]*Sin[a + b*x])/(7*b*Sec[a + b*x]^(7/3)*Sqrt[Sin[a + b*x]^2])","A",2,2,10,0.2000,1,"{3772, 2643}"
31,1,54,0,0.0335746,"\int (c \sec (a+b x))^{4/3} \, dx","Int[(c*Sec[a + b*x])^(4/3),x]","\frac{3 c \sin (a+b x) \sqrt[3]{c \sec (a+b x)} \, _2F_1\left(-\frac{1}{6},\frac{1}{2};\frac{5}{6};\cos ^2(a+b x)\right)}{b \sqrt{\sin ^2(a+b x)}}","\frac{3 c \sin (a+b x) \sqrt[3]{c \sec (a+b x)} \, _2F_1\left(-\frac{1}{6},\frac{1}{2};\frac{5}{6};\cos ^2(a+b x)\right)}{b \sqrt{\sin ^2(a+b x)}}",1,"(3*c*Hypergeometric2F1[-1/6, 1/2, 5/6, Cos[a + b*x]^2]*(c*Sec[a + b*x])^(1/3)*Sin[a + b*x])/(b*Sqrt[Sin[a + b*x]^2])","A",2,2,12,0.1667,1,"{3772, 2643}"
32,1,54,0,0.0295325,"\int (c \sec (a+b x))^{2/3} \, dx","Int[(c*Sec[a + b*x])^(2/3),x]","-\frac{3 c \sin (a+b x) \, _2F_1\left(\frac{1}{6},\frac{1}{2};\frac{7}{6};\cos ^2(a+b x)\right)}{b \sqrt{\sin ^2(a+b x)} \sqrt[3]{c \sec (a+b x)}}","-\frac{3 c \sin (a+b x) \, _2F_1\left(\frac{1}{6},\frac{1}{2};\frac{7}{6};\cos ^2(a+b x)\right)}{b \sqrt{\sin ^2(a+b x)} \sqrt[3]{c \sec (a+b x)}}",1,"(-3*c*Hypergeometric2F1[1/6, 1/2, 7/6, Cos[a + b*x]^2]*Sin[a + b*x])/(b*(c*Sec[a + b*x])^(1/3)*Sqrt[Sin[a + b*x]^2])","A",2,2,12,0.1667,1,"{3772, 2643}"
33,1,56,0,0.0349386,"\int \sqrt[3]{c \sec (a+b x)} \, dx","Int[(c*Sec[a + b*x])^(1/3),x]","-\frac{3 c \sin (a+b x) \, _2F_1\left(\frac{1}{3},\frac{1}{2};\frac{4}{3};\cos ^2(a+b x)\right)}{2 b \sqrt{\sin ^2(a+b x)} (c \sec (a+b x))^{2/3}}","-\frac{3 c \sin (a+b x) \, _2F_1\left(\frac{1}{3},\frac{1}{2};\frac{4}{3};\cos ^2(a+b x)\right)}{2 b \sqrt{\sin ^2(a+b x)} (c \sec (a+b x))^{2/3}}",1,"(-3*c*Hypergeometric2F1[1/3, 1/2, 4/3, Cos[a + b*x]^2]*Sin[a + b*x])/(2*b*(c*Sec[a + b*x])^(2/3)*Sqrt[Sin[a + b*x]^2])","A",2,2,12,0.1667,1,"{3772, 2643}"
34,1,56,0,0.0324897,"\int \frac{1}{\sqrt[3]{c \sec (a+b x)}} \, dx","Int[(c*Sec[a + b*x])^(-1/3),x]","-\frac{3 c \sin (a+b x) \, _2F_1\left(\frac{1}{2},\frac{2}{3};\frac{5}{3};\cos ^2(a+b x)\right)}{4 b \sqrt{\sin ^2(a+b x)} (c \sec (a+b x))^{4/3}}","-\frac{3 c \sin (a+b x) \, _2F_1\left(\frac{1}{2},\frac{2}{3};\frac{5}{3};\cos ^2(a+b x)\right)}{4 b \sqrt{\sin ^2(a+b x)} (c \sec (a+b x))^{4/3}}",1,"(-3*c*Hypergeometric2F1[1/2, 2/3, 5/3, Cos[a + b*x]^2]*Sin[a + b*x])/(4*b*(c*Sec[a + b*x])^(4/3)*Sqrt[Sin[a + b*x]^2])","A",2,2,12,0.1667,1,"{3772, 2643}"
35,1,56,0,0.0282795,"\int \frac{1}{(c \sec (a+b x))^{2/3}} \, dx","Int[(c*Sec[a + b*x])^(-2/3),x]","-\frac{3 c \sin (a+b x) \, _2F_1\left(\frac{1}{2},\frac{5}{6};\frac{11}{6};\cos ^2(a+b x)\right)}{5 b \sqrt{\sin ^2(a+b x)} (c \sec (a+b x))^{5/3}}","-\frac{3 c \sin (a+b x) \, _2F_1\left(\frac{1}{2},\frac{5}{6};\frac{11}{6};\cos ^2(a+b x)\right)}{5 b \sqrt{\sin ^2(a+b x)} (c \sec (a+b x))^{5/3}}",1,"(-3*c*Hypergeometric2F1[1/2, 5/6, 11/6, Cos[a + b*x]^2]*Sin[a + b*x])/(5*b*(c*Sec[a + b*x])^(5/3)*Sqrt[Sin[a + b*x]^2])","A",2,2,12,0.1667,1,"{3772, 2643}"
36,1,56,0,0.0286994,"\int \frac{1}{(c \sec (a+b x))^{4/3}} \, dx","Int[(c*Sec[a + b*x])^(-4/3),x]","-\frac{3 c \sin (a+b x) \, _2F_1\left(\frac{1}{2},\frac{7}{6};\frac{13}{6};\cos ^2(a+b x)\right)}{7 b \sqrt{\sin ^2(a+b x)} (c \sec (a+b x))^{7/3}}","-\frac{3 c \sin (a+b x) \, _2F_1\left(\frac{1}{2},\frac{7}{6};\frac{13}{6};\cos ^2(a+b x)\right)}{7 b \sqrt{\sin ^2(a+b x)} (c \sec (a+b x))^{7/3}}",1,"(-3*c*Hypergeometric2F1[1/2, 7/6, 13/6, Cos[a + b*x]^2]*Sin[a + b*x])/(7*b*(c*Sec[a + b*x])^(7/3)*Sqrt[Sin[a + b*x]^2])","A",2,2,12,0.1667,1,"{3772, 2643}"
37,1,70,0,0.0328775,"\int \sec ^n(a+b x) \, dx","Int[Sec[a + b*x]^n,x]","-\frac{\sin (a+b x) \sec ^{n-1}(a+b x) \, _2F_1\left(\frac{1}{2},\frac{1-n}{2};\frac{3-n}{2};\cos ^2(a+b x)\right)}{b (1-n) \sqrt{\sin ^2(a+b x)}}","-\frac{\sin (a+b x) \sec ^{n-1}(a+b x) \, _2F_1\left(\frac{1}{2},\frac{1-n}{2};\frac{3-n}{2};\cos ^2(a+b x)\right)}{b (1-n) \sqrt{\sin ^2(a+b x)}}",1,"-((Hypergeometric2F1[1/2, (1 - n)/2, (3 - n)/2, Cos[a + b*x]^2]*Sec[a + b*x]^(-1 + n)*Sin[a + b*x])/(b*(1 - n)*Sqrt[Sin[a + b*x]^2]))","A",2,2,8,0.2500,1,"{3772, 2643}"
38,1,73,0,0.0311051,"\int (c \sec (a+b x))^n \, dx","Int[(c*Sec[a + b*x])^n,x]","-\frac{c \sin (a+b x) (c \sec (a+b x))^{n-1} \, _2F_1\left(\frac{1}{2},\frac{1-n}{2};\frac{3-n}{2};\cos ^2(a+b x)\right)}{b (1-n) \sqrt{\sin ^2(a+b x)}}","-\frac{c \sin (a+b x) (c \sec (a+b x))^{n-1} \, _2F_1\left(\frac{1}{2},\frac{1-n}{2};\frac{3-n}{2};\cos ^2(a+b x)\right)}{b (1-n) \sqrt{\sin ^2(a+b x)}}",1,"-((c*Hypergeometric2F1[1/2, (1 - n)/2, (3 - n)/2, Cos[a + b*x]^2]*(c*Sec[a + b*x])^(-1 + n)*Sin[a + b*x])/(b*(1 - n)*Sqrt[Sin[a + b*x]^2]))","A",2,2,10,0.2000,1,"{3772, 2643}"
39,1,50,0,0.016905,"\int \sec ^2(x)^{7/2} \, dx","Int[(Sec[x]^2)^(7/2),x]","\frac{1}{6} \tan (x) \sec ^2(x)^{5/2}+\frac{5}{24} \tan (x) \sec ^2(x)^{3/2}+\frac{5}{16} \tan (x) \sqrt{\sec ^2(x)}+\frac{5}{16} \sinh ^{-1}(\tan (x))","\frac{1}{6} \tan (x) \sec ^2(x)^{5/2}+\frac{5}{24} \tan (x) \sec ^2(x)^{3/2}+\frac{5}{16} \tan (x) \sqrt{\sec ^2(x)}+\frac{5}{16} \sinh ^{-1}(\tan (x))",1,"(5*ArcSinh[Tan[x]])/16 + (5*Sqrt[Sec[x]^2]*Tan[x])/16 + (5*(Sec[x]^2)^(3/2)*Tan[x])/24 + ((Sec[x]^2)^(5/2)*Tan[x])/6","A",5,3,8,0.3750,1,"{4122, 195, 215}"
40,1,36,0,0.0124014,"\int \sec ^2(x)^{5/2} \, dx","Int[(Sec[x]^2)^(5/2),x]","\frac{1}{4} \tan (x) \sec ^2(x)^{3/2}+\frac{3}{8} \tan (x) \sqrt{\sec ^2(x)}+\frac{3}{8} \sinh ^{-1}(\tan (x))","\frac{1}{4} \tan (x) \sec ^2(x)^{3/2}+\frac{3}{8} \tan (x) \sqrt{\sec ^2(x)}+\frac{3}{8} \sinh ^{-1}(\tan (x))",1,"(3*ArcSinh[Tan[x]])/8 + (3*Sqrt[Sec[x]^2]*Tan[x])/8 + ((Sec[x]^2)^(3/2)*Tan[x])/4","A",4,3,8,0.3750,1,"{4122, 195, 215}"
41,1,22,0,0.0085539,"\int \sec ^2(x)^{3/2} \, dx","Int[(Sec[x]^2)^(3/2),x]","\frac{1}{2} \tan (x) \sqrt{\sec ^2(x)}+\frac{1}{2} \sinh ^{-1}(\tan (x))","\frac{1}{2} \tan (x) \sqrt{\sec ^2(x)}+\frac{1}{2} \sinh ^{-1}(\tan (x))",1,"ArcSinh[Tan[x]]/2 + (Sqrt[Sec[x]^2]*Tan[x])/2","A",3,3,8,0.3750,1,"{4122, 195, 215}"
42,1,3,0,0.005895,"\int \sqrt{\sec ^2(x)} \, dx","Int[Sqrt[Sec[x]^2],x]","\sinh ^{-1}(\tan (x))","\sinh ^{-1}(\tan (x))",1,"ArcSinh[Tan[x]]","A",2,2,8,0.2500,1,"{4122, 215}"
43,1,11,0,0.0073548,"\int \frac{1}{\sqrt{\sec ^2(x)}} \, dx","Int[1/Sqrt[Sec[x]^2],x]","\frac{\tan (x)}{\sqrt{\sec ^2(x)}}","\frac{\tan (x)}{\sqrt{\sec ^2(x)}}",1,"Tan[x]/Sqrt[Sec[x]^2]","A",2,2,8,0.2500,1,"{4122, 191}"
44,1,29,0,0.0105769,"\int \frac{1}{\sec ^2(x)^{3/2}} \, dx","Int[(Sec[x]^2)^(-3/2),x]","\frac{2 \tan (x)}{3 \sqrt{\sec ^2(x)}}+\frac{\tan (x)}{3 \sec ^2(x)^{3/2}}","\frac{2 \tan (x)}{3 \sqrt{\sec ^2(x)}}+\frac{\tan (x)}{3 \sec ^2(x)^{3/2}}",1,"Tan[x]/(3*(Sec[x]^2)^(3/2)) + (2*Tan[x])/(3*Sqrt[Sec[x]^2])","A",3,3,8,0.3750,1,"{4122, 192, 191}"
45,1,43,0,0.0149745,"\int \frac{1}{\sec ^2(x)^{5/2}} \, dx","Int[(Sec[x]^2)^(-5/2),x]","\frac{8 \tan (x)}{15 \sqrt{\sec ^2(x)}}+\frac{4 \tan (x)}{15 \sec ^2(x)^{3/2}}+\frac{\tan (x)}{5 \sec ^2(x)^{5/2}}","\frac{8 \tan (x)}{15 \sqrt{\sec ^2(x)}}+\frac{4 \tan (x)}{15 \sec ^2(x)^{3/2}}+\frac{\tan (x)}{5 \sec ^2(x)^{5/2}}",1,"Tan[x]/(5*(Sec[x]^2)^(5/2)) + (4*Tan[x])/(15*(Sec[x]^2)^(3/2)) + (8*Tan[x])/(15*Sqrt[Sec[x]^2])","A",4,3,8,0.3750,1,"{4122, 192, 191}"
46,1,57,0,0.0188078,"\int \frac{1}{\sec ^2(x)^{7/2}} \, dx","Int[(Sec[x]^2)^(-7/2),x]","\frac{16 \tan (x)}{35 \sqrt{\sec ^2(x)}}+\frac{8 \tan (x)}{35 \sec ^2(x)^{3/2}}+\frac{6 \tan (x)}{35 \sec ^2(x)^{5/2}}+\frac{\tan (x)}{7 \sec ^2(x)^{7/2}}","\frac{16 \tan (x)}{35 \sqrt{\sec ^2(x)}}+\frac{8 \tan (x)}{35 \sec ^2(x)^{3/2}}+\frac{6 \tan (x)}{35 \sec ^2(x)^{5/2}}+\frac{\tan (x)}{7 \sec ^2(x)^{7/2}}",1,"Tan[x]/(7*(Sec[x]^2)^(7/2)) + (6*Tan[x])/(35*(Sec[x]^2)^(5/2)) + (8*Tan[x])/(35*(Sec[x]^2)^(3/2)) + (16*Tan[x])/(35*Sqrt[Sec[x]^2])","A",5,3,8,0.3750,1,"{4122, 192, 191}"
47,1,84,0,0.0413025,"\int \left(a \sec ^2(x)\right)^{7/2} \, dx","Int[(a*Sec[x]^2)^(7/2),x]","\frac{5}{16} a^3 \tan (x) \sqrt{a \sec ^2(x)}+\frac{5}{24} a^2 \tan (x) \left(a \sec ^2(x)\right)^{3/2}+\frac{5}{16} a^{7/2} \tanh ^{-1}\left(\frac{\sqrt{a} \tan (x)}{\sqrt{a \sec ^2(x)}}\right)+\frac{1}{6} a \tan (x) \left(a \sec ^2(x)\right)^{5/2}","\frac{5}{16} a^3 \tan (x) \sqrt{a \sec ^2(x)}+\frac{5}{24} a^2 \tan (x) \left(a \sec ^2(x)\right)^{3/2}+\frac{5}{16} a^{7/2} \tanh ^{-1}\left(\frac{\sqrt{a} \tan (x)}{\sqrt{a \sec ^2(x)}}\right)+\frac{1}{6} a \tan (x) \left(a \sec ^2(x)\right)^{5/2}",1,"(5*a^(7/2)*ArcTanh[(Sqrt[a]*Tan[x])/Sqrt[a*Sec[x]^2]])/16 + (5*a^3*Sqrt[a*Sec[x]^2]*Tan[x])/16 + (5*a^2*(a*Sec[x]^2)^(3/2)*Tan[x])/24 + (a*(a*Sec[x]^2)^(5/2)*Tan[x])/6","A",6,4,10,0.4000,1,"{4122, 195, 217, 206}"
48,1,65,0,0.0313453,"\int \left(a \sec ^2(x)\right)^{5/2} \, dx","Int[(a*Sec[x]^2)^(5/2),x]","\frac{3}{8} a^2 \tan (x) \sqrt{a \sec ^2(x)}+\frac{3}{8} a^{5/2} \tanh ^{-1}\left(\frac{\sqrt{a} \tan (x)}{\sqrt{a \sec ^2(x)}}\right)+\frac{1}{4} a \tan (x) \left(a \sec ^2(x)\right)^{3/2}","\frac{3}{8} a^2 \tan (x) \sqrt{a \sec ^2(x)}+\frac{3}{8} a^{5/2} \tanh ^{-1}\left(\frac{\sqrt{a} \tan (x)}{\sqrt{a \sec ^2(x)}}\right)+\frac{1}{4} a \tan (x) \left(a \sec ^2(x)\right)^{3/2}",1,"(3*a^(5/2)*ArcTanh[(Sqrt[a]*Tan[x])/Sqrt[a*Sec[x]^2]])/8 + (3*a^2*Sqrt[a*Sec[x]^2]*Tan[x])/8 + (a*(a*Sec[x]^2)^(3/2)*Tan[x])/4","A",5,4,10,0.4000,1,"{4122, 195, 217, 206}"
49,1,46,0,0.0223066,"\int \left(a \sec ^2(x)\right)^{3/2} \, dx","Int[(a*Sec[x]^2)^(3/2),x]","\frac{1}{2} a^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a} \tan (x)}{\sqrt{a \sec ^2(x)}}\right)+\frac{1}{2} a \tan (x) \sqrt{a \sec ^2(x)}","\frac{1}{2} a^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a} \tan (x)}{\sqrt{a \sec ^2(x)}}\right)+\frac{1}{2} a \tan (x) \sqrt{a \sec ^2(x)}",1,"(a^(3/2)*ArcTanh[(Sqrt[a]*Tan[x])/Sqrt[a*Sec[x]^2]])/2 + (a*Sqrt[a*Sec[x]^2]*Tan[x])/2","A",4,4,10,0.4000,1,"{4122, 195, 217, 206}"
50,1,25,0,0.0148376,"\int \sqrt{a \sec ^2(x)} \, dx","Int[Sqrt[a*Sec[x]^2],x]","\sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a} \tan (x)}{\sqrt{a \sec ^2(x)}}\right)","\sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a} \tan (x)}{\sqrt{a \sec ^2(x)}}\right)",1,"Sqrt[a]*ArcTanh[(Sqrt[a]*Tan[x])/Sqrt[a*Sec[x]^2]]","A",3,3,10,0.3000,1,"{4122, 217, 206}"
51,1,13,0,0.0286669,"\int \frac{1}{\sqrt{a \sec ^2(x)}} \, dx","Int[1/Sqrt[a*Sec[x]^2],x]","\frac{\tan (x)}{\sqrt{a \sec ^2(x)}}","\frac{\tan (x)}{\sqrt{a \sec ^2(x)}}",1,"Tan[x]/Sqrt[a*Sec[x]^2]","A",2,2,10,0.2000,1,"{4122, 191}"
52,1,36,0,0.0182093,"\int \frac{1}{\left(a \sec ^2(x)\right)^{3/2}} \, dx","Int[(a*Sec[x]^2)^(-3/2),x]","\frac{2 \tan (x)}{3 a \sqrt{a \sec ^2(x)}}+\frac{\tan (x)}{3 \left(a \sec ^2(x)\right)^{3/2}}","\frac{2 \tan (x)}{3 a \sqrt{a \sec ^2(x)}}+\frac{\tan (x)}{3 \left(a \sec ^2(x)\right)^{3/2}}",1,"Tan[x]/(3*(a*Sec[x]^2)^(3/2)) + (2*Tan[x])/(3*a*Sqrt[a*Sec[x]^2])","A",3,3,10,0.3000,1,"{4122, 192, 191}"
53,1,55,0,0.0266371,"\int \frac{1}{\left(a \sec ^2(x)\right)^{5/2}} \, dx","Int[(a*Sec[x]^2)^(-5/2),x]","\frac{8 \tan (x)}{15 a^2 \sqrt{a \sec ^2(x)}}+\frac{4 \tan (x)}{15 a \left(a \sec ^2(x)\right)^{3/2}}+\frac{\tan (x)}{5 \left(a \sec ^2(x)\right)^{5/2}}","\frac{8 \tan (x)}{15 a^2 \sqrt{a \sec ^2(x)}}+\frac{4 \tan (x)}{15 a \left(a \sec ^2(x)\right)^{3/2}}+\frac{\tan (x)}{5 \left(a \sec ^2(x)\right)^{5/2}}",1,"Tan[x]/(5*(a*Sec[x]^2)^(5/2)) + (4*Tan[x])/(15*a*(a*Sec[x]^2)^(3/2)) + (8*Tan[x])/(15*a^2*Sqrt[a*Sec[x]^2])","A",4,3,10,0.3000,1,"{4122, 192, 191}"
54,1,74,0,0.0349597,"\int \frac{1}{\left(a \sec ^2(x)\right)^{7/2}} \, dx","Int[(a*Sec[x]^2)^(-7/2),x]","\frac{16 \tan (x)}{35 a^3 \sqrt{a \sec ^2(x)}}+\frac{8 \tan (x)}{35 a^2 \left(a \sec ^2(x)\right)^{3/2}}+\frac{6 \tan (x)}{35 a \left(a \sec ^2(x)\right)^{5/2}}+\frac{\tan (x)}{7 \left(a \sec ^2(x)\right)^{7/2}}","\frac{16 \tan (x)}{35 a^3 \sqrt{a \sec ^2(x)}}+\frac{8 \tan (x)}{35 a^2 \left(a \sec ^2(x)\right)^{3/2}}+\frac{6 \tan (x)}{35 a \left(a \sec ^2(x)\right)^{5/2}}+\frac{\tan (x)}{7 \left(a \sec ^2(x)\right)^{7/2}}",1,"Tan[x]/(7*(a*Sec[x]^2)^(7/2)) + (6*Tan[x])/(35*a*(a*Sec[x]^2)^(5/2)) + (8*Tan[x])/(35*a^2*(a*Sec[x]^2)^(3/2)) + (16*Tan[x])/(35*a^3*Sqrt[a*Sec[x]^2])","A",5,3,10,0.3000,1,"{4122, 192, 191}"
55,1,117,0,0.0522832,"\int \left(a \sec ^3(x)\right)^{5/2} \, dx","Int[(a*Sec[x]^3)^(5/2),x]","\frac{2}{13} a^2 \tan (x) \sec ^4(x) \sqrt{a \sec ^3(x)}+\frac{22}{117} a^2 \tan (x) \sec ^2(x) \sqrt{a \sec ^3(x)}+\frac{154}{585} a^2 \tan (x) \sqrt{a \sec ^3(x)}-\frac{154}{195} a^2 \cos ^{\frac{3}{2}}(x) E\left(\left.\frac{x}{2}\right|2\right) \sqrt{a \sec ^3(x)}+\frac{154}{195} a^2 \sin (x) \cos (x) \sqrt{a \sec ^3(x)}","\frac{2}{13} a^2 \tan (x) \sec ^4(x) \sqrt{a \sec ^3(x)}+\frac{22}{117} a^2 \tan (x) \sec ^2(x) \sqrt{a \sec ^3(x)}+\frac{154}{585} a^2 \tan (x) \sqrt{a \sec ^3(x)}-\frac{154}{195} a^2 \cos ^{\frac{3}{2}}(x) E\left(\left.\frac{x}{2}\right|2\right) \sqrt{a \sec ^3(x)}+\frac{154}{195} a^2 \sin (x) \cos (x) \sqrt{a \sec ^3(x)}",1,"(-154*a^2*Cos[x]^(3/2)*EllipticE[x/2, 2]*Sqrt[a*Sec[x]^3])/195 + (154*a^2*Cos[x]*Sqrt[a*Sec[x]^3]*Sin[x])/195 + (154*a^2*Sqrt[a*Sec[x]^3]*Tan[x])/585 + (22*a^2*Sec[x]^2*Sqrt[a*Sec[x]^3]*Tan[x])/117 + (2*a^2*Sec[x]^4*Sqrt[a*Sec[x]^3]*Tan[x])/13","A",7,4,10,0.4000,1,"{4123, 3768, 3771, 2639}"
56,1,65,0,0.0353327,"\int \left(a \sec ^3(x)\right)^{3/2} \, dx","Int[(a*Sec[x]^3)^(3/2),x]","\frac{10}{21} a \sin (x) \sqrt{a \sec ^3(x)}+\frac{2}{7} a \tan (x) \sec (x) \sqrt{a \sec ^3(x)}+\frac{10}{21} a \cos ^{\frac{3}{2}}(x) F\left(\left.\frac{x}{2}\right|2\right) \sqrt{a \sec ^3(x)}","\frac{10}{21} a \sin (x) \sqrt{a \sec ^3(x)}+\frac{2}{7} a \tan (x) \sec (x) \sqrt{a \sec ^3(x)}+\frac{10}{21} a \cos ^{\frac{3}{2}}(x) F\left(\left.\frac{x}{2}\right|2\right) \sqrt{a \sec ^3(x)}",1,"(10*a*Cos[x]^(3/2)*EllipticF[x/2, 2]*Sqrt[a*Sec[x]^3])/21 + (10*a*Sqrt[a*Sec[x]^3]*Sin[x])/21 + (2*a*Sec[x]*Sqrt[a*Sec[x]^3]*Tan[x])/7","A",5,4,10,0.4000,1,"{4123, 3768, 3771, 2641}"
57,1,42,0,0.0256077,"\int \sqrt{a \sec ^3(x)} \, dx","Int[Sqrt[a*Sec[x]^3],x]","2 \sin (x) \cos (x) \sqrt{a \sec ^3(x)}-2 \cos ^{\frac{3}{2}}(x) E\left(\left.\frac{x}{2}\right|2\right) \sqrt{a \sec ^3(x)}","2 \sin (x) \cos (x) \sqrt{a \sec ^3(x)}-2 \cos ^{\frac{3}{2}}(x) E\left(\left.\frac{x}{2}\right|2\right) \sqrt{a \sec ^3(x)}",1,"-2*Cos[x]^(3/2)*EllipticE[x/2, 2]*Sqrt[a*Sec[x]^3] + 2*Cos[x]*Sqrt[a*Sec[x]^3]*Sin[x]","A",4,4,10,0.4000,1,"{4123, 3768, 3771, 2639}"
58,1,44,0,0.0270201,"\int \frac{1}{\sqrt{a \sec ^3(x)}} \, dx","Int[1/Sqrt[a*Sec[x]^3],x]","\frac{2 \tan (x)}{3 \sqrt{a \sec ^3(x)}}+\frac{2 F\left(\left.\frac{x}{2}\right|2\right)}{3 \cos ^{\frac{3}{2}}(x) \sqrt{a \sec ^3(x)}}","\frac{2 \tan (x)}{3 \sqrt{a \sec ^3(x)}}+\frac{2 F\left(\left.\frac{x}{2}\right|2\right)}{3 \cos ^{\frac{3}{2}}(x) \sqrt{a \sec ^3(x)}}",1,"(2*EllipticF[x/2, 2])/(3*Cos[x]^(3/2)*Sqrt[a*Sec[x]^3]) + (2*Tan[x])/(3*Sqrt[a*Sec[x]^3])","A",4,4,10,0.4000,1,"{4123, 3769, 3771, 2641}"
59,1,73,0,0.0367949,"\int \frac{1}{\left(a \sec ^3(x)\right)^{3/2}} \, dx","Int[(a*Sec[x]^3)^(-3/2),x]","\frac{14 \sin (x)}{45 a \sqrt{a \sec ^3(x)}}+\frac{2 \sin (x) \cos ^2(x)}{9 a \sqrt{a \sec ^3(x)}}+\frac{14 E\left(\left.\frac{x}{2}\right|2\right)}{15 a \cos ^{\frac{3}{2}}(x) \sqrt{a \sec ^3(x)}}","\frac{14 \sin (x)}{45 a \sqrt{a \sec ^3(x)}}+\frac{2 \sin (x) \cos ^2(x)}{9 a \sqrt{a \sec ^3(x)}}+\frac{14 E\left(\left.\frac{x}{2}\right|2\right)}{15 a \cos ^{\frac{3}{2}}(x) \sqrt{a \sec ^3(x)}}",1,"(14*EllipticE[x/2, 2])/(15*a*Cos[x]^(3/2)*Sqrt[a*Sec[x]^3]) + (14*Sin[x])/(45*a*Sqrt[a*Sec[x]^3]) + (2*Cos[x]^2*Sin[x])/(9*a*Sqrt[a*Sec[x]^3])","A",5,4,10,0.4000,1,"{4123, 3769, 3771, 2639}"
60,1,117,0,0.0561162,"\int \frac{1}{\left(a \sec ^3(x)\right)^{5/2}} \, dx","Int[(a*Sec[x]^3)^(-5/2),x]","\frac{26 \tan (x)}{77 a^2 \sqrt{a \sec ^3(x)}}+\frac{2 \sin (x) \cos ^5(x)}{15 a^2 \sqrt{a \sec ^3(x)}}+\frac{26 \sin (x) \cos ^3(x)}{165 a^2 \sqrt{a \sec ^3(x)}}+\frac{26 F\left(\left.\frac{x}{2}\right|2\right)}{77 a^2 \cos ^{\frac{3}{2}}(x) \sqrt{a \sec ^3(x)}}+\frac{78 \sin (x) \cos (x)}{385 a^2 \sqrt{a \sec ^3(x)}}","\frac{26 \tan (x)}{77 a^2 \sqrt{a \sec ^3(x)}}+\frac{2 \sin (x) \cos ^5(x)}{15 a^2 \sqrt{a \sec ^3(x)}}+\frac{26 \sin (x) \cos ^3(x)}{165 a^2 \sqrt{a \sec ^3(x)}}+\frac{26 F\left(\left.\frac{x}{2}\right|2\right)}{77 a^2 \cos ^{\frac{3}{2}}(x) \sqrt{a \sec ^3(x)}}+\frac{78 \sin (x) \cos (x)}{385 a^2 \sqrt{a \sec ^3(x)}}",1,"(26*EllipticF[x/2, 2])/(77*a^2*Cos[x]^(3/2)*Sqrt[a*Sec[x]^3]) + (78*Cos[x]*Sin[x])/(385*a^2*Sqrt[a*Sec[x]^3]) + (26*Cos[x]^3*Sin[x])/(165*a^2*Sqrt[a*Sec[x]^3]) + (2*Cos[x]^5*Sin[x])/(15*a^2*Sqrt[a*Sec[x]^3]) + (26*Tan[x])/(77*a^2*Sqrt[a*Sec[x]^3])","A",7,4,10,0.4000,1,"{4123, 3769, 3771, 2641}"
61,1,163,0,0.0390895,"\int \left(a \sec ^4(x)\right)^{7/2} \, dx","Int[(a*Sec[x]^4)^(7/2),x]","a^3 \sin (x) \cos (x) \sqrt{a \sec ^4(x)}+\frac{1}{13} a^3 \sin ^2(x) \tan ^{11}(x) \sqrt{a \sec ^4(x)}+\frac{6}{11} a^3 \sin ^2(x) \tan ^9(x) \sqrt{a \sec ^4(x)}+\frac{5}{3} a^3 \sin ^2(x) \tan ^7(x) \sqrt{a \sec ^4(x)}+\frac{20}{7} a^3 \sin ^2(x) \tan ^5(x) \sqrt{a \sec ^4(x)}+3 a^3 \sin ^2(x) \tan ^3(x) \sqrt{a \sec ^4(x)}+2 a^3 \sin ^2(x) \tan (x) \sqrt{a \sec ^4(x)}","a^3 \sin (x) \cos (x) \sqrt{a \sec ^4(x)}+\frac{1}{13} a^3 \sin ^2(x) \tan ^{11}(x) \sqrt{a \sec ^4(x)}+\frac{6}{11} a^3 \sin ^2(x) \tan ^9(x) \sqrt{a \sec ^4(x)}+\frac{5}{3} a^3 \sin ^2(x) \tan ^7(x) \sqrt{a \sec ^4(x)}+\frac{20}{7} a^3 \sin ^2(x) \tan ^5(x) \sqrt{a \sec ^4(x)}+3 a^3 \sin ^2(x) \tan ^3(x) \sqrt{a \sec ^4(x)}+2 a^3 \sin ^2(x) \tan (x) \sqrt{a \sec ^4(x)}",1,"a^3*Cos[x]*Sqrt[a*Sec[x]^4]*Sin[x] + 2*a^3*Sqrt[a*Sec[x]^4]*Sin[x]^2*Tan[x] + 3*a^3*Sqrt[a*Sec[x]^4]*Sin[x]^2*Tan[x]^3 + (20*a^3*Sqrt[a*Sec[x]^4]*Sin[x]^2*Tan[x]^5)/7 + (5*a^3*Sqrt[a*Sec[x]^4]*Sin[x]^2*Tan[x]^7)/3 + (6*a^3*Sqrt[a*Sec[x]^4]*Sin[x]^2*Tan[x]^9)/11 + (a^3*Sqrt[a*Sec[x]^4]*Sin[x]^2*Tan[x]^11)/13","A",3,2,10,0.2000,1,"{4123, 3767}"
62,1,117,0,0.0303353,"\int \left(a \sec ^4(x)\right)^{5/2} \, dx","Int[(a*Sec[x]^4)^(5/2),x]","a^2 \sin (x) \cos (x) \sqrt{a \sec ^4(x)}+\frac{1}{9} a^2 \sin ^2(x) \tan ^7(x) \sqrt{a \sec ^4(x)}+\frac{4}{7} a^2 \sin ^2(x) \tan ^5(x) \sqrt{a \sec ^4(x)}+\frac{6}{5} a^2 \sin ^2(x) \tan ^3(x) \sqrt{a \sec ^4(x)}+\frac{4}{3} a^2 \sin ^2(x) \tan (x) \sqrt{a \sec ^4(x)}","a^2 \sin (x) \cos (x) \sqrt{a \sec ^4(x)}+\frac{1}{9} a^2 \sin ^2(x) \tan ^7(x) \sqrt{a \sec ^4(x)}+\frac{4}{7} a^2 \sin ^2(x) \tan ^5(x) \sqrt{a \sec ^4(x)}+\frac{6}{5} a^2 \sin ^2(x) \tan ^3(x) \sqrt{a \sec ^4(x)}+\frac{4}{3} a^2 \sin ^2(x) \tan (x) \sqrt{a \sec ^4(x)}",1,"a^2*Cos[x]*Sqrt[a*Sec[x]^4]*Sin[x] + (4*a^2*Sqrt[a*Sec[x]^4]*Sin[x]^2*Tan[x])/3 + (6*a^2*Sqrt[a*Sec[x]^4]*Sin[x]^2*Tan[x]^3)/5 + (4*a^2*Sqrt[a*Sec[x]^4]*Sin[x]^2*Tan[x]^5)/7 + (a^2*Sqrt[a*Sec[x]^4]*Sin[x]^2*Tan[x]^7)/9","A",3,2,10,0.2000,1,"{4123, 3767}"
63,1,61,0,0.0220653,"\int \left(a \sec ^4(x)\right)^{3/2} \, dx","Int[(a*Sec[x]^4)^(3/2),x]","a \sin (x) \cos (x) \sqrt{a \sec ^4(x)}+\frac{1}{5} a \sin ^2(x) \tan ^3(x) \sqrt{a \sec ^4(x)}+\frac{2}{3} a \sin ^2(x) \tan (x) \sqrt{a \sec ^4(x)}","a \sin (x) \cos (x) \sqrt{a \sec ^4(x)}+\frac{1}{5} a \sin ^2(x) \tan ^3(x) \sqrt{a \sec ^4(x)}+\frac{2}{3} a \sin ^2(x) \tan (x) \sqrt{a \sec ^4(x)}",1,"a*Cos[x]*Sqrt[a*Sec[x]^4]*Sin[x] + (2*a*Sqrt[a*Sec[x]^4]*Sin[x]^2*Tan[x])/3 + (a*Sqrt[a*Sec[x]^4]*Sin[x]^2*Tan[x]^3)/5","A",3,2,10,0.2000,1,"{4123, 3767}"
64,1,15,0,0.0158969,"\int \sqrt{a \sec ^4(x)} \, dx","Int[Sqrt[a*Sec[x]^4],x]","\sin (x) \cos (x) \sqrt{a \sec ^4(x)}","\sin (x) \cos (x) \sqrt{a \sec ^4(x)}",1,"Cos[x]*Sqrt[a*Sec[x]^4]*Sin[x]","A",3,3,10,0.3000,1,"{4123, 3767, 8}"
65,1,36,0,0.0146596,"\int \frac{1}{\sqrt{a \sec ^4(x)}} \, dx","Int[1/Sqrt[a*Sec[x]^4],x]","\frac{x \sec ^2(x)}{2 \sqrt{a \sec ^4(x)}}+\frac{\tan (x)}{2 \sqrt{a \sec ^4(x)}}","\frac{x \sec ^2(x)}{2 \sqrt{a \sec ^4(x)}}+\frac{\tan (x)}{2 \sqrt{a \sec ^4(x)}}",1,"(x*Sec[x]^2)/(2*Sqrt[a*Sec[x]^4]) + Tan[x]/(2*Sqrt[a*Sec[x]^4])","A",3,3,10,0.3000,1,"{4123, 2635, 8}"
66,1,86,0,0.0319133,"\int \frac{1}{\left(a \sec ^4(x)\right)^{3/2}} \, dx","Int[(a*Sec[x]^4)^(-3/2),x]","\frac{5 x \sec ^2(x)}{16 a \sqrt{a \sec ^4(x)}}+\frac{5 \tan (x)}{16 a \sqrt{a \sec ^4(x)}}+\frac{\sin (x) \cos ^3(x)}{6 a \sqrt{a \sec ^4(x)}}+\frac{5 \sin (x) \cos (x)}{24 a \sqrt{a \sec ^4(x)}}","\frac{5 x \sec ^2(x)}{16 a \sqrt{a \sec ^4(x)}}+\frac{5 \tan (x)}{16 a \sqrt{a \sec ^4(x)}}+\frac{\sin (x) \cos ^3(x)}{6 a \sqrt{a \sec ^4(x)}}+\frac{5 \sin (x) \cos (x)}{24 a \sqrt{a \sec ^4(x)}}",1,"(5*x*Sec[x]^2)/(16*a*Sqrt[a*Sec[x]^4]) + (5*Cos[x]*Sin[x])/(24*a*Sqrt[a*Sec[x]^4]) + (Cos[x]^3*Sin[x])/(6*a*Sqrt[a*Sec[x]^4]) + (5*Tan[x])/(16*a*Sqrt[a*Sec[x]^4])","A",5,3,10,0.3000,1,"{4123, 2635, 8}"
67,1,132,0,0.0508577,"\int \frac{1}{\left(a \sec ^4(x)\right)^{5/2}} \, dx","Int[(a*Sec[x]^4)^(-5/2),x]","\frac{63 x \sec ^2(x)}{256 a^2 \sqrt{a \sec ^4(x)}}+\frac{63 \tan (x)}{256 a^2 \sqrt{a \sec ^4(x)}}+\frac{\sin (x) \cos ^7(x)}{10 a^2 \sqrt{a \sec ^4(x)}}+\frac{9 \sin (x) \cos ^5(x)}{80 a^2 \sqrt{a \sec ^4(x)}}+\frac{21 \sin (x) \cos ^3(x)}{160 a^2 \sqrt{a \sec ^4(x)}}+\frac{21 \sin (x) \cos (x)}{128 a^2 \sqrt{a \sec ^4(x)}}","\frac{63 x \sec ^2(x)}{256 a^2 \sqrt{a \sec ^4(x)}}+\frac{63 \tan (x)}{256 a^2 \sqrt{a \sec ^4(x)}}+\frac{\sin (x) \cos ^7(x)}{10 a^2 \sqrt{a \sec ^4(x)}}+\frac{9 \sin (x) \cos ^5(x)}{80 a^2 \sqrt{a \sec ^4(x)}}+\frac{21 \sin (x) \cos ^3(x)}{160 a^2 \sqrt{a \sec ^4(x)}}+\frac{21 \sin (x) \cos (x)}{128 a^2 \sqrt{a \sec ^4(x)}}",1,"(63*x*Sec[x]^2)/(256*a^2*Sqrt[a*Sec[x]^4]) + (21*Cos[x]*Sin[x])/(128*a^2*Sqrt[a*Sec[x]^4]) + (21*Cos[x]^3*Sin[x])/(160*a^2*Sqrt[a*Sec[x]^4]) + (9*Cos[x]^5*Sin[x])/(80*a^2*Sqrt[a*Sec[x]^4]) + (Cos[x]^7*Sin[x])/(10*a^2*Sqrt[a*Sec[x]^4]) + (63*Tan[x])/(256*a^2*Sqrt[a*Sec[x]^4])","A",7,3,10,0.3000,1,"{4123, 2635, 8}"
68,1,81,0,0.0532608,"\int \left((b \sec (c+d x))^p\right)^n \, dx","Int[((b*Sec[c + d*x])^p)^n,x]","-\frac{\sin (c+d x) \cos (c+d x) \left((b \sec (c+d x))^p\right)^n \, _2F_1\left(\frac{1}{2},\frac{1}{2} (1-n p);\frac{1}{2} (3-n p);\cos ^2(c+d x)\right)}{d (1-n p) \sqrt{\sin ^2(c+d x)}}","-\frac{\sin (c+d x) \cos (c+d x) \left((b \sec (c+d x))^p\right)^n \, _2F_1\left(\frac{1}{2},\frac{1}{2} (1-n p);\frac{1}{2} (3-n p);\cos ^2(c+d x)\right)}{d (1-n p) \sqrt{\sin ^2(c+d x)}}",1,"-((Cos[c + d*x]*Hypergeometric2F1[1/2, (1 - n*p)/2, (3 - n*p)/2, Cos[c + d*x]^2]*((b*Sec[c + d*x])^p)^n*Sin[c + d*x])/(d*(1 - n*p)*Sqrt[Sin[c + d*x]^2]))","A",3,3,12,0.2500,1,"{4123, 3772, 2643}"
69,1,83,0,0.0495264,"\int \left(a (b \sec (c+d x))^p\right)^n \, dx","Int[(a*(b*Sec[c + d*x])^p)^n,x]","-\frac{\sin (c+d x) \cos (c+d x) \, _2F_1\left(\frac{1}{2},\frac{1}{2} (1-n p);\frac{1}{2} (3-n p);\cos ^2(c+d x)\right) \left(a (b \sec (c+d x))^p\right)^n}{d (1-n p) \sqrt{\sin ^2(c+d x)}}","-\frac{\sin (c+d x) \cos (c+d x) \, _2F_1\left(\frac{1}{2},\frac{1}{2} (1-n p);\frac{1}{2} (3-n p);\cos ^2(c+d x)\right) \left(a (b \sec (c+d x))^p\right)^n}{d (1-n p) \sqrt{\sin ^2(c+d x)}}",1,"-((Cos[c + d*x]*Hypergeometric2F1[1/2, (1 - n*p)/2, (3 - n*p)/2, Cos[c + d*x]^2]*(a*(b*Sec[c + d*x])^p)^n*Sin[c + d*x])/(d*(1 - n*p)*Sqrt[Sin[c + d*x]^2]))","A",3,3,14,0.2143,1,"{4123, 3772, 2643}"
70,1,97,0,0.0604263,"\int \sec ^4(c+d x) \sqrt{b \sec (c+d x)} \, dx","Int[Sec[c + d*x]^4*Sqrt[b*Sec[c + d*x]],x]","\frac{2 \sin (c+d x) (b \sec (c+d x))^{7/2}}{7 b^3 d}+\frac{10 \sin (c+d x) (b \sec (c+d x))^{3/2}}{21 b d}+\frac{10 \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 \sin (c+d x) (b \sec (c+d x))^{7/2}}{7 b^3 d}+\frac{10 \sin (c+d x) (b \sec (c+d x))^{3/2}}{21 b d}+\frac{10 \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}",1,"(10*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2]*Sqrt[b*Sec[c + d*x]])/(21*d) + (10*(b*Sec[c + d*x])^(3/2)*Sin[c + d*x])/(21*b*d) + (2*(b*Sec[c + d*x])^(7/2)*Sin[c + d*x])/(7*b^3*d)","A",5,4,21,0.1905,1,"{16, 3768, 3771, 2641}"
71,1,95,0,0.0606493,"\int \sec ^3(c+d x) \sqrt{b \sec (c+d x)} \, dx","Int[Sec[c + d*x]^3*Sqrt[b*Sec[c + d*x]],x]","\frac{2 \sin (c+d x) (b \sec (c+d x))^{5/2}}{5 b^2 d}+\frac{6 \sin (c+d x) \sqrt{b \sec (c+d x)}}{5 d}-\frac{6 b 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 \sin (c+d x) (b \sec (c+d x))^{5/2}}{5 b^2 d}+\frac{6 \sin (c+d x) \sqrt{b \sec (c+d x)}}{5 d}-\frac{6 b 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)}}",1,"(-6*b*EllipticE[(c + d*x)/2, 2])/(5*d*Sqrt[Cos[c + d*x]]*Sqrt[b*Sec[c + d*x]]) + (6*Sqrt[b*Sec[c + d*x]]*Sin[c + d*x])/(5*d) + (2*(b*Sec[c + d*x])^(5/2)*Sin[c + d*x])/(5*b^2*d)","A",5,4,21,0.1905,1,"{16, 3768, 3771, 2639}"
72,1,69,0,0.0420639,"\int \sec ^2(c+d x) \sqrt{b \sec (c+d x)} \, dx","Int[Sec[c + d*x]^2*Sqrt[b*Sec[c + d*x]],x]","\frac{2 \sin (c+d x) (b \sec (c+d x))^{3/2}}{3 b d}+\frac{2 \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 \sin (c+d x) (b \sec (c+d x))^{3/2}}{3 b d}+\frac{2 \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*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2]*Sqrt[b*Sec[c + d*x]])/(3*d) + (2*(b*Sec[c + d*x])^(3/2)*Sin[c + d*x])/(3*b*d)","A",4,4,21,0.1905,1,"{16, 3768, 3771, 2641}"
73,1,63,0,0.0407368,"\int \sec (c+d x) \sqrt{b \sec (c+d x)} \, dx","Int[Sec[c + d*x]*Sqrt[b*Sec[c + d*x]],x]","\frac{2 \sin (c+d x) \sqrt{b \sec (c+d x)}}{d}-\frac{2 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 \sin (c+d x) \sqrt{b \sec (c+d x)}}{d}-\frac{2 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)}}",1,"(-2*b*EllipticE[(c + d*x)/2, 2])/(d*Sqrt[Cos[c + d*x]]*Sqrt[b*Sec[c + d*x]]) + (2*Sqrt[b*Sec[c + d*x]]*Sin[c + d*x])/d","A",4,4,19,0.2105,1,"{16, 3768, 3771, 2639}"
74,1,38,0,0.0202235,"\int \sqrt{b \sec (c+d x)} \, dx","Int[Sqrt[b*Sec[c + d*x]],x]","\frac{2 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \sec (c+d x)}}{d}","\frac{2 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \sec (c+d x)}}{d}",1,"(2*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2]*Sqrt[b*Sec[c + d*x]])/d","A",2,2,12,0.1667,1,"{3771, 2641}"
75,1,39,0,0.0296558,"\int \cos (c+d x) \sqrt{b \sec (c+d x)} \, dx","Int[Cos[c + d*x]*Sqrt[b*Sec[c + d*x]],x]","\frac{2 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 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)}}",1,"(2*b*EllipticE[(c + d*x)/2, 2])/(d*Sqrt[Cos[c + d*x]]*Sqrt[b*Sec[c + d*x]])","A",3,3,19,0.1579,1,"{16, 3771, 2639}"
76,1,67,0,0.0516895,"\int \cos ^2(c+d x) \sqrt{b \sec (c+d x)} \, dx","Int[Cos[c + d*x]^2*Sqrt[b*Sec[c + d*x]],x]","\frac{2 b \sin (c+d x)}{3 d \sqrt{b \sec (c+d x)}}+\frac{2 \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)}{3 d \sqrt{b \sec (c+d x)}}+\frac{2 \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*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2]*Sqrt[b*Sec[c + d*x]])/(3*d) + (2*b*Sin[c + d*x])/(3*d*Sqrt[b*Sec[c + d*x]])","A",4,4,21,0.1905,1,"{16, 3769, 3771, 2641}"
77,1,70,0,0.0514325,"\int \cos ^3(c+d x) \sqrt{b \sec (c+d x)} \, dx","Int[Cos[c + d*x]^3*Sqrt[b*Sec[c + d*x]],x]","\frac{2 b^2 \sin (c+d x)}{5 d (b \sec (c+d x))^{3/2}}+\frac{6 b 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^2 \sin (c+d x)}{5 d (b \sec (c+d x))^{3/2}}+\frac{6 b 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)}}",1,"(6*b*EllipticE[(c + d*x)/2, 2])/(5*d*Sqrt[Cos[c + d*x]]*Sqrt[b*Sec[c + d*x]]) + (2*b^2*Sin[c + d*x])/(5*d*(b*Sec[c + d*x])^(3/2))","A",4,4,21,0.1905,1,"{16, 3769, 3771, 2639}"
78,1,95,0,0.0701063,"\int \cos ^4(c+d x) \sqrt{b \sec (c+d x)} \, dx","Int[Cos[c + d*x]^4*Sqrt[b*Sec[c + d*x]],x]","\frac{2 b^3 \sin (c+d x)}{7 d (b \sec (c+d x))^{5/2}}+\frac{10 b \sin (c+d x)}{21 d \sqrt{b \sec (c+d x)}}+\frac{10 \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^3 \sin (c+d x)}{7 d (b \sec (c+d x))^{5/2}}+\frac{10 b \sin (c+d x)}{21 d \sqrt{b \sec (c+d x)}}+\frac{10 \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}",1,"(10*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2]*Sqrt[b*Sec[c + d*x]])/(21*d) + (2*b^3*Sin[c + d*x])/(7*d*(b*Sec[c + d*x])^(5/2)) + (10*b*Sin[c + d*x])/(21*d*Sqrt[b*Sec[c + d*x]])","A",5,4,21,0.1905,1,"{16, 3769, 3771, 2641}"
79,1,98,0,0.0693045,"\int \cos ^5(c+d x) \sqrt{b \sec (c+d x)} \, dx","Int[Cos[c + d*x]^5*Sqrt[b*Sec[c + d*x]],x]","\frac{2 b^4 \sin (c+d x)}{9 d (b \sec (c+d x))^{7/2}}+\frac{14 b^2 \sin (c+d x)}{45 d (b \sec (c+d x))^{3/2}}+\frac{14 b E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{15 d \sqrt{\cos (c+d x)} \sqrt{b \sec (c+d x)}}","\frac{2 b^4 \sin (c+d x)}{9 d (b \sec (c+d x))^{7/2}}+\frac{14 b^2 \sin (c+d x)}{45 d (b \sec (c+d x))^{3/2}}+\frac{14 b E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{15 d \sqrt{\cos (c+d x)} \sqrt{b \sec (c+d x)}}",1,"(14*b*EllipticE[(c + d*x)/2, 2])/(15*d*Sqrt[Cos[c + d*x]]*Sqrt[b*Sec[c + d*x]]) + (2*b^4*Sin[c + d*x])/(9*d*(b*Sec[c + d*x])^(7/2)) + (14*b^2*Sin[c + d*x])/(45*d*(b*Sec[c + d*x])^(3/2))","A",5,4,21,0.1905,1,"{16, 3769, 3771, 2639}"
80,1,95,0,0.0594839,"\int \sec ^3(c+d x) (b \sec (c+d x))^{3/2} \, dx","Int[Sec[c + d*x]^3*(b*Sec[c + d*x])^(3/2),x]","\frac{2 \sin (c+d x) (b \sec (c+d x))^{7/2}}{7 b^2 d}+\frac{10 \sin (c+d x) (b \sec (c+d x))^{3/2}}{21 d}+\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 d}","\frac{2 \sin (c+d x) (b \sec (c+d x))^{7/2}}{7 b^2 d}+\frac{10 \sin (c+d x) (b \sec (c+d x))^{3/2}}{21 d}+\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 d}",1,"(10*b*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2]*Sqrt[b*Sec[c + d*x]])/(21*d) + (10*(b*Sec[c + d*x])^(3/2)*Sin[c + d*x])/(21*d) + (2*(b*Sec[c + d*x])^(7/2)*Sin[c + d*x])/(7*b^2*d)","A",5,4,21,0.1905,1,"{16, 3768, 3771, 2641}"
81,1,98,0,0.0591151,"\int \sec ^2(c+d x) (b \sec (c+d x))^{3/2} \, dx","Int[Sec[c + d*x]^2*(b*Sec[c + d*x])^(3/2),x]","-\frac{6 b^2 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 \sin (c+d x) (b \sec (c+d x))^{5/2}}{5 b d}+\frac{6 b \sin (c+d x) \sqrt{b \sec (c+d x)}}{5 d}","-\frac{6 b^2 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 \sin (c+d x) (b \sec (c+d x))^{5/2}}{5 b d}+\frac{6 b \sin (c+d x) \sqrt{b \sec (c+d x)}}{5 d}",1,"(-6*b^2*EllipticE[(c + d*x)/2, 2])/(5*d*Sqrt[Cos[c + d*x]]*Sqrt[b*Sec[c + d*x]]) + (6*b*Sqrt[b*Sec[c + d*x]]*Sin[c + d*x])/(5*d) + (2*(b*Sec[c + d*x])^(5/2)*Sin[c + d*x])/(5*b*d)","A",5,4,21,0.1905,1,"{16, 3768, 3771, 2639}"
82,1,67,0,0.0407184,"\int \sec (c+d x) (b \sec (c+d x))^{3/2} \, dx","Int[Sec[c + d*x]*(b*Sec[c + d*x])^(3/2),x]","\frac{2 \sin (c+d x) (b \sec (c+d x))^{3/2}}{3 d}+\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 d}","\frac{2 \sin (c+d x) (b \sec (c+d x))^{3/2}}{3 d}+\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 d}",1,"(2*b*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2]*Sqrt[b*Sec[c + d*x]])/(3*d) + (2*(b*Sec[c + d*x])^(3/2)*Sin[c + d*x])/(3*d)","A",4,4,19,0.2105,1,"{16, 3768, 3771, 2641}"
83,1,66,0,0.0335228,"\int (b \sec (c+d x))^{3/2} \, dx","Int[(b*Sec[c + d*x])^(3/2),x]","\frac{2 b \sin (c+d x) \sqrt{b \sec (c+d x)}}{d}-\frac{2 b^2 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 \sin (c+d x) \sqrt{b \sec (c+d x)}}{d}-\frac{2 b^2 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*b^2*EllipticE[(c + d*x)/2, 2])/(d*Sqrt[Cos[c + d*x]]*Sqrt[b*Sec[c + d*x]]) + (2*b*Sqrt[b*Sec[c + d*x]]*Sin[c + d*x])/d","A",3,3,12,0.2500,1,"{3768, 3771, 2639}"
84,1,39,0,0.030127,"\int \cos (c+d x) (b \sec (c+d x))^{3/2} \, dx","Int[Cos[c + d*x]*(b*Sec[c + d*x])^(3/2),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)}}{d}","\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)}}{d}",1,"(2*b*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2]*Sqrt[b*Sec[c + d*x]])/d","A",3,3,19,0.1579,1,"{16, 3771, 2641}"
85,1,41,0,0.0378043,"\int \cos ^2(c+d x) (b \sec (c+d x))^{3/2} \, dx","Int[Cos[c + d*x]^2*(b*Sec[c + d*x])^(3/2),x]","\frac{2 b^2 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^2 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*b^2*EllipticE[(c + d*x)/2, 2])/(d*Sqrt[Cos[c + d*x]]*Sqrt[b*Sec[c + d*x]])","A",3,3,21,0.1429,1,"{16, 3771, 2639}"
86,1,70,0,0.0542509,"\int \cos ^3(c+d x) (b \sec (c+d x))^{3/2} \, dx","Int[Cos[c + d*x]^3*(b*Sec[c + d*x])^(3/2),x]","\frac{2 b^2 \sin (c+d x)}{3 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 d}","\frac{2 b^2 \sin (c+d x)}{3 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 d}",1,"(2*b*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2]*Sqrt[b*Sec[c + d*x]])/(3*d) + (2*b^2*Sin[c + d*x])/(3*d*Sqrt[b*Sec[c + d*x]])","A",4,4,21,0.1905,1,"{16, 3769, 3771, 2641}"
87,1,72,0,0.0541705,"\int \cos ^4(c+d x) (b \sec (c+d x))^{3/2} \, dx","Int[Cos[c + d*x]^4*(b*Sec[c + d*x])^(3/2),x]","\frac{2 b^3 \sin (c+d x)}{5 d (b \sec (c+d x))^{3/2}}+\frac{6 b^2 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^3 \sin (c+d x)}{5 d (b \sec (c+d x))^{3/2}}+\frac{6 b^2 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)}}",1,"(6*b^2*EllipticE[(c + d*x)/2, 2])/(5*d*Sqrt[Cos[c + d*x]]*Sqrt[b*Sec[c + d*x]]) + (2*b^3*Sin[c + d*x])/(5*d*(b*Sec[c + d*x])^(3/2))","A",4,4,21,0.1905,1,"{16, 3769, 3771, 2639}"
88,1,98,0,0.0730224,"\int \cos ^5(c+d x) (b \sec (c+d x))^{3/2} \, dx","Int[Cos[c + d*x]^5*(b*Sec[c + d*x])^(3/2),x]","\frac{2 b^4 \sin (c+d x)}{7 d (b \sec (c+d x))^{5/2}}+\frac{10 b^2 \sin (c+d x)}{21 d \sqrt{b \sec (c+d x)}}+\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 d}","\frac{2 b^4 \sin (c+d x)}{7 d (b \sec (c+d x))^{5/2}}+\frac{10 b^2 \sin (c+d x)}{21 d \sqrt{b \sec (c+d x)}}+\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 d}",1,"(10*b*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2]*Sqrt[b*Sec[c + d*x]])/(21*d) + (2*b^4*Sin[c + d*x])/(7*d*(b*Sec[c + d*x])^(5/2)) + (10*b^2*Sin[c + d*x])/(21*d*Sqrt[b*Sec[c + d*x]])","A",5,4,21,0.1905,1,"{16, 3769, 3771, 2641}"
89,1,100,0,0.0747851,"\int \cos ^6(c+d x) (b \sec (c+d x))^{3/2} \, dx","Int[Cos[c + d*x]^6*(b*Sec[c + d*x])^(3/2),x]","\frac{2 b^5 \sin (c+d x)}{9 d (b \sec (c+d x))^{7/2}}+\frac{14 b^3 \sin (c+d x)}{45 d (b \sec (c+d x))^{3/2}}+\frac{14 b^2 E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{15 d \sqrt{\cos (c+d x)} \sqrt{b \sec (c+d x)}}","\frac{2 b^5 \sin (c+d x)}{9 d (b \sec (c+d x))^{7/2}}+\frac{14 b^3 \sin (c+d x)}{45 d (b \sec (c+d x))^{3/2}}+\frac{14 b^2 E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{15 d \sqrt{\cos (c+d x)} \sqrt{b \sec (c+d x)}}",1,"(14*b^2*EllipticE[(c + d*x)/2, 2])/(15*d*Sqrt[Cos[c + d*x]]*Sqrt[b*Sec[c + d*x]]) + (2*b^5*Sin[c + d*x])/(9*d*(b*Sec[c + d*x])^(7/2)) + (14*b^3*Sin[c + d*x])/(45*d*(b*Sec[c + d*x])^(3/2))","A",5,4,21,0.1905,1,"{16, 3769, 3771, 2639}"
90,1,98,0,0.0588525,"\int \sec ^2(c+d x) (b \sec (c+d x))^{5/2} \, dx","Int[Sec[c + d*x]^2*(b*Sec[c + d*x])^(5/2),x]","\frac{10 b^2 \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 \sin (c+d x) (b \sec (c+d x))^{7/2}}{7 b d}+\frac{10 b \sin (c+d x) (b \sec (c+d x))^{3/2}}{21 d}","\frac{10 b^2 \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 \sin (c+d x) (b \sec (c+d x))^{7/2}}{7 b d}+\frac{10 b \sin (c+d x) (b \sec (c+d x))^{3/2}}{21 d}",1,"(10*b^2*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2]*Sqrt[b*Sec[c + d*x]])/(21*d) + (10*b*(b*Sec[c + d*x])^(3/2)*Sin[c + d*x])/(21*d) + (2*(b*Sec[c + d*x])^(7/2)*Sin[c + d*x])/(7*b*d)","A",5,4,21,0.1905,1,"{16, 3768, 3771, 2641}"
91,1,97,0,0.0567826,"\int \sec (c+d x) (b \sec (c+d x))^{5/2} \, dx","Int[Sec[c + d*x]*(b*Sec[c + d*x])^(5/2),x]","\frac{6 b^2 \sin (c+d x) \sqrt{b \sec (c+d x)}}{5 d}-\frac{6 b^3 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 \sin (c+d x) (b \sec (c+d x))^{5/2}}{5 d}","\frac{6 b^2 \sin (c+d x) \sqrt{b \sec (c+d x)}}{5 d}-\frac{6 b^3 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 \sin (c+d x) (b \sec (c+d x))^{5/2}}{5 d}",1,"(-6*b^3*EllipticE[(c + d*x)/2, 2])/(5*d*Sqrt[Cos[c + d*x]]*Sqrt[b*Sec[c + d*x]]) + (6*b^2*Sqrt[b*Sec[c + d*x]]*Sin[c + d*x])/(5*d) + (2*(b*Sec[c + d*x])^(5/2)*Sin[c + d*x])/(5*d)","A",5,4,19,0.2105,1,"{16, 3768, 3771, 2639}"
92,1,70,0,0.0323627,"\int (b \sec (c+d x))^{5/2} \, dx","Int[(b*Sec[c + d*x])^(5/2),x]","\frac{2 b^2 \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) (b \sec (c+d x))^{3/2}}{3 d}","\frac{2 b^2 \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) (b \sec (c+d x))^{3/2}}{3 d}",1,"(2*b^2*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2]*Sqrt[b*Sec[c + d*x]])/(3*d) + (2*b*(b*Sec[c + d*x])^(3/2)*Sin[c + d*x])/(3*d)","A",3,3,12,0.2500,1,"{3768, 3771, 2641}"
93,1,68,0,0.0445958,"\int \cos (c+d x) (b \sec (c+d x))^{5/2} \, dx","Int[Cos[c + d*x]*(b*Sec[c + d*x])^(5/2),x]","\frac{2 b^2 \sin (c+d x) \sqrt{b \sec (c+d x)}}{d}-\frac{2 b^3 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^2 \sin (c+d x) \sqrt{b \sec (c+d x)}}{d}-\frac{2 b^3 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*b^3*EllipticE[(c + d*x)/2, 2])/(d*Sqrt[Cos[c + d*x]]*Sqrt[b*Sec[c + d*x]]) + (2*b^2*Sqrt[b*Sec[c + d*x]]*Sin[c + d*x])/d","A",4,4,19,0.2105,1,"{16, 3768, 3771, 2639}"
94,1,41,0,0.0379056,"\int \cos ^2(c+d x) (b \sec (c+d x))^{5/2} \, dx","Int[Cos[c + d*x]^2*(b*Sec[c + d*x])^(5/2),x]","\frac{2 b^2 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \sec (c+d x)}}{d}","\frac{2 b^2 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \sec (c+d x)}}{d}",1,"(2*b^2*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2]*Sqrt[b*Sec[c + d*x]])/d","A",3,3,21,0.1429,1,"{16, 3771, 2641}"
95,1,41,0,0.0367042,"\int \cos ^3(c+d x) (b \sec (c+d x))^{5/2} \, dx","Int[Cos[c + d*x]^3*(b*Sec[c + d*x])^(5/2),x]","\frac{2 b^3 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^3 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*b^3*EllipticE[(c + d*x)/2, 2])/(d*Sqrt[Cos[c + d*x]]*Sqrt[b*Sec[c + d*x]])","A",3,3,21,0.1429,1,"{16, 3771, 2639}"
96,1,72,0,0.0546094,"\int \cos ^4(c+d x) (b \sec (c+d x))^{5/2} \, dx","Int[Cos[c + d*x]^4*(b*Sec[c + d*x])^(5/2),x]","\frac{2 b^3 \sin (c+d x)}{3 d \sqrt{b \sec (c+d x)}}+\frac{2 b^2 \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^3 \sin (c+d x)}{3 d \sqrt{b \sec (c+d x)}}+\frac{2 b^2 \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^2*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2]*Sqrt[b*Sec[c + d*x]])/(3*d) + (2*b^3*Sin[c + d*x])/(3*d*Sqrt[b*Sec[c + d*x]])","A",4,4,21,0.1905,1,"{16, 3769, 3771, 2641}"
97,1,72,0,0.0537524,"\int \cos ^5(c+d x) (b \sec (c+d x))^{5/2} \, dx","Int[Cos[c + d*x]^5*(b*Sec[c + d*x])^(5/2),x]","\frac{2 b^4 \sin (c+d x)}{5 d (b \sec (c+d x))^{3/2}}+\frac{6 b^3 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^4 \sin (c+d x)}{5 d (b \sec (c+d x))^{3/2}}+\frac{6 b^3 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)}}",1,"(6*b^3*EllipticE[(c + d*x)/2, 2])/(5*d*Sqrt[Cos[c + d*x]]*Sqrt[b*Sec[c + d*x]]) + (2*b^4*Sin[c + d*x])/(5*d*(b*Sec[c + d*x])^(3/2))","A",4,4,21,0.1905,1,"{16, 3769, 3771, 2639}"
98,1,100,0,0.0714372,"\int \cos ^6(c+d x) (b \sec (c+d x))^{5/2} \, dx","Int[Cos[c + d*x]^6*(b*Sec[c + d*x])^(5/2),x]","\frac{2 b^5 \sin (c+d x)}{7 d (b \sec (c+d x))^{5/2}}+\frac{10 b^3 \sin (c+d x)}{21 d \sqrt{b \sec (c+d x)}}+\frac{10 b^2 \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^5 \sin (c+d x)}{7 d (b \sec (c+d x))^{5/2}}+\frac{10 b^3 \sin (c+d x)}{21 d \sqrt{b \sec (c+d x)}}+\frac{10 b^2 \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}",1,"(10*b^2*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2]*Sqrt[b*Sec[c + d*x]])/(21*d) + (2*b^5*Sin[c + d*x])/(7*d*(b*Sec[c + d*x])^(5/2)) + (10*b^3*Sin[c + d*x])/(21*d*Sqrt[b*Sec[c + d*x]])","A",5,4,21,0.1905,1,"{16, 3769, 3771, 2641}"
99,1,100,0,0.0740449,"\int \cos ^7(c+d x) (b \sec (c+d x))^{5/2} \, dx","Int[Cos[c + d*x]^7*(b*Sec[c + d*x])^(5/2),x]","\frac{2 b^6 \sin (c+d x)}{9 d (b \sec (c+d x))^{7/2}}+\frac{14 b^4 \sin (c+d x)}{45 d (b \sec (c+d x))^{3/2}}+\frac{14 b^3 E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{15 d \sqrt{\cos (c+d x)} \sqrt{b \sec (c+d x)}}","\frac{2 b^6 \sin (c+d x)}{9 d (b \sec (c+d x))^{7/2}}+\frac{14 b^4 \sin (c+d x)}{45 d (b \sec (c+d x))^{3/2}}+\frac{14 b^3 E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{15 d \sqrt{\cos (c+d x)} \sqrt{b \sec (c+d x)}}",1,"(14*b^3*EllipticE[(c + d*x)/2, 2])/(15*d*Sqrt[Cos[c + d*x]]*Sqrt[b*Sec[c + d*x]]) + (2*b^6*Sin[c + d*x])/(9*d*(b*Sec[c + d*x])^(7/2)) + (14*b^4*Sin[c + d*x])/(45*d*(b*Sec[c + d*x])^(3/2))","A",5,4,21,0.1905,1,"{16, 3769, 3771, 2639}"
100,1,98,0,0.0484491,"\int (b \sec (c+d x))^{7/2} \, dx","Int[(b*Sec[c + d*x])^(7/2),x]","\frac{6 b^3 \sin (c+d x) \sqrt{b \sec (c+d x)}}{5 d}-\frac{6 b^4 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))^{5/2}}{5 d}","\frac{6 b^3 \sin (c+d x) \sqrt{b \sec (c+d x)}}{5 d}-\frac{6 b^4 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))^{5/2}}{5 d}",1,"(-6*b^4*EllipticE[(c + d*x)/2, 2])/(5*d*Sqrt[Cos[c + d*x]]*Sqrt[b*Sec[c + d*x]]) + (6*b^3*Sqrt[b*Sec[c + d*x]]*Sin[c + d*x])/(5*d) + (2*b*(b*Sec[c + d*x])^(5/2)*Sin[c + d*x])/(5*d)","A",4,3,12,0.2500,1,"{3768, 3771, 2639}"
101,1,100,0,0.0574047,"\int \frac{\sec ^5(c+d x)}{\sqrt{b \sec (c+d x)}} \, dx","Int[Sec[c + d*x]^5/Sqrt[b*Sec[c + d*x]],x]","\frac{2 \sin (c+d x) (b \sec (c+d x))^{7/2}}{7 b^4 d}+\frac{10 \sin (c+d x) (b \sec (c+d x))^{3/2}}{21 b^2 d}+\frac{10 \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 d}","\frac{2 \sin (c+d x) (b \sec (c+d x))^{7/2}}{7 b^4 d}+\frac{10 \sin (c+d x) (b \sec (c+d x))^{3/2}}{21 b^2 d}+\frac{10 \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 d}",1,"(10*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2]*Sqrt[b*Sec[c + d*x]])/(21*b*d) + (10*(b*Sec[c + d*x])^(3/2)*Sin[c + d*x])/(21*b^2*d) + (2*(b*Sec[c + d*x])^(7/2)*Sin[c + d*x])/(7*b^4*d)","A",5,4,21,0.1905,1,"{16, 3768, 3771, 2641}"
102,1,97,0,0.0586433,"\int \frac{\sec ^4(c+d x)}{\sqrt{b \sec (c+d x)}} \, dx","Int[Sec[c + d*x]^4/Sqrt[b*Sec[c + d*x]],x]","\frac{2 \sin (c+d x) (b \sec (c+d x))^{5/2}}{5 b^3 d}+\frac{6 \sin (c+d x) \sqrt{b \sec (c+d x)}}{5 b d}-\frac{6 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 \sin (c+d x) (b \sec (c+d x))^{5/2}}{5 b^3 d}+\frac{6 \sin (c+d x) \sqrt{b \sec (c+d x)}}{5 b d}-\frac{6 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)}}",1,"(-6*EllipticE[(c + d*x)/2, 2])/(5*d*Sqrt[Cos[c + d*x]]*Sqrt[b*Sec[c + d*x]]) + (6*Sqrt[b*Sec[c + d*x]]*Sin[c + d*x])/(5*b*d) + (2*(b*Sec[c + d*x])^(5/2)*Sin[c + d*x])/(5*b^3*d)","A",5,4,21,0.1905,1,"{16, 3768, 3771, 2639}"
103,1,72,0,0.0394617,"\int \frac{\sec ^3(c+d x)}{\sqrt{b \sec (c+d x)}} \, dx","Int[Sec[c + d*x]^3/Sqrt[b*Sec[c + d*x]],x]","\frac{2 \sin (c+d x) (b \sec (c+d x))^{3/2}}{3 b^2 d}+\frac{2 \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 d}","\frac{2 \sin (c+d x) (b \sec (c+d x))^{3/2}}{3 b^2 d}+\frac{2 \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 d}",1,"(2*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2]*Sqrt[b*Sec[c + d*x]])/(3*b*d) + (2*(b*Sec[c + d*x])^(3/2)*Sin[c + d*x])/(3*b^2*d)","A",4,4,21,0.1905,1,"{16, 3768, 3771, 2641}"
104,1,65,0,0.0401477,"\int \frac{\sec ^2(c+d x)}{\sqrt{b \sec (c+d x)}} \, dx","Int[Sec[c + d*x]^2/Sqrt[b*Sec[c + d*x]],x]","\frac{2 \sin (c+d x) \sqrt{b \sec (c+d x)}}{b d}-\frac{2 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 \sin (c+d x) \sqrt{b \sec (c+d x)}}{b d}-\frac{2 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*EllipticE[(c + d*x)/2, 2])/(d*Sqrt[Cos[c + d*x]]*Sqrt[b*Sec[c + d*x]]) + (2*Sqrt[b*Sec[c + d*x]]*Sin[c + d*x])/(b*d)","A",4,4,21,0.1905,1,"{16, 3768, 3771, 2639}"
105,1,41,0,0.0212964,"\int \frac{\sec (c+d x)}{\sqrt{b \sec (c+d x)}} \, dx","Int[Sec[c + d*x]/Sqrt[b*Sec[c + d*x]],x]","\frac{2 \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 \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}",1,"(2*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2]*Sqrt[b*Sec[c + d*x]])/(b*d)","A",3,3,19,0.1579,1,"{16, 3771, 2641}"
106,1,38,0,0.0190712,"\int \frac{1}{\sqrt{b \sec (c+d x)}} \, dx","Int[1/Sqrt[b*Sec[c + d*x]],x]","\frac{2 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 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*EllipticE[(c + d*x)/2, 2])/(d*Sqrt[Cos[c + d*x]]*Sqrt[b*Sec[c + d*x]])","A",2,2,12,0.1667,1,"{3771, 2639}"
107,1,69,0,0.0434153,"\int \frac{\cos (c+d x)}{\sqrt{b \sec (c+d x)}} \, dx","Int[Cos[c + d*x]/Sqrt[b*Sec[c + d*x]],x]","\frac{2 \sin (c+d x)}{3 d \sqrt{b \sec (c+d x)}}+\frac{2 \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 d}","\frac{2 \sin (c+d x)}{3 d \sqrt{b \sec (c+d x)}}+\frac{2 \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 d}",1,"(2*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2]*Sqrt[b*Sec[c + d*x]])/(3*b*d) + (2*Sin[c + d*x])/(3*d*Sqrt[b*Sec[c + d*x]])","A",4,4,19,0.2105,1,"{16, 3769, 3771, 2641}"
108,1,67,0,0.0507569,"\int \frac{\cos ^2(c+d x)}{\sqrt{b \sec (c+d x)}} \, dx","Int[Cos[c + d*x]^2/Sqrt[b*Sec[c + d*x]],x]","\frac{2 b \sin (c+d x)}{5 d (b \sec (c+d x))^{3/2}}+\frac{6 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)}{5 d (b \sec (c+d x))^{3/2}}+\frac{6 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)}}",1,"(6*EllipticE[(c + d*x)/2, 2])/(5*d*Sqrt[Cos[c + d*x]]*Sqrt[b*Sec[c + d*x]]) + (2*b*Sin[c + d*x])/(5*d*(b*Sec[c + d*x])^(3/2))","A",4,4,21,0.1905,1,"{16, 3769, 3771, 2639}"
109,1,97,0,0.0690577,"\int \frac{\cos ^3(c+d x)}{\sqrt{b \sec (c+d x)}} \, dx","Int[Cos[c + d*x]^3/Sqrt[b*Sec[c + d*x]],x]","\frac{2 b^2 \sin (c+d x)}{7 d (b \sec (c+d x))^{5/2}}+\frac{10 \sin (c+d x)}{21 d \sqrt{b \sec (c+d x)}}+\frac{10 \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 d}","\frac{2 b^2 \sin (c+d x)}{7 d (b \sec (c+d x))^{5/2}}+\frac{10 \sin (c+d x)}{21 d \sqrt{b \sec (c+d x)}}+\frac{10 \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 d}",1,"(10*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2]*Sqrt[b*Sec[c + d*x]])/(21*b*d) + (2*b^2*Sin[c + d*x])/(7*d*(b*Sec[c + d*x])^(5/2)) + (10*Sin[c + d*x])/(21*d*Sqrt[b*Sec[c + d*x]])","A",5,4,21,0.1905,1,"{16, 3769, 3771, 2641}"
110,1,95,0,0.069369,"\int \frac{\cos ^4(c+d x)}{\sqrt{b \sec (c+d x)}} \, dx","Int[Cos[c + d*x]^4/Sqrt[b*Sec[c + d*x]],x]","\frac{2 b^3 \sin (c+d x)}{9 d (b \sec (c+d x))^{7/2}}+\frac{14 b \sin (c+d x)}{45 d (b \sec (c+d x))^{3/2}}+\frac{14 E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{15 d \sqrt{\cos (c+d x)} \sqrt{b \sec (c+d x)}}","\frac{2 b^3 \sin (c+d x)}{9 d (b \sec (c+d x))^{7/2}}+\frac{14 b \sin (c+d x)}{45 d (b \sec (c+d x))^{3/2}}+\frac{14 E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{15 d \sqrt{\cos (c+d x)} \sqrt{b \sec (c+d x)}}",1,"(14*EllipticE[(c + d*x)/2, 2])/(15*d*Sqrt[Cos[c + d*x]]*Sqrt[b*Sec[c + d*x]]) + (2*b^3*Sin[c + d*x])/(9*d*(b*Sec[c + d*x])^(7/2)) + (14*b*Sin[c + d*x])/(45*d*(b*Sec[c + d*x])^(3/2))","A",5,4,21,0.1905,1,"{16, 3769, 3771, 2639}"
111,1,100,0,0.0586986,"\int \frac{\sec ^6(c+d x)}{(b \sec (c+d x))^{3/2}} \, dx","Int[Sec[c + d*x]^6/(b*Sec[c + d*x])^(3/2),x]","\frac{2 \sin (c+d x) (b \sec (c+d x))^{7/2}}{7 b^5 d}+\frac{10 \sin (c+d x) (b \sec (c+d x))^{3/2}}{21 b^3 d}+\frac{10 \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^2 d}","\frac{2 \sin (c+d x) (b \sec (c+d x))^{7/2}}{7 b^5 d}+\frac{10 \sin (c+d x) (b \sec (c+d x))^{3/2}}{21 b^3 d}+\frac{10 \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^2 d}",1,"(10*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2]*Sqrt[b*Sec[c + d*x]])/(21*b^2*d) + (10*(b*Sec[c + d*x])^(3/2)*Sin[c + d*x])/(21*b^3*d) + (2*(b*Sec[c + d*x])^(7/2)*Sin[c + d*x])/(7*b^5*d)","A",5,4,21,0.1905,1,"{16, 3768, 3771, 2641}"
112,1,100,0,0.0576487,"\int \frac{\sec ^5(c+d x)}{(b \sec (c+d x))^{3/2}} \, dx","Int[Sec[c + d*x]^5/(b*Sec[c + d*x])^(3/2),x]","\frac{2 \sin (c+d x) (b \sec (c+d x))^{5/2}}{5 b^4 d}+\frac{6 \sin (c+d x) \sqrt{b \sec (c+d x)}}{5 b^2 d}-\frac{6 E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{5 b d \sqrt{\cos (c+d x)} \sqrt{b \sec (c+d x)}}","\frac{2 \sin (c+d x) (b \sec (c+d x))^{5/2}}{5 b^4 d}+\frac{6 \sin (c+d x) \sqrt{b \sec (c+d x)}}{5 b^2 d}-\frac{6 E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{5 b d \sqrt{\cos (c+d x)} \sqrt{b \sec (c+d x)}}",1,"(-6*EllipticE[(c + d*x)/2, 2])/(5*b*d*Sqrt[Cos[c + d*x]]*Sqrt[b*Sec[c + d*x]]) + (6*Sqrt[b*Sec[c + d*x]]*Sin[c + d*x])/(5*b^2*d) + (2*(b*Sec[c + d*x])^(5/2)*Sin[c + d*x])/(5*b^4*d)","A",5,4,21,0.1905,1,"{16, 3768, 3771, 2639}"
113,1,72,0,0.0377128,"\int \frac{\sec ^4(c+d x)}{(b \sec (c+d x))^{3/2}} \, dx","Int[Sec[c + d*x]^4/(b*Sec[c + d*x])^(3/2),x]","\frac{2 \sin (c+d x) (b \sec (c+d x))^{3/2}}{3 b^3 d}+\frac{2 \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 \sin (c+d x) (b \sec (c+d x))^{3/2}}{3 b^3 d}+\frac{2 \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}",1,"(2*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2]*Sqrt[b*Sec[c + d*x]])/(3*b^2*d) + (2*(b*Sec[c + d*x])^(3/2)*Sin[c + d*x])/(3*b^3*d)","A",4,4,21,0.1905,1,"{16, 3768, 3771, 2641}"
114,1,68,0,0.0395441,"\int \frac{\sec ^3(c+d x)}{(b \sec (c+d x))^{3/2}} \, dx","Int[Sec[c + d*x]^3/(b*Sec[c + d*x])^(3/2),x]","\frac{2 \sin (c+d x) \sqrt{b \sec (c+d x)}}{b^2 d}-\frac{2 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 \sin (c+d x) \sqrt{b \sec (c+d x)}}{b^2 d}-\frac{2 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*EllipticE[(c + d*x)/2, 2])/(b*d*Sqrt[Cos[c + d*x]]*Sqrt[b*Sec[c + d*x]]) + (2*Sqrt[b*Sec[c + d*x]]*Sin[c + d*x])/(b^2*d)","A",4,4,21,0.1905,1,"{16, 3768, 3771, 2639}"
115,1,41,0,0.023263,"\int \frac{\sec ^2(c+d x)}{(b \sec (c+d x))^{3/2}} \, dx","Int[Sec[c + d*x]^2/(b*Sec[c + d*x])^(3/2),x]","\frac{2 \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 \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}",1,"(2*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2]*Sqrt[b*Sec[c + d*x]])/(b^2*d)","A",3,3,21,0.1429,1,"{16, 3771, 2641}"
116,1,41,0,0.021754,"\int \frac{\sec (c+d x)}{(b \sec (c+d x))^{3/2}} \, dx","Int[Sec[c + d*x]/(b*Sec[c + d*x])^(3/2),x]","\frac{2 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 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*EllipticE[(c + d*x)/2, 2])/(b*d*Sqrt[Cos[c + d*x]]*Sqrt[b*Sec[c + d*x]])","A",3,3,19,0.1579,1,"{16, 3771, 2639}"
117,1,72,0,0.0329195,"\int \frac{1}{(b \sec (c+d x))^{3/2}} \, dx","Int[(b*Sec[c + d*x])^(-3/2),x]","\frac{2 \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 \sin (c+d x)}{3 b d \sqrt{b \sec (c+d x)}}","\frac{2 \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 \sin (c+d x)}{3 b d \sqrt{b \sec (c+d x)}}",1,"(2*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2]*Sqrt[b*Sec[c + d*x]])/(3*b^2*d) + (2*Sin[c + d*x])/(3*b*d*Sqrt[b*Sec[c + d*x]])","A",3,3,12,0.2500,1,"{3769, 3771, 2641}"
118,1,69,0,0.0448313,"\int \frac{\cos (c+d x)}{(b \sec (c+d x))^{3/2}} \, dx","Int[Cos[c + d*x]/(b*Sec[c + d*x])^(3/2),x]","\frac{2 \sin (c+d x)}{5 d (b \sec (c+d x))^{3/2}}+\frac{6 E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{5 b d \sqrt{\cos (c+d x)} \sqrt{b \sec (c+d x)}}","\frac{2 \sin (c+d x)}{5 d (b \sec (c+d x))^{3/2}}+\frac{6 E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{5 b d \sqrt{\cos (c+d x)} \sqrt{b \sec (c+d x)}}",1,"(6*EllipticE[(c + d*x)/2, 2])/(5*b*d*Sqrt[Cos[c + d*x]]*Sqrt[b*Sec[c + d*x]]) + (2*Sin[c + d*x])/(5*d*(b*Sec[c + d*x])^(3/2))","A",4,4,19,0.2105,1,"{16, 3769, 3771, 2639}"
119,1,98,0,0.0721163,"\int \frac{\cos ^2(c+d x)}{(b \sec (c+d x))^{3/2}} \, dx","Int[Cos[c + d*x]^2/(b*Sec[c + d*x])^(3/2),x]","\frac{10 \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^2 d}+\frac{10 \sin (c+d x)}{21 b d \sqrt{b \sec (c+d x)}}+\frac{2 b \sin (c+d x)}{7 d (b \sec (c+d x))^{5/2}}","\frac{10 \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^2 d}+\frac{10 \sin (c+d x)}{21 b d \sqrt{b \sec (c+d x)}}+\frac{2 b \sin (c+d x)}{7 d (b \sec (c+d x))^{5/2}}",1,"(10*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2]*Sqrt[b*Sec[c + d*x]])/(21*b^2*d) + (2*b*Sin[c + d*x])/(7*d*(b*Sec[c + d*x])^(5/2)) + (10*Sin[c + d*x])/(21*b*d*Sqrt[b*Sec[c + d*x]])","A",5,4,21,0.1905,1,"{16, 3769, 3771, 2641}"
120,1,97,0,0.0712229,"\int \frac{\cos ^3(c+d x)}{(b \sec (c+d x))^{3/2}} \, dx","Int[Cos[c + d*x]^3/(b*Sec[c + d*x])^(3/2),x]","\frac{2 b^2 \sin (c+d x)}{9 d (b \sec (c+d x))^{7/2}}+\frac{14 \sin (c+d x)}{45 d (b \sec (c+d x))^{3/2}}+\frac{14 E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{15 b d \sqrt{\cos (c+d x)} \sqrt{b \sec (c+d x)}}","\frac{2 b^2 \sin (c+d x)}{9 d (b \sec (c+d x))^{7/2}}+\frac{14 \sin (c+d x)}{45 d (b \sec (c+d x))^{3/2}}+\frac{14 E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{15 b d \sqrt{\cos (c+d x)} \sqrt{b \sec (c+d x)}}",1,"(14*EllipticE[(c + d*x)/2, 2])/(15*b*d*Sqrt[Cos[c + d*x]]*Sqrt[b*Sec[c + d*x]]) + (2*b^2*Sin[c + d*x])/(9*d*(b*Sec[c + d*x])^(7/2)) + (14*Sin[c + d*x])/(45*d*(b*Sec[c + d*x])^(3/2))","A",5,4,21,0.1905,1,"{16, 3769, 3771, 2639}"
121,1,100,0,0.0571708,"\int \frac{\sec ^7(c+d x)}{(b \sec (c+d x))^{5/2}} \, dx","Int[Sec[c + d*x]^7/(b*Sec[c + d*x])^(5/2),x]","\frac{2 \sin (c+d x) (b \sec (c+d x))^{7/2}}{7 b^6 d}+\frac{10 \sin (c+d x) (b \sec (c+d x))^{3/2}}{21 b^4 d}+\frac{10 \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^3 d}","\frac{2 \sin (c+d x) (b \sec (c+d x))^{7/2}}{7 b^6 d}+\frac{10 \sin (c+d x) (b \sec (c+d x))^{3/2}}{21 b^4 d}+\frac{10 \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^3 d}",1,"(10*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2]*Sqrt[b*Sec[c + d*x]])/(21*b^3*d) + (10*(b*Sec[c + d*x])^(3/2)*Sin[c + d*x])/(21*b^4*d) + (2*(b*Sec[c + d*x])^(7/2)*Sin[c + d*x])/(7*b^6*d)","A",5,4,21,0.1905,1,"{16, 3768, 3771, 2641}"
122,1,100,0,0.058089,"\int \frac{\sec ^6(c+d x)}{(b \sec (c+d x))^{5/2}} \, dx","Int[Sec[c + d*x]^6/(b*Sec[c + d*x])^(5/2),x]","\frac{2 \sin (c+d x) (b \sec (c+d x))^{5/2}}{5 b^5 d}+\frac{6 \sin (c+d x) \sqrt{b \sec (c+d x)}}{5 b^3 d}-\frac{6 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 \sin (c+d x) (b \sec (c+d x))^{5/2}}{5 b^5 d}+\frac{6 \sin (c+d x) \sqrt{b \sec (c+d x)}}{5 b^3 d}-\frac{6 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)}}",1,"(-6*EllipticE[(c + d*x)/2, 2])/(5*b^2*d*Sqrt[Cos[c + d*x]]*Sqrt[b*Sec[c + d*x]]) + (6*Sqrt[b*Sec[c + d*x]]*Sin[c + d*x])/(5*b^3*d) + (2*(b*Sec[c + d*x])^(5/2)*Sin[c + d*x])/(5*b^5*d)","A",5,4,21,0.1905,1,"{16, 3768, 3771, 2639}"
123,1,72,0,0.0383166,"\int \frac{\sec ^5(c+d x)}{(b \sec (c+d x))^{5/2}} \, dx","Int[Sec[c + d*x]^5/(b*Sec[c + d*x])^(5/2),x]","\frac{2 \sin (c+d x) (b \sec (c+d x))^{3/2}}{3 b^4 d}+\frac{2 \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 \sin (c+d x) (b \sec (c+d x))^{3/2}}{3 b^4 d}+\frac{2 \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*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2]*Sqrt[b*Sec[c + d*x]])/(3*b^3*d) + (2*(b*Sec[c + d*x])^(3/2)*Sin[c + d*x])/(3*b^4*d)","A",4,4,21,0.1905,1,"{16, 3768, 3771, 2641}"
124,1,68,0,0.0383202,"\int \frac{\sec ^4(c+d x)}{(b \sec (c+d x))^{5/2}} \, dx","Int[Sec[c + d*x]^4/(b*Sec[c + d*x])^(5/2),x]","\frac{2 \sin (c+d x) \sqrt{b \sec (c+d x)}}{b^3 d}-\frac{2 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 \sin (c+d x) \sqrt{b \sec (c+d x)}}{b^3 d}-\frac{2 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*EllipticE[(c + d*x)/2, 2])/(b^2*d*Sqrt[Cos[c + d*x]]*Sqrt[b*Sec[c + d*x]]) + (2*Sqrt[b*Sec[c + d*x]]*Sin[c + d*x])/(b^3*d)","A",4,4,21,0.1905,1,"{16, 3768, 3771, 2639}"
125,1,41,0,0.0218402,"\int \frac{\sec ^3(c+d x)}{(b \sec (c+d x))^{5/2}} \, dx","Int[Sec[c + d*x]^3/(b*Sec[c + d*x])^(5/2),x]","\frac{2 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \sec (c+d x)}}{b^3 d}","\frac{2 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \sec (c+d x)}}{b^3 d}",1,"(2*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2]*Sqrt[b*Sec[c + d*x]])/(b^3*d)","A",3,3,21,0.1429,1,"{16, 3771, 2641}"
126,1,41,0,0.0226226,"\int \frac{\sec ^2(c+d x)}{(b \sec (c+d x))^{5/2}} \, dx","Int[Sec[c + d*x]^2/(b*Sec[c + d*x])^(5/2),x]","\frac{2 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 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*EllipticE[(c + d*x)/2, 2])/(b^2*d*Sqrt[Cos[c + d*x]]*Sqrt[b*Sec[c + d*x]])","A",3,3,21,0.1429,1,"{16, 3771, 2639}"
127,1,72,0,0.0400432,"\int \frac{\sec (c+d x)}{(b \sec (c+d x))^{5/2}} \, dx","Int[Sec[c + d*x]/(b*Sec[c + d*x])^(5/2),x]","\frac{2 \sin (c+d x)}{3 b^2 d \sqrt{b \sec (c+d x)}}+\frac{2 \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 \sin (c+d x)}{3 b^2 d \sqrt{b \sec (c+d x)}}+\frac{2 \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*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2]*Sqrt[b*Sec[c + d*x]])/(3*b^3*d) + (2*Sin[c + d*x])/(3*b^2*d*Sqrt[b*Sec[c + d*x]])","A",4,4,19,0.2105,1,"{16, 3769, 3771, 2641}"
128,1,72,0,0.0337027,"\int \frac{1}{(b \sec (c+d x))^{5/2}} \, dx","Int[(b*Sec[c + d*x])^(-5/2),x]","\frac{6 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 \sin (c+d x)}{5 b d (b \sec (c+d x))^{3/2}}","\frac{6 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 \sin (c+d x)}{5 b d (b \sec (c+d x))^{3/2}}",1,"(6*EllipticE[(c + d*x)/2, 2])/(5*b^2*d*Sqrt[Cos[c + d*x]]*Sqrt[b*Sec[c + d*x]]) + (2*Sin[c + d*x])/(5*b*d*(b*Sec[c + d*x])^(3/2))","A",3,3,12,0.2500,1,"{3769, 3771, 2639}"
129,1,97,0,0.0634044,"\int \frac{\cos (c+d x)}{(b \sec (c+d x))^{5/2}} \, dx","Int[Cos[c + d*x]/(b*Sec[c + d*x])^(5/2),x]","\frac{10 \sin (c+d x)}{21 b^2 d \sqrt{b \sec (c+d x)}}+\frac{10 \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^3 d}+\frac{2 \sin (c+d x)}{7 d (b \sec (c+d x))^{5/2}}","\frac{10 \sin (c+d x)}{21 b^2 d \sqrt{b \sec (c+d x)}}+\frac{10 \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^3 d}+\frac{2 \sin (c+d x)}{7 d (b \sec (c+d x))^{5/2}}",1,"(10*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2]*Sqrt[b*Sec[c + d*x]])/(21*b^3*d) + (2*Sin[c + d*x])/(7*d*(b*Sec[c + d*x])^(5/2)) + (10*Sin[c + d*x])/(21*b^2*d*Sqrt[b*Sec[c + d*x]])","A",5,4,19,0.2105,1,"{16, 3769, 3771, 2641}"
130,1,98,0,0.0723242,"\int \frac{\cos ^2(c+d x)}{(b \sec (c+d x))^{5/2}} \, dx","Int[Cos[c + d*x]^2/(b*Sec[c + d*x])^(5/2),x]","\frac{14 E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{15 b^2 d \sqrt{\cos (c+d x)} \sqrt{b \sec (c+d x)}}+\frac{14 \sin (c+d x)}{45 b d (b \sec (c+d x))^{3/2}}+\frac{2 b \sin (c+d x)}{9 d (b \sec (c+d x))^{7/2}}","\frac{14 E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{15 b^2 d \sqrt{\cos (c+d x)} \sqrt{b \sec (c+d x)}}+\frac{14 \sin (c+d x)}{45 b d (b \sec (c+d x))^{3/2}}+\frac{2 b \sin (c+d x)}{9 d (b \sec (c+d x))^{7/2}}",1,"(14*EllipticE[(c + d*x)/2, 2])/(15*b^2*d*Sqrt[Cos[c + d*x]]*Sqrt[b*Sec[c + d*x]]) + (2*b*Sin[c + d*x])/(9*d*(b*Sec[c + d*x])^(7/2)) + (14*Sin[c + d*x])/(45*b*d*(b*Sec[c + d*x])^(3/2))","A",5,4,21,0.1905,1,"{16, 3769, 3771, 2639}"
131,1,100,0,0.0512744,"\int \frac{1}{(b \sec (c+d x))^{7/2}} \, dx","Int[(b*Sec[c + d*x])^(-7/2),x]","\frac{10 \sin (c+d x)}{21 b^3 d \sqrt{b \sec (c+d x)}}+\frac{10 \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 \sin (c+d x)}{7 b d (b \sec (c+d x))^{5/2}}","\frac{10 \sin (c+d x)}{21 b^3 d \sqrt{b \sec (c+d x)}}+\frac{10 \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 \sin (c+d x)}{7 b d (b \sec (c+d x))^{5/2}}",1,"(10*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2]*Sqrt[b*Sec[c + d*x]])/(21*b^4*d) + (2*Sin[c + d*x])/(7*b*d*(b*Sec[c + d*x])^(5/2)) + (10*Sin[c + d*x])/(21*b^3*d*Sqrt[b*Sec[c + d*x]])","A",4,3,12,0.2500,1,"{3769, 3771, 2641}"
132,1,107,0,0.0332845,"\int \sec ^{\frac{9}{2}}(c+d x) \sqrt{b \sec (c+d x)} \, dx","Int[Sec[c + d*x]^(9/2)*Sqrt[b*Sec[c + d*x]],x]","\frac{\sin (c+d x) \sec ^{\frac{7}{2}}(c+d x) \sqrt{b \sec (c+d x)}}{4 d}+\frac{3 \sin (c+d x) \sec ^{\frac{3}{2}}(c+d x) \sqrt{b \sec (c+d x)}}{8 d}+\frac{3 \sqrt{b \sec (c+d x)} \tanh ^{-1}(\sin (c+d x))}{8 d \sqrt{\sec (c+d x)}}","\frac{\sin (c+d x) \sec ^{\frac{7}{2}}(c+d x) \sqrt{b \sec (c+d x)}}{4 d}+\frac{3 \sin (c+d x) \sec ^{\frac{3}{2}}(c+d x) \sqrt{b \sec (c+d x)}}{8 d}+\frac{3 \sqrt{b \sec (c+d x)} \tanh ^{-1}(\sin (c+d x))}{8 d \sqrt{\sec (c+d x)}}",1,"(3*ArcTanh[Sin[c + d*x]]*Sqrt[b*Sec[c + d*x]])/(8*d*Sqrt[Sec[c + d*x]]) + (3*Sec[c + d*x]^(3/2)*Sqrt[b*Sec[c + d*x]]*Sin[c + d*x])/(8*d) + (Sec[c + d*x]^(7/2)*Sqrt[b*Sec[c + d*x]]*Sin[c + d*x])/(4*d)","A",4,3,23,0.1304,1,"{17, 3768, 3770}"
133,1,70,0,0.0165725,"\int \sec ^{\frac{7}{2}}(c+d x) \sqrt{b \sec (c+d x)} \, dx","Int[Sec[c + d*x]^(7/2)*Sqrt[b*Sec[c + d*x]],x]","\frac{\sin ^3(c+d x) \sec ^{\frac{5}{2}}(c+d x) \sqrt{b \sec (c+d x)}}{3 d}+\frac{\sin (c+d x) \sqrt{\sec (c+d x)} \sqrt{b \sec (c+d x)}}{d}","\frac{\sin ^3(c+d x) \sec ^{\frac{5}{2}}(c+d x) \sqrt{b \sec (c+d x)}}{3 d}+\frac{\sin (c+d x) \sqrt{\sec (c+d x)} \sqrt{b \sec (c+d x)}}{d}",1,"(Sqrt[Sec[c + d*x]]*Sqrt[b*Sec[c + d*x]]*Sin[c + d*x])/d + (Sec[c + d*x]^(5/2)*Sqrt[b*Sec[c + d*x]]*Sin[c + d*x]^3)/(3*d)","A",3,2,23,0.08696,1,"{17, 3767}"
134,1,72,0,0.0192353,"\int \sec ^{\frac{5}{2}}(c+d x) \sqrt{b \sec (c+d x)} \, dx","Int[Sec[c + d*x]^(5/2)*Sqrt[b*Sec[c + d*x]],x]","\frac{\sin (c+d x) \sec ^{\frac{3}{2}}(c+d x) \sqrt{b \sec (c+d x)}}{2 d}+\frac{\sqrt{b \sec (c+d x)} \tanh ^{-1}(\sin (c+d x))}{2 d \sqrt{\sec (c+d x)}}","\frac{\sin (c+d x) \sec ^{\frac{3}{2}}(c+d x) \sqrt{b \sec (c+d x)}}{2 d}+\frac{\sqrt{b \sec (c+d x)} \tanh ^{-1}(\sin (c+d x))}{2 d \sqrt{\sec (c+d x)}}",1,"(ArcTanh[Sin[c + d*x]]*Sqrt[b*Sec[c + d*x]])/(2*d*Sqrt[Sec[c + d*x]]) + (Sec[c + d*x]^(3/2)*Sqrt[b*Sec[c + d*x]]*Sin[c + d*x])/(2*d)","A",3,3,23,0.1304,1,"{17, 3768, 3770}"
135,1,32,0,0.0117126,"\int \sec ^{\frac{3}{2}}(c+d x) \sqrt{b \sec (c+d x)} \, dx","Int[Sec[c + d*x]^(3/2)*Sqrt[b*Sec[c + d*x]],x]","\frac{\sin (c+d x) \sqrt{\sec (c+d x)} \sqrt{b \sec (c+d x)}}{d}","\frac{\sin (c+d x) \sqrt{\sec (c+d x)} \sqrt{b \sec (c+d x)}}{d}",1,"(Sqrt[Sec[c + d*x]]*Sqrt[b*Sec[c + d*x]]*Sin[c + d*x])/d","A",3,3,23,0.1304,1,"{17, 3767, 8}"
136,1,33,0,0.006833,"\int \sqrt{\sec (c+d x)} \sqrt{b \sec (c+d x)} \, dx","Int[Sqrt[Sec[c + d*x]]*Sqrt[b*Sec[c + d*x]],x]","\frac{\sqrt{b \sec (c+d x)} \tanh ^{-1}(\sin (c+d x))}{d \sqrt{\sec (c+d x)}}","\frac{\sqrt{b \sec (c+d x)} \tanh ^{-1}(\sin (c+d x))}{d \sqrt{\sec (c+d x)}}",1,"(ArcTanh[Sin[c + d*x]]*Sqrt[b*Sec[c + d*x]])/(d*Sqrt[Sec[c + d*x]])","A",2,2,23,0.08696,1,"{17, 3770}"
137,1,24,0,0.0022498,"\int \frac{\sqrt{b \sec (c+d x)}}{\sqrt{\sec (c+d x)}} \, dx","Int[Sqrt[b*Sec[c + d*x]]/Sqrt[Sec[c + d*x]],x]","\frac{x \sqrt{b \sec (c+d x)}}{\sqrt{\sec (c+d x)}}","\frac{x \sqrt{b \sec (c+d x)}}{\sqrt{\sec (c+d x)}}",1,"(x*Sqrt[b*Sec[c + d*x]])/Sqrt[Sec[c + d*x]]","A",2,2,23,0.08696,1,"{17, 8}"
138,1,32,0,0.0066801,"\int \frac{\sqrt{b \sec (c+d x)}}{\sec ^{\frac{3}{2}}(c+d x)} \, dx","Int[Sqrt[b*Sec[c + d*x]]/Sec[c + d*x]^(3/2),x]","\frac{\sin (c+d x) \sqrt{b \sec (c+d x)}}{d \sqrt{\sec (c+d x)}}","\frac{\sin (c+d x) \sqrt{b \sec (c+d x)}}{d \sqrt{\sec (c+d x)}}",1,"(Sqrt[b*Sec[c + d*x]]*Sin[c + d*x])/(d*Sqrt[Sec[c + d*x]])","A",2,2,23,0.08696,1,"{17, 2637}"
139,1,63,0,0.0137245,"\int \frac{\sqrt{b \sec (c+d x)}}{\sec ^{\frac{5}{2}}(c+d x)} \, dx","Int[Sqrt[b*Sec[c + d*x]]/Sec[c + d*x]^(5/2),x]","\frac{x \sqrt{b \sec (c+d x)}}{2 \sqrt{\sec (c+d x)}}+\frac{\sin (c+d x) \sqrt{b \sec (c+d x)}}{2 d \sec ^{\frac{3}{2}}(c+d x)}","\frac{x \sqrt{b \sec (c+d x)}}{2 \sqrt{\sec (c+d x)}}+\frac{\sin (c+d x) \sqrt{b \sec (c+d x)}}{2 d \sec ^{\frac{3}{2}}(c+d x)}",1,"(x*Sqrt[b*Sec[c + d*x]])/(2*Sqrt[Sec[c + d*x]]) + (Sqrt[b*Sec[c + d*x]]*Sin[c + d*x])/(2*d*Sec[c + d*x]^(3/2))","A",3,3,23,0.1304,1,"{17, 2635, 8}"
140,1,70,0,0.0163579,"\int \frac{\sqrt{b \sec (c+d x)}}{\sec ^{\frac{7}{2}}(c+d x)} \, dx","Int[Sqrt[b*Sec[c + d*x]]/Sec[c + d*x]^(7/2),x]","\frac{\sin (c+d x) \sqrt{b \sec (c+d x)}}{d \sqrt{\sec (c+d x)}}-\frac{\sin ^3(c+d x) \sqrt{b \sec (c+d x)}}{3 d \sqrt{\sec (c+d x)}}","\frac{\sin (c+d x) \sqrt{b \sec (c+d x)}}{d \sqrt{\sec (c+d x)}}-\frac{\sin ^3(c+d x) \sqrt{b \sec (c+d x)}}{3 d \sqrt{\sec (c+d x)}}",1,"(Sqrt[b*Sec[c + d*x]]*Sin[c + d*x])/(d*Sqrt[Sec[c + d*x]]) - (Sqrt[b*Sec[c + d*x]]*Sin[c + d*x]^3)/(3*d*Sqrt[Sec[c + d*x]])","A",3,2,23,0.08696,1,"{17, 2633}"
141,1,98,0,0.0251071,"\int \frac{\sqrt{b \sec (c+d x)}}{\sec ^{\frac{9}{2}}(c+d x)} \, dx","Int[Sqrt[b*Sec[c + d*x]]/Sec[c + d*x]^(9/2),x]","\frac{3 x \sqrt{b \sec (c+d x)}}{8 \sqrt{\sec (c+d x)}}+\frac{3 \sin (c+d x) \sqrt{b \sec (c+d x)}}{8 d \sec ^{\frac{3}{2}}(c+d x)}+\frac{\sin (c+d x) \sqrt{b \sec (c+d x)}}{4 d \sec ^{\frac{7}{2}}(c+d x)}","\frac{3 x \sqrt{b \sec (c+d x)}}{8 \sqrt{\sec (c+d x)}}+\frac{3 \sin (c+d x) \sqrt{b \sec (c+d x)}}{8 d \sec ^{\frac{3}{2}}(c+d x)}+\frac{\sin (c+d x) \sqrt{b \sec (c+d x)}}{4 d \sec ^{\frac{7}{2}}(c+d x)}",1,"(3*x*Sqrt[b*Sec[c + d*x]])/(8*Sqrt[Sec[c + d*x]]) + (Sqrt[b*Sec[c + d*x]]*Sin[c + d*x])/(4*d*Sec[c + d*x]^(7/2)) + (3*Sqrt[b*Sec[c + d*x]]*Sin[c + d*x])/(8*d*Sec[c + d*x]^(3/2))","A",4,3,23,0.1304,1,"{17, 2635, 8}"
142,1,110,0,0.0348635,"\int \sec ^{\frac{7}{2}}(c+d x) (b \sec (c+d x))^{3/2} \, dx","Int[Sec[c + d*x]^(7/2)*(b*Sec[c + d*x])^(3/2),x]","\frac{b \sin (c+d x) \sec ^{\frac{7}{2}}(c+d x) \sqrt{b \sec (c+d x)}}{4 d}+\frac{3 b \sin (c+d x) \sec ^{\frac{3}{2}}(c+d x) \sqrt{b \sec (c+d x)}}{8 d}+\frac{3 b \sqrt{b \sec (c+d x)} \tanh ^{-1}(\sin (c+d x))}{8 d \sqrt{\sec (c+d x)}}","\frac{b \sin (c+d x) \sec ^{\frac{7}{2}}(c+d x) \sqrt{b \sec (c+d x)}}{4 d}+\frac{3 b \sin (c+d x) \sec ^{\frac{3}{2}}(c+d x) \sqrt{b \sec (c+d x)}}{8 d}+\frac{3 b \sqrt{b \sec (c+d x)} \tanh ^{-1}(\sin (c+d x))}{8 d \sqrt{\sec (c+d x)}}",1,"(3*b*ArcTanh[Sin[c + d*x]]*Sqrt[b*Sec[c + d*x]])/(8*d*Sqrt[Sec[c + d*x]]) + (3*b*Sec[c + d*x]^(3/2)*Sqrt[b*Sec[c + d*x]]*Sin[c + d*x])/(8*d) + (b*Sec[c + d*x]^(7/2)*Sqrt[b*Sec[c + d*x]]*Sin[c + d*x])/(4*d)","A",4,3,23,0.1304,1,"{17, 3768, 3770}"
143,1,72,0,0.0169584,"\int \sec ^{\frac{5}{2}}(c+d x) (b \sec (c+d x))^{3/2} \, dx","Int[Sec[c + d*x]^(5/2)*(b*Sec[c + d*x])^(3/2),x]","\frac{b \sin ^3(c+d x) \sec ^{\frac{5}{2}}(c+d x) \sqrt{b \sec (c+d x)}}{3 d}+\frac{b \sin (c+d x) \sqrt{\sec (c+d x)} \sqrt{b \sec (c+d x)}}{d}","\frac{b \sin ^3(c+d x) \sec ^{\frac{5}{2}}(c+d x) \sqrt{b \sec (c+d x)}}{3 d}+\frac{b \sin (c+d x) \sqrt{\sec (c+d x)} \sqrt{b \sec (c+d x)}}{d}",1,"(b*Sqrt[Sec[c + d*x]]*Sqrt[b*Sec[c + d*x]]*Sin[c + d*x])/d + (b*Sec[c + d*x]^(5/2)*Sqrt[b*Sec[c + d*x]]*Sin[c + d*x]^3)/(3*d)","A",3,2,23,0.08696,1,"{17, 3767}"
144,1,74,0,0.0207255,"\int \sec ^{\frac{3}{2}}(c+d x) (b \sec (c+d x))^{3/2} \, dx","Int[Sec[c + d*x]^(3/2)*(b*Sec[c + d*x])^(3/2),x]","\frac{b \sin (c+d x) \sec ^{\frac{3}{2}}(c+d x) \sqrt{b \sec (c+d x)}}{2 d}+\frac{b \sqrt{b \sec (c+d x)} \tanh ^{-1}(\sin (c+d x))}{2 d \sqrt{\sec (c+d x)}}","\frac{b \sin (c+d x) \sec ^{\frac{3}{2}}(c+d x) \sqrt{b \sec (c+d x)}}{2 d}+\frac{b \sqrt{b \sec (c+d x)} \tanh ^{-1}(\sin (c+d x))}{2 d \sqrt{\sec (c+d x)}}",1,"(b*ArcTanh[Sin[c + d*x]]*Sqrt[b*Sec[c + d*x]])/(2*d*Sqrt[Sec[c + d*x]]) + (b*Sec[c + d*x]^(3/2)*Sqrt[b*Sec[c + d*x]]*Sin[c + d*x])/(2*d)","A",3,3,23,0.1304,1,"{17, 3768, 3770}"
145,1,33,0,0.0113825,"\int \sqrt{\sec (c+d x)} (b \sec (c+d x))^{3/2} \, dx","Int[Sqrt[Sec[c + d*x]]*(b*Sec[c + d*x])^(3/2),x]","\frac{b \sin (c+d x) \sqrt{\sec (c+d x)} \sqrt{b \sec (c+d x)}}{d}","\frac{b \sin (c+d x) \sqrt{\sec (c+d x)} \sqrt{b \sec (c+d x)}}{d}",1,"(b*Sqrt[Sec[c + d*x]]*Sqrt[b*Sec[c + d*x]]*Sin[c + d*x])/d","A",3,3,23,0.1304,1,"{17, 3767, 8}"
146,1,34,0,0.0074038,"\int \frac{(b \sec (c+d x))^{3/2}}{\sqrt{\sec (c+d x)}} \, dx","Int[(b*Sec[c + d*x])^(3/2)/Sqrt[Sec[c + d*x]],x]","\frac{b \sqrt{b \sec (c+d x)} \tanh ^{-1}(\sin (c+d x))}{d \sqrt{\sec (c+d x)}}","\frac{b \sqrt{b \sec (c+d x)} \tanh ^{-1}(\sin (c+d x))}{d \sqrt{\sec (c+d x)}}",1,"(b*ArcTanh[Sin[c + d*x]]*Sqrt[b*Sec[c + d*x]])/(d*Sqrt[Sec[c + d*x]])","A",2,2,23,0.08696,1,"{17, 3770}"
147,1,25,0,0.002594,"\int \frac{(b \sec (c+d x))^{3/2}}{\sec ^{\frac{3}{2}}(c+d x)} \, dx","Int[(b*Sec[c + d*x])^(3/2)/Sec[c + d*x]^(3/2),x]","\frac{b x \sqrt{b \sec (c+d x)}}{\sqrt{\sec (c+d x)}}","\frac{b x \sqrt{b \sec (c+d x)}}{\sqrt{\sec (c+d x)}}",1,"(b*x*Sqrt[b*Sec[c + d*x]])/Sqrt[Sec[c + d*x]]","A",2,2,23,0.08696,1,"{17, 8}"
148,1,33,0,0.0074591,"\int \frac{(b \sec (c+d x))^{3/2}}{\sec ^{\frac{5}{2}}(c+d x)} \, dx","Int[(b*Sec[c + d*x])^(3/2)/Sec[c + d*x]^(5/2),x]","\frac{b \sin (c+d x) \sqrt{b \sec (c+d x)}}{d \sqrt{\sec (c+d x)}}","\frac{b \sin (c+d x) \sqrt{b \sec (c+d x)}}{d \sqrt{\sec (c+d x)}}",1,"(b*Sqrt[b*Sec[c + d*x]]*Sin[c + d*x])/(d*Sqrt[Sec[c + d*x]])","A",2,2,23,0.08696,1,"{17, 2637}"
149,1,65,0,0.0146445,"\int \frac{(b \sec (c+d x))^{3/2}}{\sec ^{\frac{7}{2}}(c+d x)} \, dx","Int[(b*Sec[c + d*x])^(3/2)/Sec[c + d*x]^(7/2),x]","\frac{b x \sqrt{b \sec (c+d x)}}{2 \sqrt{\sec (c+d x)}}+\frac{b \sin (c+d x) \sqrt{b \sec (c+d x)}}{2 d \sec ^{\frac{3}{2}}(c+d x)}","\frac{b x \sqrt{b \sec (c+d x)}}{2 \sqrt{\sec (c+d x)}}+\frac{b \sin (c+d x) \sqrt{b \sec (c+d x)}}{2 d \sec ^{\frac{3}{2}}(c+d x)}",1,"(b*x*Sqrt[b*Sec[c + d*x]])/(2*Sqrt[Sec[c + d*x]]) + (b*Sqrt[b*Sec[c + d*x]]*Sin[c + d*x])/(2*d*Sec[c + d*x]^(3/2))","A",3,3,23,0.1304,1,"{17, 2635, 8}"
150,1,72,0,0.0170607,"\int \frac{(b \sec (c+d x))^{3/2}}{\sec ^{\frac{9}{2}}(c+d x)} \, dx","Int[(b*Sec[c + d*x])^(3/2)/Sec[c + d*x]^(9/2),x]","\frac{b \sin (c+d x) \sqrt{b \sec (c+d x)}}{d \sqrt{\sec (c+d x)}}-\frac{b \sin ^3(c+d x) \sqrt{b \sec (c+d x)}}{3 d \sqrt{\sec (c+d x)}}","\frac{b \sin (c+d x) \sqrt{b \sec (c+d x)}}{d \sqrt{\sec (c+d x)}}-\frac{b \sin ^3(c+d x) \sqrt{b \sec (c+d x)}}{3 d \sqrt{\sec (c+d x)}}",1,"(b*Sqrt[b*Sec[c + d*x]]*Sin[c + d*x])/(d*Sqrt[Sec[c + d*x]]) - (b*Sqrt[b*Sec[c + d*x]]*Sin[c + d*x]^3)/(3*d*Sqrt[Sec[c + d*x]])","A",3,2,23,0.08696,1,"{17, 2633}"
151,1,101,0,0.0275267,"\int \frac{(b \sec (c+d x))^{3/2}}{\sec ^{\frac{11}{2}}(c+d x)} \, dx","Int[(b*Sec[c + d*x])^(3/2)/Sec[c + d*x]^(11/2),x]","\frac{3 b x \sqrt{b \sec (c+d x)}}{8 \sqrt{\sec (c+d x)}}+\frac{3 b \sin (c+d x) \sqrt{b \sec (c+d x)}}{8 d \sec ^{\frac{3}{2}}(c+d x)}+\frac{b \sin (c+d x) \sqrt{b \sec (c+d x)}}{4 d \sec ^{\frac{7}{2}}(c+d x)}","\frac{3 b x \sqrt{b \sec (c+d x)}}{8 \sqrt{\sec (c+d x)}}+\frac{3 b \sin (c+d x) \sqrt{b \sec (c+d x)}}{8 d \sec ^{\frac{3}{2}}(c+d x)}+\frac{b \sin (c+d x) \sqrt{b \sec (c+d x)}}{4 d \sec ^{\frac{7}{2}}(c+d x)}",1,"(3*b*x*Sqrt[b*Sec[c + d*x]])/(8*Sqrt[Sec[c + d*x]]) + (b*Sqrt[b*Sec[c + d*x]]*Sin[c + d*x])/(4*d*Sec[c + d*x]^(7/2)) + (3*b*Sqrt[b*Sec[c + d*x]]*Sin[c + d*x])/(8*d*Sec[c + d*x]^(3/2))","A",4,3,23,0.1304,1,"{17, 2635, 8}"
152,1,116,0,0.0239371,"\int \sec ^{\frac{7}{2}}(c+d x) (b \sec (c+d x))^{5/2} \, dx","Int[Sec[c + d*x]^(7/2)*(b*Sec[c + d*x])^(5/2),x]","\frac{b^2 \sin ^5(c+d x) \sec ^{\frac{9}{2}}(c+d x) \sqrt{b \sec (c+d x)}}{5 d}+\frac{2 b^2 \sin ^3(c+d x) \sec ^{\frac{5}{2}}(c+d x) \sqrt{b \sec (c+d x)}}{3 d}+\frac{b^2 \sin (c+d x) \sqrt{\sec (c+d x)} \sqrt{b \sec (c+d x)}}{d}","\frac{b^2 \sin ^5(c+d x) \sec ^{\frac{9}{2}}(c+d x) \sqrt{b \sec (c+d x)}}{5 d}+\frac{2 b^2 \sin ^3(c+d x) \sec ^{\frac{5}{2}}(c+d x) \sqrt{b \sec (c+d x)}}{3 d}+\frac{b^2 \sin (c+d x) \sqrt{\sec (c+d x)} \sqrt{b \sec (c+d x)}}{d}",1,"(b^2*Sqrt[Sec[c + d*x]]*Sqrt[b*Sec[c + d*x]]*Sin[c + d*x])/d + (2*b^2*Sec[c + d*x]^(5/2)*Sqrt[b*Sec[c + d*x]]*Sin[c + d*x]^3)/(3*d) + (b^2*Sec[c + d*x]^(9/2)*Sqrt[b*Sec[c + d*x]]*Sin[c + d*x]^5)/(5*d)","A",3,2,23,0.08696,1,"{17, 3767}"
153,1,76,0,0.0174445,"\int \sec ^{\frac{3}{2}}(c+d x) (b \sec (c+d x))^{5/2} \, dx","Int[Sec[c + d*x]^(3/2)*(b*Sec[c + d*x])^(5/2),x]","\frac{b^2 \sin ^3(c+d x) \sec ^{\frac{5}{2}}(c+d x) \sqrt{b \sec (c+d x)}}{3 d}+\frac{b^2 \sin (c+d x) \sqrt{\sec (c+d x)} \sqrt{b \sec (c+d x)}}{d}","\frac{b^2 \sin ^3(c+d x) \sec ^{\frac{5}{2}}(c+d x) \sqrt{b \sec (c+d x)}}{3 d}+\frac{b^2 \sin (c+d x) \sqrt{\sec (c+d x)} \sqrt{b \sec (c+d x)}}{d}",1,"(b^2*Sqrt[Sec[c + d*x]]*Sqrt[b*Sec[c + d*x]]*Sin[c + d*x])/d + (b^2*Sec[c + d*x]^(5/2)*Sqrt[b*Sec[c + d*x]]*Sin[c + d*x]^3)/(3*d)","A",3,2,23,0.08696,1,"{17, 3767}"
154,1,78,0,0.020254,"\int \sqrt{\sec (c+d x)} (b \sec (c+d x))^{5/2} \, dx","Int[Sqrt[Sec[c + d*x]]*(b*Sec[c + d*x])^(5/2),x]","\frac{b^2 \sin (c+d x) \sec ^{\frac{3}{2}}(c+d x) \sqrt{b \sec (c+d x)}}{2 d}+\frac{b^2 \sqrt{b \sec (c+d x)} \tanh ^{-1}(\sin (c+d x))}{2 d \sqrt{\sec (c+d x)}}","\frac{b^2 \sin (c+d x) \sec ^{\frac{3}{2}}(c+d x) \sqrt{b \sec (c+d x)}}{2 d}+\frac{b^2 \sqrt{b \sec (c+d x)} \tanh ^{-1}(\sin (c+d x))}{2 d \sqrt{\sec (c+d x)}}",1,"(b^2*ArcTanh[Sin[c + d*x]]*Sqrt[b*Sec[c + d*x]])/(2*d*Sqrt[Sec[c + d*x]]) + (b^2*Sec[c + d*x]^(3/2)*Sqrt[b*Sec[c + d*x]]*Sin[c + d*x])/(2*d)","A",3,3,23,0.1304,1,"{17, 3768, 3770}"
155,1,35,0,0.011894,"\int \frac{(b \sec (c+d x))^{5/2}}{\sqrt{\sec (c+d x)}} \, dx","Int[(b*Sec[c + d*x])^(5/2)/Sqrt[Sec[c + d*x]],x]","\frac{b^2 \sin (c+d x) \sqrt{\sec (c+d x)} \sqrt{b \sec (c+d x)}}{d}","\frac{b^2 \sin (c+d x) \sqrt{\sec (c+d x)} \sqrt{b \sec (c+d x)}}{d}",1,"(b^2*Sqrt[Sec[c + d*x]]*Sqrt[b*Sec[c + d*x]]*Sin[c + d*x])/d","A",3,3,23,0.1304,1,"{17, 3767, 8}"
156,1,36,0,0.00772,"\int \frac{(b \sec (c+d x))^{5/2}}{\sec ^{\frac{3}{2}}(c+d x)} \, dx","Int[(b*Sec[c + d*x])^(5/2)/Sec[c + d*x]^(3/2),x]","\frac{b^2 \sqrt{b \sec (c+d x)} \tanh ^{-1}(\sin (c+d x))}{d \sqrt{\sec (c+d x)}}","\frac{b^2 \sqrt{b \sec (c+d x)} \tanh ^{-1}(\sin (c+d x))}{d \sqrt{\sec (c+d x)}}",1,"(b^2*ArcTanh[Sin[c + d*x]]*Sqrt[b*Sec[c + d*x]])/(d*Sqrt[Sec[c + d*x]])","A",2,2,23,0.08696,1,"{17, 3770}"
157,1,27,0,0.0026389,"\int \frac{(b \sec (c+d x))^{5/2}}{\sec ^{\frac{5}{2}}(c+d x)} \, dx","Int[(b*Sec[c + d*x])^(5/2)/Sec[c + d*x]^(5/2),x]","\frac{b^2 x \sqrt{b \sec (c+d x)}}{\sqrt{\sec (c+d x)}}","\frac{b^2 x \sqrt{b \sec (c+d x)}}{\sqrt{\sec (c+d x)}}",1,"(b^2*x*Sqrt[b*Sec[c + d*x]])/Sqrt[Sec[c + d*x]]","A",2,2,23,0.08696,1,"{17, 8}"
158,1,35,0,0.0070795,"\int \frac{(b \sec (c+d x))^{5/2}}{\sec ^{\frac{7}{2}}(c+d x)} \, dx","Int[(b*Sec[c + d*x])^(5/2)/Sec[c + d*x]^(7/2),x]","\frac{b^2 \sin (c+d x) \sqrt{b \sec (c+d x)}}{d \sqrt{\sec (c+d x)}}","\frac{b^2 \sin (c+d x) \sqrt{b \sec (c+d x)}}{d \sqrt{\sec (c+d x)}}",1,"(b^2*Sqrt[b*Sec[c + d*x]]*Sin[c + d*x])/(d*Sqrt[Sec[c + d*x]])","A",2,2,23,0.08696,1,"{17, 2637}"
159,1,69,0,0.0154454,"\int \frac{(b \sec (c+d x))^{5/2}}{\sec ^{\frac{9}{2}}(c+d x)} \, dx","Int[(b*Sec[c + d*x])^(5/2)/Sec[c + d*x]^(9/2),x]","\frac{b^2 x \sqrt{b \sec (c+d x)}}{2 \sqrt{\sec (c+d x)}}+\frac{b^2 \sin (c+d x) \sqrt{b \sec (c+d x)}}{2 d \sec ^{\frac{3}{2}}(c+d x)}","\frac{b^2 x \sqrt{b \sec (c+d x)}}{2 \sqrt{\sec (c+d x)}}+\frac{b^2 \sin (c+d x) \sqrt{b \sec (c+d x)}}{2 d \sec ^{\frac{3}{2}}(c+d x)}",1,"(b^2*x*Sqrt[b*Sec[c + d*x]])/(2*Sqrt[Sec[c + d*x]]) + (b^2*Sqrt[b*Sec[c + d*x]]*Sin[c + d*x])/(2*d*Sec[c + d*x]^(3/2))","A",3,3,23,0.1304,1,"{17, 2635, 8}"
160,1,76,0,0.0168081,"\int \frac{(b \sec (c+d x))^{5/2}}{\sec ^{\frac{11}{2}}(c+d x)} \, dx","Int[(b*Sec[c + d*x])^(5/2)/Sec[c + d*x]^(11/2),x]","\frac{b^2 \sin (c+d x) \sqrt{b \sec (c+d x)}}{d \sqrt{\sec (c+d x)}}-\frac{b^2 \sin ^3(c+d x) \sqrt{b \sec (c+d x)}}{3 d \sqrt{\sec (c+d x)}}","\frac{b^2 \sin (c+d x) \sqrt{b \sec (c+d x)}}{d \sqrt{\sec (c+d x)}}-\frac{b^2 \sin ^3(c+d x) \sqrt{b \sec (c+d x)}}{3 d \sqrt{\sec (c+d x)}}",1,"(b^2*Sqrt[b*Sec[c + d*x]]*Sin[c + d*x])/(d*Sqrt[Sec[c + d*x]]) - (b^2*Sqrt[b*Sec[c + d*x]]*Sin[c + d*x]^3)/(3*d*Sqrt[Sec[c + d*x]])","A",3,2,23,0.08696,1,"{17, 2633}"
161,1,72,0,0.0192948,"\int \frac{\sec ^{\frac{7}{2}}(c+d x)}{\sqrt{b \sec (c+d x)}} \, dx","Int[Sec[c + d*x]^(7/2)/Sqrt[b*Sec[c + d*x]],x]","\frac{\sin (c+d x) \sec ^{\frac{5}{2}}(c+d x)}{2 d \sqrt{b \sec (c+d x)}}+\frac{\sqrt{\sec (c+d x)} \tanh ^{-1}(\sin (c+d x))}{2 d \sqrt{b \sec (c+d x)}}","\frac{\sin (c+d x) \sec ^{\frac{5}{2}}(c+d x)}{2 d \sqrt{b \sec (c+d x)}}+\frac{\sqrt{\sec (c+d x)} \tanh ^{-1}(\sin (c+d x))}{2 d \sqrt{b \sec (c+d x)}}",1,"(ArcTanh[Sin[c + d*x]]*Sqrt[Sec[c + d*x]])/(2*d*Sqrt[b*Sec[c + d*x]]) + (Sec[c + d*x]^(5/2)*Sin[c + d*x])/(2*d*Sqrt[b*Sec[c + d*x]])","A",3,3,23,0.1304,1,"{17, 3768, 3770}"
162,1,32,0,0.0114377,"\int \frac{\sec ^{\frac{5}{2}}(c+d x)}{\sqrt{b \sec (c+d x)}} \, dx","Int[Sec[c + d*x]^(5/2)/Sqrt[b*Sec[c + d*x]],x]","\frac{\sin (c+d x) \sec ^{\frac{3}{2}}(c+d x)}{d \sqrt{b \sec (c+d x)}}","\frac{\sin (c+d x) \sec ^{\frac{3}{2}}(c+d x)}{d \sqrt{b \sec (c+d x)}}",1,"(Sec[c + d*x]^(3/2)*Sin[c + d*x])/(d*Sqrt[b*Sec[c + d*x]])","A",3,3,23,0.1304,1,"{17, 3767, 8}"
163,1,33,0,0.0074269,"\int \frac{\sec ^{\frac{3}{2}}(c+d x)}{\sqrt{b \sec (c+d x)}} \, dx","Int[Sec[c + d*x]^(3/2)/Sqrt[b*Sec[c + d*x]],x]","\frac{\sqrt{\sec (c+d x)} \tanh ^{-1}(\sin (c+d x))}{d \sqrt{b \sec (c+d x)}}","\frac{\sqrt{\sec (c+d x)} \tanh ^{-1}(\sin (c+d x))}{d \sqrt{b \sec (c+d x)}}",1,"(ArcTanh[Sin[c + d*x]]*Sqrt[Sec[c + d*x]])/(d*Sqrt[b*Sec[c + d*x]])","A",2,2,23,0.08696,1,"{17, 3770}"
164,1,24,0,0.0022741,"\int \frac{\sqrt{\sec (c+d x)}}{\sqrt{b \sec (c+d x)}} \, dx","Int[Sqrt[Sec[c + d*x]]/Sqrt[b*Sec[c + d*x]],x]","\frac{x \sqrt{\sec (c+d x)}}{\sqrt{b \sec (c+d x)}}","\frac{x \sqrt{\sec (c+d x)}}{\sqrt{b \sec (c+d x)}}",1,"(x*Sqrt[Sec[c + d*x]])/Sqrt[b*Sec[c + d*x]]","A",2,2,23,0.08696,1,"{17, 8}"
165,1,32,0,0.0066139,"\int \frac{1}{\sqrt{\sec (c+d x)} \sqrt{b \sec (c+d x)}} \, dx","Int[1/(Sqrt[Sec[c + d*x]]*Sqrt[b*Sec[c + d*x]]),x]","\frac{\sin (c+d x) \sqrt{\sec (c+d x)}}{d \sqrt{b \sec (c+d x)}}","\frac{\sin (c+d x) \sqrt{\sec (c+d x)}}{d \sqrt{b \sec (c+d x)}}",1,"(Sqrt[Sec[c + d*x]]*Sin[c + d*x])/(d*Sqrt[b*Sec[c + d*x]])","A",2,2,23,0.08696,1,"{18, 2637}"
166,1,63,0,0.0135085,"\int \frac{1}{\sec ^{\frac{3}{2}}(c+d x) \sqrt{b \sec (c+d x)}} \, dx","Int[1/(Sec[c + d*x]^(3/2)*Sqrt[b*Sec[c + d*x]]),x]","\frac{x \sqrt{\sec (c+d x)}}{2 \sqrt{b \sec (c+d x)}}+\frac{\sin (c+d x)}{2 d \sqrt{\sec (c+d x)} \sqrt{b \sec (c+d x)}}","\frac{x \sqrt{\sec (c+d x)}}{2 \sqrt{b \sec (c+d x)}}+\frac{\sin (c+d x)}{2 d \sqrt{\sec (c+d x)} \sqrt{b \sec (c+d x)}}",1,"(x*Sqrt[Sec[c + d*x]])/(2*Sqrt[b*Sec[c + d*x]]) + Sin[c + d*x]/(2*d*Sqrt[Sec[c + d*x]]*Sqrt[b*Sec[c + d*x]])","A",3,3,23,0.1304,1,"{18, 2635, 8}"
167,1,70,0,0.0157183,"\int \frac{1}{\sec ^{\frac{5}{2}}(c+d x) \sqrt{b \sec (c+d x)}} \, dx","Int[1/(Sec[c + d*x]^(5/2)*Sqrt[b*Sec[c + d*x]]),x]","\frac{\sin (c+d x) \sqrt{\sec (c+d x)}}{d \sqrt{b \sec (c+d x)}}-\frac{\sin ^3(c+d x) \sqrt{\sec (c+d x)}}{3 d \sqrt{b \sec (c+d x)}}","\frac{\sin (c+d x) \sqrt{\sec (c+d x)}}{d \sqrt{b \sec (c+d x)}}-\frac{\sin ^3(c+d x) \sqrt{\sec (c+d x)}}{3 d \sqrt{b \sec (c+d x)}}",1,"(Sqrt[Sec[c + d*x]]*Sin[c + d*x])/(d*Sqrt[b*Sec[c + d*x]]) - (Sqrt[Sec[c + d*x]]*Sin[c + d*x]^3)/(3*d*Sqrt[b*Sec[c + d*x]])","A",3,2,23,0.08696,1,"{18, 2633}"
168,1,78,0,0.0201799,"\int \frac{\sec ^{\frac{9}{2}}(c+d x)}{(b \sec (c+d x))^{3/2}} \, dx","Int[Sec[c + d*x]^(9/2)/(b*Sec[c + d*x])^(3/2),x]","\frac{\sin (c+d x) \sec ^{\frac{5}{2}}(c+d x)}{2 b d \sqrt{b \sec (c+d x)}}+\frac{\sqrt{\sec (c+d x)} \tanh ^{-1}(\sin (c+d x))}{2 b d \sqrt{b \sec (c+d x)}}","\frac{\sin (c+d x) \sec ^{\frac{5}{2}}(c+d x)}{2 b d \sqrt{b \sec (c+d x)}}+\frac{\sqrt{\sec (c+d x)} \tanh ^{-1}(\sin (c+d x))}{2 b d \sqrt{b \sec (c+d x)}}",1,"(ArcTanh[Sin[c + d*x]]*Sqrt[Sec[c + d*x]])/(2*b*d*Sqrt[b*Sec[c + d*x]]) + (Sec[c + d*x]^(5/2)*Sin[c + d*x])/(2*b*d*Sqrt[b*Sec[c + d*x]])","A",3,3,23,0.1304,1,"{17, 3768, 3770}"
169,1,35,0,0.0118306,"\int \frac{\sec ^{\frac{7}{2}}(c+d x)}{(b \sec (c+d x))^{3/2}} \, dx","Int[Sec[c + d*x]^(7/2)/(b*Sec[c + d*x])^(3/2),x]","\frac{\sin (c+d x) \sec ^{\frac{3}{2}}(c+d x)}{b d \sqrt{b \sec (c+d x)}}","\frac{\sin (c+d x) \sec ^{\frac{3}{2}}(c+d x)}{b d \sqrt{b \sec (c+d x)}}",1,"(Sec[c + d*x]^(3/2)*Sin[c + d*x])/(b*d*Sqrt[b*Sec[c + d*x]])","A",3,3,23,0.1304,1,"{17, 3767, 8}"
170,1,36,0,0.0074694,"\int \frac{\sec ^{\frac{5}{2}}(c+d x)}{(b \sec (c+d x))^{3/2}} \, dx","Int[Sec[c + d*x]^(5/2)/(b*Sec[c + d*x])^(3/2),x]","\frac{\sqrt{\sec (c+d x)} \tanh ^{-1}(\sin (c+d x))}{b d \sqrt{b \sec (c+d x)}}","\frac{\sqrt{\sec (c+d x)} \tanh ^{-1}(\sin (c+d x))}{b d \sqrt{b \sec (c+d x)}}",1,"(ArcTanh[Sin[c + d*x]]*Sqrt[Sec[c + d*x]])/(b*d*Sqrt[b*Sec[c + d*x]])","A",2,2,23,0.08696,1,"{17, 3770}"
171,1,27,0,0.0027357,"\int \frac{\sec ^{\frac{3}{2}}(c+d x)}{(b \sec (c+d x))^{3/2}} \, dx","Int[Sec[c + d*x]^(3/2)/(b*Sec[c + d*x])^(3/2),x]","\frac{x \sqrt{\sec (c+d x)}}{b \sqrt{b \sec (c+d x)}}","\frac{x \sqrt{\sec (c+d x)}}{b \sqrt{b \sec (c+d x)}}",1,"(x*Sqrt[Sec[c + d*x]])/(b*Sqrt[b*Sec[c + d*x]])","A",2,2,23,0.08696,1,"{17, 8}"
172,1,35,0,0.007553,"\int \frac{\sqrt{\sec (c+d x)}}{(b \sec (c+d x))^{3/2}} \, dx","Int[Sqrt[Sec[c + d*x]]/(b*Sec[c + d*x])^(3/2),x]","\frac{\sin (c+d x) \sqrt{\sec (c+d x)}}{b d \sqrt{b \sec (c+d x)}}","\frac{\sin (c+d x) \sqrt{\sec (c+d x)}}{b d \sqrt{b \sec (c+d x)}}",1,"(Sqrt[Sec[c + d*x]]*Sin[c + d*x])/(b*d*Sqrt[b*Sec[c + d*x]])","A",2,2,23,0.08696,1,"{17, 2637}"
173,1,69,0,0.0141337,"\int \frac{1}{\sqrt{\sec (c+d x)} (b \sec (c+d x))^{3/2}} \, dx","Int[1/(Sqrt[Sec[c + d*x]]*(b*Sec[c + d*x])^(3/2)),x]","\frac{x \sqrt{\sec (c+d x)}}{2 b \sqrt{b \sec (c+d x)}}+\frac{\sin (c+d x)}{2 b d \sqrt{\sec (c+d x)} \sqrt{b \sec (c+d x)}}","\frac{x \sqrt{\sec (c+d x)}}{2 b \sqrt{b \sec (c+d x)}}+\frac{\sin (c+d x)}{2 b d \sqrt{\sec (c+d x)} \sqrt{b \sec (c+d x)}}",1,"(x*Sqrt[Sec[c + d*x]])/(2*b*Sqrt[b*Sec[c + d*x]]) + Sin[c + d*x]/(2*b*d*Sqrt[Sec[c + d*x]]*Sqrt[b*Sec[c + d*x]])","A",3,3,23,0.1304,1,"{18, 2635, 8}"
174,1,76,0,0.0168956,"\int \frac{1}{\sec ^{\frac{3}{2}}(c+d x) (b \sec (c+d x))^{3/2}} \, dx","Int[1/(Sec[c + d*x]^(3/2)*(b*Sec[c + d*x])^(3/2)),x]","\frac{\sin (c+d x) \sqrt{\sec (c+d x)}}{b d \sqrt{b \sec (c+d x)}}-\frac{\sin ^3(c+d x) \sqrt{\sec (c+d x)}}{3 b d \sqrt{b \sec (c+d x)}}","\frac{\sin (c+d x) \sqrt{\sec (c+d x)}}{b d \sqrt{b \sec (c+d x)}}-\frac{\sin ^3(c+d x) \sqrt{\sec (c+d x)}}{3 b d \sqrt{b \sec (c+d x)}}",1,"(Sqrt[Sec[c + d*x]]*Sin[c + d*x])/(b*d*Sqrt[b*Sec[c + d*x]]) - (Sqrt[Sec[c + d*x]]*Sin[c + d*x]^3)/(3*b*d*Sqrt[b*Sec[c + d*x]])","A",3,2,23,0.08696,1,"{18, 2633}"
175,1,107,0,0.027397,"\int \frac{1}{\sec ^{\frac{5}{2}}(c+d x) (b \sec (c+d x))^{3/2}} \, dx","Int[1/(Sec[c + d*x]^(5/2)*(b*Sec[c + d*x])^(3/2)),x]","\frac{3 x \sqrt{\sec (c+d x)}}{8 b \sqrt{b \sec (c+d x)}}+\frac{\sin (c+d x)}{4 b d \sec ^{\frac{5}{2}}(c+d x) \sqrt{b \sec (c+d x)}}+\frac{3 \sin (c+d x)}{8 b d \sqrt{\sec (c+d x)} \sqrt{b \sec (c+d x)}}","\frac{3 x \sqrt{\sec (c+d x)}}{8 b \sqrt{b \sec (c+d x)}}+\frac{\sin (c+d x)}{4 b d \sec ^{\frac{5}{2}}(c+d x) \sqrt{b \sec (c+d x)}}+\frac{3 \sin (c+d x)}{8 b d \sqrt{\sec (c+d x)} \sqrt{b \sec (c+d x)}}",1,"(3*x*Sqrt[Sec[c + d*x]])/(8*b*Sqrt[b*Sec[c + d*x]]) + Sin[c + d*x]/(4*b*d*Sec[c + d*x]^(5/2)*Sqrt[b*Sec[c + d*x]]) + (3*Sin[c + d*x])/(8*b*d*Sqrt[Sec[c + d*x]]*Sqrt[b*Sec[c + d*x]])","A",4,3,23,0.1304,1,"{18, 2635, 8}"
176,1,78,0,0.0202177,"\int \frac{\sec ^{\frac{11}{2}}(c+d x)}{(b \sec (c+d x))^{5/2}} \, dx","Int[Sec[c + d*x]^(11/2)/(b*Sec[c + d*x])^(5/2),x]","\frac{\sin (c+d x) \sec ^{\frac{5}{2}}(c+d x)}{2 b^2 d \sqrt{b \sec (c+d x)}}+\frac{\sqrt{\sec (c+d x)} \tanh ^{-1}(\sin (c+d x))}{2 b^2 d \sqrt{b \sec (c+d x)}}","\frac{\sin (c+d x) \sec ^{\frac{5}{2}}(c+d x)}{2 b^2 d \sqrt{b \sec (c+d x)}}+\frac{\sqrt{\sec (c+d x)} \tanh ^{-1}(\sin (c+d x))}{2 b^2 d \sqrt{b \sec (c+d x)}}",1,"(ArcTanh[Sin[c + d*x]]*Sqrt[Sec[c + d*x]])/(2*b^2*d*Sqrt[b*Sec[c + d*x]]) + (Sec[c + d*x]^(5/2)*Sin[c + d*x])/(2*b^2*d*Sqrt[b*Sec[c + d*x]])","A",3,3,23,0.1304,1,"{17, 3768, 3770}"
177,1,35,0,0.0115766,"\int \frac{\sec ^{\frac{9}{2}}(c+d x)}{(b \sec (c+d x))^{5/2}} \, dx","Int[Sec[c + d*x]^(9/2)/(b*Sec[c + d*x])^(5/2),x]","\frac{\sin (c+d x) \sec ^{\frac{3}{2}}(c+d x)}{b^2 d \sqrt{b \sec (c+d x)}}","\frac{\sin (c+d x) \sec ^{\frac{3}{2}}(c+d x)}{b^2 d \sqrt{b \sec (c+d x)}}",1,"(Sec[c + d*x]^(3/2)*Sin[c + d*x])/(b^2*d*Sqrt[b*Sec[c + d*x]])","A",3,3,23,0.1304,1,"{17, 3767, 8}"
178,1,36,0,0.0077274,"\int \frac{\sec ^{\frac{7}{2}}(c+d x)}{(b \sec (c+d x))^{5/2}} \, dx","Int[Sec[c + d*x]^(7/2)/(b*Sec[c + d*x])^(5/2),x]","\frac{\sqrt{\sec (c+d x)} \tanh ^{-1}(\sin (c+d x))}{b^2 d \sqrt{b \sec (c+d x)}}","\frac{\sqrt{\sec (c+d x)} \tanh ^{-1}(\sin (c+d x))}{b^2 d \sqrt{b \sec (c+d x)}}",1,"(ArcTanh[Sin[c + d*x]]*Sqrt[Sec[c + d*x]])/(b^2*d*Sqrt[b*Sec[c + d*x]])","A",2,2,23,0.08696,1,"{17, 3770}"
179,1,27,0,0.0026661,"\int \frac{\sec ^{\frac{5}{2}}(c+d x)}{(b \sec (c+d x))^{5/2}} \, dx","Int[Sec[c + d*x]^(5/2)/(b*Sec[c + d*x])^(5/2),x]","\frac{x \sqrt{\sec (c+d x)}}{b^2 \sqrt{b \sec (c+d x)}}","\frac{x \sqrt{\sec (c+d x)}}{b^2 \sqrt{b \sec (c+d x)}}",1,"(x*Sqrt[Sec[c + d*x]])/(b^2*Sqrt[b*Sec[c + d*x]])","A",2,2,23,0.08696,1,"{17, 8}"
180,1,35,0,0.0069425,"\int \frac{\sec ^{\frac{3}{2}}(c+d x)}{(b \sec (c+d x))^{5/2}} \, dx","Int[Sec[c + d*x]^(3/2)/(b*Sec[c + d*x])^(5/2),x]","\frac{\sin (c+d x) \sqrt{\sec (c+d x)}}{b^2 d \sqrt{b \sec (c+d x)}}","\frac{\sin (c+d x) \sqrt{\sec (c+d x)}}{b^2 d \sqrt{b \sec (c+d x)}}",1,"(Sqrt[Sec[c + d*x]]*Sin[c + d*x])/(b^2*d*Sqrt[b*Sec[c + d*x]])","A",2,2,23,0.08696,1,"{17, 2637}"
181,1,69,0,0.0146361,"\int \frac{\sqrt{\sec (c+d x)}}{(b \sec (c+d x))^{5/2}} \, dx","Int[Sqrt[Sec[c + d*x]]/(b*Sec[c + d*x])^(5/2),x]","\frac{x \sqrt{\sec (c+d x)}}{2 b^2 \sqrt{b \sec (c+d x)}}+\frac{\sin (c+d x)}{2 b^2 d \sqrt{\sec (c+d x)} \sqrt{b \sec (c+d x)}}","\frac{x \sqrt{\sec (c+d x)}}{2 b^2 \sqrt{b \sec (c+d x)}}+\frac{\sin (c+d x)}{2 b^2 d \sqrt{\sec (c+d x)} \sqrt{b \sec (c+d x)}}",1,"(x*Sqrt[Sec[c + d*x]])/(2*b^2*Sqrt[b*Sec[c + d*x]]) + Sin[c + d*x]/(2*b^2*d*Sqrt[Sec[c + d*x]]*Sqrt[b*Sec[c + d*x]])","A",3,3,23,0.1304,1,"{17, 2635, 8}"
182,1,76,0,0.0167266,"\int \frac{1}{\sqrt{\sec (c+d x)} (b \sec (c+d x))^{5/2}} \, dx","Int[1/(Sqrt[Sec[c + d*x]]*(b*Sec[c + d*x])^(5/2)),x]","\frac{\sin (c+d x) \sqrt{\sec (c+d x)}}{b^2 d \sqrt{b \sec (c+d x)}}-\frac{\sin ^3(c+d x) \sqrt{\sec (c+d x)}}{3 b^2 d \sqrt{b \sec (c+d x)}}","\frac{\sin (c+d x) \sqrt{\sec (c+d x)}}{b^2 d \sqrt{b \sec (c+d x)}}-\frac{\sin ^3(c+d x) \sqrt{\sec (c+d x)}}{3 b^2 d \sqrt{b \sec (c+d x)}}",1,"(Sqrt[Sec[c + d*x]]*Sin[c + d*x])/(b^2*d*Sqrt[b*Sec[c + d*x]]) - (Sqrt[Sec[c + d*x]]*Sin[c + d*x]^3)/(3*b^2*d*Sqrt[b*Sec[c + d*x]])","A",3,2,23,0.08696,1,"{18, 2633}"
183,1,107,0,0.0284181,"\int \frac{1}{\sec ^{\frac{3}{2}}(c+d x) (b \sec (c+d x))^{5/2}} \, dx","Int[1/(Sec[c + d*x]^(3/2)*(b*Sec[c + d*x])^(5/2)),x]","\frac{3 x \sqrt{\sec (c+d x)}}{8 b^2 \sqrt{b \sec (c+d x)}}+\frac{\sin (c+d x)}{4 b^2 d \sec ^{\frac{5}{2}}(c+d x) \sqrt{b \sec (c+d x)}}+\frac{3 \sin (c+d x)}{8 b^2 d \sqrt{\sec (c+d x)} \sqrt{b \sec (c+d x)}}","\frac{3 x \sqrt{\sec (c+d x)}}{8 b^2 \sqrt{b \sec (c+d x)}}+\frac{\sin (c+d x)}{4 b^2 d \sec ^{\frac{5}{2}}(c+d x) \sqrt{b \sec (c+d x)}}+\frac{3 \sin (c+d x)}{8 b^2 d \sqrt{\sec (c+d x)} \sqrt{b \sec (c+d x)}}",1,"(3*x*Sqrt[Sec[c + d*x]])/(8*b^2*Sqrt[b*Sec[c + d*x]]) + Sin[c + d*x]/(4*b^2*d*Sec[c + d*x]^(5/2)*Sqrt[b*Sec[c + d*x]]) + (3*Sin[c + d*x])/(8*b^2*d*Sqrt[Sec[c + d*x]]*Sqrt[b*Sec[c + d*x]])","A",4,3,23,0.1304,1,"{18, 2635, 8}"
184,1,58,0,0.0325862,"\int \sec ^2(c+d x) \sqrt[3]{b \sec (c+d x)} \, dx","Int[Sec[c + d*x]^2*(b*Sec[c + d*x])^(1/3),x]","\frac{3 \sin (c+d x) (b \sec (c+d x))^{4/3} \, _2F_1\left(-\frac{2}{3},\frac{1}{2};\frac{1}{3};\cos ^2(c+d x)\right)}{4 b d \sqrt{\sin ^2(c+d x)}}","\frac{3 \sin (c+d x) (b \sec (c+d x))^{4/3} \, _2F_1\left(-\frac{2}{3},\frac{1}{2};\frac{1}{3};\cos ^2(c+d x)\right)}{4 b d \sqrt{\sin ^2(c+d x)}}",1,"(3*Hypergeometric2F1[-2/3, 1/2, 1/3, Cos[c + d*x]^2]*(b*Sec[c + d*x])^(4/3)*Sin[c + d*x])/(4*b*d*Sqrt[Sin[c + d*x]^2])","A",3,3,21,0.1429,1,"{16, 3772, 2643}"
185,1,53,0,0.0308292,"\int \sec (c+d x) \sqrt[3]{b \sec (c+d x)} \, dx","Int[Sec[c + d*x]*(b*Sec[c + d*x])^(1/3),x]","\frac{3 \sin (c+d x) \sqrt[3]{b \sec (c+d x)} \, _2F_1\left(-\frac{1}{6},\frac{1}{2};\frac{5}{6};\cos ^2(c+d x)\right)}{d \sqrt{\sin ^2(c+d x)}}","\frac{3 \sin (c+d x) \sqrt[3]{b \sec (c+d x)} \, _2F_1\left(-\frac{1}{6},\frac{1}{2};\frac{5}{6};\cos ^2(c+d x)\right)}{d \sqrt{\sin ^2(c+d x)}}",1,"(3*Hypergeometric2F1[-1/6, 1/2, 5/6, Cos[c + d*x]^2]*(b*Sec[c + d*x])^(1/3)*Sin[c + d*x])/(d*Sqrt[Sin[c + d*x]^2])","A",3,3,19,0.1579,1,"{16, 3772, 2643}"
186,1,56,0,0.0249474,"\int \sqrt[3]{b \sec (c+d x)} \, dx","Int[(b*Sec[c + d*x])^(1/3),x]","-\frac{3 b \sin (c+d x) \, _2F_1\left(\frac{1}{3},\frac{1}{2};\frac{4}{3};\cos ^2(c+d x)\right)}{2 d \sqrt{\sin ^2(c+d x)} (b \sec (c+d x))^{2/3}}","-\frac{3 b \sin (c+d x) \, _2F_1\left(\frac{1}{3},\frac{1}{2};\frac{4}{3};\cos ^2(c+d x)\right)}{2 d \sqrt{\sin ^2(c+d x)} (b \sec (c+d x))^{2/3}}",1,"(-3*b*Hypergeometric2F1[1/3, 1/2, 4/3, Cos[c + d*x]^2]*Sin[c + d*x])/(2*d*(b*Sec[c + d*x])^(2/3)*Sqrt[Sin[c + d*x]^2])","A",2,2,12,0.1667,1,"{3772, 2643}"
187,1,58,0,0.0358247,"\int \cos (c+d x) \sqrt[3]{b \sec (c+d x)} \, dx","Int[Cos[c + d*x]*(b*Sec[c + d*x])^(1/3),x]","-\frac{3 b^2 \sin (c+d x) \, _2F_1\left(\frac{1}{2},\frac{5}{6};\frac{11}{6};\cos ^2(c+d x)\right)}{5 d \sqrt{\sin ^2(c+d x)} (b \sec (c+d x))^{5/3}}","-\frac{3 b^2 \sin (c+d x) \, _2F_1\left(\frac{1}{2},\frac{5}{6};\frac{11}{6};\cos ^2(c+d x)\right)}{5 d \sqrt{\sin ^2(c+d x)} (b \sec (c+d x))^{5/3}}",1,"(-3*b^2*Hypergeometric2F1[1/2, 5/6, 11/6, Cos[c + d*x]^2]*Sin[c + d*x])/(5*d*(b*Sec[c + d*x])^(5/3)*Sqrt[Sin[c + d*x]^2])","A",3,3,19,0.1579,1,"{16, 3772, 2643}"
188,1,58,0,0.0432759,"\int \cos ^2(c+d x) \sqrt[3]{b \sec (c+d x)} \, dx","Int[Cos[c + d*x]^2*(b*Sec[c + d*x])^(1/3),x]","-\frac{3 b^3 \sin (c+d x) \, _2F_1\left(\frac{1}{2},\frac{4}{3};\frac{7}{3};\cos ^2(c+d x)\right)}{8 d \sqrt{\sin ^2(c+d x)} (b \sec (c+d x))^{8/3}}","-\frac{3 b^3 \sin (c+d x) \, _2F_1\left(\frac{1}{2},\frac{4}{3};\frac{7}{3};\cos ^2(c+d x)\right)}{8 d \sqrt{\sin ^2(c+d x)} (b \sec (c+d x))^{8/3}}",1,"(-3*b^3*Hypergeometric2F1[1/2, 4/3, 7/3, Cos[c + d*x]^2]*Sin[c + d*x])/(8*d*(b*Sec[c + d*x])^(8/3)*Sqrt[Sin[c + d*x]^2])","A",3,3,21,0.1429,1,"{16, 3772, 2643}"
189,1,58,0,0.0309513,"\int \sec ^2(c+d x) (b \sec (c+d x))^{4/3} \, dx","Int[Sec[c + d*x]^2*(b*Sec[c + d*x])^(4/3),x]","\frac{3 \sin (c+d x) (b \sec (c+d x))^{7/3} \, _2F_1\left(-\frac{7}{6},\frac{1}{2};-\frac{1}{6};\cos ^2(c+d x)\right)}{7 b d \sqrt{\sin ^2(c+d x)}}","\frac{3 \sin (c+d x) (b \sec (c+d x))^{7/3} \, _2F_1\left(-\frac{7}{6},\frac{1}{2};-\frac{1}{6};\cos ^2(c+d x)\right)}{7 b d \sqrt{\sin ^2(c+d x)}}",1,"(3*Hypergeometric2F1[-7/6, 1/2, -1/6, Cos[c + d*x]^2]*(b*Sec[c + d*x])^(7/3)*Sin[c + d*x])/(7*b*d*Sqrt[Sin[c + d*x]^2])","A",3,3,21,0.1429,1,"{16, 3772, 2643}"
190,1,55,0,0.0302989,"\int \sec (c+d x) (b \sec (c+d x))^{4/3} \, dx","Int[Sec[c + d*x]*(b*Sec[c + d*x])^(4/3),x]","\frac{3 \sin (c+d x) (b \sec (c+d x))^{4/3} \, _2F_1\left(-\frac{2}{3},\frac{1}{2};\frac{1}{3};\cos ^2(c+d x)\right)}{4 d \sqrt{\sin ^2(c+d x)}}","\frac{3 \sin (c+d x) (b \sec (c+d x))^{4/3} \, _2F_1\left(-\frac{2}{3},\frac{1}{2};\frac{1}{3};\cos ^2(c+d x)\right)}{4 d \sqrt{\sin ^2(c+d x)}}",1,"(3*Hypergeometric2F1[-2/3, 1/2, 1/3, Cos[c + d*x]^2]*(b*Sec[c + d*x])^(4/3)*Sin[c + d*x])/(4*d*Sqrt[Sin[c + d*x]^2])","A",3,3,19,0.1579,1,"{16, 3772, 2643}"
191,1,54,0,0.026934,"\int (b \sec (c+d x))^{4/3} \, dx","Int[(b*Sec[c + d*x])^(4/3),x]","\frac{3 b \sin (c+d x) \sqrt[3]{b \sec (c+d x)} \, _2F_1\left(-\frac{1}{6},\frac{1}{2};\frac{5}{6};\cos ^2(c+d x)\right)}{d \sqrt{\sin ^2(c+d x)}}","\frac{3 b \sin (c+d x) \sqrt[3]{b \sec (c+d x)} \, _2F_1\left(-\frac{1}{6},\frac{1}{2};\frac{5}{6};\cos ^2(c+d x)\right)}{d \sqrt{\sin ^2(c+d x)}}",1,"(3*b*Hypergeometric2F1[-1/6, 1/2, 5/6, Cos[c + d*x]^2]*(b*Sec[c + d*x])^(1/3)*Sin[c + d*x])/(d*Sqrt[Sin[c + d*x]^2])","A",2,2,12,0.1667,1,"{3772, 2643}"
192,1,58,0,0.0381933,"\int \cos (c+d x) (b \sec (c+d x))^{4/3} \, dx","Int[Cos[c + d*x]*(b*Sec[c + d*x])^(4/3),x]","-\frac{3 b^2 \sin (c+d x) \, _2F_1\left(\frac{1}{3},\frac{1}{2};\frac{4}{3};\cos ^2(c+d x)\right)}{2 d \sqrt{\sin ^2(c+d x)} (b \sec (c+d x))^{2/3}}","-\frac{3 b^2 \sin (c+d x) \, _2F_1\left(\frac{1}{3},\frac{1}{2};\frac{4}{3};\cos ^2(c+d x)\right)}{2 d \sqrt{\sin ^2(c+d x)} (b \sec (c+d x))^{2/3}}",1,"(-3*b^2*Hypergeometric2F1[1/3, 1/2, 4/3, Cos[c + d*x]^2]*Sin[c + d*x])/(2*d*(b*Sec[c + d*x])^(2/3)*Sqrt[Sin[c + d*x]^2])","A",3,3,19,0.1579,1,"{16, 3772, 2643}"
193,1,58,0,0.0460992,"\int \cos ^2(c+d x) (b \sec (c+d x))^{4/3} \, dx","Int[Cos[c + d*x]^2*(b*Sec[c + d*x])^(4/3),x]","-\frac{3 b^3 \sin (c+d x) \, _2F_1\left(\frac{1}{2},\frac{5}{6};\frac{11}{6};\cos ^2(c+d x)\right)}{5 d \sqrt{\sin ^2(c+d x)} (b \sec (c+d x))^{5/3}}","-\frac{3 b^3 \sin (c+d x) \, _2F_1\left(\frac{1}{2},\frac{5}{6};\frac{11}{6};\cos ^2(c+d x)\right)}{5 d \sqrt{\sin ^2(c+d x)} (b \sec (c+d x))^{5/3}}",1,"(-3*b^3*Hypergeometric2F1[1/2, 5/6, 11/6, Cos[c + d*x]^2]*Sin[c + d*x])/(5*d*(b*Sec[c + d*x])^(5/3)*Sqrt[Sin[c + d*x]^2])","A",3,3,21,0.1429,1,"{16, 3772, 2643}"
194,1,58,0,0.0311336,"\int \frac{\sec ^2(c+d x)}{\sqrt[3]{b \sec (c+d x)}} \, dx","Int[Sec[c + d*x]^2/(b*Sec[c + d*x])^(1/3),x]","\frac{3 \sin (c+d x) (b \sec (c+d x))^{2/3} \, _2F_1\left(-\frac{1}{3},\frac{1}{2};\frac{2}{3};\cos ^2(c+d x)\right)}{2 b d \sqrt{\sin ^2(c+d x)}}","\frac{3 \sin (c+d x) (b \sec (c+d x))^{2/3} \, _2F_1\left(-\frac{1}{3},\frac{1}{2};\frac{2}{3};\cos ^2(c+d x)\right)}{2 b d \sqrt{\sin ^2(c+d x)}}",1,"(3*Hypergeometric2F1[-1/3, 1/2, 2/3, Cos[c + d*x]^2]*(b*Sec[c + d*x])^(2/3)*Sin[c + d*x])/(2*b*d*Sqrt[Sin[c + d*x]^2])","A",3,3,21,0.1429,1,"{16, 3772, 2643}"
195,1,53,0,0.0313008,"\int \frac{\sec (c+d x)}{\sqrt[3]{b \sec (c+d x)}} \, dx","Int[Sec[c + d*x]/(b*Sec[c + d*x])^(1/3),x]","-\frac{3 \sin (c+d x) \, _2F_1\left(\frac{1}{6},\frac{1}{2};\frac{7}{6};\cos ^2(c+d x)\right)}{d \sqrt{\sin ^2(c+d x)} \sqrt[3]{b \sec (c+d x)}}","-\frac{3 \sin (c+d x) \, _2F_1\left(\frac{1}{6},\frac{1}{2};\frac{7}{6};\cos ^2(c+d x)\right)}{d \sqrt{\sin ^2(c+d x)} \sqrt[3]{b \sec (c+d x)}}",1,"(-3*Hypergeometric2F1[1/6, 1/2, 7/6, Cos[c + d*x]^2]*Sin[c + d*x])/(d*(b*Sec[c + d*x])^(1/3)*Sqrt[Sin[c + d*x]^2])","A",3,3,19,0.1579,1,"{16, 3772, 2643}"
196,1,56,0,0.025305,"\int \frac{1}{\sqrt[3]{b \sec (c+d x)}} \, dx","Int[(b*Sec[c + d*x])^(-1/3),x]","-\frac{3 b \sin (c+d x) \, _2F_1\left(\frac{1}{2},\frac{2}{3};\frac{5}{3};\cos ^2(c+d x)\right)}{4 d \sqrt{\sin ^2(c+d x)} (b \sec (c+d x))^{4/3}}","-\frac{3 b \sin (c+d x) \, _2F_1\left(\frac{1}{2},\frac{2}{3};\frac{5}{3};\cos ^2(c+d x)\right)}{4 d \sqrt{\sin ^2(c+d x)} (b \sec (c+d x))^{4/3}}",1,"(-3*b*Hypergeometric2F1[1/2, 2/3, 5/3, Cos[c + d*x]^2]*Sin[c + d*x])/(4*d*(b*Sec[c + d*x])^(4/3)*Sqrt[Sin[c + d*x]^2])","A",2,2,12,0.1667,1,"{3772, 2643}"
197,1,58,0,0.0374952,"\int \frac{\cos (c+d x)}{\sqrt[3]{b \sec (c+d x)}} \, dx","Int[Cos[c + d*x]/(b*Sec[c + d*x])^(1/3),x]","-\frac{3 b^2 \sin (c+d x) \, _2F_1\left(\frac{1}{2},\frac{7}{6};\frac{13}{6};\cos ^2(c+d x)\right)}{7 d \sqrt{\sin ^2(c+d x)} (b \sec (c+d x))^{7/3}}","-\frac{3 b^2 \sin (c+d x) \, _2F_1\left(\frac{1}{2},\frac{7}{6};\frac{13}{6};\cos ^2(c+d x)\right)}{7 d \sqrt{\sin ^2(c+d x)} (b \sec (c+d x))^{7/3}}",1,"(-3*b^2*Hypergeometric2F1[1/2, 7/6, 13/6, Cos[c + d*x]^2]*Sin[c + d*x])/(7*d*(b*Sec[c + d*x])^(7/3)*Sqrt[Sin[c + d*x]^2])","A",3,3,19,0.1579,1,"{16, 3772, 2643}"
198,1,58,0,0.04462,"\int \frac{\cos ^2(c+d x)}{\sqrt[3]{b \sec (c+d x)}} \, dx","Int[Cos[c + d*x]^2/(b*Sec[c + d*x])^(1/3),x]","-\frac{3 b^3 \sin (c+d x) \, _2F_1\left(\frac{1}{2},\frac{5}{3};\frac{8}{3};\cos ^2(c+d x)\right)}{10 d \sqrt{\sin ^2(c+d x)} (b \sec (c+d x))^{10/3}}","-\frac{3 b^3 \sin (c+d x) \, _2F_1\left(\frac{1}{2},\frac{5}{3};\frac{8}{3};\cos ^2(c+d x)\right)}{10 d \sqrt{\sin ^2(c+d x)} (b \sec (c+d x))^{10/3}}",1,"(-3*b^3*Hypergeometric2F1[1/2, 5/3, 8/3, Cos[c + d*x]^2]*Sin[c + d*x])/(10*d*(b*Sec[c + d*x])^(10/3)*Sqrt[Sin[c + d*x]^2])","A",3,3,21,0.1429,1,"{16, 3772, 2643}"
199,1,56,0,0.031286,"\int \frac{\sec ^2(c+d x)}{(b \sec (c+d x))^{4/3}} \, dx","Int[Sec[c + d*x]^2/(b*Sec[c + d*x])^(4/3),x]","-\frac{3 \sin (c+d x) \, _2F_1\left(\frac{1}{6},\frac{1}{2};\frac{7}{6};\cos ^2(c+d x)\right)}{b d \sqrt{\sin ^2(c+d x)} \sqrt[3]{b \sec (c+d x)}}","-\frac{3 \sin (c+d x) \, _2F_1\left(\frac{1}{6},\frac{1}{2};\frac{7}{6};\cos ^2(c+d x)\right)}{b d \sqrt{\sin ^2(c+d x)} \sqrt[3]{b \sec (c+d x)}}",1,"(-3*Hypergeometric2F1[1/6, 1/2, 7/6, Cos[c + d*x]^2]*Sin[c + d*x])/(b*d*(b*Sec[c + d*x])^(1/3)*Sqrt[Sin[c + d*x]^2])","A",3,3,21,0.1429,1,"{16, 3772, 2643}"
200,1,55,0,0.02957,"\int \frac{\sec (c+d x)}{(b \sec (c+d x))^{4/3}} \, dx","Int[Sec[c + d*x]/(b*Sec[c + d*x])^(4/3),x]","-\frac{3 \sin (c+d x) \, _2F_1\left(\frac{1}{2},\frac{2}{3};\frac{5}{3};\cos ^2(c+d x)\right)}{4 d \sqrt{\sin ^2(c+d x)} (b \sec (c+d x))^{4/3}}","-\frac{3 \sin (c+d x) \, _2F_1\left(\frac{1}{2},\frac{2}{3};\frac{5}{3};\cos ^2(c+d x)\right)}{4 d \sqrt{\sin ^2(c+d x)} (b \sec (c+d x))^{4/3}}",1,"(-3*Hypergeometric2F1[1/2, 2/3, 5/3, Cos[c + d*x]^2]*Sin[c + d*x])/(4*d*(b*Sec[c + d*x])^(4/3)*Sqrt[Sin[c + d*x]^2])","A",3,3,19,0.1579,1,"{16, 3772, 2643}"
201,1,56,0,0.0259363,"\int \frac{1}{(b \sec (c+d x))^{4/3}} \, dx","Int[(b*Sec[c + d*x])^(-4/3),x]","-\frac{3 b \sin (c+d x) \, _2F_1\left(\frac{1}{2},\frac{7}{6};\frac{13}{6};\cos ^2(c+d x)\right)}{7 d \sqrt{\sin ^2(c+d x)} (b \sec (c+d x))^{7/3}}","-\frac{3 b \sin (c+d x) \, _2F_1\left(\frac{1}{2},\frac{7}{6};\frac{13}{6};\cos ^2(c+d x)\right)}{7 d \sqrt{\sin ^2(c+d x)} (b \sec (c+d x))^{7/3}}",1,"(-3*b*Hypergeometric2F1[1/2, 7/6, 13/6, Cos[c + d*x]^2]*Sin[c + d*x])/(7*d*(b*Sec[c + d*x])^(7/3)*Sqrt[Sin[c + d*x]^2])","A",2,2,12,0.1667,1,"{3772, 2643}"
202,1,58,0,0.0380579,"\int \frac{\cos (c+d x)}{(b \sec (c+d x))^{4/3}} \, dx","Int[Cos[c + d*x]/(b*Sec[c + d*x])^(4/3),x]","-\frac{3 b^2 \sin (c+d x) \, _2F_1\left(\frac{1}{2},\frac{5}{3};\frac{8}{3};\cos ^2(c+d x)\right)}{10 d \sqrt{\sin ^2(c+d x)} (b \sec (c+d x))^{10/3}}","-\frac{3 b^2 \sin (c+d x) \, _2F_1\left(\frac{1}{2},\frac{5}{3};\frac{8}{3};\cos ^2(c+d x)\right)}{10 d \sqrt{\sin ^2(c+d x)} (b \sec (c+d x))^{10/3}}",1,"(-3*b^2*Hypergeometric2F1[1/2, 5/3, 8/3, Cos[c + d*x]^2]*Sin[c + d*x])/(10*d*(b*Sec[c + d*x])^(10/3)*Sqrt[Sin[c + d*x]^2])","A",3,3,19,0.1579,1,"{16, 3772, 2643}"
203,1,58,0,0.0472666,"\int \frac{\cos ^2(c+d x)}{(b \sec (c+d x))^{4/3}} \, dx","Int[Cos[c + d*x]^2/(b*Sec[c + d*x])^(4/3),x]","-\frac{3 b^3 \sin (c+d x) \, _2F_1\left(\frac{1}{2},\frac{13}{6};\frac{19}{6};\cos ^2(c+d x)\right)}{13 d \sqrt{\sin ^2(c+d x)} (b \sec (c+d x))^{13/3}}","-\frac{3 b^3 \sin (c+d x) \, _2F_1\left(\frac{1}{2},\frac{13}{6};\frac{19}{6};\cos ^2(c+d x)\right)}{13 d \sqrt{\sin ^2(c+d x)} (b \sec (c+d x))^{13/3}}",1,"(-3*b^3*Hypergeometric2F1[1/2, 13/6, 19/6, Cos[c + d*x]^2]*Sin[c + d*x])/(13*d*(b*Sec[c + d*x])^(13/3)*Sqrt[Sin[c + d*x]^2])","A",3,3,21,0.1429,1,"{16, 3772, 2643}"
204,1,81,0,0.0402926,"\int \sec ^m(c+d x) (b \sec (c+d x))^{4/3} \, dx","Int[Sec[c + d*x]^m*(b*Sec[c + d*x])^(4/3),x]","\frac{3 b \sin (c+d x) \sqrt[3]{b \sec (c+d x)} \sec ^m(c+d x) \, _2F_1\left(\frac{1}{2},\frac{1}{6} (-3 m-1);\frac{1}{6} (5-3 m);\cos ^2(c+d x)\right)}{d (3 m+1) \sqrt{\sin ^2(c+d x)}}","\frac{3 b \sin (c+d x) \sqrt[3]{b \sec (c+d x)} \sec ^m(c+d x) \, _2F_1\left(\frac{1}{2},\frac{1}{6} (-3 m-1);\frac{1}{6} (5-3 m);\cos ^2(c+d x)\right)}{d (3 m+1) \sqrt{\sin ^2(c+d x)}}",1,"(3*b*Hypergeometric2F1[1/2, (-1 - 3*m)/6, (5 - 3*m)/6, Cos[c + d*x]^2]*Sec[c + d*x]^m*(b*Sec[c + d*x])^(1/3)*Sin[c + d*x])/(d*(1 + 3*m)*Sqrt[Sin[c + d*x]^2])","A",3,3,21,0.1429,1,"{20, 3772, 2643}"
205,1,82,0,0.0386954,"\int \sec ^m(c+d x) (b \sec (c+d x))^{2/3} \, dx","Int[Sec[c + d*x]^m*(b*Sec[c + d*x])^(2/3),x]","-\frac{3 \sin (c+d x) (b \sec (c+d x))^{2/3} \sec ^{m-1}(c+d x) \, _2F_1\left(\frac{1}{2},\frac{1}{6} (1-3 m);\frac{1}{6} (7-3 m);\cos ^2(c+d x)\right)}{d (1-3 m) \sqrt{\sin ^2(c+d x)}}","-\frac{3 \sin (c+d x) (b \sec (c+d x))^{2/3} \sec ^{m-1}(c+d x) \, _2F_1\left(\frac{1}{2},\frac{1}{6} (1-3 m);\frac{1}{6} (7-3 m);\cos ^2(c+d x)\right)}{d (1-3 m) \sqrt{\sin ^2(c+d x)}}",1,"(-3*Hypergeometric2F1[1/2, (1 - 3*m)/6, (7 - 3*m)/6, Cos[c + d*x]^2]*Sec[c + d*x]^(-1 + m)*(b*Sec[c + d*x])^(2/3)*Sin[c + d*x])/(d*(1 - 3*m)*Sqrt[Sin[c + d*x]^2])","A",3,3,21,0.1429,1,"{20, 3772, 2643}"
206,1,82,0,0.0406077,"\int \sec ^m(c+d x) \sqrt[3]{b \sec (c+d x)} \, dx","Int[Sec[c + d*x]^m*(b*Sec[c + d*x])^(1/3),x]","-\frac{3 \sin (c+d x) \sqrt[3]{b \sec (c+d x)} \sec ^{m-1}(c+d x) \, _2F_1\left(\frac{1}{2},\frac{1}{6} (2-3 m);\frac{1}{6} (8-3 m);\cos ^2(c+d x)\right)}{d (2-3 m) \sqrt{\sin ^2(c+d x)}}","-\frac{3 \sin (c+d x) \sqrt[3]{b \sec (c+d x)} \sec ^{m-1}(c+d x) \, _2F_1\left(\frac{1}{2},\frac{1}{6} (2-3 m);\frac{1}{6} (8-3 m);\cos ^2(c+d x)\right)}{d (2-3 m) \sqrt{\sin ^2(c+d x)}}",1,"(-3*Hypergeometric2F1[1/2, (2 - 3*m)/6, (8 - 3*m)/6, Cos[c + d*x]^2]*Sec[c + d*x]^(-1 + m)*(b*Sec[c + d*x])^(1/3)*Sin[c + d*x])/(d*(2 - 3*m)*Sqrt[Sin[c + d*x]^2])","A",3,3,21,0.1429,1,"{20, 3772, 2643}"
207,1,82,0,0.0390033,"\int \frac{\sec ^m(c+d x)}{\sqrt[3]{b \sec (c+d x)}} \, dx","Int[Sec[c + d*x]^m/(b*Sec[c + d*x])^(1/3),x]","-\frac{3 \sin (c+d x) \sec ^{m-1}(c+d x) \, _2F_1\left(\frac{1}{2},\frac{1}{6} (4-3 m);\frac{1}{6} (10-3 m);\cos ^2(c+d x)\right)}{d (4-3 m) \sqrt{\sin ^2(c+d x)} \sqrt[3]{b \sec (c+d x)}}","-\frac{3 \sin (c+d x) \sec ^{m-1}(c+d x) \, _2F_1\left(\frac{1}{2},\frac{1}{6} (4-3 m);\frac{1}{6} (10-3 m);\cos ^2(c+d x)\right)}{d (4-3 m) \sqrt{\sin ^2(c+d x)} \sqrt[3]{b \sec (c+d x)}}",1,"(-3*Hypergeometric2F1[1/2, (4 - 3*m)/6, (10 - 3*m)/6, Cos[c + d*x]^2]*Sec[c + d*x]^(-1 + m)*Sin[c + d*x])/(d*(4 - 3*m)*(b*Sec[c + d*x])^(1/3)*Sqrt[Sin[c + d*x]^2])","A",3,3,21,0.1429,1,"{20, 3772, 2643}"
208,1,82,0,0.0406255,"\int \frac{\sec ^m(c+d x)}{(b \sec (c+d x))^{2/3}} \, dx","Int[Sec[c + d*x]^m/(b*Sec[c + d*x])^(2/3),x]","-\frac{3 \sin (c+d x) \sec ^{m-1}(c+d x) \, _2F_1\left(\frac{1}{2},\frac{1}{6} (5-3 m);\frac{1}{6} (11-3 m);\cos ^2(c+d x)\right)}{d (5-3 m) \sqrt{\sin ^2(c+d x)} (b \sec (c+d x))^{2/3}}","-\frac{3 \sin (c+d x) \sec ^{m-1}(c+d x) \, _2F_1\left(\frac{1}{2},\frac{1}{6} (5-3 m);\frac{1}{6} (11-3 m);\cos ^2(c+d x)\right)}{d (5-3 m) \sqrt{\sin ^2(c+d x)} (b \sec (c+d x))^{2/3}}",1,"(-3*Hypergeometric2F1[1/2, (5 - 3*m)/6, (11 - 3*m)/6, Cos[c + d*x]^2]*Sec[c + d*x]^(-1 + m)*Sin[c + d*x])/(d*(5 - 3*m)*(b*Sec[c + d*x])^(2/3)*Sqrt[Sin[c + d*x]^2])","A",3,3,21,0.1429,1,"{20, 3772, 2643}"
209,1,85,0,0.0429287,"\int \frac{\sec ^m(c+d x)}{(b \sec (c+d x))^{4/3}} \, dx","Int[Sec[c + d*x]^m/(b*Sec[c + d*x])^(4/3),x]","-\frac{3 \sin (c+d x) \sec ^{m-2}(c+d x) \, _2F_1\left(\frac{1}{2},\frac{1}{6} (7-3 m);\frac{1}{6} (13-3 m);\cos ^2(c+d x)\right)}{b d (7-3 m) \sqrt{\sin ^2(c+d x)} \sqrt[3]{b \sec (c+d x)}}","-\frac{3 \sin (c+d x) \sec ^{m-2}(c+d x) \, _2F_1\left(\frac{1}{2},\frac{1}{6} (7-3 m);\frac{1}{6} (13-3 m);\cos ^2(c+d x)\right)}{b d (7-3 m) \sqrt{\sin ^2(c+d x)} \sqrt[3]{b \sec (c+d x)}}",1,"(-3*Hypergeometric2F1[1/2, (7 - 3*m)/6, (13 - 3*m)/6, Cos[c + d*x]^2]*Sec[c + d*x]^(-2 + m)*Sin[c + d*x])/(b*d*(7 - 3*m)*(b*Sec[c + d*x])^(1/3)*Sqrt[Sin[c + d*x]^2])","A",3,3,21,0.1429,1,"{20, 3772, 2643}"
210,1,89,0,0.0385914,"\int \sec ^m(c+d x) (b \sec (c+d x))^n \, dx","Int[Sec[c + d*x]^m*(b*Sec[c + d*x])^n,x]","-\frac{\sin (c+d x) \sec ^{m-1}(c+d x) (b \sec (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{1}{2} (-m-n+1);\frac{1}{2} (-m-n+3);\cos ^2(c+d x)\right)}{d (-m-n+1) \sqrt{\sin ^2(c+d x)}}","-\frac{\sin (c+d x) \sec ^{m-1}(c+d x) (b \sec (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{1}{2} (-m-n+1);\frac{1}{2} (-m-n+3);\cos ^2(c+d x)\right)}{d (-m-n+1) \sqrt{\sin ^2(c+d x)}}",1,"-((Hypergeometric2F1[1/2, (1 - m - n)/2, (3 - m - n)/2, Cos[c + d*x]^2]*Sec[c + d*x]^(-1 + m)*(b*Sec[c + d*x])^n*Sin[c + d*x])/(d*(1 - m - n)*Sqrt[Sin[c + d*x]^2]))","A",3,3,19,0.1579,1,"{20, 3772, 2643}"
211,1,72,0,0.0442525,"\int \sec ^2(c+d x) (b \sec (c+d x))^n \, dx","Int[Sec[c + d*x]^2*(b*Sec[c + d*x])^n,x]","\frac{\sin (c+d x) (b \sec (c+d x))^{n+1} \, _2F_1\left(\frac{1}{2},\frac{1}{2} (-n-1);\frac{1-n}{2};\cos ^2(c+d x)\right)}{b d (n+1) \sqrt{\sin ^2(c+d x)}}","\frac{\sin (c+d x) (b \sec (c+d x))^{n+1} \, _2F_1\left(\frac{1}{2},\frac{1}{2} (-n-1);\frac{1-n}{2};\cos ^2(c+d x)\right)}{b d (n+1) \sqrt{\sin ^2(c+d x)}}",1,"(Hypergeometric2F1[1/2, (-1 - n)/2, (1 - n)/2, Cos[c + d*x]^2]*(b*Sec[c + d*x])^(1 + n)*Sin[c + d*x])/(b*d*(1 + n)*Sqrt[Sin[c + d*x]^2])","A",3,3,19,0.1579,1,"{16, 3772, 2643}"
212,1,61,0,0.0366607,"\int \sec (c+d x) (b \sec (c+d x))^n \, dx","Int[Sec[c + d*x]*(b*Sec[c + d*x])^n,x]","\frac{\sin (c+d x) (b \sec (c+d x))^n \, _2F_1\left(\frac{1}{2},-\frac{n}{2};\frac{2-n}{2};\cos ^2(c+d x)\right)}{d n \sqrt{\sin ^2(c+d x)}}","\frac{\sin (c+d x) (b \sec (c+d x))^n \, _2F_1\left(\frac{1}{2},-\frac{n}{2};\frac{2-n}{2};\cos ^2(c+d x)\right)}{d n \sqrt{\sin ^2(c+d x)}}",1,"(Hypergeometric2F1[1/2, -n/2, (2 - n)/2, Cos[c + d*x]^2]*(b*Sec[c + d*x])^n*Sin[c + d*x])/(d*n*Sqrt[Sin[c + d*x]^2])","A",3,3,17,0.1765,1,"{16, 3772, 2643}"
213,1,73,0,0.0336746,"\int (b \sec (c+d x))^n \, dx","Int[(b*Sec[c + d*x])^n,x]","-\frac{b \sin (c+d x) (b \sec (c+d x))^{n-1} \, _2F_1\left(\frac{1}{2},\frac{1-n}{2};\frac{3-n}{2};\cos ^2(c+d x)\right)}{d (1-n) \sqrt{\sin ^2(c+d x)}}","-\frac{b \sin (c+d x) (b \sec (c+d x))^{n-1} \, _2F_1\left(\frac{1}{2},\frac{1-n}{2};\frac{3-n}{2};\cos ^2(c+d x)\right)}{d (1-n) \sqrt{\sin ^2(c+d x)}}",1,"-((b*Hypergeometric2F1[1/2, (1 - n)/2, (3 - n)/2, Cos[c + d*x]^2]*(b*Sec[c + d*x])^(-1 + n)*Sin[c + d*x])/(d*(1 - n)*Sqrt[Sin[c + d*x]^2]))","A",2,2,10,0.2000,1,"{3772, 2643}"
214,1,75,0,0.0492554,"\int \cos (c+d x) (b \sec (c+d x))^n \, dx","Int[Cos[c + d*x]*(b*Sec[c + d*x])^n,x]","-\frac{b^2 \sin (c+d x) (b \sec (c+d x))^{n-2} \, _2F_1\left(\frac{1}{2},\frac{2-n}{2};\frac{4-n}{2};\cos ^2(c+d x)\right)}{d (2-n) \sqrt{\sin ^2(c+d x)}}","-\frac{b^2 \sin (c+d x) (b \sec (c+d x))^{n-2} \, _2F_1\left(\frac{1}{2},\frac{2-n}{2};\frac{4-n}{2};\cos ^2(c+d x)\right)}{d (2-n) \sqrt{\sin ^2(c+d x)}}",1,"-((b^2*Hypergeometric2F1[1/2, (2 - n)/2, (4 - n)/2, Cos[c + d*x]^2]*(b*Sec[c + d*x])^(-2 + n)*Sin[c + d*x])/(d*(2 - n)*Sqrt[Sin[c + d*x]^2]))","A",3,3,17,0.1765,1,"{16, 3772, 2643}"
215,1,75,0,0.0553529,"\int \cos ^2(c+d x) (b \sec (c+d x))^n \, dx","Int[Cos[c + d*x]^2*(b*Sec[c + d*x])^n,x]","-\frac{b^3 \sin (c+d x) (b \sec (c+d x))^{n-3} \, _2F_1\left(\frac{1}{2},\frac{3-n}{2};\frac{5-n}{2};\cos ^2(c+d x)\right)}{d (3-n) \sqrt{\sin ^2(c+d x)}}","-\frac{b^3 \sin (c+d x) (b \sec (c+d x))^{n-3} \, _2F_1\left(\frac{1}{2},\frac{3-n}{2};\frac{5-n}{2};\cos ^2(c+d x)\right)}{d (3-n) \sqrt{\sin ^2(c+d x)}}",1,"-((b^3*Hypergeometric2F1[1/2, (3 - n)/2, (5 - n)/2, Cos[c + d*x]^2]*(b*Sec[c + d*x])^(-3 + n)*Sin[c + d*x])/(d*(3 - n)*Sqrt[Sin[c + d*x]^2]))","A",3,3,19,0.1579,1,"{16, 3772, 2643}"
216,1,75,0,0.0558594,"\int \cos ^3(c+d x) (b \sec (c+d x))^n \, dx","Int[Cos[c + d*x]^3*(b*Sec[c + d*x])^n,x]","-\frac{b^4 \sin (c+d x) (b \sec (c+d x))^{n-4} \, _2F_1\left(\frac{1}{2},\frac{4-n}{2};\frac{6-n}{2};\cos ^2(c+d x)\right)}{d (4-n) \sqrt{\sin ^2(c+d x)}}","-\frac{b^4 \sin (c+d x) (b \sec (c+d x))^{n-4} \, _2F_1\left(\frac{1}{2},\frac{4-n}{2};\frac{6-n}{2};\cos ^2(c+d x)\right)}{d (4-n) \sqrt{\sin ^2(c+d x)}}",1,"-((b^4*Hypergeometric2F1[1/2, (4 - n)/2, (6 - n)/2, Cos[c + d*x]^2]*(b*Sec[c + d*x])^(-4 + n)*Sin[c + d*x])/(d*(4 - n)*Sqrt[Sin[c + d*x]^2]))","A",3,3,19,0.1579,1,"{16, 3772, 2643}"
217,1,80,0,0.0400818,"\int \sec ^{\frac{5}{2}}(c+d x) (b \sec (c+d x))^n \, dx","Int[Sec[c + d*x]^(5/2)*(b*Sec[c + d*x])^n,x]","\frac{2 \sin (c+d x) \sec ^{\frac{3}{2}}(c+d x) (b \sec (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{1}{4} (-2 n-3);\frac{1}{4} (1-2 n);\cos ^2(c+d x)\right)}{d (2 n+3) \sqrt{\sin ^2(c+d x)}}","\frac{2 \sin (c+d x) \sec ^{\frac{3}{2}}(c+d x) (b \sec (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{1}{4} (-2 n-3);\frac{1}{4} (1-2 n);\cos ^2(c+d x)\right)}{d (2 n+3) \sqrt{\sin ^2(c+d x)}}",1,"(2*Hypergeometric2F1[1/2, (-3 - 2*n)/4, (1 - 2*n)/4, Cos[c + d*x]^2]*Sec[c + d*x]^(3/2)*(b*Sec[c + d*x])^n*Sin[c + d*x])/(d*(3 + 2*n)*Sqrt[Sin[c + d*x]^2])","A",3,3,21,0.1429,1,"{20, 3772, 2643}"
218,1,80,0,0.0382578,"\int \sec ^{\frac{3}{2}}(c+d x) (b \sec (c+d x))^n \, dx","Int[Sec[c + d*x]^(3/2)*(b*Sec[c + d*x])^n,x]","\frac{2 \sin (c+d x) \sqrt{\sec (c+d x)} (b \sec (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{1}{4} (-2 n-1);\frac{1}{4} (3-2 n);\cos ^2(c+d x)\right)}{d (2 n+1) \sqrt{\sin ^2(c+d x)}}","\frac{2 \sin (c+d x) \sqrt{\sec (c+d x)} (b \sec (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{1}{4} (-2 n-1);\frac{1}{4} (3-2 n);\cos ^2(c+d x)\right)}{d (2 n+1) \sqrt{\sin ^2(c+d x)}}",1,"(2*Hypergeometric2F1[1/2, (-1 - 2*n)/4, (3 - 2*n)/4, Cos[c + d*x]^2]*Sqrt[Sec[c + d*x]]*(b*Sec[c + d*x])^n*Sin[c + d*x])/(d*(1 + 2*n)*Sqrt[Sin[c + d*x]^2])","A",3,3,21,0.1429,1,"{20, 3772, 2643}"
219,1,80,0,0.0381516,"\int \sqrt{\sec (c+d x)} (b \sec (c+d x))^n \, dx","Int[Sqrt[Sec[c + d*x]]*(b*Sec[c + d*x])^n,x]","-\frac{2 \sin (c+d x) (b \sec (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{1}{4} (1-2 n);\frac{1}{4} (5-2 n);\cos ^2(c+d x)\right)}{d (1-2 n) \sqrt{\sin ^2(c+d x)} \sqrt{\sec (c+d x)}}","-\frac{2 \sin (c+d x) (b \sec (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{1}{4} (1-2 n);\frac{1}{4} (5-2 n);\cos ^2(c+d x)\right)}{d (1-2 n) \sqrt{\sin ^2(c+d x)} \sqrt{\sec (c+d x)}}",1,"(-2*Hypergeometric2F1[1/2, (1 - 2*n)/4, (5 - 2*n)/4, Cos[c + d*x]^2]*(b*Sec[c + d*x])^n*Sin[c + d*x])/(d*(1 - 2*n)*Sqrt[Sec[c + d*x]]*Sqrt[Sin[c + d*x]^2])","A",3,3,21,0.1429,1,"{20, 3772, 2643}"
220,1,80,0,0.0389261,"\int \frac{(b \sec (c+d x))^n}{\sqrt{\sec (c+d x)}} \, dx","Int[(b*Sec[c + d*x])^n/Sqrt[Sec[c + d*x]],x]","-\frac{2 \sin (c+d x) (b \sec (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{1}{4} (3-2 n);\frac{1}{4} (7-2 n);\cos ^2(c+d x)\right)}{d (3-2 n) \sqrt{\sin ^2(c+d x)} \sec ^{\frac{3}{2}}(c+d x)}","-\frac{2 \sin (c+d x) (b \sec (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{1}{4} (3-2 n);\frac{1}{4} (7-2 n);\cos ^2(c+d x)\right)}{d (3-2 n) \sqrt{\sin ^2(c+d x)} \sec ^{\frac{3}{2}}(c+d x)}",1,"(-2*Hypergeometric2F1[1/2, (3 - 2*n)/4, (7 - 2*n)/4, Cos[c + d*x]^2]*(b*Sec[c + d*x])^n*Sin[c + d*x])/(d*(3 - 2*n)*Sec[c + d*x]^(3/2)*Sqrt[Sin[c + d*x]^2])","A",3,3,21,0.1429,1,"{20, 3772, 2643}"
221,1,80,0,0.0398434,"\int \frac{(b \sec (c+d x))^n}{\sec ^{\frac{3}{2}}(c+d x)} \, dx","Int[(b*Sec[c + d*x])^n/Sec[c + d*x]^(3/2),x]","-\frac{2 \sin (c+d x) (b \sec (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{1}{4} (5-2 n);\frac{1}{4} (9-2 n);\cos ^2(c+d x)\right)}{d (5-2 n) \sqrt{\sin ^2(c+d x)} \sec ^{\frac{5}{2}}(c+d x)}","-\frac{2 \sin (c+d x) (b \sec (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{1}{4} (5-2 n);\frac{1}{4} (9-2 n);\cos ^2(c+d x)\right)}{d (5-2 n) \sqrt{\sin ^2(c+d x)} \sec ^{\frac{5}{2}}(c+d x)}",1,"(-2*Hypergeometric2F1[1/2, (5 - 2*n)/4, (9 - 2*n)/4, Cos[c + d*x]^2]*(b*Sec[c + d*x])^n*Sin[c + d*x])/(d*(5 - 2*n)*Sec[c + d*x]^(5/2)*Sqrt[Sin[c + d*x]^2])","A",3,3,21,0.1429,1,"{20, 3772, 2643}"
222,1,80,0,0.038628,"\int \frac{(b \sec (c+d x))^n}{\sec ^{\frac{5}{2}}(c+d x)} \, dx","Int[(b*Sec[c + d*x])^n/Sec[c + d*x]^(5/2),x]","-\frac{2 \sin (c+d x) (b \sec (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{1}{4} (7-2 n);\frac{1}{4} (11-2 n);\cos ^2(c+d x)\right)}{d (7-2 n) \sqrt{\sin ^2(c+d x)} \sec ^{\frac{7}{2}}(c+d x)}","-\frac{2 \sin (c+d x) (b \sec (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{1}{4} (7-2 n);\frac{1}{4} (11-2 n);\cos ^2(c+d x)\right)}{d (7-2 n) \sqrt{\sin ^2(c+d x)} \sec ^{\frac{7}{2}}(c+d x)}",1,"(-2*Hypergeometric2F1[1/2, (7 - 2*n)/4, (11 - 2*n)/4, Cos[c + d*x]^2]*(b*Sec[c + d*x])^n*Sin[c + d*x])/(d*(7 - 2*n)*Sec[c + d*x]^(7/2)*Sqrt[Sin[c + d*x]^2])","A",3,3,21,0.1429,1,"{20, 3772, 2643}"
223,1,20,0,0.0351707,"\int (d \sec (a+b x))^{7/2} \sin (a+b x) \, dx","Int[(d*Sec[a + b*x])^(7/2)*Sin[a + b*x],x]","\frac{2 d (d \sec (a+b x))^{5/2}}{5 b}","\frac{2 d (d \sec (a+b x))^{5/2}}{5 b}",1,"(2*d*(d*Sec[a + b*x])^(5/2))/(5*b)","A",2,2,19,0.1053,1,"{2622, 30}"
224,1,20,0,0.0359804,"\int (d \sec (a+b x))^{5/2} \sin (a+b x) \, dx","Int[(d*Sec[a + b*x])^(5/2)*Sin[a + b*x],x]","\frac{2 d (d \sec (a+b x))^{3/2}}{3 b}","\frac{2 d (d \sec (a+b x))^{3/2}}{3 b}",1,"(2*d*(d*Sec[a + b*x])^(3/2))/(3*b)","A",2,2,19,0.1053,1,"{2622, 30}"
225,1,18,0,0.0362843,"\int (d \sec (a+b x))^{3/2} \sin (a+b x) \, dx","Int[(d*Sec[a + b*x])^(3/2)*Sin[a + b*x],x]","\frac{2 d \sqrt{d \sec (a+b x)}}{b}","\frac{2 d \sqrt{d \sec (a+b x)}}{b}",1,"(2*d*Sqrt[d*Sec[a + b*x]])/b","A",2,2,19,0.1053,1,"{2622, 30}"
226,1,18,0,0.032692,"\int \sqrt{d \sec (a+b x)} \sin (a+b x) \, dx","Int[Sqrt[d*Sec[a + b*x]]*Sin[a + b*x],x]","-\frac{2 d}{b \sqrt{d \sec (a+b x)}}","-\frac{2 d}{b \sqrt{d \sec (a+b x)}}",1,"(-2*d)/(b*Sqrt[d*Sec[a + b*x]])","A",2,2,19,0.1053,1,"{2622, 30}"
227,1,20,0,0.0326505,"\int \frac{\sin (a+b x)}{\sqrt{d \sec (a+b x)}} \, dx","Int[Sin[a + b*x]/Sqrt[d*Sec[a + b*x]],x]","-\frac{2 d}{3 b (d \sec (a+b x))^{3/2}}","-\frac{2 d}{3 b (d \sec (a+b x))^{3/2}}",1,"(-2*d)/(3*b*(d*Sec[a + b*x])^(3/2))","A",2,2,19,0.1053,1,"{2622, 30}"
228,1,41,0,0.048539,"\int (d \sec (a+b x))^{5/2} \sin ^3(a+b x) \, dx","Int[(d*Sec[a + b*x])^(5/2)*Sin[a + b*x]^3,x]","\frac{2 d^3}{b \sqrt{d \sec (a+b x)}}+\frac{2 d (d \sec (a+b x))^{3/2}}{3 b}","\frac{2 d^3}{b \sqrt{d \sec (a+b x)}}+\frac{2 d (d \sec (a+b x))^{3/2}}{3 b}",1,"(2*d^3)/(b*Sqrt[d*Sec[a + b*x]]) + (2*d*(d*Sec[a + b*x])^(3/2))/(3*b)","A",3,2,21,0.09524,1,"{2622, 14}"
229,1,43,0,0.0485292,"\int (d \sec (a+b x))^{9/2} \sin ^3(a+b x) \, dx","Int[(d*Sec[a + b*x])^(9/2)*Sin[a + b*x]^3,x]","\frac{2 d (d \sec (a+b x))^{7/2}}{7 b}-\frac{2 d^3 (d \sec (a+b x))^{3/2}}{3 b}","\frac{2 d (d \sec (a+b x))^{7/2}}{7 b}-\frac{2 d^3 (d \sec (a+b x))^{3/2}}{3 b}",1,"(-2*d^3*(d*Sec[a + b*x])^(3/2))/(3*b) + (2*d*(d*Sec[a + b*x])^(7/2))/(7*b)","A",3,2,21,0.09524,1,"{2622, 14}"
230,1,128,0,0.2039314,"\int (d \csc (a+b x))^{9/2} \sqrt{c \sec (a+b x)} \, dx","Int[(d*Csc[a + b*x])^(9/2)*Sqrt[c*Sec[a + b*x]],x]","-\frac{4 c d^3 (d \csc (a+b x))^{3/2}}{7 b \sqrt{c \sec (a+b x)}}+\frac{4 d^4 \sqrt{\sin (2 a+2 b x)} F\left(\left.a+b x-\frac{\pi }{4}\right|2\right) \sqrt{c \sec (a+b x)} \sqrt{d \csc (a+b x)}}{7 b}-\frac{2 c d (d \csc (a+b x))^{7/2}}{7 b \sqrt{c \sec (a+b x)}}","-\frac{4 c d^3 (d \csc (a+b x))^{3/2}}{7 b \sqrt{c \sec (a+b x)}}+\frac{4 d^4 \sqrt{\sin (2 a+2 b x)} F\left(\left.a+b x-\frac{\pi }{4}\right|2\right) \sqrt{c \sec (a+b x)} \sqrt{d \csc (a+b x)}}{7 b}-\frac{2 c d (d \csc (a+b x))^{7/2}}{7 b \sqrt{c \sec (a+b x)}}",1,"(-4*c*d^3*(d*Csc[a + b*x])^(3/2))/(7*b*Sqrt[c*Sec[a + b*x]]) - (2*c*d*(d*Csc[a + b*x])^(7/2))/(7*b*Sqrt[c*Sec[a + b*x]]) + (4*d^4*Sqrt[d*Csc[a + b*x]]*EllipticF[a - Pi/4 + b*x, 2]*Sqrt[c*Sec[a + b*x]]*Sqrt[Sin[2*a + 2*b*x]])/(7*b)","A",5,4,25,0.1600,1,"{2625, 2630, 2573, 2641}"
231,1,69,0,0.0970203,"\int (d \csc (a+b x))^{7/2} \sqrt{c \sec (a+b x)} \, dx","Int[(d*Csc[a + b*x])^(7/2)*Sqrt[c*Sec[a + b*x]],x]","-\frac{8 c d^3 \sqrt{d \csc (a+b x)}}{5 b \sqrt{c \sec (a+b x)}}-\frac{2 c d (d \csc (a+b x))^{5/2}}{5 b \sqrt{c \sec (a+b x)}}","-\frac{8 c d^3 \sqrt{d \csc (a+b x)}}{5 b \sqrt{c \sec (a+b x)}}-\frac{2 c d (d \csc (a+b x))^{5/2}}{5 b \sqrt{c \sec (a+b x)}}",1,"(-8*c*d^3*Sqrt[d*Csc[a + b*x]])/(5*b*Sqrt[c*Sec[a + b*x]]) - (2*c*d*(d*Csc[a + b*x])^(5/2))/(5*b*Sqrt[c*Sec[a + b*x]])","A",2,2,25,0.08000,1,"{2625, 2619}"
232,1,93,0,0.1434908,"\int (d \csc (a+b x))^{5/2} \sqrt{c \sec (a+b x)} \, dx","Int[(d*Csc[a + b*x])^(5/2)*Sqrt[c*Sec[a + b*x]],x]","\frac{2 d^2 \sqrt{\sin (2 a+2 b x)} F\left(\left.a+b x-\frac{\pi }{4}\right|2\right) \sqrt{c \sec (a+b x)} \sqrt{d \csc (a+b x)}}{3 b}-\frac{2 c d (d \csc (a+b x))^{3/2}}{3 b \sqrt{c \sec (a+b x)}}","\frac{2 d^2 \sqrt{\sin (2 a+2 b x)} F\left(\left.a+b x-\frac{\pi }{4}\right|2\right) \sqrt{c \sec (a+b x)} \sqrt{d \csc (a+b x)}}{3 b}-\frac{2 c d (d \csc (a+b x))^{3/2}}{3 b \sqrt{c \sec (a+b x)}}",1,"(-2*c*d*(d*Csc[a + b*x])^(3/2))/(3*b*Sqrt[c*Sec[a + b*x]]) + (2*d^2*Sqrt[d*Csc[a + b*x]]*EllipticF[a - Pi/4 + b*x, 2]*Sqrt[c*Sec[a + b*x]]*Sqrt[Sin[2*a + 2*b*x]])/(3*b)","A",4,4,25,0.1600,1,"{2625, 2630, 2573, 2641}"
233,1,31,0,0.0486029,"\int (d \csc (a+b x))^{3/2} \sqrt{c \sec (a+b x)} \, dx","Int[(d*Csc[a + b*x])^(3/2)*Sqrt[c*Sec[a + b*x]],x]","-\frac{2 c d \sqrt{d \csc (a+b x)}}{b \sqrt{c \sec (a+b x)}}","-\frac{2 c d \sqrt{d \csc (a+b x)}}{b \sqrt{c \sec (a+b x)}}",1,"(-2*c*d*Sqrt[d*Csc[a + b*x]])/(b*Sqrt[c*Sec[a + b*x]])","A",1,1,25,0.04000,1,"{2619}"
234,1,53,0,0.0927454,"\int \sqrt{d \csc (a+b x)} \sqrt{c \sec (a+b x)} \, dx","Int[Sqrt[d*Csc[a + b*x]]*Sqrt[c*Sec[a + b*x]],x]","\frac{\sqrt{\sin (2 a+2 b x)} F\left(\left.a+b x-\frac{\pi }{4}\right|2\right) \sqrt{c \sec (a+b x)} \sqrt{d \csc (a+b x)}}{b}","\frac{\sqrt{\sin (2 a+2 b x)} F\left(\left.a+b x-\frac{\pi }{4}\right|2\right) \sqrt{c \sec (a+b x)} \sqrt{d \csc (a+b x)}}{b}",1,"(Sqrt[d*Csc[a + b*x]]*EllipticF[a - Pi/4 + b*x, 2]*Sqrt[c*Sec[a + b*x]]*Sqrt[Sin[2*a + 2*b*x]])/b","A",3,3,25,0.1200,1,"{2630, 2573, 2641}"
235,1,270,0,0.1404809,"\int \frac{\sqrt{c \sec (a+b x)}}{\sqrt{d \csc (a+b x)}} \, dx","Int[Sqrt[c*Sec[a + b*x]]/Sqrt[d*Csc[a + b*x]],x]","-\frac{\tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (a+b x)}\right) \sqrt{c \sec (a+b x)}}{\sqrt{2} b \sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)}}+\frac{\tan ^{-1}\left(\sqrt{2} \sqrt{\tan (a+b x)}+1\right) \sqrt{c \sec (a+b x)}}{\sqrt{2} b \sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)}}+\frac{\sqrt{c \sec (a+b x)} \log \left(\tan (a+b x)-\sqrt{2} \sqrt{\tan (a+b x)}+1\right)}{2 \sqrt{2} b \sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)}}-\frac{\sqrt{c \sec (a+b x)} \log \left(\tan (a+b x)+\sqrt{2} \sqrt{\tan (a+b x)}+1\right)}{2 \sqrt{2} b \sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)}}","-\frac{\tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (a+b x)}\right) \sqrt{c \sec (a+b x)}}{\sqrt{2} b \sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)}}+\frac{\tan ^{-1}\left(\sqrt{2} \sqrt{\tan (a+b x)}+1\right) \sqrt{c \sec (a+b x)}}{\sqrt{2} b \sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)}}+\frac{\sqrt{c \sec (a+b x)} \log \left(\tan (a+b x)-\sqrt{2} \sqrt{\tan (a+b x)}+1\right)}{2 \sqrt{2} b \sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)}}-\frac{\sqrt{c \sec (a+b x)} \log \left(\tan (a+b x)+\sqrt{2} \sqrt{\tan (a+b x)}+1\right)}{2 \sqrt{2} b \sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)}}",1,"-((ArcTan[1 - Sqrt[2]*Sqrt[Tan[a + b*x]]]*Sqrt[c*Sec[a + b*x]])/(Sqrt[2]*b*Sqrt[d*Csc[a + b*x]]*Sqrt[Tan[a + b*x]])) + (ArcTan[1 + Sqrt[2]*Sqrt[Tan[a + b*x]]]*Sqrt[c*Sec[a + b*x]])/(Sqrt[2]*b*Sqrt[d*Csc[a + b*x]]*Sqrt[Tan[a + b*x]]) + (Log[1 - Sqrt[2]*Sqrt[Tan[a + b*x]] + Tan[a + b*x]]*Sqrt[c*Sec[a + b*x]])/(2*Sqrt[2]*b*Sqrt[d*Csc[a + b*x]]*Sqrt[Tan[a + b*x]]) - (Log[1 + Sqrt[2]*Sqrt[Tan[a + b*x]] + Tan[a + b*x]]*Sqrt[c*Sec[a + b*x]])/(2*Sqrt[2]*b*Sqrt[d*Csc[a + b*x]]*Sqrt[Tan[a + b*x]])","A",12,9,25,0.3600,1,"{2629, 3476, 329, 297, 1162, 617, 204, 1165, 628}"
236,1,93,0,0.1474862,"\int \frac{\sqrt{c \sec (a+b x)}}{(d \csc (a+b x))^{3/2}} \, dx","Int[Sqrt[c*Sec[a + b*x]]/(d*Csc[a + b*x])^(3/2),x]","\frac{\sqrt{\sin (2 a+2 b x)} F\left(\left.a+b x-\frac{\pi }{4}\right|2\right) \sqrt{c \sec (a+b x)} \sqrt{d \csc (a+b x)}}{2 b d^2}-\frac{c}{b d \sqrt{c \sec (a+b x)} \sqrt{d \csc (a+b x)}}","\frac{\sqrt{\sin (2 a+2 b x)} F\left(\left.a+b x-\frac{\pi }{4}\right|2\right) \sqrt{c \sec (a+b x)} \sqrt{d \csc (a+b x)}}{2 b d^2}-\frac{c}{b d \sqrt{c \sec (a+b x)} \sqrt{d \csc (a+b x)}}",1,"-(c/(b*d*Sqrt[d*Csc[a + b*x]]*Sqrt[c*Sec[a + b*x]])) + (Sqrt[d*Csc[a + b*x]]*EllipticF[a - Pi/4 + b*x, 2]*Sqrt[c*Sec[a + b*x]]*Sqrt[Sin[2*a + 2*b*x]])/(2*b*d^2)","A",4,4,25,0.1600,1,"{2627, 2630, 2573, 2641}"
237,1,322,0,0.2118075,"\int \frac{\sqrt{c \sec (a+b x)}}{(d \csc (a+b x))^{5/2}} \, dx","Int[Sqrt[c*Sec[a + b*x]]/(d*Csc[a + b*x])^(5/2),x]","-\frac{3 \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (a+b x)}\right) \sqrt{c \sec (a+b x)}}{4 \sqrt{2} b d^2 \sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)}}+\frac{3 \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (a+b x)}+1\right) \sqrt{c \sec (a+b x)}}{4 \sqrt{2} b d^2 \sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)}}+\frac{3 \sqrt{c \sec (a+b x)} \log \left(\tan (a+b x)-\sqrt{2} \sqrt{\tan (a+b x)}+1\right)}{8 \sqrt{2} b d^2 \sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)}}-\frac{3 \sqrt{c \sec (a+b x)} \log \left(\tan (a+b x)+\sqrt{2} \sqrt{\tan (a+b x)}+1\right)}{8 \sqrt{2} b d^2 \sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)}}-\frac{c}{2 b d \sqrt{c \sec (a+b x)} (d \csc (a+b x))^{3/2}}","-\frac{3 \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (a+b x)}\right) \sqrt{c \sec (a+b x)}}{4 \sqrt{2} b d^2 \sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)}}+\frac{3 \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (a+b x)}+1\right) \sqrt{c \sec (a+b x)}}{4 \sqrt{2} b d^2 \sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)}}+\frac{3 \sqrt{c \sec (a+b x)} \log \left(\tan (a+b x)-\sqrt{2} \sqrt{\tan (a+b x)}+1\right)}{8 \sqrt{2} b d^2 \sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)}}-\frac{3 \sqrt{c \sec (a+b x)} \log \left(\tan (a+b x)+\sqrt{2} \sqrt{\tan (a+b x)}+1\right)}{8 \sqrt{2} b d^2 \sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)}}-\frac{c}{2 b d \sqrt{c \sec (a+b x)} (d \csc (a+b x))^{3/2}}",1,"-c/(2*b*d*(d*Csc[a + b*x])^(3/2)*Sqrt[c*Sec[a + b*x]]) - (3*ArcTan[1 - Sqrt[2]*Sqrt[Tan[a + b*x]]]*Sqrt[c*Sec[a + b*x]])/(4*Sqrt[2]*b*d^2*Sqrt[d*Csc[a + b*x]]*Sqrt[Tan[a + b*x]]) + (3*ArcTan[1 + Sqrt[2]*Sqrt[Tan[a + b*x]]]*Sqrt[c*Sec[a + b*x]])/(4*Sqrt[2]*b*d^2*Sqrt[d*Csc[a + b*x]]*Sqrt[Tan[a + b*x]]) + (3*Log[1 - Sqrt[2]*Sqrt[Tan[a + b*x]] + Tan[a + b*x]]*Sqrt[c*Sec[a + b*x]])/(8*Sqrt[2]*b*d^2*Sqrt[d*Csc[a + b*x]]*Sqrt[Tan[a + b*x]]) - (3*Log[1 + Sqrt[2]*Sqrt[Tan[a + b*x]] + Tan[a + b*x]]*Sqrt[c*Sec[a + b*x]])/(8*Sqrt[2]*b*d^2*Sqrt[d*Csc[a + b*x]]*Sqrt[Tan[a + b*x]])","A",13,10,25,0.4000,1,"{2627, 2629, 3476, 329, 297, 1162, 617, 204, 1165, 628}"
238,1,104,0,0.1624642,"\int (d \csc (a+b x))^{9/2} (c \sec (a+b x))^{3/2} \, dx","Int[(d*Csc[a + b*x])^(9/2)*(c*Sec[a + b*x])^(3/2),x]","\frac{64 c d^5 \sqrt{c \sec (a+b x)}}{21 b \sqrt{d \csc (a+b x)}}-\frac{16 c d^3 \sqrt{c \sec (a+b x)} (d \csc (a+b x))^{3/2}}{21 b}-\frac{2 c d \sqrt{c \sec (a+b x)} (d \csc (a+b x))^{7/2}}{7 b}","\frac{64 c d^5 \sqrt{c \sec (a+b x)}}{21 b \sqrt{d \csc (a+b x)}}-\frac{16 c d^3 \sqrt{c \sec (a+b x)} (d \csc (a+b x))^{3/2}}{21 b}-\frac{2 c d \sqrt{c \sec (a+b x)} (d \csc (a+b x))^{7/2}}{7 b}",1,"(64*c*d^5*Sqrt[c*Sec[a + b*x]])/(21*b*Sqrt[d*Csc[a + b*x]]) - (16*c*d^3*(d*Csc[a + b*x])^(3/2)*Sqrt[c*Sec[a + b*x]])/(21*b) - (2*c*d*(d*Csc[a + b*x])^(7/2)*Sqrt[c*Sec[a + b*x]])/(7*b)","A",3,2,25,0.08000,1,"{2625, 2619}"
239,1,166,0,0.2679057,"\int (d \csc (a+b x))^{7/2} (c \sec (a+b x))^{3/2} \, dx","Int[(d*Csc[a + b*x])^(7/2)*(c*Sec[a + b*x])^(3/2),x]","-\frac{24 c^2 d^4 E\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{5 b \sqrt{\sin (2 a+2 b x)} \sqrt{c \sec (a+b x)} \sqrt{d \csc (a+b x)}}+\frac{24 c d^5 \sqrt{c \sec (a+b x)}}{5 b (d \csc (a+b x))^{3/2}}-\frac{12 c d^3 \sqrt{c \sec (a+b x)} \sqrt{d \csc (a+b x)}}{5 b}-\frac{2 c d \sqrt{c \sec (a+b x)} (d \csc (a+b x))^{5/2}}{5 b}","-\frac{24 c^2 d^4 E\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{5 b \sqrt{\sin (2 a+2 b x)} \sqrt{c \sec (a+b x)} \sqrt{d \csc (a+b x)}}+\frac{24 c d^5 \sqrt{c \sec (a+b x)}}{5 b (d \csc (a+b x))^{3/2}}-\frac{12 c d^3 \sqrt{c \sec (a+b x)} \sqrt{d \csc (a+b x)}}{5 b}-\frac{2 c d \sqrt{c \sec (a+b x)} (d \csc (a+b x))^{5/2}}{5 b}",1,"(24*c*d^5*Sqrt[c*Sec[a + b*x]])/(5*b*(d*Csc[a + b*x])^(3/2)) - (12*c*d^3*Sqrt[d*Csc[a + b*x]]*Sqrt[c*Sec[a + b*x]])/(5*b) - (2*c*d*(d*Csc[a + b*x])^(5/2)*Sqrt[c*Sec[a + b*x]])/(5*b) - (24*c^2*d^4*EllipticE[a - Pi/4 + b*x, 2])/(5*b*Sqrt[d*Csc[a + b*x]]*Sqrt[c*Sec[a + b*x]]*Sqrt[Sin[2*a + 2*b*x]])","A",6,5,25,0.2000,1,"{2625, 2626, 2630, 2572, 2639}"
240,1,69,0,0.1028384,"\int (d \csc (a+b x))^{5/2} (c \sec (a+b x))^{3/2} \, dx","Int[(d*Csc[a + b*x])^(5/2)*(c*Sec[a + b*x])^(3/2),x]","\frac{8 c d^3 \sqrt{c \sec (a+b x)}}{3 b \sqrt{d \csc (a+b x)}}-\frac{2 c d \sqrt{c \sec (a+b x)} (d \csc (a+b x))^{3/2}}{3 b}","\frac{8 c d^3 \sqrt{c \sec (a+b x)}}{3 b \sqrt{d \csc (a+b x)}}-\frac{2 c d \sqrt{c \sec (a+b x)} (d \csc (a+b x))^{3/2}}{3 b}",1,"(8*c*d^3*Sqrt[c*Sec[a + b*x]])/(3*b*Sqrt[d*Csc[a + b*x]]) - (2*c*d*(d*Csc[a + b*x])^(3/2)*Sqrt[c*Sec[a + b*x]])/(3*b)","A",2,2,25,0.08000,1,"{2625, 2619}"
241,1,125,0,0.2047326,"\int (d \csc (a+b x))^{3/2} (c \sec (a+b x))^{3/2} \, dx","Int[(d*Csc[a + b*x])^(3/2)*(c*Sec[a + b*x])^(3/2),x]","-\frac{4 c^2 d^2 E\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{b \sqrt{\sin (2 a+2 b x)} \sqrt{c \sec (a+b x)} \sqrt{d \csc (a+b x)}}+\frac{4 c d^3 \sqrt{c \sec (a+b x)}}{b (d \csc (a+b x))^{3/2}}-\frac{2 c d \sqrt{c \sec (a+b x)} \sqrt{d \csc (a+b x)}}{b}","-\frac{4 c^2 d^2 E\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{b \sqrt{\sin (2 a+2 b x)} \sqrt{c \sec (a+b x)} \sqrt{d \csc (a+b x)}}+\frac{4 c d^3 \sqrt{c \sec (a+b x)}}{b (d \csc (a+b x))^{3/2}}-\frac{2 c d \sqrt{c \sec (a+b x)} \sqrt{d \csc (a+b x)}}{b}",1,"(4*c*d^3*Sqrt[c*Sec[a + b*x]])/(b*(d*Csc[a + b*x])^(3/2)) - (2*c*d*Sqrt[d*Csc[a + b*x]]*Sqrt[c*Sec[a + b*x]])/b - (4*c^2*d^2*EllipticE[a - Pi/4 + b*x, 2])/(b*Sqrt[d*Csc[a + b*x]]*Sqrt[c*Sec[a + b*x]]*Sqrt[Sin[2*a + 2*b*x]])","A",5,5,25,0.2000,1,"{2625, 2626, 2630, 2572, 2639}"
242,1,31,0,0.0476698,"\int \sqrt{d \csc (a+b x)} (c \sec (a+b x))^{3/2} \, dx","Int[Sqrt[d*Csc[a + b*x]]*(c*Sec[a + b*x])^(3/2),x]","\frac{2 c d \sqrt{c \sec (a+b x)}}{b \sqrt{d \csc (a+b x)}}","\frac{2 c d \sqrt{c \sec (a+b x)}}{b \sqrt{d \csc (a+b x)}}",1,"(2*c*d*Sqrt[c*Sec[a + b*x]])/(b*Sqrt[d*Csc[a + b*x]])","A",1,1,25,0.04000,1,"{2619}"
243,1,89,0,0.1430641,"\int \frac{(c \sec (a+b x))^{3/2}}{\sqrt{d \csc (a+b x)}} \, dx","Int[(c*Sec[a + b*x])^(3/2)/Sqrt[d*Csc[a + b*x]],x]","\frac{2 c d \sqrt{c \sec (a+b x)}}{b (d \csc (a+b x))^{3/2}}-\frac{2 c^2 E\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{b \sqrt{\sin (2 a+2 b x)} \sqrt{c \sec (a+b x)} \sqrt{d \csc (a+b x)}}","\frac{2 c d \sqrt{c \sec (a+b x)}}{b (d \csc (a+b x))^{3/2}}-\frac{2 c^2 E\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{b \sqrt{\sin (2 a+2 b x)} \sqrt{c \sec (a+b x)} \sqrt{d \csc (a+b x)}}",1,"(2*c*d*Sqrt[c*Sec[a + b*x]])/(b*(d*Csc[a + b*x])^(3/2)) - (2*c^2*EllipticE[a - Pi/4 + b*x, 2])/(b*Sqrt[d*Csc[a + b*x]]*Sqrt[c*Sec[a + b*x]]*Sqrt[Sin[2*a + 2*b*x]])","A",4,4,25,0.1600,1,"{2626, 2630, 2572, 2639}"
244,1,327,0,0.2193898,"\int \frac{(c \sec (a+b x))^{3/2}}{(d \csc (a+b x))^{3/2}} \, dx","Int[(c*Sec[a + b*x])^(3/2)/(d*Csc[a + b*x])^(3/2),x]","\frac{c^2 \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (a+b x)}\right) \sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)}}{\sqrt{2} b d^2 \sqrt{c \sec (a+b x)}}-\frac{c^2 \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (a+b x)}+1\right) \sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)}}{\sqrt{2} b d^2 \sqrt{c \sec (a+b x)}}+\frac{c^2 \sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)} \log \left(\tan (a+b x)-\sqrt{2} \sqrt{\tan (a+b x)}+1\right)}{2 \sqrt{2} b d^2 \sqrt{c \sec (a+b x)}}-\frac{c^2 \sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)} \log \left(\tan (a+b x)+\sqrt{2} \sqrt{\tan (a+b x)}+1\right)}{2 \sqrt{2} b d^2 \sqrt{c \sec (a+b x)}}+\frac{2 c \sqrt{c \sec (a+b x)}}{b d \sqrt{d \csc (a+b x)}}","\frac{c^2 \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (a+b x)}\right) \sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)}}{\sqrt{2} b d^2 \sqrt{c \sec (a+b x)}}-\frac{c^2 \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (a+b x)}+1\right) \sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)}}{\sqrt{2} b d^2 \sqrt{c \sec (a+b x)}}+\frac{c^2 \sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)} \log \left(\tan (a+b x)-\sqrt{2} \sqrt{\tan (a+b x)}+1\right)}{2 \sqrt{2} b d^2 \sqrt{c \sec (a+b x)}}-\frac{c^2 \sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)} \log \left(\tan (a+b x)+\sqrt{2} \sqrt{\tan (a+b x)}+1\right)}{2 \sqrt{2} b d^2 \sqrt{c \sec (a+b x)}}+\frac{2 c \sqrt{c \sec (a+b x)}}{b d \sqrt{d \csc (a+b x)}}",1,"(2*c*Sqrt[c*Sec[a + b*x]])/(b*d*Sqrt[d*Csc[a + b*x]]) + (c^2*ArcTan[1 - Sqrt[2]*Sqrt[Tan[a + b*x]]]*Sqrt[d*Csc[a + b*x]]*Sqrt[Tan[a + b*x]])/(Sqrt[2]*b*d^2*Sqrt[c*Sec[a + b*x]]) - (c^2*ArcTan[1 + Sqrt[2]*Sqrt[Tan[a + b*x]]]*Sqrt[d*Csc[a + b*x]]*Sqrt[Tan[a + b*x]])/(Sqrt[2]*b*d^2*Sqrt[c*Sec[a + b*x]]) + (c^2*Sqrt[d*Csc[a + b*x]]*Log[1 - Sqrt[2]*Sqrt[Tan[a + b*x]] + Tan[a + b*x]]*Sqrt[Tan[a + b*x]])/(2*Sqrt[2]*b*d^2*Sqrt[c*Sec[a + b*x]]) - (c^2*Sqrt[d*Csc[a + b*x]]*Log[1 + Sqrt[2]*Sqrt[Tan[a + b*x]] + Tan[a + b*x]]*Sqrt[Tan[a + b*x]])/(2*Sqrt[2]*b*d^2*Sqrt[c*Sec[a + b*x]])","A",13,10,25,0.4000,1,"{2624, 2629, 3476, 329, 211, 1165, 628, 1162, 617, 204}"
245,1,94,0,0.1526839,"\int \frac{(c \sec (a+b x))^{3/2}}{(d \csc (a+b x))^{5/2}} \, dx","Int[(c*Sec[a + b*x])^(3/2)/(d*Csc[a + b*x])^(5/2),x]","\frac{2 c \sqrt{c \sec (a+b x)}}{b d (d \csc (a+b x))^{3/2}}-\frac{3 c^2 E\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{b d^2 \sqrt{\sin (2 a+2 b x)} \sqrt{c \sec (a+b x)} \sqrt{d \csc (a+b x)}}","\frac{2 c \sqrt{c \sec (a+b x)}}{b d (d \csc (a+b x))^{3/2}}-\frac{3 c^2 E\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{b d^2 \sqrt{\sin (2 a+2 b x)} \sqrt{c \sec (a+b x)} \sqrt{d \csc (a+b x)}}",1,"(2*c*Sqrt[c*Sec[a + b*x]])/(b*d*(d*Csc[a + b*x])^(3/2)) - (3*c^2*EllipticE[a - Pi/4 + b*x, 2])/(b*d^2*Sqrt[d*Csc[a + b*x]]*Sqrt[c*Sec[a + b*x]]*Sqrt[Sin[2*a + 2*b*x]])","A",4,4,25,0.1600,1,"{2624, 2630, 2572, 2639}"
246,1,166,0,0.2647528,"\int (d \csc (a+b x))^{9/2} (c \sec (a+b x))^{5/2} \, dx","Int[(d*Csc[a + b*x])^(9/2)*(c*Sec[a + b*x])^(5/2),x]","\frac{40 c^2 d^4 \sqrt{\sin (2 a+2 b x)} F\left(\left.a+b x-\frac{\pi }{4}\right|2\right) \sqrt{c \sec (a+b x)} \sqrt{d \csc (a+b x)}}{21 b}+\frac{40 c d^5 (c \sec (a+b x))^{3/2}}{21 b \sqrt{d \csc (a+b x)}}-\frac{20 c d^3 (c \sec (a+b x))^{3/2} (d \csc (a+b x))^{3/2}}{21 b}-\frac{2 c d (c \sec (a+b x))^{3/2} (d \csc (a+b x))^{7/2}}{7 b}","\frac{40 c^2 d^4 \sqrt{\sin (2 a+2 b x)} F\left(\left.a+b x-\frac{\pi }{4}\right|2\right) \sqrt{c \sec (a+b x)} \sqrt{d \csc (a+b x)}}{21 b}+\frac{40 c d^5 (c \sec (a+b x))^{3/2}}{21 b \sqrt{d \csc (a+b x)}}-\frac{20 c d^3 (c \sec (a+b x))^{3/2} (d \csc (a+b x))^{3/2}}{21 b}-\frac{2 c d (c \sec (a+b x))^{3/2} (d \csc (a+b x))^{7/2}}{7 b}",1,"(40*c*d^5*(c*Sec[a + b*x])^(3/2))/(21*b*Sqrt[d*Csc[a + b*x]]) - (20*c*d^3*(d*Csc[a + b*x])^(3/2)*(c*Sec[a + b*x])^(3/2))/(21*b) - (2*c*d*(d*Csc[a + b*x])^(7/2)*(c*Sec[a + b*x])^(3/2))/(7*b) + (40*c^2*d^4*Sqrt[d*Csc[a + b*x]]*EllipticF[a - Pi/4 + b*x, 2]*Sqrt[c*Sec[a + b*x]]*Sqrt[Sin[2*a + 2*b*x]])/(21*b)","A",6,5,25,0.2000,1,"{2625, 2626, 2630, 2573, 2641}"
247,1,106,0,0.1621005,"\int (d \csc (a+b x))^{7/2} (c \sec (a+b x))^{5/2} \, dx","Int[(d*Csc[a + b*x])^(7/2)*(c*Sec[a + b*x])^(5/2),x]","-\frac{64 c^3 d^3 \sqrt{d \csc (a+b x)}}{15 b \sqrt{c \sec (a+b x)}}+\frac{16 c d^3 (c \sec (a+b x))^{3/2} \sqrt{d \csc (a+b x)}}{15 b}-\frac{2 c d (c \sec (a+b x))^{3/2} (d \csc (a+b x))^{5/2}}{5 b}","-\frac{64 c^3 d^3 \sqrt{d \csc (a+b x)}}{15 b \sqrt{c \sec (a+b x)}}+\frac{16 c d^3 (c \sec (a+b x))^{3/2} \sqrt{d \csc (a+b x)}}{15 b}-\frac{2 c d (c \sec (a+b x))^{3/2} (d \csc (a+b x))^{5/2}}{5 b}",1,"(-64*c^3*d^3*Sqrt[d*Csc[a + b*x]])/(15*b*Sqrt[c*Sec[a + b*x]]) + (16*c*d^3*Sqrt[d*Csc[a + b*x]]*(c*Sec[a + b*x])^(3/2))/(15*b) - (2*c*d*(d*Csc[a + b*x])^(5/2)*(c*Sec[a + b*x])^(3/2))/(5*b)","A",3,3,25,0.1200,1,"{2625, 2626, 2619}"
248,1,131,0,0.2044,"\int (d \csc (a+b x))^{5/2} (c \sec (a+b x))^{5/2} \, dx","Int[(d*Csc[a + b*x])^(5/2)*(c*Sec[a + b*x])^(5/2),x]","\frac{4 c^2 d^2 \sqrt{\sin (2 a+2 b x)} F\left(\left.a+b x-\frac{\pi }{4}\right|2\right) \sqrt{c \sec (a+b x)} \sqrt{d \csc (a+b x)}}{3 b}+\frac{4 c d^3 (c \sec (a+b x))^{3/2}}{3 b \sqrt{d \csc (a+b x)}}-\frac{2 c d (c \sec (a+b x))^{3/2} (d \csc (a+b x))^{3/2}}{3 b}","\frac{4 c^2 d^2 \sqrt{\sin (2 a+2 b x)} F\left(\left.a+b x-\frac{\pi }{4}\right|2\right) \sqrt{c \sec (a+b x)} \sqrt{d \csc (a+b x)}}{3 b}+\frac{4 c d^3 (c \sec (a+b x))^{3/2}}{3 b \sqrt{d \csc (a+b x)}}-\frac{2 c d (c \sec (a+b x))^{3/2} (d \csc (a+b x))^{3/2}}{3 b}",1,"(4*c*d^3*(c*Sec[a + b*x])^(3/2))/(3*b*Sqrt[d*Csc[a + b*x]]) - (2*c*d*(d*Csc[a + b*x])^(3/2)*(c*Sec[a + b*x])^(3/2))/(3*b) + (4*c^2*d^2*Sqrt[d*Csc[a + b*x]]*EllipticF[a - Pi/4 + b*x, 2]*Sqrt[c*Sec[a + b*x]]*Sqrt[Sin[2*a + 2*b*x]])/(3*b)","A",5,5,25,0.2000,1,"{2625, 2626, 2630, 2573, 2641}"
249,1,69,0,0.1024233,"\int (d \csc (a+b x))^{3/2} (c \sec (a+b x))^{5/2} \, dx","Int[(d*Csc[a + b*x])^(3/2)*(c*Sec[a + b*x])^(5/2),x]","\frac{2 c d (c \sec (a+b x))^{3/2} \sqrt{d \csc (a+b x)}}{3 b}-\frac{8 c^3 d \sqrt{d \csc (a+b x)}}{3 b \sqrt{c \sec (a+b x)}}","\frac{2 c d (c \sec (a+b x))^{3/2} \sqrt{d \csc (a+b x)}}{3 b}-\frac{8 c^3 d \sqrt{d \csc (a+b x)}}{3 b \sqrt{c \sec (a+b x)}}",1,"(-8*c^3*d*Sqrt[d*Csc[a + b*x]])/(3*b*Sqrt[c*Sec[a + b*x]]) + (2*c*d*Sqrt[d*Csc[a + b*x]]*(c*Sec[a + b*x])^(3/2))/(3*b)","A",2,2,25,0.08000,1,"{2626, 2619}"
250,1,93,0,0.1405814,"\int \sqrt{d \csc (a+b x)} (c \sec (a+b x))^{5/2} \, dx","Int[Sqrt[d*Csc[a + b*x]]*(c*Sec[a + b*x])^(5/2),x]","\frac{2 c^2 \sqrt{\sin (2 a+2 b x)} F\left(\left.a+b x-\frac{\pi }{4}\right|2\right) \sqrt{c \sec (a+b x)} \sqrt{d \csc (a+b x)}}{3 b}+\frac{2 c d (c \sec (a+b x))^{3/2}}{3 b \sqrt{d \csc (a+b x)}}","\frac{2 c^2 \sqrt{\sin (2 a+2 b x)} F\left(\left.a+b x-\frac{\pi }{4}\right|2\right) \sqrt{c \sec (a+b x)} \sqrt{d \csc (a+b x)}}{3 b}+\frac{2 c d (c \sec (a+b x))^{3/2}}{3 b \sqrt{d \csc (a+b x)}}",1,"(2*c*d*(c*Sec[a + b*x])^(3/2))/(3*b*Sqrt[d*Csc[a + b*x]]) + (2*c^2*Sqrt[d*Csc[a + b*x]]*EllipticF[a - Pi/4 + b*x, 2]*Sqrt[c*Sec[a + b*x]]*Sqrt[Sin[2*a + 2*b*x]])/(3*b)","A",4,4,25,0.1600,1,"{2626, 2630, 2573, 2641}"
251,1,33,0,0.0494305,"\int \frac{(c \sec (a+b x))^{5/2}}{\sqrt{d \csc (a+b x)}} \, dx","Int[(c*Sec[a + b*x])^(5/2)/Sqrt[d*Csc[a + b*x]],x]","\frac{2 c d (c \sec (a+b x))^{3/2}}{3 b (d \csc (a+b x))^{3/2}}","\frac{2 c d (c \sec (a+b x))^{3/2}}{3 b (d \csc (a+b x))^{3/2}}",1,"(2*c*d*(c*Sec[a + b*x])^(3/2))/(3*b*(d*Csc[a + b*x])^(3/2))","A",1,1,25,0.04000,1,"{2619}"
252,1,98,0,0.1495937,"\int \frac{(c \sec (a+b x))^{5/2}}{(d \csc (a+b x))^{3/2}} \, dx","Int[(c*Sec[a + b*x])^(5/2)/(d*Csc[a + b*x])^(3/2),x]","\frac{2 c (c \sec (a+b x))^{3/2}}{3 b d \sqrt{d \csc (a+b x)}}-\frac{c^2 \sqrt{\sin (2 a+2 b x)} F\left(\left.a+b x-\frac{\pi }{4}\right|2\right) \sqrt{c \sec (a+b x)} \sqrt{d \csc (a+b x)}}{3 b d^2}","\frac{2 c (c \sec (a+b x))^{3/2}}{3 b d \sqrt{d \csc (a+b x)}}-\frac{c^2 \sqrt{\sin (2 a+2 b x)} F\left(\left.a+b x-\frac{\pi }{4}\right|2\right) \sqrt{c \sec (a+b x)} \sqrt{d \csc (a+b x)}}{3 b d^2}",1,"(2*c*(c*Sec[a + b*x])^(3/2))/(3*b*d*Sqrt[d*Csc[a + b*x]]) - (c^2*Sqrt[d*Csc[a + b*x]]*EllipticF[a - Pi/4 + b*x, 2]*Sqrt[c*Sec[a + b*x]]*Sqrt[Sin[2*a + 2*b*x]])/(3*b*d^2)","A",4,4,25,0.1600,1,"{2624, 2630, 2573, 2641}"
253,1,329,0,0.2169211,"\int \frac{(c \sec (a+b x))^{5/2}}{(d \csc (a+b x))^{5/2}} \, dx","Int[(c*Sec[a + b*x])^(5/2)/(d*Csc[a + b*x])^(5/2),x]","\frac{c^2 \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (a+b x)}\right) \sqrt{c \sec (a+b x)}}{\sqrt{2} b d^2 \sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)}}-\frac{c^2 \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (a+b x)}+1\right) \sqrt{c \sec (a+b x)}}{\sqrt{2} b d^2 \sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)}}-\frac{c^2 \sqrt{c \sec (a+b x)} \log \left(\tan (a+b x)-\sqrt{2} \sqrt{\tan (a+b x)}+1\right)}{2 \sqrt{2} b d^2 \sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)}}+\frac{c^2 \sqrt{c \sec (a+b x)} \log \left(\tan (a+b x)+\sqrt{2} \sqrt{\tan (a+b x)}+1\right)}{2 \sqrt{2} b d^2 \sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)}}+\frac{2 c (c \sec (a+b x))^{3/2}}{3 b d (d \csc (a+b x))^{3/2}}","\frac{c^2 \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (a+b x)}\right) \sqrt{c \sec (a+b x)}}{\sqrt{2} b d^2 \sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)}}-\frac{c^2 \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (a+b x)}+1\right) \sqrt{c \sec (a+b x)}}{\sqrt{2} b d^2 \sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)}}-\frac{c^2 \sqrt{c \sec (a+b x)} \log \left(\tan (a+b x)-\sqrt{2} \sqrt{\tan (a+b x)}+1\right)}{2 \sqrt{2} b d^2 \sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)}}+\frac{c^2 \sqrt{c \sec (a+b x)} \log \left(\tan (a+b x)+\sqrt{2} \sqrt{\tan (a+b x)}+1\right)}{2 \sqrt{2} b d^2 \sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)}}+\frac{2 c (c \sec (a+b x))^{3/2}}{3 b d (d \csc (a+b x))^{3/2}}",1,"(2*c*(c*Sec[a + b*x])^(3/2))/(3*b*d*(d*Csc[a + b*x])^(3/2)) + (c^2*ArcTan[1 - Sqrt[2]*Sqrt[Tan[a + b*x]]]*Sqrt[c*Sec[a + b*x]])/(Sqrt[2]*b*d^2*Sqrt[d*Csc[a + b*x]]*Sqrt[Tan[a + b*x]]) - (c^2*ArcTan[1 + Sqrt[2]*Sqrt[Tan[a + b*x]]]*Sqrt[c*Sec[a + b*x]])/(Sqrt[2]*b*d^2*Sqrt[d*Csc[a + b*x]]*Sqrt[Tan[a + b*x]]) - (c^2*Log[1 - Sqrt[2]*Sqrt[Tan[a + b*x]] + Tan[a + b*x]]*Sqrt[c*Sec[a + b*x]])/(2*Sqrt[2]*b*d^2*Sqrt[d*Csc[a + b*x]]*Sqrt[Tan[a + b*x]]) + (c^2*Log[1 + Sqrt[2]*Sqrt[Tan[a + b*x]] + Tan[a + b*x]]*Sqrt[c*Sec[a + b*x]])/(2*Sqrt[2]*b*d^2*Sqrt[d*Csc[a + b*x]]*Sqrt[Tan[a + b*x]])","A",13,10,25,0.4000,1,"{2624, 2629, 3476, 329, 297, 1162, 617, 204, 1165, 628}"
254,1,69,0,0.0996172,"\int \frac{(d \csc (a+b x))^{9/2}}{\sqrt{c \sec (a+b x)}} \, dx","Int[(d*Csc[a + b*x])^(9/2)/Sqrt[c*Sec[a + b*x]],x]","-\frac{8 c d^3 (d \csc (a+b x))^{3/2}}{21 b (c \sec (a+b x))^{3/2}}-\frac{2 c d (d \csc (a+b x))^{7/2}}{7 b (c \sec (a+b x))^{3/2}}","-\frac{8 c d^3 (d \csc (a+b x))^{3/2}}{21 b (c \sec (a+b x))^{3/2}}-\frac{2 c d (d \csc (a+b x))^{7/2}}{7 b (c \sec (a+b x))^{3/2}}",1,"(-8*c*d^3*(d*Csc[a + b*x])^(3/2))/(21*b*(c*Sec[a + b*x])^(3/2)) - (2*c*d*(d*Csc[a + b*x])^(7/2))/(7*b*(c*Sec[a + b*x])^(3/2))","A",2,2,25,0.08000,1,"{2625, 2619}"
255,1,128,0,0.1927314,"\int \frac{(d \csc (a+b x))^{7/2}}{\sqrt{c \sec (a+b x)}} \, dx","Int[(d*Csc[a + b*x])^(7/2)/Sqrt[c*Sec[a + b*x]],x]","-\frac{4 c d^3 \sqrt{d \csc (a+b x)}}{5 b (c \sec (a+b x))^{3/2}}-\frac{4 d^4 E\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{5 b \sqrt{\sin (2 a+2 b x)} \sqrt{c \sec (a+b x)} \sqrt{d \csc (a+b x)}}-\frac{2 c d (d \csc (a+b x))^{5/2}}{5 b (c \sec (a+b x))^{3/2}}","-\frac{4 c d^3 \sqrt{d \csc (a+b x)}}{5 b (c \sec (a+b x))^{3/2}}-\frac{4 d^4 E\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{5 b \sqrt{\sin (2 a+2 b x)} \sqrt{c \sec (a+b x)} \sqrt{d \csc (a+b x)}}-\frac{2 c d (d \csc (a+b x))^{5/2}}{5 b (c \sec (a+b x))^{3/2}}",1,"(-4*c*d^3*Sqrt[d*Csc[a + b*x]])/(5*b*(c*Sec[a + b*x])^(3/2)) - (2*c*d*(d*Csc[a + b*x])^(5/2))/(5*b*(c*Sec[a + b*x])^(3/2)) - (4*d^4*EllipticE[a - Pi/4 + b*x, 2])/(5*b*Sqrt[d*Csc[a + b*x]]*Sqrt[c*Sec[a + b*x]]*Sqrt[Sin[2*a + 2*b*x]])","A",5,4,25,0.1600,1,"{2625, 2630, 2572, 2639}"
256,1,33,0,0.0480831,"\int \frac{(d \csc (a+b x))^{5/2}}{\sqrt{c \sec (a+b x)}} \, dx","Int[(d*Csc[a + b*x])^(5/2)/Sqrt[c*Sec[a + b*x]],x]","-\frac{2 c d (d \csc (a+b x))^{3/2}}{3 b (c \sec (a+b x))^{3/2}}","-\frac{2 c d (d \csc (a+b x))^{3/2}}{3 b (c \sec (a+b x))^{3/2}}",1,"(-2*c*d*(d*Csc[a + b*x])^(3/2))/(3*b*(c*Sec[a + b*x])^(3/2))","A",1,1,25,0.04000,1,"{2619}"
257,1,89,0,0.1392635,"\int \frac{(d \csc (a+b x))^{3/2}}{\sqrt{c \sec (a+b x)}} \, dx","Int[(d*Csc[a + b*x])^(3/2)/Sqrt[c*Sec[a + b*x]],x]","-\frac{2 d^2 E\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{b \sqrt{\sin (2 a+2 b x)} \sqrt{c \sec (a+b x)} \sqrt{d \csc (a+b x)}}-\frac{2 c d \sqrt{d \csc (a+b x)}}{b (c \sec (a+b x))^{3/2}}","-\frac{2 d^2 E\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{b \sqrt{\sin (2 a+2 b x)} \sqrt{c \sec (a+b x)} \sqrt{d \csc (a+b x)}}-\frac{2 c d \sqrt{d \csc (a+b x)}}{b (c \sec (a+b x))^{3/2}}",1,"(-2*c*d*Sqrt[d*Csc[a + b*x]])/(b*(c*Sec[a + b*x])^(3/2)) - (2*d^2*EllipticE[a - Pi/4 + b*x, 2])/(b*Sqrt[d*Csc[a + b*x]]*Sqrt[c*Sec[a + b*x]]*Sqrt[Sin[2*a + 2*b*x]])","A",4,4,25,0.1600,1,"{2625, 2630, 2572, 2639}"
258,1,270,0,0.1309259,"\int \frac{\sqrt{d \csc (a+b x)}}{\sqrt{c \sec (a+b x)}} \, dx","Int[Sqrt[d*Csc[a + b*x]]/Sqrt[c*Sec[a + b*x]],x]","-\frac{\sqrt{\tan (a+b x)} \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (a+b x)}\right) \sqrt{d \csc (a+b x)}}{\sqrt{2} b \sqrt{c \sec (a+b x)}}+\frac{\tan ^{-1}\left(\sqrt{2} \sqrt{\tan (a+b x)}+1\right) \sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)}}{\sqrt{2} b \sqrt{c \sec (a+b x)}}-\frac{\sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)} \log \left(\tan (a+b x)-\sqrt{2} \sqrt{\tan (a+b x)}+1\right)}{2 \sqrt{2} b \sqrt{c \sec (a+b x)}}+\frac{\sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)} \log \left(\tan (a+b x)+\sqrt{2} \sqrt{\tan (a+b x)}+1\right)}{2 \sqrt{2} b \sqrt{c \sec (a+b x)}}","-\frac{\sqrt{\tan (a+b x)} \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (a+b x)}\right) \sqrt{d \csc (a+b x)}}{\sqrt{2} b \sqrt{c \sec (a+b x)}}+\frac{\tan ^{-1}\left(\sqrt{2} \sqrt{\tan (a+b x)}+1\right) \sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)}}{\sqrt{2} b \sqrt{c \sec (a+b x)}}-\frac{\sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)} \log \left(\tan (a+b x)-\sqrt{2} \sqrt{\tan (a+b x)}+1\right)}{2 \sqrt{2} b \sqrt{c \sec (a+b x)}}+\frac{\sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)} \log \left(\tan (a+b x)+\sqrt{2} \sqrt{\tan (a+b x)}+1\right)}{2 \sqrt{2} b \sqrt{c \sec (a+b x)}}",1,"-((ArcTan[1 - Sqrt[2]*Sqrt[Tan[a + b*x]]]*Sqrt[d*Csc[a + b*x]]*Sqrt[Tan[a + b*x]])/(Sqrt[2]*b*Sqrt[c*Sec[a + b*x]])) + (ArcTan[1 + Sqrt[2]*Sqrt[Tan[a + b*x]]]*Sqrt[d*Csc[a + b*x]]*Sqrt[Tan[a + b*x]])/(Sqrt[2]*b*Sqrt[c*Sec[a + b*x]]) - (Sqrt[d*Csc[a + b*x]]*Log[1 - Sqrt[2]*Sqrt[Tan[a + b*x]] + Tan[a + b*x]]*Sqrt[Tan[a + b*x]])/(2*Sqrt[2]*b*Sqrt[c*Sec[a + b*x]]) + (Sqrt[d*Csc[a + b*x]]*Log[1 + Sqrt[2]*Sqrt[Tan[a + b*x]] + Tan[a + b*x]]*Sqrt[Tan[a + b*x]])/(2*Sqrt[2]*b*Sqrt[c*Sec[a + b*x]])","A",12,9,25,0.3600,1,"{2629, 3476, 329, 211, 1165, 628, 1162, 617, 204}"
259,1,53,0,0.0884838,"\int \frac{1}{\sqrt{d \csc (a+b x)} \sqrt{c \sec (a+b x)}} \, dx","Int[1/(Sqrt[d*Csc[a + b*x]]*Sqrt[c*Sec[a + b*x]]),x]","\frac{E\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{b \sqrt{\sin (2 a+2 b x)} \sqrt{c \sec (a+b x)} \sqrt{d \csc (a+b x)}}","\frac{E\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{b \sqrt{\sin (2 a+2 b x)} \sqrt{c \sec (a+b x)} \sqrt{d \csc (a+b x)}}",1,"EllipticE[a - Pi/4 + b*x, 2]/(b*Sqrt[d*Csc[a + b*x]]*Sqrt[c*Sec[a + b*x]]*Sqrt[Sin[2*a + 2*b*x]])","A",3,3,25,0.1200,1,"{2630, 2572, 2639}"
260,1,322,0,0.2040938,"\int \frac{1}{(d \csc (a+b x))^{3/2} \sqrt{c \sec (a+b x)}} \, dx","Int[1/((d*Csc[a + b*x])^(3/2)*Sqrt[c*Sec[a + b*x]]),x]","-\frac{\tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (a+b x)}\right) \sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)}}{4 \sqrt{2} b d^2 \sqrt{c \sec (a+b x)}}+\frac{\tan ^{-1}\left(\sqrt{2} \sqrt{\tan (a+b x)}+1\right) \sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)}}{4 \sqrt{2} b d^2 \sqrt{c \sec (a+b x)}}-\frac{\sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)} \log \left(\tan (a+b x)-\sqrt{2} \sqrt{\tan (a+b x)}+1\right)}{8 \sqrt{2} b d^2 \sqrt{c \sec (a+b x)}}+\frac{\sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)} \log \left(\tan (a+b x)+\sqrt{2} \sqrt{\tan (a+b x)}+1\right)}{8 \sqrt{2} b d^2 \sqrt{c \sec (a+b x)}}-\frac{c}{2 b d (c \sec (a+b x))^{3/2} \sqrt{d \csc (a+b x)}}","-\frac{\tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (a+b x)}\right) \sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)}}{4 \sqrt{2} b d^2 \sqrt{c \sec (a+b x)}}+\frac{\tan ^{-1}\left(\sqrt{2} \sqrt{\tan (a+b x)}+1\right) \sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)}}{4 \sqrt{2} b d^2 \sqrt{c \sec (a+b x)}}-\frac{\sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)} \log \left(\tan (a+b x)-\sqrt{2} \sqrt{\tan (a+b x)}+1\right)}{8 \sqrt{2} b d^2 \sqrt{c \sec (a+b x)}}+\frac{\sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)} \log \left(\tan (a+b x)+\sqrt{2} \sqrt{\tan (a+b x)}+1\right)}{8 \sqrt{2} b d^2 \sqrt{c \sec (a+b x)}}-\frac{c}{2 b d (c \sec (a+b x))^{3/2} \sqrt{d \csc (a+b x)}}",1,"-c/(2*b*d*Sqrt[d*Csc[a + b*x]]*(c*Sec[a + b*x])^(3/2)) - (ArcTan[1 - Sqrt[2]*Sqrt[Tan[a + b*x]]]*Sqrt[d*Csc[a + b*x]]*Sqrt[Tan[a + b*x]])/(4*Sqrt[2]*b*d^2*Sqrt[c*Sec[a + b*x]]) + (ArcTan[1 + Sqrt[2]*Sqrt[Tan[a + b*x]]]*Sqrt[d*Csc[a + b*x]]*Sqrt[Tan[a + b*x]])/(4*Sqrt[2]*b*d^2*Sqrt[c*Sec[a + b*x]]) - (Sqrt[d*Csc[a + b*x]]*Log[1 - Sqrt[2]*Sqrt[Tan[a + b*x]] + Tan[a + b*x]]*Sqrt[Tan[a + b*x]])/(8*Sqrt[2]*b*d^2*Sqrt[c*Sec[a + b*x]]) + (Sqrt[d*Csc[a + b*x]]*Log[1 + Sqrt[2]*Sqrt[Tan[a + b*x]] + Tan[a + b*x]]*Sqrt[Tan[a + b*x]])/(8*Sqrt[2]*b*d^2*Sqrt[c*Sec[a + b*x]])","A",13,10,25,0.4000,1,"{2627, 2629, 3476, 329, 211, 1165, 628, 1162, 617, 204}"
261,1,95,0,0.1411207,"\int \frac{1}{(d \csc (a+b x))^{5/2} \sqrt{c \sec (a+b x)}} \, dx","Int[1/((d*Csc[a + b*x])^(5/2)*Sqrt[c*Sec[a + b*x]]),x]","\frac{E\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{2 b d^2 \sqrt{\sin (2 a+2 b x)} \sqrt{c \sec (a+b x)} \sqrt{d \csc (a+b x)}}-\frac{c}{3 b d (c \sec (a+b x))^{3/2} (d \csc (a+b x))^{3/2}}","\frac{E\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{2 b d^2 \sqrt{\sin (2 a+2 b x)} \sqrt{c \sec (a+b x)} \sqrt{d \csc (a+b x)}}-\frac{c}{3 b d (c \sec (a+b x))^{3/2} (d \csc (a+b x))^{3/2}}",1,"-c/(3*b*d*(d*Csc[a + b*x])^(3/2)*(c*Sec[a + b*x])^(3/2)) + EllipticE[a - Pi/4 + b*x, 2]/(2*b*d^2*Sqrt[d*Csc[a + b*x]]*Sqrt[c*Sec[a + b*x]]*Sqrt[Sin[2*a + 2*b*x]])","A",4,4,25,0.1600,1,"{2627, 2630, 2572, 2639}"
262,1,110,0,0.1539959,"\int \frac{(d \csc (a+b x))^{11/2}}{(c \sec (a+b x))^{3/2}} \, dx","Int[(d*Csc[a + b*x])^(11/2)/(c*Sec[a + b*x])^(3/2),x]","\frac{8 d^5 \sqrt{d \csc (a+b x)}}{45 b c \sqrt{c \sec (a+b x)}}+\frac{2 d^3 (d \csc (a+b x))^{5/2}}{45 b c \sqrt{c \sec (a+b x)}}-\frac{2 d (d \csc (a+b x))^{9/2}}{9 b c \sqrt{c \sec (a+b x)}}","\frac{8 d^5 \sqrt{d \csc (a+b x)}}{45 b c \sqrt{c \sec (a+b x)}}+\frac{2 d^3 (d \csc (a+b x))^{5/2}}{45 b c \sqrt{c \sec (a+b x)}}-\frac{2 d (d \csc (a+b x))^{9/2}}{9 b c \sqrt{c \sec (a+b x)}}",1,"(8*d^5*Sqrt[d*Csc[a + b*x]])/(45*b*c*Sqrt[c*Sec[a + b*x]]) + (2*d^3*(d*Csc[a + b*x])^(5/2))/(45*b*c*Sqrt[c*Sec[a + b*x]]) - (2*d*(d*Csc[a + b*x])^(9/2))/(9*b*c*Sqrt[c*Sec[a + b*x]])","A",3,3,25,0.1200,1,"{2623, 2625, 2619}"
263,1,135,0,0.1996188,"\int \frac{(d \csc (a+b x))^{9/2}}{(c \sec (a+b x))^{3/2}} \, dx","Int[(d*Csc[a + b*x])^(9/2)/(c*Sec[a + b*x])^(3/2),x]","-\frac{2 d^4 \sqrt{\sin (2 a+2 b x)} F\left(\left.a+b x-\frac{\pi }{4}\right|2\right) \sqrt{c \sec (a+b x)} \sqrt{d \csc (a+b x)}}{21 b c^2}+\frac{2 d^3 (d \csc (a+b x))^{3/2}}{21 b c \sqrt{c \sec (a+b x)}}-\frac{2 d (d \csc (a+b x))^{7/2}}{7 b c \sqrt{c \sec (a+b x)}}","-\frac{2 d^4 \sqrt{\sin (2 a+2 b x)} F\left(\left.a+b x-\frac{\pi }{4}\right|2\right) \sqrt{c \sec (a+b x)} \sqrt{d \csc (a+b x)}}{21 b c^2}+\frac{2 d^3 (d \csc (a+b x))^{3/2}}{21 b c \sqrt{c \sec (a+b x)}}-\frac{2 d (d \csc (a+b x))^{7/2}}{7 b c \sqrt{c \sec (a+b x)}}",1,"(2*d^3*(d*Csc[a + b*x])^(3/2))/(21*b*c*Sqrt[c*Sec[a + b*x]]) - (2*d*(d*Csc[a + b*x])^(7/2))/(7*b*c*Sqrt[c*Sec[a + b*x]]) - (2*d^4*Sqrt[d*Csc[a + b*x]]*EllipticF[a - Pi/4 + b*x, 2]*Sqrt[c*Sec[a + b*x]]*Sqrt[Sin[2*a + 2*b*x]])/(21*b*c^2)","A",5,5,25,0.2000,1,"{2623, 2625, 2630, 2573, 2641}"
264,1,33,0,0.0533232,"\int \frac{(d \csc (a+b x))^{7/2}}{(c \sec (a+b x))^{3/2}} \, dx","Int[(d*Csc[a + b*x])^(7/2)/(c*Sec[a + b*x])^(3/2),x]","-\frac{2 c d (d \csc (a+b x))^{5/2}}{5 b (c \sec (a+b x))^{5/2}}","-\frac{2 c d (d \csc (a+b x))^{5/2}}{5 b (c \sec (a+b x))^{5/2}}",1,"(-2*c*d*(d*Csc[a + b*x])^(5/2))/(5*b*(c*Sec[a + b*x])^(5/2))","A",1,1,25,0.04000,1,"{2619}"
265,1,98,0,0.1475185,"\int \frac{(d \csc (a+b x))^{5/2}}{(c \sec (a+b x))^{3/2}} \, dx","Int[(d*Csc[a + b*x])^(5/2)/(c*Sec[a + b*x])^(3/2),x]","-\frac{d^2 \sqrt{\sin (2 a+2 b x)} F\left(\left.a+b x-\frac{\pi }{4}\right|2\right) \sqrt{c \sec (a+b x)} \sqrt{d \csc (a+b x)}}{3 b c^2}-\frac{2 d (d \csc (a+b x))^{3/2}}{3 b c \sqrt{c \sec (a+b x)}}","-\frac{d^2 \sqrt{\sin (2 a+2 b x)} F\left(\left.a+b x-\frac{\pi }{4}\right|2\right) \sqrt{c \sec (a+b x)} \sqrt{d \csc (a+b x)}}{3 b c^2}-\frac{2 d (d \csc (a+b x))^{3/2}}{3 b c \sqrt{c \sec (a+b x)}}",1,"(-2*d*(d*Csc[a + b*x])^(3/2))/(3*b*c*Sqrt[c*Sec[a + b*x]]) - (d^2*Sqrt[d*Csc[a + b*x]]*EllipticF[a - Pi/4 + b*x, 2]*Sqrt[c*Sec[a + b*x]]*Sqrt[Sin[2*a + 2*b*x]])/(3*b*c^2)","A",4,4,25,0.1600,1,"{2623, 2630, 2573, 2641}"
266,1,327,0,0.215005,"\int \frac{(d \csc (a+b x))^{3/2}}{(c \sec (a+b x))^{3/2}} \, dx","Int[(d*Csc[a + b*x])^(3/2)/(c*Sec[a + b*x])^(3/2),x]","\frac{d^2 \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (a+b x)}\right) \sqrt{c \sec (a+b x)}}{\sqrt{2} b c^2 \sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)}}-\frac{d^2 \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (a+b x)}+1\right) \sqrt{c \sec (a+b x)}}{\sqrt{2} b c^2 \sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)}}-\frac{d^2 \sqrt{c \sec (a+b x)} \log \left(\tan (a+b x)-\sqrt{2} \sqrt{\tan (a+b x)}+1\right)}{2 \sqrt{2} b c^2 \sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)}}+\frac{d^2 \sqrt{c \sec (a+b x)} \log \left(\tan (a+b x)+\sqrt{2} \sqrt{\tan (a+b x)}+1\right)}{2 \sqrt{2} b c^2 \sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)}}-\frac{2 d \sqrt{d \csc (a+b x)}}{b c \sqrt{c \sec (a+b x)}}","\frac{d^2 \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (a+b x)}\right) \sqrt{c \sec (a+b x)}}{\sqrt{2} b c^2 \sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)}}-\frac{d^2 \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (a+b x)}+1\right) \sqrt{c \sec (a+b x)}}{\sqrt{2} b c^2 \sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)}}-\frac{d^2 \sqrt{c \sec (a+b x)} \log \left(\tan (a+b x)-\sqrt{2} \sqrt{\tan (a+b x)}+1\right)}{2 \sqrt{2} b c^2 \sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)}}+\frac{d^2 \sqrt{c \sec (a+b x)} \log \left(\tan (a+b x)+\sqrt{2} \sqrt{\tan (a+b x)}+1\right)}{2 \sqrt{2} b c^2 \sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)}}-\frac{2 d \sqrt{d \csc (a+b x)}}{b c \sqrt{c \sec (a+b x)}}",1,"(-2*d*Sqrt[d*Csc[a + b*x]])/(b*c*Sqrt[c*Sec[a + b*x]]) + (d^2*ArcTan[1 - Sqrt[2]*Sqrt[Tan[a + b*x]]]*Sqrt[c*Sec[a + b*x]])/(Sqrt[2]*b*c^2*Sqrt[d*Csc[a + b*x]]*Sqrt[Tan[a + b*x]]) - (d^2*ArcTan[1 + Sqrt[2]*Sqrt[Tan[a + b*x]]]*Sqrt[c*Sec[a + b*x]])/(Sqrt[2]*b*c^2*Sqrt[d*Csc[a + b*x]]*Sqrt[Tan[a + b*x]]) - (d^2*Log[1 - Sqrt[2]*Sqrt[Tan[a + b*x]] + Tan[a + b*x]]*Sqrt[c*Sec[a + b*x]])/(2*Sqrt[2]*b*c^2*Sqrt[d*Csc[a + b*x]]*Sqrt[Tan[a + b*x]]) + (d^2*Log[1 + Sqrt[2]*Sqrt[Tan[a + b*x]] + Tan[a + b*x]]*Sqrt[c*Sec[a + b*x]])/(2*Sqrt[2]*b*c^2*Sqrt[d*Csc[a + b*x]]*Sqrt[Tan[a + b*x]])","A",13,10,25,0.4000,1,"{2623, 2629, 3476, 329, 297, 1162, 617, 204, 1165, 628}"
267,1,92,0,0.1429544,"\int \frac{\sqrt{d \csc (a+b x)}}{(c \sec (a+b x))^{3/2}} \, dx","Int[Sqrt[d*Csc[a + b*x]]/(c*Sec[a + b*x])^(3/2),x]","\frac{\sqrt{\sin (2 a+2 b x)} F\left(\left.a+b x-\frac{\pi }{4}\right|2\right) \sqrt{c \sec (a+b x)} \sqrt{d \csc (a+b x)}}{2 b c^2}+\frac{d}{b c \sqrt{c \sec (a+b x)} \sqrt{d \csc (a+b x)}}","\frac{\sqrt{\sin (2 a+2 b x)} F\left(\left.a+b x-\frac{\pi }{4}\right|2\right) \sqrt{c \sec (a+b x)} \sqrt{d \csc (a+b x)}}{2 b c^2}+\frac{d}{b c \sqrt{c \sec (a+b x)} \sqrt{d \csc (a+b x)}}",1,"d/(b*c*Sqrt[d*Csc[a + b*x]]*Sqrt[c*Sec[a + b*x]]) + (Sqrt[d*Csc[a + b*x]]*EllipticF[a - Pi/4 + b*x, 2]*Sqrt[c*Sec[a + b*x]]*Sqrt[Sin[2*a + 2*b*x]])/(2*b*c^2)","A",4,4,25,0.1600,1,"{2628, 2630, 2573, 2641}"
268,1,322,0,0.2134148,"\int \frac{1}{\sqrt{d \csc (a+b x)} (c \sec (a+b x))^{3/2}} \, dx","Int[1/(Sqrt[d*Csc[a + b*x]]*(c*Sec[a + b*x])^(3/2)),x]","-\frac{\tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (a+b x)}\right) \sqrt{c \sec (a+b x)}}{4 \sqrt{2} b c^2 \sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)}}+\frac{\tan ^{-1}\left(\sqrt{2} \sqrt{\tan (a+b x)}+1\right) \sqrt{c \sec (a+b x)}}{4 \sqrt{2} b c^2 \sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)}}+\frac{\sqrt{c \sec (a+b x)} \log \left(\tan (a+b x)-\sqrt{2} \sqrt{\tan (a+b x)}+1\right)}{8 \sqrt{2} b c^2 \sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)}}-\frac{\sqrt{c \sec (a+b x)} \log \left(\tan (a+b x)+\sqrt{2} \sqrt{\tan (a+b x)}+1\right)}{8 \sqrt{2} b c^2 \sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)}}+\frac{d}{2 b c \sqrt{c \sec (a+b x)} (d \csc (a+b x))^{3/2}}","-\frac{\tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (a+b x)}\right) \sqrt{c \sec (a+b x)}}{4 \sqrt{2} b c^2 \sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)}}+\frac{\tan ^{-1}\left(\sqrt{2} \sqrt{\tan (a+b x)}+1\right) \sqrt{c \sec (a+b x)}}{4 \sqrt{2} b c^2 \sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)}}+\frac{\sqrt{c \sec (a+b x)} \log \left(\tan (a+b x)-\sqrt{2} \sqrt{\tan (a+b x)}+1\right)}{8 \sqrt{2} b c^2 \sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)}}-\frac{\sqrt{c \sec (a+b x)} \log \left(\tan (a+b x)+\sqrt{2} \sqrt{\tan (a+b x)}+1\right)}{8 \sqrt{2} b c^2 \sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)}}+\frac{d}{2 b c \sqrt{c \sec (a+b x)} (d \csc (a+b x))^{3/2}}",1,"d/(2*b*c*(d*Csc[a + b*x])^(3/2)*Sqrt[c*Sec[a + b*x]]) - (ArcTan[1 - Sqrt[2]*Sqrt[Tan[a + b*x]]]*Sqrt[c*Sec[a + b*x]])/(4*Sqrt[2]*b*c^2*Sqrt[d*Csc[a + b*x]]*Sqrt[Tan[a + b*x]]) + (ArcTan[1 + Sqrt[2]*Sqrt[Tan[a + b*x]]]*Sqrt[c*Sec[a + b*x]])/(4*Sqrt[2]*b*c^2*Sqrt[d*Csc[a + b*x]]*Sqrt[Tan[a + b*x]]) + (Log[1 - Sqrt[2]*Sqrt[Tan[a + b*x]] + Tan[a + b*x]]*Sqrt[c*Sec[a + b*x]])/(8*Sqrt[2]*b*c^2*Sqrt[d*Csc[a + b*x]]*Sqrt[Tan[a + b*x]]) - (Log[1 + Sqrt[2]*Sqrt[Tan[a + b*x]] + Tan[a + b*x]]*Sqrt[c*Sec[a + b*x]])/(8*Sqrt[2]*b*c^2*Sqrt[d*Csc[a + b*x]]*Sqrt[Tan[a + b*x]])","A",13,10,25,0.4000,1,"{2628, 2629, 3476, 329, 297, 1162, 617, 204, 1165, 628}"
269,1,135,0,0.2071164,"\int \frac{1}{(d \csc (a+b x))^{3/2} (c \sec (a+b x))^{3/2}} \, dx","Int[1/((d*Csc[a + b*x])^(3/2)*(c*Sec[a + b*x])^(3/2)),x]","\frac{\sqrt{\sin (2 a+2 b x)} F\left(\left.a+b x-\frac{\pi }{4}\right|2\right) \sqrt{c \sec (a+b x)} \sqrt{d \csc (a+b x)}}{12 b c^2 d^2}-\frac{c}{3 b d (c \sec (a+b x))^{5/2} \sqrt{d \csc (a+b x)}}+\frac{1}{6 b c d \sqrt{c \sec (a+b x)} \sqrt{d \csc (a+b x)}}","\frac{\sqrt{\sin (2 a+2 b x)} F\left(\left.a+b x-\frac{\pi }{4}\right|2\right) \sqrt{c \sec (a+b x)} \sqrt{d \csc (a+b x)}}{12 b c^2 d^2}-\frac{c}{3 b d (c \sec (a+b x))^{5/2} \sqrt{d \csc (a+b x)}}+\frac{1}{6 b c d \sqrt{c \sec (a+b x)} \sqrt{d \csc (a+b x)}}",1,"-c/(3*b*d*Sqrt[d*Csc[a + b*x]]*(c*Sec[a + b*x])^(5/2)) + 1/(6*b*c*d*Sqrt[d*Csc[a + b*x]]*Sqrt[c*Sec[a + b*x]]) + (Sqrt[d*Csc[a + b*x]]*EllipticF[a - Pi/4 + b*x, 2]*Sqrt[c*Sec[a + b*x]]*Sqrt[Sin[2*a + 2*b*x]])/(12*b*c^2*d^2)","A",5,5,25,0.2000,1,"{2627, 2628, 2630, 2573, 2641}"
270,1,371,0,0.297432,"\int \frac{1}{(d \csc (a+b x))^{5/2} (c \sec (a+b x))^{3/2}} \, dx","Int[1/((d*Csc[a + b*x])^(5/2)*(c*Sec[a + b*x])^(3/2)),x]","-\frac{3 \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (a+b x)}\right) \sqrt{c \sec (a+b x)}}{32 \sqrt{2} b c^2 d^2 \sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)}}+\frac{3 \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (a+b x)}+1\right) \sqrt{c \sec (a+b x)}}{32 \sqrt{2} b c^2 d^2 \sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)}}+\frac{3 \sqrt{c \sec (a+b x)} \log \left(\tan (a+b x)-\sqrt{2} \sqrt{\tan (a+b x)}+1\right)}{64 \sqrt{2} b c^2 d^2 \sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)}}-\frac{3 \sqrt{c \sec (a+b x)} \log \left(\tan (a+b x)+\sqrt{2} \sqrt{\tan (a+b x)}+1\right)}{64 \sqrt{2} b c^2 d^2 \sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)}}-\frac{c}{4 b d (c \sec (a+b x))^{5/2} (d \csc (a+b x))^{3/2}}+\frac{3}{16 b c d \sqrt{c \sec (a+b x)} (d \csc (a+b x))^{3/2}}","-\frac{3 \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (a+b x)}\right) \sqrt{c \sec (a+b x)}}{32 \sqrt{2} b c^2 d^2 \sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)}}+\frac{3 \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (a+b x)}+1\right) \sqrt{c \sec (a+b x)}}{32 \sqrt{2} b c^2 d^2 \sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)}}+\frac{3 \sqrt{c \sec (a+b x)} \log \left(\tan (a+b x)-\sqrt{2} \sqrt{\tan (a+b x)}+1\right)}{64 \sqrt{2} b c^2 d^2 \sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)}}-\frac{3 \sqrt{c \sec (a+b x)} \log \left(\tan (a+b x)+\sqrt{2} \sqrt{\tan (a+b x)}+1\right)}{64 \sqrt{2} b c^2 d^2 \sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)}}-\frac{c}{4 b d (c \sec (a+b x))^{5/2} (d \csc (a+b x))^{3/2}}+\frac{3}{16 b c d \sqrt{c \sec (a+b x)} (d \csc (a+b x))^{3/2}}",1,"-c/(4*b*d*(d*Csc[a + b*x])^(3/2)*(c*Sec[a + b*x])^(5/2)) + 3/(16*b*c*d*(d*Csc[a + b*x])^(3/2)*Sqrt[c*Sec[a + b*x]]) - (3*ArcTan[1 - Sqrt[2]*Sqrt[Tan[a + b*x]]]*Sqrt[c*Sec[a + b*x]])/(32*Sqrt[2]*b*c^2*d^2*Sqrt[d*Csc[a + b*x]]*Sqrt[Tan[a + b*x]]) + (3*ArcTan[1 + Sqrt[2]*Sqrt[Tan[a + b*x]]]*Sqrt[c*Sec[a + b*x]])/(32*Sqrt[2]*b*c^2*d^2*Sqrt[d*Csc[a + b*x]]*Sqrt[Tan[a + b*x]]) + (3*Log[1 - Sqrt[2]*Sqrt[Tan[a + b*x]] + Tan[a + b*x]]*Sqrt[c*Sec[a + b*x]])/(64*Sqrt[2]*b*c^2*d^2*Sqrt[d*Csc[a + b*x]]*Sqrt[Tan[a + b*x]]) - (3*Log[1 + Sqrt[2]*Sqrt[Tan[a + b*x]] + Tan[a + b*x]]*Sqrt[c*Sec[a + b*x]])/(64*Sqrt[2]*b*c^2*d^2*Sqrt[d*Csc[a + b*x]]*Sqrt[Tan[a + b*x]])","A",14,11,25,0.4400,1,"{2627, 2628, 2629, 3476, 329, 297, 1162, 617, 204, 1165, 628}"
271,1,33,0,0.0540944,"\int \frac{(d \csc (a+b x))^{9/2}}{(c \sec (a+b x))^{5/2}} \, dx","Int[(d*Csc[a + b*x])^(9/2)/(c*Sec[a + b*x])^(5/2),x]","-\frac{2 c d (d \csc (a+b x))^{7/2}}{7 b (c \sec (a+b x))^{7/2}}","-\frac{2 c d (d \csc (a+b x))^{7/2}}{7 b (c \sec (a+b x))^{7/2}}",1,"(-2*c*d*(d*Csc[a + b*x])^(7/2))/(7*b*(c*Sec[a + b*x])^(7/2))","A",1,1,25,0.04000,1,"{2619}"
272,1,135,0,0.2022317,"\int \frac{(d \csc (a+b x))^{7/2}}{(c \sec (a+b x))^{5/2}} \, dx","Int[(d*Csc[a + b*x])^(7/2)/(c*Sec[a + b*x])^(5/2),x]","\frac{6 d^4 E\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{5 b c^2 \sqrt{\sin (2 a+2 b x)} \sqrt{c \sec (a+b x)} \sqrt{d \csc (a+b x)}}+\frac{6 d^3 \sqrt{d \csc (a+b x)}}{5 b c (c \sec (a+b x))^{3/2}}-\frac{2 d (d \csc (a+b x))^{5/2}}{5 b c (c \sec (a+b x))^{3/2}}","\frac{6 d^4 E\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{5 b c^2 \sqrt{\sin (2 a+2 b x)} \sqrt{c \sec (a+b x)} \sqrt{d \csc (a+b x)}}+\frac{6 d^3 \sqrt{d \csc (a+b x)}}{5 b c (c \sec (a+b x))^{3/2}}-\frac{2 d (d \csc (a+b x))^{5/2}}{5 b c (c \sec (a+b x))^{3/2}}",1,"(6*d^3*Sqrt[d*Csc[a + b*x]])/(5*b*c*(c*Sec[a + b*x])^(3/2)) - (2*d*(d*Csc[a + b*x])^(5/2))/(5*b*c*(c*Sec[a + b*x])^(3/2)) + (6*d^4*EllipticE[a - Pi/4 + b*x, 2])/(5*b*c^2*Sqrt[d*Csc[a + b*x]]*Sqrt[c*Sec[a + b*x]]*Sqrt[Sin[2*a + 2*b*x]])","A",5,5,25,0.2000,1,"{2623, 2625, 2630, 2572, 2639}"
273,1,329,0,0.214465,"\int \frac{(d \csc (a+b x))^{5/2}}{(c \sec (a+b x))^{5/2}} \, dx","Int[(d*Csc[a + b*x])^(5/2)/(c*Sec[a + b*x])^(5/2),x]","\frac{d^2 \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (a+b x)}\right) \sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)}}{\sqrt{2} b c^2 \sqrt{c \sec (a+b x)}}-\frac{d^2 \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (a+b x)}+1\right) \sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)}}{\sqrt{2} b c^2 \sqrt{c \sec (a+b x)}}+\frac{d^2 \sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)} \log \left(\tan (a+b x)-\sqrt{2} \sqrt{\tan (a+b x)}+1\right)}{2 \sqrt{2} b c^2 \sqrt{c \sec (a+b x)}}-\frac{d^2 \sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)} \log \left(\tan (a+b x)+\sqrt{2} \sqrt{\tan (a+b x)}+1\right)}{2 \sqrt{2} b c^2 \sqrt{c \sec (a+b x)}}-\frac{2 d (d \csc (a+b x))^{3/2}}{3 b c (c \sec (a+b x))^{3/2}}","\frac{d^2 \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (a+b x)}\right) \sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)}}{\sqrt{2} b c^2 \sqrt{c \sec (a+b x)}}-\frac{d^2 \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (a+b x)}+1\right) \sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)}}{\sqrt{2} b c^2 \sqrt{c \sec (a+b x)}}+\frac{d^2 \sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)} \log \left(\tan (a+b x)-\sqrt{2} \sqrt{\tan (a+b x)}+1\right)}{2 \sqrt{2} b c^2 \sqrt{c \sec (a+b x)}}-\frac{d^2 \sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)} \log \left(\tan (a+b x)+\sqrt{2} \sqrt{\tan (a+b x)}+1\right)}{2 \sqrt{2} b c^2 \sqrt{c \sec (a+b x)}}-\frac{2 d (d \csc (a+b x))^{3/2}}{3 b c (c \sec (a+b x))^{3/2}}",1,"(-2*d*(d*Csc[a + b*x])^(3/2))/(3*b*c*(c*Sec[a + b*x])^(3/2)) + (d^2*ArcTan[1 - Sqrt[2]*Sqrt[Tan[a + b*x]]]*Sqrt[d*Csc[a + b*x]]*Sqrt[Tan[a + b*x]])/(Sqrt[2]*b*c^2*Sqrt[c*Sec[a + b*x]]) - (d^2*ArcTan[1 + Sqrt[2]*Sqrt[Tan[a + b*x]]]*Sqrt[d*Csc[a + b*x]]*Sqrt[Tan[a + b*x]])/(Sqrt[2]*b*c^2*Sqrt[c*Sec[a + b*x]]) + (d^2*Sqrt[d*Csc[a + b*x]]*Log[1 - Sqrt[2]*Sqrt[Tan[a + b*x]] + Tan[a + b*x]]*Sqrt[Tan[a + b*x]])/(2*Sqrt[2]*b*c^2*Sqrt[c*Sec[a + b*x]]) - (d^2*Sqrt[d*Csc[a + b*x]]*Log[1 + Sqrt[2]*Sqrt[Tan[a + b*x]] + Tan[a + b*x]]*Sqrt[Tan[a + b*x]])/(2*Sqrt[2]*b*c^2*Sqrt[c*Sec[a + b*x]])","A",13,10,25,0.4000,1,"{2623, 2629, 3476, 329, 211, 1165, 628, 1162, 617, 204}"
274,1,94,0,0.1469609,"\int \frac{(d \csc (a+b x))^{3/2}}{(c \sec (a+b x))^{5/2}} \, dx","Int[(d*Csc[a + b*x])^(3/2)/(c*Sec[a + b*x])^(5/2),x]","-\frac{3 d^2 E\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{b c^2 \sqrt{\sin (2 a+2 b x)} \sqrt{c \sec (a+b x)} \sqrt{d \csc (a+b x)}}-\frac{2 d \sqrt{d \csc (a+b x)}}{b c (c \sec (a+b x))^{3/2}}","-\frac{3 d^2 E\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{b c^2 \sqrt{\sin (2 a+2 b x)} \sqrt{c \sec (a+b x)} \sqrt{d \csc (a+b x)}}-\frac{2 d \sqrt{d \csc (a+b x)}}{b c (c \sec (a+b x))^{3/2}}",1,"(-2*d*Sqrt[d*Csc[a + b*x]])/(b*c*(c*Sec[a + b*x])^(3/2)) - (3*d^2*EllipticE[a - Pi/4 + b*x, 2])/(b*c^2*Sqrt[d*Csc[a + b*x]]*Sqrt[c*Sec[a + b*x]]*Sqrt[Sin[2*a + 2*b*x]])","A",4,4,25,0.1600,1,"{2623, 2630, 2572, 2639}"
275,1,322,0,0.2034369,"\int \frac{\sqrt{d \csc (a+b x)}}{(c \sec (a+b x))^{5/2}} \, dx","Int[Sqrt[d*Csc[a + b*x]]/(c*Sec[a + b*x])^(5/2),x]","-\frac{3 \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (a+b x)}\right) \sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)}}{4 \sqrt{2} b c^2 \sqrt{c \sec (a+b x)}}+\frac{3 \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (a+b x)}+1\right) \sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)}}{4 \sqrt{2} b c^2 \sqrt{c \sec (a+b x)}}-\frac{3 \sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)} \log \left(\tan (a+b x)-\sqrt{2} \sqrt{\tan (a+b x)}+1\right)}{8 \sqrt{2} b c^2 \sqrt{c \sec (a+b x)}}+\frac{3 \sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)} \log \left(\tan (a+b x)+\sqrt{2} \sqrt{\tan (a+b x)}+1\right)}{8 \sqrt{2} b c^2 \sqrt{c \sec (a+b x)}}+\frac{d}{2 b c (c \sec (a+b x))^{3/2} \sqrt{d \csc (a+b x)}}","-\frac{3 \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (a+b x)}\right) \sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)}}{4 \sqrt{2} b c^2 \sqrt{c \sec (a+b x)}}+\frac{3 \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (a+b x)}+1\right) \sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)}}{4 \sqrt{2} b c^2 \sqrt{c \sec (a+b x)}}-\frac{3 \sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)} \log \left(\tan (a+b x)-\sqrt{2} \sqrt{\tan (a+b x)}+1\right)}{8 \sqrt{2} b c^2 \sqrt{c \sec (a+b x)}}+\frac{3 \sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)} \log \left(\tan (a+b x)+\sqrt{2} \sqrt{\tan (a+b x)}+1\right)}{8 \sqrt{2} b c^2 \sqrt{c \sec (a+b x)}}+\frac{d}{2 b c (c \sec (a+b x))^{3/2} \sqrt{d \csc (a+b x)}}",1,"d/(2*b*c*Sqrt[d*Csc[a + b*x]]*(c*Sec[a + b*x])^(3/2)) - (3*ArcTan[1 - Sqrt[2]*Sqrt[Tan[a + b*x]]]*Sqrt[d*Csc[a + b*x]]*Sqrt[Tan[a + b*x]])/(4*Sqrt[2]*b*c^2*Sqrt[c*Sec[a + b*x]]) + (3*ArcTan[1 + Sqrt[2]*Sqrt[Tan[a + b*x]]]*Sqrt[d*Csc[a + b*x]]*Sqrt[Tan[a + b*x]])/(4*Sqrt[2]*b*c^2*Sqrt[c*Sec[a + b*x]]) - (3*Sqrt[d*Csc[a + b*x]]*Log[1 - Sqrt[2]*Sqrt[Tan[a + b*x]] + Tan[a + b*x]]*Sqrt[Tan[a + b*x]])/(8*Sqrt[2]*b*c^2*Sqrt[c*Sec[a + b*x]]) + (3*Sqrt[d*Csc[a + b*x]]*Log[1 + Sqrt[2]*Sqrt[Tan[a + b*x]] + Tan[a + b*x]]*Sqrt[Tan[a + b*x]])/(8*Sqrt[2]*b*c^2*Sqrt[c*Sec[a + b*x]])","A",13,10,25,0.4000,1,"{2628, 2629, 3476, 329, 211, 1165, 628, 1162, 617, 204}"
276,1,95,0,0.1418493,"\int \frac{1}{\sqrt{d \csc (a+b x)} (c \sec (a+b x))^{5/2}} \, dx","Int[1/(Sqrt[d*Csc[a + b*x]]*(c*Sec[a + b*x])^(5/2)),x]","\frac{E\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{2 b c^2 \sqrt{\sin (2 a+2 b x)} \sqrt{c \sec (a+b x)} \sqrt{d \csc (a+b x)}}+\frac{d}{3 b c (c \sec (a+b x))^{3/2} (d \csc (a+b x))^{3/2}}","\frac{E\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{2 b c^2 \sqrt{\sin (2 a+2 b x)} \sqrt{c \sec (a+b x)} \sqrt{d \csc (a+b x)}}+\frac{d}{3 b c (c \sec (a+b x))^{3/2} (d \csc (a+b x))^{3/2}}",1,"d/(3*b*c*(d*Csc[a + b*x])^(3/2)*(c*Sec[a + b*x])^(3/2)) + EllipticE[a - Pi/4 + b*x, 2]/(2*b*c^2*Sqrt[d*Csc[a + b*x]]*Sqrt[c*Sec[a + b*x]]*Sqrt[Sin[2*a + 2*b*x]])","A",4,4,25,0.1600,1,"{2628, 2630, 2572, 2639}"
277,1,371,0,0.2905644,"\int \frac{1}{(d \csc (a+b x))^{3/2} (c \sec (a+b x))^{5/2}} \, dx","Int[1/((d*Csc[a + b*x])^(3/2)*(c*Sec[a + b*x])^(5/2)),x]","-\frac{3 \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (a+b x)}\right) \sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)}}{32 \sqrt{2} b c^2 d^2 \sqrt{c \sec (a+b x)}}+\frac{3 \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (a+b x)}+1\right) \sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)}}{32 \sqrt{2} b c^2 d^2 \sqrt{c \sec (a+b x)}}-\frac{3 \sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)} \log \left(\tan (a+b x)-\sqrt{2} \sqrt{\tan (a+b x)}+1\right)}{64 \sqrt{2} b c^2 d^2 \sqrt{c \sec (a+b x)}}+\frac{3 \sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)} \log \left(\tan (a+b x)+\sqrt{2} \sqrt{\tan (a+b x)}+1\right)}{64 \sqrt{2} b c^2 d^2 \sqrt{c \sec (a+b x)}}-\frac{c}{4 b d (c \sec (a+b x))^{7/2} \sqrt{d \csc (a+b x)}}+\frac{1}{16 b c d (c \sec (a+b x))^{3/2} \sqrt{d \csc (a+b x)}}","-\frac{3 \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (a+b x)}\right) \sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)}}{32 \sqrt{2} b c^2 d^2 \sqrt{c \sec (a+b x)}}+\frac{3 \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (a+b x)}+1\right) \sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)}}{32 \sqrt{2} b c^2 d^2 \sqrt{c \sec (a+b x)}}-\frac{3 \sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)} \log \left(\tan (a+b x)-\sqrt{2} \sqrt{\tan (a+b x)}+1\right)}{64 \sqrt{2} b c^2 d^2 \sqrt{c \sec (a+b x)}}+\frac{3 \sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)} \log \left(\tan (a+b x)+\sqrt{2} \sqrt{\tan (a+b x)}+1\right)}{64 \sqrt{2} b c^2 d^2 \sqrt{c \sec (a+b x)}}-\frac{c}{4 b d (c \sec (a+b x))^{7/2} \sqrt{d \csc (a+b x)}}+\frac{1}{16 b c d (c \sec (a+b x))^{3/2} \sqrt{d \csc (a+b x)}}",1,"-c/(4*b*d*Sqrt[d*Csc[a + b*x]]*(c*Sec[a + b*x])^(7/2)) + 1/(16*b*c*d*Sqrt[d*Csc[a + b*x]]*(c*Sec[a + b*x])^(3/2)) - (3*ArcTan[1 - Sqrt[2]*Sqrt[Tan[a + b*x]]]*Sqrt[d*Csc[a + b*x]]*Sqrt[Tan[a + b*x]])/(32*Sqrt[2]*b*c^2*d^2*Sqrt[c*Sec[a + b*x]]) + (3*ArcTan[1 + Sqrt[2]*Sqrt[Tan[a + b*x]]]*Sqrt[d*Csc[a + b*x]]*Sqrt[Tan[a + b*x]])/(32*Sqrt[2]*b*c^2*d^2*Sqrt[c*Sec[a + b*x]]) - (3*Sqrt[d*Csc[a + b*x]]*Log[1 - Sqrt[2]*Sqrt[Tan[a + b*x]] + Tan[a + b*x]]*Sqrt[Tan[a + b*x]])/(64*Sqrt[2]*b*c^2*d^2*Sqrt[c*Sec[a + b*x]]) + (3*Sqrt[d*Csc[a + b*x]]*Log[1 + Sqrt[2]*Sqrt[Tan[a + b*x]] + Tan[a + b*x]]*Sqrt[Tan[a + b*x]])/(64*Sqrt[2]*b*c^2*d^2*Sqrt[c*Sec[a + b*x]])","A",14,11,25,0.4400,1,"{2627, 2628, 2629, 3476, 329, 211, 1165, 628, 1162, 617, 204}"
278,1,135,0,0.2055755,"\int \frac{1}{(d \csc (a+b x))^{5/2} (c \sec (a+b x))^{5/2}} \, dx","Int[1/((d*Csc[a + b*x])^(5/2)*(c*Sec[a + b*x])^(5/2)),x]","\frac{3 E\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{20 b c^2 d^2 \sqrt{\sin (2 a+2 b x)} \sqrt{c \sec (a+b x)} \sqrt{d \csc (a+b x)}}-\frac{c}{5 b d (c \sec (a+b x))^{7/2} (d \csc (a+b x))^{3/2}}+\frac{1}{10 b c d (c \sec (a+b x))^{3/2} (d \csc (a+b x))^{3/2}}","\frac{3 E\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{20 b c^2 d^2 \sqrt{\sin (2 a+2 b x)} \sqrt{c \sec (a+b x)} \sqrt{d \csc (a+b x)}}-\frac{c}{5 b d (c \sec (a+b x))^{7/2} (d \csc (a+b x))^{3/2}}+\frac{1}{10 b c d (c \sec (a+b x))^{3/2} (d \csc (a+b x))^{3/2}}",1,"-c/(5*b*d*(d*Csc[a + b*x])^(3/2)*(c*Sec[a + b*x])^(7/2)) + 1/(10*b*c*d*(d*Csc[a + b*x])^(3/2)*(c*Sec[a + b*x])^(3/2)) + (3*EllipticE[a - Pi/4 + b*x, 2])/(20*b*c^2*d^2*Sqrt[d*Csc[a + b*x]]*Sqrt[c*Sec[a + b*x]]*Sqrt[Sin[2*a + 2*b*x]])","A",5,5,25,0.2000,1,"{2627, 2628, 2630, 2572, 2639}"
279,1,406,0,0.3895987,"\int \frac{1}{(d \csc (a+b x))^{7/2} (c \sec (a+b x))^{5/2}} \, dx","Int[1/((d*Csc[a + b*x])^(7/2)*(c*Sec[a + b*x])^(5/2)),x]","-\frac{5 \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (a+b x)}\right) \sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)}}{128 \sqrt{2} b c^2 d^4 \sqrt{c \sec (a+b x)}}+\frac{5 \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (a+b x)}+1\right) \sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)}}{128 \sqrt{2} b c^2 d^4 \sqrt{c \sec (a+b x)}}-\frac{5 \sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)} \log \left(\tan (a+b x)-\sqrt{2} \sqrt{\tan (a+b x)}+1\right)}{256 \sqrt{2} b c^2 d^4 \sqrt{c \sec (a+b x)}}+\frac{5 \sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)} \log \left(\tan (a+b x)+\sqrt{2} \sqrt{\tan (a+b x)}+1\right)}{256 \sqrt{2} b c^2 d^4 \sqrt{c \sec (a+b x)}}-\frac{5 c}{48 b d^3 (c \sec (a+b x))^{7/2} \sqrt{d \csc (a+b x)}}+\frac{5}{192 b c d^3 (c \sec (a+b x))^{3/2} \sqrt{d \csc (a+b x)}}-\frac{c}{6 b d (c \sec (a+b x))^{7/2} (d \csc (a+b x))^{5/2}}","-\frac{5 \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (a+b x)}\right) \sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)}}{128 \sqrt{2} b c^2 d^4 \sqrt{c \sec (a+b x)}}+\frac{5 \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (a+b x)}+1\right) \sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)}}{128 \sqrt{2} b c^2 d^4 \sqrt{c \sec (a+b x)}}-\frac{5 \sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)} \log \left(\tan (a+b x)-\sqrt{2} \sqrt{\tan (a+b x)}+1\right)}{256 \sqrt{2} b c^2 d^4 \sqrt{c \sec (a+b x)}}+\frac{5 \sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)} \log \left(\tan (a+b x)+\sqrt{2} \sqrt{\tan (a+b x)}+1\right)}{256 \sqrt{2} b c^2 d^4 \sqrt{c \sec (a+b x)}}-\frac{5 c}{48 b d^3 (c \sec (a+b x))^{7/2} \sqrt{d \csc (a+b x)}}+\frac{5}{192 b c d^3 (c \sec (a+b x))^{3/2} \sqrt{d \csc (a+b x)}}-\frac{c}{6 b d (c \sec (a+b x))^{7/2} (d \csc (a+b x))^{5/2}}",1,"-c/(6*b*d*(d*Csc[a + b*x])^(5/2)*(c*Sec[a + b*x])^(7/2)) - (5*c)/(48*b*d^3*Sqrt[d*Csc[a + b*x]]*(c*Sec[a + b*x])^(7/2)) + 5/(192*b*c*d^3*Sqrt[d*Csc[a + b*x]]*(c*Sec[a + b*x])^(3/2)) - (5*ArcTan[1 - Sqrt[2]*Sqrt[Tan[a + b*x]]]*Sqrt[d*Csc[a + b*x]]*Sqrt[Tan[a + b*x]])/(128*Sqrt[2]*b*c^2*d^4*Sqrt[c*Sec[a + b*x]]) + (5*ArcTan[1 + Sqrt[2]*Sqrt[Tan[a + b*x]]]*Sqrt[d*Csc[a + b*x]]*Sqrt[Tan[a + b*x]])/(128*Sqrt[2]*b*c^2*d^4*Sqrt[c*Sec[a + b*x]]) - (5*Sqrt[d*Csc[a + b*x]]*Log[1 - Sqrt[2]*Sqrt[Tan[a + b*x]] + Tan[a + b*x]]*Sqrt[Tan[a + b*x]])/(256*Sqrt[2]*b*c^2*d^4*Sqrt[c*Sec[a + b*x]]) + (5*Sqrt[d*Csc[a + b*x]]*Log[1 + Sqrt[2]*Sqrt[Tan[a + b*x]] + Tan[a + b*x]]*Sqrt[Tan[a + b*x]])/(256*Sqrt[2]*b*c^2*d^4*Sqrt[c*Sec[a + b*x]])","A",15,11,25,0.4400,1,"{2627, 2628, 2629, 3476, 329, 211, 1165, 628, 1162, 617, 204}"
280,1,81,0,0.073849,"\int \csc ^n(e+f x) \sec ^m(e+f x) \, dx","Int[Csc[e + f*x]^n*Sec[e + f*x]^m,x]","\frac{\cos ^2(e+f x)^{\frac{m+1}{2}} \sec ^{m+1}(e+f x) \csc ^{n-1}(e+f x) \, _2F_1\left(\frac{m+1}{2},\frac{1-n}{2};\frac{3-n}{2};\sin ^2(e+f x)\right)}{f (1-n)}","\frac{\cos ^2(e+f x)^{\frac{m+1}{2}} \sec ^{m+1}(e+f x) \csc ^{n-1}(e+f x) \, _2F_1\left(\frac{m+1}{2},\frac{1-n}{2};\frac{3-n}{2};\sin ^2(e+f x)\right)}{f (1-n)}",1,"((Cos[e + f*x]^2)^((1 + m)/2)*Csc[e + f*x]^(-1 + n)*Hypergeometric2F1[(1 + m)/2, (1 - n)/2, (3 - n)/2, Sin[e + f*x]^2]*Sec[e + f*x]^(1 + m))/(f*(1 - n))","A",2,2,17,0.1176,1,"{2631, 2577}"
281,1,86,0,0.0864896,"\int \csc ^n(e+f x) (a \sec (e+f x))^m \, dx","Int[Csc[e + f*x]^n*(a*Sec[e + f*x])^m,x]","\frac{\cos ^2(e+f x)^{\frac{m+1}{2}} \csc ^{n-1}(e+f x) (a \sec (e+f x))^{m+1} \, _2F_1\left(\frac{m+1}{2},\frac{1-n}{2};\frac{3-n}{2};\sin ^2(e+f x)\right)}{a f (1-n)}","\frac{\cos ^2(e+f x)^{\frac{m+1}{2}} \csc ^{n-1}(e+f x) (a \sec (e+f x))^{m+1} \, _2F_1\left(\frac{m+1}{2},\frac{1-n}{2};\frac{3-n}{2};\sin ^2(e+f x)\right)}{a f (1-n)}",1,"((Cos[e + f*x]^2)^((1 + m)/2)*Csc[e + f*x]^(-1 + n)*Hypergeometric2F1[(1 + m)/2, (1 - n)/2, (3 - n)/2, Sin[e + f*x]^2]*(a*Sec[e + f*x])^(1 + m))/(a*f*(1 - n))","A",2,2,19,0.1053,1,"{2631, 2577}"
282,1,84,0,0.0868945,"\int (b \csc (e+f x))^n \sec ^m(e+f x) \, dx","Int[(b*Csc[e + f*x])^n*Sec[e + f*x]^m,x]","\frac{b \cos ^2(e+f x)^{\frac{m+1}{2}} \sec ^{m+1}(e+f x) (b \csc (e+f x))^{n-1} \, _2F_1\left(\frac{m+1}{2},\frac{1-n}{2};\frac{3-n}{2};\sin ^2(e+f x)\right)}{f (1-n)}","\frac{b \cos ^2(e+f x)^{\frac{m+1}{2}} \sec ^{m+1}(e+f x) (b \csc (e+f x))^{n-1} \, _2F_1\left(\frac{m+1}{2},\frac{1-n}{2};\frac{3-n}{2};\sin ^2(e+f x)\right)}{f (1-n)}",1,"(b*(Cos[e + f*x]^2)^((1 + m)/2)*(b*Csc[e + f*x])^(-1 + n)*Hypergeometric2F1[(1 + m)/2, (1 - n)/2, (3 - n)/2, Sin[e + f*x]^2]*Sec[e + f*x]^(1 + m))/(f*(1 - n))","A",2,2,19,0.1053,1,"{2631, 2577}"
283,1,89,0,0.0942339,"\int (b \csc (e+f x))^n (a \sec (e+f x))^m \, dx","Int[(b*Csc[e + f*x])^n*(a*Sec[e + f*x])^m,x]","\frac{b \cos ^2(e+f x)^{\frac{m+1}{2}} (a \sec (e+f x))^{m+1} (b \csc (e+f x))^{n-1} \, _2F_1\left(\frac{m+1}{2},\frac{1-n}{2};\frac{3-n}{2};\sin ^2(e+f x)\right)}{a f (1-n)}","\frac{b \cos ^2(e+f x)^{\frac{m+1}{2}} (a \sec (e+f x))^{m+1} (b \csc (e+f x))^{n-1} \, _2F_1\left(\frac{m+1}{2},\frac{1-n}{2};\frac{3-n}{2};\sin ^2(e+f x)\right)}{a f (1-n)}",1,"(b*(Cos[e + f*x]^2)^((1 + m)/2)*(b*Csc[e + f*x])^(-1 + n)*Hypergeometric2F1[(1 + m)/2, (1 - n)/2, (3 - n)/2, Sin[e + f*x]^2]*(a*Sec[e + f*x])^(1 + m))/(a*f*(1 - n))","A",2,2,21,0.09524,1,"{2631, 2577}"
284,1,48,0,0.0508996,"\int (b \csc (e+f x))^n \sec ^5(e+f x) \, dx","Int[(b*Csc[e + f*x])^n*Sec[e + f*x]^5,x]","\frac{(b \csc (e+f x))^{n+5} \, _2F_1\left(3,\frac{n+5}{2};\frac{n+7}{2};\csc ^2(e+f x)\right)}{b^5 f (n+5)}","\frac{(b \csc (e+f x))^{n+5} \, _2F_1\left(3,\frac{n+5}{2};\frac{n+7}{2};\csc ^2(e+f x)\right)}{b^5 f (n+5)}",1,"((b*Csc[e + f*x])^(5 + n)*Hypergeometric2F1[3, (5 + n)/2, (7 + n)/2, Csc[e + f*x]^2])/(b^5*f*(5 + n))","A",2,2,19,0.1053,1,"{2621, 364}"
285,1,49,0,0.0510699,"\int (b \csc (e+f x))^n \sec ^3(e+f x) \, dx","Int[(b*Csc[e + f*x])^n*Sec[e + f*x]^3,x]","-\frac{(b \csc (e+f x))^{n+3} \, _2F_1\left(2,\frac{n+3}{2};\frac{n+5}{2};\csc ^2(e+f x)\right)}{b^3 f (n+3)}","-\frac{(b \csc (e+f x))^{n+3} \, _2F_1\left(2,\frac{n+3}{2};\frac{n+5}{2};\csc ^2(e+f x)\right)}{b^3 f (n+3)}",1,"-(((b*Csc[e + f*x])^(3 + n)*Hypergeometric2F1[2, (3 + n)/2, (5 + n)/2, Csc[e + f*x]^2])/(b^3*f*(3 + n)))","A",2,2,19,0.1053,1,"{2621, 364}"
286,1,48,0,0.0355939,"\int (b \csc (e+f x))^n \sec (e+f x) \, dx","Int[(b*Csc[e + f*x])^n*Sec[e + f*x],x]","\frac{(b \csc (e+f x))^{n+1} \, _2F_1\left(1,\frac{n+1}{2};\frac{n+3}{2};\csc ^2(e+f x)\right)}{b f (n+1)}","\frac{(b \csc (e+f x))^{n+1} \, _2F_1\left(1,\frac{n+1}{2};\frac{n+3}{2};\csc ^2(e+f x)\right)}{b f (n+1)}",1,"((b*Csc[e + f*x])^(1 + n)*Hypergeometric2F1[1, (1 + n)/2, (3 + n)/2, Csc[e + f*x]^2])/(b*f*(1 + n))","A",2,2,17,0.1176,1,"{2621, 364}"
287,1,24,0,0.0335722,"\int \cos (e+f x) (b \csc (e+f x))^n \, dx","Int[Cos[e + f*x]*(b*Csc[e + f*x])^n,x]","\frac{b (b \csc (e+f x))^{n-1}}{f (1-n)}","\frac{b (b \csc (e+f x))^{n-1}}{f (1-n)}",1,"(b*(b*Csc[e + f*x])^(-1 + n))/(f*(1 - n))","A",2,2,17,0.1176,1,"{2621, 30}"
288,1,52,0,0.0516861,"\int \cos ^3(e+f x) (b \csc (e+f x))^n \, dx","Int[Cos[e + f*x]^3*(b*Csc[e + f*x])^n,x]","\frac{b (b \csc (e+f x))^{n-1}}{f (1-n)}-\frac{b^3 (b \csc (e+f x))^{n-3}}{f (3-n)}","\frac{b (b \csc (e+f x))^{n-1}}{f (1-n)}-\frac{b^3 (b \csc (e+f x))^{n-3}}{f (3-n)}",1,"-((b^3*(b*Csc[e + f*x])^(-3 + n))/(f*(3 - n))) + (b*(b*Csc[e + f*x])^(-1 + n))/(f*(1 - n))","A",3,2,19,0.1053,1,"{2621, 14}"
289,1,78,0,0.0642744,"\int \cos ^5(e+f x) (b \csc (e+f x))^n \, dx","Int[Cos[e + f*x]^5*(b*Csc[e + f*x])^n,x]","\frac{b^5 (b \csc (e+f x))^{n-5}}{f (5-n)}-\frac{2 b^3 (b \csc (e+f x))^{n-3}}{f (3-n)}+\frac{b (b \csc (e+f x))^{n-1}}{f (1-n)}","\frac{b^5 (b \csc (e+f x))^{n-5}}{f (5-n)}-\frac{2 b^3 (b \csc (e+f x))^{n-3}}{f (3-n)}+\frac{b (b \csc (e+f x))^{n-1}}{f (1-n)}",1,"(b^5*(b*Csc[e + f*x])^(-5 + n))/(f*(5 - n)) - (2*b^3*(b*Csc[e + f*x])^(-3 + n))/(f*(3 - n)) + (b*(b*Csc[e + f*x])^(-1 + n))/(f*(1 - n))","A",3,2,19,0.1053,1,"{2621, 270}"
290,1,72,0,0.0798404,"\int (b \csc (e+f x))^n \sec ^6(e+f x) \, dx","Int[(b*Csc[e + f*x])^n*Sec[e + f*x]^6,x]","\frac{b \sqrt{\cos ^2(e+f x)} \sec (e+f x) (b \csc (e+f x))^{n-1} \, _2F_1\left(\frac{7}{2},\frac{1-n}{2};\frac{3-n}{2};\sin ^2(e+f x)\right)}{f (1-n)}","\frac{b \sqrt{\cos ^2(e+f x)} \sec (e+f x) (b \csc (e+f x))^{n-1} \, _2F_1\left(\frac{7}{2},\frac{1-n}{2};\frac{3-n}{2};\sin ^2(e+f x)\right)}{f (1-n)}",1,"(b*Sqrt[Cos[e + f*x]^2]*(b*Csc[e + f*x])^(-1 + n)*Hypergeometric2F1[7/2, (1 - n)/2, (3 - n)/2, Sin[e + f*x]^2]*Sec[e + f*x])/(f*(1 - n))","A",2,2,19,0.1053,1,"{2631, 2577}"
291,1,72,0,0.0794841,"\int (b \csc (e+f x))^n \sec ^4(e+f x) \, dx","Int[(b*Csc[e + f*x])^n*Sec[e + f*x]^4,x]","\frac{b \sqrt{\cos ^2(e+f x)} \sec (e+f x) (b \csc (e+f x))^{n-1} \, _2F_1\left(\frac{5}{2},\frac{1-n}{2};\frac{3-n}{2};\sin ^2(e+f x)\right)}{f (1-n)}","\frac{b \sqrt{\cos ^2(e+f x)} \sec (e+f x) (b \csc (e+f x))^{n-1} \, _2F_1\left(\frac{5}{2},\frac{1-n}{2};\frac{3-n}{2};\sin ^2(e+f x)\right)}{f (1-n)}",1,"(b*Sqrt[Cos[e + f*x]^2]*(b*Csc[e + f*x])^(-1 + n)*Hypergeometric2F1[5/2, (1 - n)/2, (3 - n)/2, Sin[e + f*x]^2]*Sec[e + f*x])/(f*(1 - n))","A",2,2,19,0.1053,1,"{2631, 2577}"
292,1,72,0,0.0782317,"\int (b \csc (e+f x))^n \sec ^2(e+f x) \, dx","Int[(b*Csc[e + f*x])^n*Sec[e + f*x]^2,x]","\frac{b \sqrt{\cos ^2(e+f x)} \sec (e+f x) (b \csc (e+f x))^{n-1} \, _2F_1\left(\frac{3}{2},\frac{1-n}{2};\frac{3-n}{2};\sin ^2(e+f x)\right)}{f (1-n)}","\frac{b \sqrt{\cos ^2(e+f x)} \sec (e+f x) (b \csc (e+f x))^{n-1} \, _2F_1\left(\frac{3}{2},\frac{1-n}{2};\frac{3-n}{2};\sin ^2(e+f x)\right)}{f (1-n)}",1,"(b*Sqrt[Cos[e + f*x]^2]*(b*Csc[e + f*x])^(-1 + n)*Hypergeometric2F1[3/2, (1 - n)/2, (3 - n)/2, Sin[e + f*x]^2]*Sec[e + f*x])/(f*(1 - n))","A",2,2,19,0.1053,1,"{2631, 2577}"
293,1,72,0,0.030244,"\int (b \csc (e+f x))^n \, dx","Int[(b*Csc[e + f*x])^n,x]","\frac{b \cos (e+f x) (b \csc (e+f x))^{n-1} \, _2F_1\left(\frac{1}{2},\frac{1-n}{2};\frac{3-n}{2};\sin ^2(e+f x)\right)}{f (1-n) \sqrt{\cos ^2(e+f x)}}","\frac{b \cos (e+f x) (b \csc (e+f x))^{n-1} \, _2F_1\left(\frac{1}{2},\frac{1-n}{2};\frac{3-n}{2};\sin ^2(e+f x)\right)}{f (1-n) \sqrt{\cos ^2(e+f x)}}",1,"(b*Cos[e + f*x]*(b*Csc[e + f*x])^(-1 + n)*Hypergeometric2F1[1/2, (1 - n)/2, (3 - n)/2, Sin[e + f*x]^2])/(f*(1 - n)*Sqrt[Cos[e + f*x]^2])","A",2,2,10,0.2000,1,"{3772, 2643}"
294,1,72,0,0.0796031,"\int \cos ^2(e+f x) (b \csc (e+f x))^n \, dx","Int[Cos[e + f*x]^2*(b*Csc[e + f*x])^n,x]","\frac{b \cos (e+f x) (b \csc (e+f x))^{n-1} \, _2F_1\left(-\frac{1}{2},\frac{1-n}{2};\frac{3-n}{2};\sin ^2(e+f x)\right)}{f (1-n) \sqrt{\cos ^2(e+f x)}}","\frac{b \cos (e+f x) (b \csc (e+f x))^{n-1} \, _2F_1\left(-\frac{1}{2},\frac{1-n}{2};\frac{3-n}{2};\sin ^2(e+f x)\right)}{f (1-n) \sqrt{\cos ^2(e+f x)}}",1,"(b*Cos[e + f*x]*(b*Csc[e + f*x])^(-1 + n)*Hypergeometric2F1[-1/2, (1 - n)/2, (3 - n)/2, Sin[e + f*x]^2])/(f*(1 - n)*Sqrt[Cos[e + f*x]^2])","A",2,2,19,0.1053,1,"{2631, 2577}"
295,1,72,0,0.0763823,"\int \cos ^4(e+f x) (b \csc (e+f x))^n \, dx","Int[Cos[e + f*x]^4*(b*Csc[e + f*x])^n,x]","\frac{b \cos (e+f x) (b \csc (e+f x))^{n-1} \, _2F_1\left(-\frac{3}{2},\frac{1-n}{2};\frac{3-n}{2};\sin ^2(e+f x)\right)}{f (1-n) \sqrt{\cos ^2(e+f x)}}","\frac{b \cos (e+f x) (b \csc (e+f x))^{n-1} \, _2F_1\left(-\frac{3}{2},\frac{1-n}{2};\frac{3-n}{2};\sin ^2(e+f x)\right)}{f (1-n) \sqrt{\cos ^2(e+f x)}}",1,"(b*Cos[e + f*x]*(b*Csc[e + f*x])^(-1 + n)*Hypergeometric2F1[-3/2, (1 - n)/2, (3 - n)/2, Sin[e + f*x]^2])/(f*(1 - n)*Sqrt[Cos[e + f*x]^2])","A",2,2,19,0.1053,1,"{2631, 2577}"
296,1,81,0,0.1149235,"\int (b \csc (e+f x))^n (c \sec (e+f x))^{3/2} \, dx","Int[(b*Csc[e + f*x])^n*(c*Sec[e + f*x])^(3/2),x]","\frac{b \cos ^2(e+f x)^{5/4} (c \sec (e+f x))^{5/2} (b \csc (e+f x))^{n-1} \, _2F_1\left(\frac{5}{4},\frac{1-n}{2};\frac{3-n}{2};\sin ^2(e+f x)\right)}{c f (1-n)}","\frac{b \cos ^2(e+f x)^{5/4} (c \sec (e+f x))^{5/2} (b \csc (e+f x))^{n-1} \, _2F_1\left(\frac{5}{4},\frac{1-n}{2};\frac{3-n}{2};\sin ^2(e+f x)\right)}{c f (1-n)}",1,"(b*(Cos[e + f*x]^2)^(5/4)*(b*Csc[e + f*x])^(-1 + n)*Hypergeometric2F1[5/4, (1 - n)/2, (3 - n)/2, Sin[e + f*x]^2]*(c*Sec[e + f*x])^(5/2))/(c*f*(1 - n))","A",2,2,23,0.08696,1,"{2631, 2577}"
297,1,81,0,0.0971722,"\int (b \csc (e+f x))^n \sqrt{c \sec (e+f x)} \, dx","Int[(b*Csc[e + f*x])^n*Sqrt[c*Sec[e + f*x]],x]","\frac{b \cos ^2(e+f x)^{3/4} (c \sec (e+f x))^{3/2} (b \csc (e+f x))^{n-1} \, _2F_1\left(\frac{3}{4},\frac{1-n}{2};\frac{3-n}{2};\sin ^2(e+f x)\right)}{c f (1-n)}","\frac{b \cos ^2(e+f x)^{3/4} (c \sec (e+f x))^{3/2} (b \csc (e+f x))^{n-1} \, _2F_1\left(\frac{3}{4},\frac{1-n}{2};\frac{3-n}{2};\sin ^2(e+f x)\right)}{c f (1-n)}",1,"(b*(Cos[e + f*x]^2)^(3/4)*(b*Csc[e + f*x])^(-1 + n)*Hypergeometric2F1[3/4, (1 - n)/2, (3 - n)/2, Sin[e + f*x]^2]*(c*Sec[e + f*x])^(3/2))/(c*f*(1 - n))","A",2,2,23,0.08696,1,"{2631, 2577}"
298,1,81,0,0.0958881,"\int \frac{(b \csc (e+f x))^n}{\sqrt{c \sec (e+f x)}} \, dx","Int[(b*Csc[e + f*x])^n/Sqrt[c*Sec[e + f*x]],x]","\frac{b \sqrt[4]{\cos ^2(e+f x)} \sqrt{c \sec (e+f x)} (b \csc (e+f x))^{n-1} \, _2F_1\left(\frac{1}{4},\frac{1-n}{2};\frac{3-n}{2};\sin ^2(e+f x)\right)}{c f (1-n)}","\frac{b \sqrt[4]{\cos ^2(e+f x)} \sqrt{c \sec (e+f x)} (b \csc (e+f x))^{n-1} \, _2F_1\left(\frac{1}{4},\frac{1-n}{2};\frac{3-n}{2};\sin ^2(e+f x)\right)}{c f (1-n)}",1,"(b*(Cos[e + f*x]^2)^(1/4)*(b*Csc[e + f*x])^(-1 + n)*Hypergeometric2F1[1/4, (1 - n)/2, (3 - n)/2, Sin[e + f*x]^2]*Sqrt[c*Sec[e + f*x]])/(c*f*(1 - n))","A",2,2,23,0.08696,1,"{2631, 2577}"
299,1,81,0,0.1072549,"\int \frac{(b \csc (e+f x))^n}{(c \sec (e+f x))^{3/2}} \, dx","Int[(b*Csc[e + f*x])^n/(c*Sec[e + f*x])^(3/2),x]","\frac{b (b \csc (e+f x))^{n-1} \, _2F_1\left(-\frac{1}{4},\frac{1-n}{2};\frac{3-n}{2};\sin ^2(e+f x)\right)}{c f (1-n) \sqrt[4]{\cos ^2(e+f x)} \sqrt{c \sec (e+f x)}}","\frac{b (b \csc (e+f x))^{n-1} \, _2F_1\left(-\frac{1}{4},\frac{1-n}{2};\frac{3-n}{2};\sin ^2(e+f x)\right)}{c f (1-n) \sqrt[4]{\cos ^2(e+f x)} \sqrt{c \sec (e+f x)}}",1,"(b*(b*Csc[e + f*x])^(-1 + n)*Hypergeometric2F1[-1/4, (1 - n)/2, (3 - n)/2, Sin[e + f*x]^2])/(c*f*(1 - n)*(Cos[e + f*x]^2)^(1/4)*Sqrt[c*Sec[e + f*x]])","A",2,2,23,0.08696,1,"{2631, 2577}"