1,1,105,0,0.1954344,"\int \sec (e+f x) (a+a \sec (e+f x)) (c-c \sec (e+f x))^4 \, dx","Int[Sec[e + f*x]*(a + a*Sec[e + f*x])*(c - c*Sec[e + f*x])^4,x]","\frac{a c^4 \tan ^5(e+f x)}{5 f}+\frac{4 a c^4 \tan ^3(e+f x)}{3 f}+\frac{7 a c^4 \tanh ^{-1}(\sin (e+f x))}{8 f}-\frac{3 a c^4 \tan (e+f x) \sec ^3(e+f x)}{4 f}-\frac{a c^4 \tan (e+f x) \sec (e+f x)}{8 f}","\frac{a c^4 \tan ^5(e+f x)}{5 f}+\frac{4 a c^4 \tan ^3(e+f x)}{3 f}+\frac{7 a c^4 \tanh ^{-1}(\sin (e+f x))}{8 f}-\frac{3 a c^4 \tan (e+f x) \sec ^3(e+f x)}{4 f}-\frac{a c^4 \tan (e+f x) \sec (e+f x)}{8 f}",1,"(7*a*c^4*ArcTanh[Sin[e + f*x]])/(8*f) - (a*c^4*Sec[e + f*x]*Tan[e + f*x])/(8*f) - (3*a*c^4*Sec[e + f*x]^3*Tan[e + f*x])/(4*f) + (4*a*c^4*Tan[e + f*x]^3)/(3*f) + (a*c^4*Tan[e + f*x]^5)/(5*f)","A",12,7,30,0.2333,1,"{3958, 2611, 3770, 2607, 30, 3768, 14}"
2,1,86,0,0.1573869,"\int \sec (e+f x) (a+a \sec (e+f x)) (c-c \sec (e+f x))^3 \, dx","Int[Sec[e + f*x]*(a + a*Sec[e + f*x])*(c - c*Sec[e + f*x])^3,x]","\frac{2 a c^3 \tan ^3(e+f x)}{3 f}+\frac{5 a c^3 \tanh ^{-1}(\sin (e+f x))}{8 f}-\frac{a c^3 \tan (e+f x) \sec ^3(e+f x)}{4 f}-\frac{3 a c^3 \tan (e+f x) \sec (e+f x)}{8 f}","\frac{2 a c^3 \tan ^3(e+f x)}{3 f}+\frac{5 a c^3 \tanh ^{-1}(\sin (e+f x))}{8 f}-\frac{a c^3 \tan (e+f x) \sec ^3(e+f x)}{4 f}-\frac{3 a c^3 \tan (e+f x) \sec (e+f x)}{8 f}",1,"(5*a*c^3*ArcTanh[Sin[e + f*x]])/(8*f) - (3*a*c^3*Sec[e + f*x]*Tan[e + f*x])/(8*f) - (a*c^3*Sec[e + f*x]^3*Tan[e + f*x])/(4*f) + (2*a*c^3*Tan[e + f*x]^3)/(3*f)","A",9,6,30,0.2000,1,"{3958, 2611, 3770, 2607, 30, 3768}"
3,1,61,0,0.1042848,"\int \sec (e+f x) (a+a \sec (e+f x)) (c-c \sec (e+f x))^2 \, dx","Int[Sec[e + f*x]*(a + a*Sec[e + f*x])*(c - c*Sec[e + f*x])^2,x]","\frac{a c^2 \tan ^3(e+f x)}{3 f}+\frac{a c^2 \tanh ^{-1}(\sin (e+f x))}{2 f}-\frac{a c^2 \tan (e+f x) \sec (e+f x)}{2 f}","\frac{a c^2 \tan ^3(e+f x)}{3 f}+\frac{a c^2 \tanh ^{-1}(\sin (e+f x))}{2 f}-\frac{a c^2 \tan (e+f x) \sec (e+f x)}{2 f}",1,"(a*c^2*ArcTanh[Sin[e + f*x]])/(2*f) - (a*c^2*Sec[e + f*x]*Tan[e + f*x])/(2*f) + (a*c^2*Tan[e + f*x]^3)/(3*f)","A",6,5,30,0.1667,1,"{3958, 2611, 3770, 2607, 30}"
4,1,38,0,0.0497687,"\int \sec (e+f x) (a+a \sec (e+f x)) (c-c \sec (e+f x)) \, dx","Int[Sec[e + f*x]*(a + a*Sec[e + f*x])*(c - c*Sec[e + f*x]),x]","\frac{a c \tanh ^{-1}(\sin (e+f x))}{2 f}-\frac{a c \tan (e+f x) \sec (e+f x)}{2 f}","\frac{a c \tanh ^{-1}(\sin (e+f x))}{2 f}-\frac{a c \tan (e+f x) \sec (e+f x)}{2 f}",1,"(a*c*ArcTanh[Sin[e + f*x]])/(2*f) - (a*c*Sec[e + f*x]*Tan[e + f*x])/(2*f)","A",3,3,28,0.1071,1,"{3958, 2611, 3770}"
5,1,42,0,0.0536762,"\int \frac{\sec (e+f x) (a+a \sec (e+f x))}{c-c \sec (e+f x)} \, dx","Int[(Sec[e + f*x]*(a + a*Sec[e + f*x]))/(c - c*Sec[e + f*x]),x]","-\frac{a \tanh ^{-1}(\sin (e+f x))}{c f}-\frac{2 a \tan (e+f x)}{f (c-c \sec (e+f x))}","-\frac{a \tanh ^{-1}(\sin (e+f x))}{c f}-\frac{2 a \tan (e+f x)}{f (c-c \sec (e+f x))}",1,"-((a*ArcTanh[Sin[e + f*x]])/(c*f)) - (2*a*Tan[e + f*x])/(f*(c - c*Sec[e + f*x]))","A",2,2,30,0.06667,1,"{3957, 3770}"
6,1,36,0,0.0502279,"\int \frac{\sec (e+f x) (a+a \sec (e+f x))}{(c-c \sec (e+f x))^2} \, dx","Int[(Sec[e + f*x]*(a + a*Sec[e + f*x]))/(c - c*Sec[e + f*x])^2,x]","-\frac{\tan (e+f x) (a \sec (e+f x)+a)}{3 f (c-c \sec (e+f x))^2}","-\frac{\tan (e+f x) (a \sec (e+f x)+a)}{3 f (c-c \sec (e+f x))^2}",1,"-((a + a*Sec[e + f*x])*Tan[e + f*x])/(3*f*(c - c*Sec[e + f*x])^2)","A",1,1,30,0.03333,1,"{3950}"
7,1,76,0,0.0980012,"\int \frac{\sec (e+f x) (a+a \sec (e+f x))}{(c-c \sec (e+f x))^3} \, dx","Int[(Sec[e + f*x]*(a + a*Sec[e + f*x]))/(c - c*Sec[e + f*x])^3,x]","-\frac{\tan (e+f x) (a \sec (e+f x)+a)}{15 c f (c-c \sec (e+f x))^2}-\frac{\tan (e+f x) (a \sec (e+f x)+a)}{5 f (c-c \sec (e+f x))^3}","-\frac{\tan (e+f x) (a \sec (e+f x)+a)}{15 c f (c-c \sec (e+f x))^2}-\frac{\tan (e+f x) (a \sec (e+f x)+a)}{5 f (c-c \sec (e+f x))^3}",1,"-((a + a*Sec[e + f*x])*Tan[e + f*x])/(5*f*(c - c*Sec[e + f*x])^3) - ((a + a*Sec[e + f*x])*Tan[e + f*x])/(15*c*f*(c - c*Sec[e + f*x])^2)","A",2,2,30,0.06667,1,"{3951, 3950}"
8,1,116,0,0.1503239,"\int \frac{\sec (e+f x) (a+a \sec (e+f x))}{(c-c \sec (e+f x))^4} \, dx","Int[(Sec[e + f*x]*(a + a*Sec[e + f*x]))/(c - c*Sec[e + f*x])^4,x]","-\frac{2 \tan (e+f x) (a \sec (e+f x)+a)}{105 f \left(c^2-c^2 \sec (e+f x)\right)^2}-\frac{2 \tan (e+f x) (a \sec (e+f x)+a)}{35 c f (c-c \sec (e+f x))^3}-\frac{\tan (e+f x) (a \sec (e+f x)+a)}{7 f (c-c \sec (e+f x))^4}","-\frac{2 \tan (e+f x) (a \sec (e+f x)+a)}{105 f \left(c^2-c^2 \sec (e+f x)\right)^2}-\frac{2 \tan (e+f x) (a \sec (e+f x)+a)}{35 c f (c-c \sec (e+f x))^3}-\frac{\tan (e+f x) (a \sec (e+f x)+a)}{7 f (c-c \sec (e+f x))^4}",1,"-((a + a*Sec[e + f*x])*Tan[e + f*x])/(7*f*(c - c*Sec[e + f*x])^4) - (2*(a + a*Sec[e + f*x])*Tan[e + f*x])/(35*c*f*(c - c*Sec[e + f*x])^3) - (2*(a + a*Sec[e + f*x])*Tan[e + f*x])/(105*f*(c^2 - c^2*Sec[e + f*x])^2)","A",3,2,30,0.06667,1,"{3951, 3950}"
9,1,158,0,0.2097732,"\int \frac{\sec (e+f x) (a+a \sec (e+f x))}{(c-c \sec (e+f x))^5} \, dx","Int[(Sec[e + f*x]*(a + a*Sec[e + f*x]))/(c - c*Sec[e + f*x])^5,x]","-\frac{2 \tan (e+f x) (a \sec (e+f x)+a)}{315 c f \left(c^2-c^2 \sec (e+f x)\right)^2}-\frac{2 \tan (e+f x) (a \sec (e+f x)+a)}{105 c^2 f (c-c \sec (e+f x))^3}-\frac{\tan (e+f x) (a \sec (e+f x)+a)}{21 c f (c-c \sec (e+f x))^4}-\frac{\tan (e+f x) (a \sec (e+f x)+a)}{9 f (c-c \sec (e+f x))^5}","-\frac{2 \tan (e+f x) (a \sec (e+f x)+a)}{315 c f \left(c^2-c^2 \sec (e+f x)\right)^2}-\frac{2 \tan (e+f x) (a \sec (e+f x)+a)}{105 c^2 f (c-c \sec (e+f x))^3}-\frac{\tan (e+f x) (a \sec (e+f x)+a)}{21 c f (c-c \sec (e+f x))^4}-\frac{\tan (e+f x) (a \sec (e+f x)+a)}{9 f (c-c \sec (e+f x))^5}",1,"-((a + a*Sec[e + f*x])*Tan[e + f*x])/(9*f*(c - c*Sec[e + f*x])^5) - ((a + a*Sec[e + f*x])*Tan[e + f*x])/(21*c*f*(c - c*Sec[e + f*x])^4) - (2*(a + a*Sec[e + f*x])*Tan[e + f*x])/(105*c^2*f*(c - c*Sec[e + f*x])^3) - (2*(a + a*Sec[e + f*x])*Tan[e + f*x])/(315*c*f*(c^2 - c^2*Sec[e + f*x])^2)","A",4,2,30,0.06667,1,"{3951, 3950}"
10,1,171,0,0.273989,"\int \sec (e+f x) (a+a \sec (e+f x))^2 (c-c \sec (e+f x))^5 \, dx","Int[Sec[e + f*x]*(a + a*Sec[e + f*x])^2*(c - c*Sec[e + f*x])^5,x]","-\frac{a^2 c^5 \tan ^7(e+f x)}{7 f}-\frac{4 a^2 c^5 \tan ^5(e+f x)}{5 f}+\frac{9 a^2 c^5 \tanh ^{-1}(\sin (e+f x))}{16 f}+\frac{a^2 c^5 \tan ^3(e+f x) \sec ^3(e+f x)}{2 f}-\frac{3 a^2 c^5 \tan (e+f x) \sec ^3(e+f x)}{8 f}+\frac{a^2 c^5 \tan ^3(e+f x) \sec (e+f x)}{4 f}-\frac{3 a^2 c^5 \tan (e+f x) \sec (e+f x)}{16 f}","-\frac{a^2 c^5 \tan ^7(e+f x)}{7 f}-\frac{4 a^2 c^5 \tan ^5(e+f x)}{5 f}+\frac{9 a^2 c^5 \tanh ^{-1}(\sin (e+f x))}{16 f}+\frac{a^2 c^5 \tan ^3(e+f x) \sec ^3(e+f x)}{2 f}-\frac{3 a^2 c^5 \tan (e+f x) \sec ^3(e+f x)}{8 f}+\frac{a^2 c^5 \tan ^3(e+f x) \sec (e+f x)}{4 f}-\frac{3 a^2 c^5 \tan (e+f x) \sec (e+f x)}{16 f}",1,"(9*a^2*c^5*ArcTanh[Sin[e + f*x]])/(16*f) - (3*a^2*c^5*Sec[e + f*x]*Tan[e + f*x])/(16*f) - (3*a^2*c^5*Sec[e + f*x]^3*Tan[e + f*x])/(8*f) + (a^2*c^5*Sec[e + f*x]*Tan[e + f*x]^3)/(4*f) + (a^2*c^5*Sec[e + f*x]^3*Tan[e + f*x]^3)/(2*f) - (4*a^2*c^5*Tan[e + f*x]^5)/(5*f) - (a^2*c^5*Tan[e + f*x]^7)/(7*f)","A",14,7,32,0.2188,1,"{3958, 2611, 3770, 2607, 30, 3768, 14}"
11,1,150,0,0.2406896,"\int \sec (e+f x) (a+a \sec (e+f x))^2 (c-c \sec (e+f x))^4 \, dx","Int[Sec[e + f*x]*(a + a*Sec[e + f*x])^2*(c - c*Sec[e + f*x])^4,x]","-\frac{2 a^2 c^4 \tan ^5(e+f x)}{5 f}+\frac{7 a^2 c^4 \tanh ^{-1}(\sin (e+f x))}{16 f}+\frac{a^2 c^4 \tan ^3(e+f x) \sec ^3(e+f x)}{6 f}-\frac{a^2 c^4 \tan (e+f x) \sec ^3(e+f x)}{8 f}+\frac{a^2 c^4 \tan ^3(e+f x) \sec (e+f x)}{4 f}-\frac{5 a^2 c^4 \tan (e+f x) \sec (e+f x)}{16 f}","-\frac{2 a^2 c^4 \tan ^5(e+f x)}{5 f}+\frac{7 a^2 c^4 \tanh ^{-1}(\sin (e+f x))}{16 f}+\frac{a^2 c^4 \tan ^3(e+f x) \sec ^3(e+f x)}{6 f}-\frac{a^2 c^4 \tan (e+f x) \sec ^3(e+f x)}{8 f}+\frac{a^2 c^4 \tan ^3(e+f x) \sec (e+f x)}{4 f}-\frac{5 a^2 c^4 \tan (e+f x) \sec (e+f x)}{16 f}",1,"(7*a^2*c^4*ArcTanh[Sin[e + f*x]])/(16*f) - (5*a^2*c^4*Sec[e + f*x]*Tan[e + f*x])/(16*f) - (a^2*c^4*Sec[e + f*x]^3*Tan[e + f*x])/(8*f) + (a^2*c^4*Sec[e + f*x]*Tan[e + f*x]^3)/(4*f) + (a^2*c^4*Sec[e + f*x]^3*Tan[e + f*x]^3)/(6*f) - (2*a^2*c^4*Tan[e + f*x]^5)/(5*f)","A",11,6,32,0.1875,1,"{3958, 2611, 3770, 2607, 30, 3768}"
12,1,94,0,0.1488507,"\int \sec (e+f x) (a+a \sec (e+f x))^2 (c-c \sec (e+f x))^3 \, dx","Int[Sec[e + f*x]*(a + a*Sec[e + f*x])^2*(c - c*Sec[e + f*x])^3,x]","-\frac{a^2 c^3 \tan ^5(e+f x)}{5 f}+\frac{3 a^2 c^3 \tanh ^{-1}(\sin (e+f x))}{8 f}+\frac{a^2 c^3 \tan ^3(e+f x) \sec (e+f x)}{4 f}-\frac{3 a^2 c^3 \tan (e+f x) \sec (e+f x)}{8 f}","-\frac{a^2 c^3 \tan ^5(e+f x)}{5 f}+\frac{3 a^2 c^3 \tanh ^{-1}(\sin (e+f x))}{8 f}+\frac{a^2 c^3 \tan ^3(e+f x) \sec (e+f x)}{4 f}-\frac{3 a^2 c^3 \tan (e+f x) \sec (e+f x)}{8 f}",1,"(3*a^2*c^3*ArcTanh[Sin[e + f*x]])/(8*f) - (3*a^2*c^3*Sec[e + f*x]*Tan[e + f*x])/(8*f) + (a^2*c^3*Sec[e + f*x]*Tan[e + f*x]^3)/(4*f) - (a^2*c^3*Tan[e + f*x]^5)/(5*f)","A",7,5,32,0.1562,1,"{3958, 2611, 3770, 2607, 30}"
13,1,73,0,0.1083316,"\int \sec (e+f x) (a+a \sec (e+f x))^2 (c-c \sec (e+f x))^2 \, dx","Int[Sec[e + f*x]*(a + a*Sec[e + f*x])^2*(c - c*Sec[e + f*x])^2,x]","\frac{3 a^2 c^2 \tanh ^{-1}(\sin (e+f x))}{8 f}+\frac{a^2 c^2 \tan ^3(e+f x) \sec (e+f x)}{4 f}-\frac{3 a^2 c^2 \tan (e+f x) \sec (e+f x)}{8 f}","\frac{3 a^2 c^2 \tanh ^{-1}(\sin (e+f x))}{8 f}+\frac{a^2 c^2 \tan ^3(e+f x) \sec (e+f x)}{4 f}-\frac{3 a^2 c^2 \tan (e+f x) \sec (e+f x)}{8 f}",1,"(3*a^2*c^2*ArcTanh[Sin[e + f*x]])/(8*f) - (3*a^2*c^2*Sec[e + f*x]*Tan[e + f*x])/(8*f) + (a^2*c^2*Sec[e + f*x]*Tan[e + f*x]^3)/(4*f)","A",4,3,32,0.09375,1,"{3958, 2611, 3770}"
14,1,61,0,0.1025268,"\int \sec (e+f x) (a+a \sec (e+f x))^2 (c-c \sec (e+f x)) \, dx","Int[Sec[e + f*x]*(a + a*Sec[e + f*x])^2*(c - c*Sec[e + f*x]),x]","-\frac{a^2 c \tan ^3(e+f x)}{3 f}+\frac{a^2 c \tanh ^{-1}(\sin (e+f x))}{2 f}-\frac{a^2 c \tan (e+f x) \sec (e+f x)}{2 f}","-\frac{a^2 c \tan ^3(e+f x)}{3 f}+\frac{a^2 c \tanh ^{-1}(\sin (e+f x))}{2 f}-\frac{a^2 c \tan (e+f x) \sec (e+f x)}{2 f}",1,"(a^2*c*ArcTanh[Sin[e + f*x]])/(2*f) - (a^2*c*Sec[e + f*x]*Tan[e + f*x])/(2*f) - (a^2*c*Tan[e + f*x]^3)/(3*f)","A",6,5,30,0.1667,1,"{3958, 2611, 3770, 2607, 30}"
15,1,74,0,0.0993604,"\int \frac{\sec (e+f x) (a+a \sec (e+f x))^2}{c-c \sec (e+f x)} \, dx","Int[(Sec[e + f*x]*(a + a*Sec[e + f*x])^2)/(c - c*Sec[e + f*x]),x]","-\frac{3 a^2 \tan (e+f x)}{c f}-\frac{3 a^2 \tanh ^{-1}(\sin (e+f x))}{c f}-\frac{2 \tan (e+f x) \left(a^2 \sec (e+f x)+a^2\right)}{f (c-c \sec (e+f x))}","-\frac{3 a^2 \tan (e+f x)}{c f}-\frac{3 a^2 \tanh ^{-1}(\sin (e+f x))}{c f}-\frac{2 \tan (e+f x) \left(a^2 \sec (e+f x)+a^2\right)}{f (c-c \sec (e+f x))}",1,"(-3*a^2*ArcTanh[Sin[e + f*x]])/(c*f) - (3*a^2*Tan[e + f*x])/(c*f) - (2*(a^2 + a^2*Sec[e + f*x])*Tan[e + f*x])/(f*(c - c*Sec[e + f*x]))","A",5,5,32,0.1562,1,"{3957, 3787, 3770, 3767, 8}"
16,1,89,0,0.1279741,"\int \frac{\sec (e+f x) (a+a \sec (e+f x))^2}{(c-c \sec (e+f x))^2} \, dx","Int[(Sec[e + f*x]*(a + a*Sec[e + f*x])^2)/(c - c*Sec[e + f*x])^2,x]","\frac{a^2 \tanh ^{-1}(\sin (e+f x))}{c^2 f}+\frac{2 a^2 \tan (e+f x)}{f \left(c^2-c^2 \sec (e+f x)\right)}-\frac{2 \tan (e+f x) \left(a^2 \sec (e+f x)+a^2\right)}{3 f (c-c \sec (e+f x))^2}","\frac{a^2 \tanh ^{-1}(\sin (e+f x))}{c^2 f}+\frac{2 a^2 \tan (e+f x)}{f \left(c^2-c^2 \sec (e+f x)\right)}-\frac{2 \tan (e+f x) \left(a^2 \sec (e+f x)+a^2\right)}{3 f (c-c \sec (e+f x))^2}",1,"(a^2*ArcTanh[Sin[e + f*x]])/(c^2*f) - (2*(a^2 + a^2*Sec[e + f*x])*Tan[e + f*x])/(3*f*(c - c*Sec[e + f*x])^2) + (2*a^2*Tan[e + f*x])/(f*(c^2 - c^2*Sec[e + f*x]))","A",3,2,32,0.06250,1,"{3957, 3770}"
17,1,38,0,0.0751821,"\int \frac{\sec (e+f x) (a+a \sec (e+f x))^2}{(c-c \sec (e+f x))^3} \, dx","Int[(Sec[e + f*x]*(a + a*Sec[e + f*x])^2)/(c - c*Sec[e + f*x])^3,x]","-\frac{\tan (e+f x) (a \sec (e+f x)+a)^2}{5 f (c-c \sec (e+f x))^3}","-\frac{\tan (e+f x) (a \sec (e+f x)+a)^2}{5 f (c-c \sec (e+f x))^3}",1,"-((a + a*Sec[e + f*x])^2*Tan[e + f*x])/(5*f*(c - c*Sec[e + f*x])^3)","A",1,1,32,0.03125,1,"{3950}"
18,1,80,0,0.1502088,"\int \frac{\sec (e+f x) (a+a \sec (e+f x))^2}{(c-c \sec (e+f x))^4} \, dx","Int[(Sec[e + f*x]*(a + a*Sec[e + f*x])^2)/(c - c*Sec[e + f*x])^4,x]","-\frac{\tan (e+f x) (a \sec (e+f x)+a)^2}{35 c f (c-c \sec (e+f x))^3}-\frac{\tan (e+f x) (a \sec (e+f x)+a)^2}{7 f (c-c \sec (e+f x))^4}","-\frac{\tan (e+f x) (a \sec (e+f x)+a)^2}{35 c f (c-c \sec (e+f x))^3}-\frac{\tan (e+f x) (a \sec (e+f x)+a)^2}{7 f (c-c \sec (e+f x))^4}",1,"-((a + a*Sec[e + f*x])^2*Tan[e + f*x])/(7*f*(c - c*Sec[e + f*x])^4) - ((a + a*Sec[e + f*x])^2*Tan[e + f*x])/(35*c*f*(c - c*Sec[e + f*x])^3)","A",2,2,32,0.06250,1,"{3951, 3950}"
19,1,121,0,0.2302758,"\int \frac{\sec (e+f x) (a+a \sec (e+f x))^2}{(c-c \sec (e+f x))^5} \, dx","Int[(Sec[e + f*x]*(a + a*Sec[e + f*x])^2)/(c - c*Sec[e + f*x])^5,x]","-\frac{2 \tan (e+f x) (a \sec (e+f x)+a)^2}{315 c^2 f (c-c \sec (e+f x))^3}-\frac{2 \tan (e+f x) (a \sec (e+f x)+a)^2}{63 c f (c-c \sec (e+f x))^4}-\frac{\tan (e+f x) (a \sec (e+f x)+a)^2}{9 f (c-c \sec (e+f x))^5}","-\frac{2 \tan (e+f x) (a \sec (e+f x)+a)^2}{315 c^2 f (c-c \sec (e+f x))^3}-\frac{2 \tan (e+f x) (a \sec (e+f x)+a)^2}{63 c f (c-c \sec (e+f x))^4}-\frac{\tan (e+f x) (a \sec (e+f x)+a)^2}{9 f (c-c \sec (e+f x))^5}",1,"-((a + a*Sec[e + f*x])^2*Tan[e + f*x])/(9*f*(c - c*Sec[e + f*x])^5) - (2*(a + a*Sec[e + f*x])^2*Tan[e + f*x])/(63*c*f*(c - c*Sec[e + f*x])^4) - (2*(a + a*Sec[e + f*x])^2*Tan[e + f*x])/(315*c^2*f*(c - c*Sec[e + f*x])^3)","A",3,2,32,0.06250,1,"{3951, 3950}"
20,1,163,0,0.3146772,"\int \frac{\sec (e+f x) (a+a \sec (e+f x))^2}{(c-c \sec (e+f x))^6} \, dx","Int[(Sec[e + f*x]*(a + a*Sec[e + f*x])^2)/(c - c*Sec[e + f*x])^6,x]","-\frac{2 \tan (e+f x) (a \sec (e+f x)+a)^2}{1155 f \left(c^2-c^2 \sec (e+f x)\right)^3}-\frac{2 \tan (e+f x) (a \sec (e+f x)+a)^2}{231 c^2 f (c-c \sec (e+f x))^4}-\frac{\tan (e+f x) (a \sec (e+f x)+a)^2}{33 c f (c-c \sec (e+f x))^5}-\frac{\tan (e+f x) (a \sec (e+f x)+a)^2}{11 f (c-c \sec (e+f x))^6}","-\frac{2 \tan (e+f x) (a \sec (e+f x)+a)^2}{1155 f \left(c^2-c^2 \sec (e+f x)\right)^3}-\frac{2 \tan (e+f x) (a \sec (e+f x)+a)^2}{231 c^2 f (c-c \sec (e+f x))^4}-\frac{\tan (e+f x) (a \sec (e+f x)+a)^2}{33 c f (c-c \sec (e+f x))^5}-\frac{\tan (e+f x) (a \sec (e+f x)+a)^2}{11 f (c-c \sec (e+f x))^6}",1,"-((a + a*Sec[e + f*x])^2*Tan[e + f*x])/(11*f*(c - c*Sec[e + f*x])^6) - ((a + a*Sec[e + f*x])^2*Tan[e + f*x])/(33*c*f*(c - c*Sec[e + f*x])^5) - (2*(a + a*Sec[e + f*x])^2*Tan[e + f*x])/(231*c^2*f*(c - c*Sec[e + f*x])^4) - (2*(a + a*Sec[e + f*x])^2*Tan[e + f*x])/(1155*f*(c^2 - c^2*Sec[e + f*x])^3)","A",4,2,32,0.06250,1,"{3951, 3950}"
21,1,227,0,0.3352346,"\int \sec (e+f x) (a+a \sec (e+f x))^3 (c-c \sec (e+f x))^6 \, dx","Int[Sec[e + f*x]*(a + a*Sec[e + f*x])^3*(c - c*Sec[e + f*x])^6,x]","\frac{a^3 c^6 \tan ^9(e+f x)}{9 f}+\frac{4 a^3 c^6 \tan ^7(e+f x)}{7 f}+\frac{55 a^3 c^6 \tanh ^{-1}(\sin (e+f x))}{128 f}-\frac{3 a^3 c^6 \tan ^5(e+f x) \sec ^3(e+f x)}{8 f}+\frac{5 a^3 c^6 \tan ^3(e+f x) \sec ^3(e+f x)}{16 f}-\frac{15 a^3 c^6 \tan (e+f x) \sec ^3(e+f x)}{64 f}-\frac{a^3 c^6 \tan ^5(e+f x) \sec (e+f x)}{6 f}+\frac{5 a^3 c^6 \tan ^3(e+f x) \sec (e+f x)}{24 f}-\frac{25 a^3 c^6 \tan (e+f x) \sec (e+f x)}{128 f}","\frac{a^3 c^6 \tan ^9(e+f x)}{9 f}+\frac{4 a^3 c^6 \tan ^7(e+f x)}{7 f}+\frac{55 a^3 c^6 \tanh ^{-1}(\sin (e+f x))}{128 f}-\frac{3 a^3 c^6 \tan ^5(e+f x) \sec ^3(e+f x)}{8 f}+\frac{5 a^3 c^6 \tan ^3(e+f x) \sec ^3(e+f x)}{16 f}-\frac{15 a^3 c^6 \tan (e+f x) \sec ^3(e+f x)}{64 f}-\frac{a^3 c^6 \tan ^5(e+f x) \sec (e+f x)}{6 f}+\frac{5 a^3 c^6 \tan ^3(e+f x) \sec (e+f x)}{24 f}-\frac{25 a^3 c^6 \tan (e+f x) \sec (e+f x)}{128 f}",1,"(55*a^3*c^6*ArcTanh[Sin[e + f*x]])/(128*f) - (25*a^3*c^6*Sec[e + f*x]*Tan[e + f*x])/(128*f) - (15*a^3*c^6*Sec[e + f*x]^3*Tan[e + f*x])/(64*f) + (5*a^3*c^6*Sec[e + f*x]*Tan[e + f*x]^3)/(24*f) + (5*a^3*c^6*Sec[e + f*x]^3*Tan[e + f*x]^3)/(16*f) - (a^3*c^6*Sec[e + f*x]*Tan[e + f*x]^5)/(6*f) - (3*a^3*c^6*Sec[e + f*x]^3*Tan[e + f*x]^5)/(8*f) + (4*a^3*c^6*Tan[e + f*x]^7)/(7*f) + (a^3*c^6*Tan[e + f*x]^9)/(9*f)","A",16,7,32,0.2188,1,"{3958, 2611, 3770, 2607, 30, 3768, 14}"
22,1,206,0,0.3018234,"\int \sec (e+f x) (a+a \sec (e+f x))^3 (c-c \sec (e+f x))^5 \, dx","Int[Sec[e + f*x]*(a + a*Sec[e + f*x])^3*(c - c*Sec[e + f*x])^5,x]","\frac{2 a^3 c^5 \tan ^7(e+f x)}{7 f}+\frac{45 a^3 c^5 \tanh ^{-1}(\sin (e+f x))}{128 f}-\frac{a^3 c^5 \tan ^5(e+f x) \sec ^3(e+f x)}{8 f}+\frac{5 a^3 c^5 \tan ^3(e+f x) \sec ^3(e+f x)}{48 f}-\frac{5 a^3 c^5 \tan (e+f x) \sec ^3(e+f x)}{64 f}-\frac{a^3 c^5 \tan ^5(e+f x) \sec (e+f x)}{6 f}+\frac{5 a^3 c^5 \tan ^3(e+f x) \sec (e+f x)}{24 f}-\frac{35 a^3 c^5 \tan (e+f x) \sec (e+f x)}{128 f}","\frac{2 a^3 c^5 \tan ^7(e+f x)}{7 f}+\frac{45 a^3 c^5 \tanh ^{-1}(\sin (e+f x))}{128 f}-\frac{a^3 c^5 \tan ^5(e+f x) \sec ^3(e+f x)}{8 f}+\frac{5 a^3 c^5 \tan ^3(e+f x) \sec ^3(e+f x)}{48 f}-\frac{5 a^3 c^5 \tan (e+f x) \sec ^3(e+f x)}{64 f}-\frac{a^3 c^5 \tan ^5(e+f x) \sec (e+f x)}{6 f}+\frac{5 a^3 c^5 \tan ^3(e+f x) \sec (e+f x)}{24 f}-\frac{35 a^3 c^5 \tan (e+f x) \sec (e+f x)}{128 f}",1,"(45*a^3*c^5*ArcTanh[Sin[e + f*x]])/(128*f) - (35*a^3*c^5*Sec[e + f*x]*Tan[e + f*x])/(128*f) - (5*a^3*c^5*Sec[e + f*x]^3*Tan[e + f*x])/(64*f) + (5*a^3*c^5*Sec[e + f*x]*Tan[e + f*x]^3)/(24*f) + (5*a^3*c^5*Sec[e + f*x]^3*Tan[e + f*x]^3)/(48*f) - (a^3*c^5*Sec[e + f*x]*Tan[e + f*x]^5)/(6*f) - (a^3*c^5*Sec[e + f*x]^3*Tan[e + f*x]^5)/(8*f) + (2*a^3*c^5*Tan[e + f*x]^7)/(7*f)","A",13,6,32,0.1875,1,"{3958, 2611, 3770, 2607, 30, 3768}"
23,1,121,0,0.1781817,"\int \sec (e+f x) (a+a \sec (e+f x))^3 (c-c \sec (e+f x))^4 \, dx","Int[Sec[e + f*x]*(a + a*Sec[e + f*x])^3*(c - c*Sec[e + f*x])^4,x]","\frac{a^3 c^4 \tan ^7(e+f x)}{7 f}+\frac{5 a^3 c^4 \tanh ^{-1}(\sin (e+f x))}{16 f}-\frac{a^3 c^4 \tan ^5(e+f x) \sec (e+f x)}{6 f}+\frac{5 a^3 c^4 \tan ^3(e+f x) \sec (e+f x)}{24 f}-\frac{5 a^3 c^4 \tan (e+f x) \sec (e+f x)}{16 f}","\frac{a^3 c^4 \tan ^7(e+f x)}{7 f}+\frac{5 a^3 c^4 \tanh ^{-1}(\sin (e+f x))}{16 f}-\frac{a^3 c^4 \tan ^5(e+f x) \sec (e+f x)}{6 f}+\frac{5 a^3 c^4 \tan ^3(e+f x) \sec (e+f x)}{24 f}-\frac{5 a^3 c^4 \tan (e+f x) \sec (e+f x)}{16 f}",1,"(5*a^3*c^4*ArcTanh[Sin[e + f*x]])/(16*f) - (5*a^3*c^4*Sec[e + f*x]*Tan[e + f*x])/(16*f) + (5*a^3*c^4*Sec[e + f*x]*Tan[e + f*x]^3)/(24*f) - (a^3*c^4*Sec[e + f*x]*Tan[e + f*x]^5)/(6*f) + (a^3*c^4*Tan[e + f*x]^7)/(7*f)","A",8,5,32,0.1562,1,"{3958, 2611, 3770, 2607, 30}"
24,1,100,0,0.1311133,"\int \sec (e+f x) (a+a \sec (e+f x))^3 (c-c \sec (e+f x))^3 \, dx","Int[Sec[e + f*x]*(a + a*Sec[e + f*x])^3*(c - c*Sec[e + f*x])^3,x]","\frac{5 a^3 c^3 \tanh ^{-1}(\sin (e+f x))}{16 f}-\frac{a^3 c^3 \tan ^5(e+f x) \sec (e+f x)}{6 f}+\frac{5 a^3 c^3 \tan ^3(e+f x) \sec (e+f x)}{24 f}-\frac{5 a^3 c^3 \tan (e+f x) \sec (e+f x)}{16 f}","\frac{5 a^3 c^3 \tanh ^{-1}(\sin (e+f x))}{16 f}-\frac{a^3 c^3 \tan ^5(e+f x) \sec (e+f x)}{6 f}+\frac{5 a^3 c^3 \tan ^3(e+f x) \sec (e+f x)}{24 f}-\frac{5 a^3 c^3 \tan (e+f x) \sec (e+f x)}{16 f}",1,"(5*a^3*c^3*ArcTanh[Sin[e + f*x]])/(16*f) - (5*a^3*c^3*Sec[e + f*x]*Tan[e + f*x])/(16*f) + (5*a^3*c^3*Sec[e + f*x]*Tan[e + f*x]^3)/(24*f) - (a^3*c^3*Sec[e + f*x]*Tan[e + f*x]^5)/(6*f)","A",5,3,32,0.09375,1,"{3958, 2611, 3770}"
25,1,94,0,0.1478007,"\int \sec (e+f x) (a+a \sec (e+f x))^3 (c-c \sec (e+f x))^2 \, dx","Int[Sec[e + f*x]*(a + a*Sec[e + f*x])^3*(c - c*Sec[e + f*x])^2,x]","\frac{a^3 c^2 \tan ^5(e+f x)}{5 f}+\frac{3 a^3 c^2 \tanh ^{-1}(\sin (e+f x))}{8 f}+\frac{a^3 c^2 \tan ^3(e+f x) \sec (e+f x)}{4 f}-\frac{3 a^3 c^2 \tan (e+f x) \sec (e+f x)}{8 f}","\frac{a^3 c^2 \tan ^5(e+f x)}{5 f}+\frac{3 a^3 c^2 \tanh ^{-1}(\sin (e+f x))}{8 f}+\frac{a^3 c^2 \tan ^3(e+f x) \sec (e+f x)}{4 f}-\frac{3 a^3 c^2 \tan (e+f x) \sec (e+f x)}{8 f}",1,"(3*a^3*c^2*ArcTanh[Sin[e + f*x]])/(8*f) - (3*a^3*c^2*Sec[e + f*x]*Tan[e + f*x])/(8*f) + (a^3*c^2*Sec[e + f*x]*Tan[e + f*x]^3)/(4*f) + (a^3*c^2*Tan[e + f*x]^5)/(5*f)","A",7,5,32,0.1562,1,"{3958, 2611, 3770, 2607, 30}"
26,1,86,0,0.1557396,"\int \sec (e+f x) (a+a \sec (e+f x))^3 (c-c \sec (e+f x)) \, dx","Int[Sec[e + f*x]*(a + a*Sec[e + f*x])^3*(c - c*Sec[e + f*x]),x]","-\frac{2 a^3 c \tan ^3(e+f x)}{3 f}+\frac{5 a^3 c \tanh ^{-1}(\sin (e+f x))}{8 f}-\frac{a^3 c \tan (e+f x) \sec ^3(e+f x)}{4 f}-\frac{3 a^3 c \tan (e+f x) \sec (e+f x)}{8 f}","-\frac{2 a^3 c \tan ^3(e+f x)}{3 f}+\frac{5 a^3 c \tanh ^{-1}(\sin (e+f x))}{8 f}-\frac{a^3 c \tan (e+f x) \sec ^3(e+f x)}{4 f}-\frac{3 a^3 c \tan (e+f x) \sec (e+f x)}{8 f}",1,"(5*a^3*c*ArcTanh[Sin[e + f*x]])/(8*f) - (3*a^3*c*Sec[e + f*x]*Tan[e + f*x])/(8*f) - (a^3*c*Sec[e + f*x]^3*Tan[e + f*x])/(4*f) - (2*a^3*c*Tan[e + f*x]^3)/(3*f)","A",9,6,30,0.2000,1,"{3958, 2611, 3770, 2607, 30, 3768}"
27,1,100,0,0.1286578,"\int \frac{\sec (e+f x) (a+a \sec (e+f x))^3}{c-c \sec (e+f x)} \, dx","Int[(Sec[e + f*x]*(a + a*Sec[e + f*x])^3)/(c - c*Sec[e + f*x]),x]","-\frac{10 a^3 \tan (e+f x)}{c f}-\frac{15 a^3 \tanh ^{-1}(\sin (e+f x))}{2 c f}-\frac{5 a^3 \tan (e+f x) \sec (e+f x)}{2 c f}-\frac{2 a \tan (e+f x) (a \sec (e+f x)+a)^2}{f (c-c \sec (e+f x))}","-\frac{10 a^3 \tan (e+f x)}{c f}-\frac{15 a^3 \tanh ^{-1}(\sin (e+f x))}{2 c f}-\frac{5 a^3 \tan (e+f x) \sec (e+f x)}{2 c f}-\frac{2 a \tan (e+f x) (a \sec (e+f x)+a)^2}{f (c-c \sec (e+f x))}",1,"(-15*a^3*ArcTanh[Sin[e + f*x]])/(2*c*f) - (10*a^3*Tan[e + f*x])/(c*f) - (5*a^3*Sec[e + f*x]*Tan[e + f*x])/(2*c*f) - (2*a*(a + a*Sec[e + f*x])^2*Tan[e + f*x])/(f*(c - c*Sec[e + f*x]))","A",6,6,32,0.1875,1,"{3957, 3788, 3767, 8, 4046, 3770}"
28,1,119,0,0.1830513,"\int \frac{\sec (e+f x) (a+a \sec (e+f x))^3}{(c-c \sec (e+f x))^2} \, dx","Int[(Sec[e + f*x]*(a + a*Sec[e + f*x])^3)/(c - c*Sec[e + f*x])^2,x]","\frac{5 a^3 \tan (e+f x)}{c^2 f}+\frac{5 a^3 \tanh ^{-1}(\sin (e+f x))}{c^2 f}+\frac{10 \tan (e+f x) \left(a^3 \sec (e+f x)+a^3\right)}{3 f \left(c^2-c^2 \sec (e+f x)\right)}-\frac{2 a \tan (e+f x) (a \sec (e+f x)+a)^2}{3 f (c-c \sec (e+f x))^2}","\frac{5 a^3 \tan (e+f x)}{c^2 f}+\frac{5 a^3 \tanh ^{-1}(\sin (e+f x))}{c^2 f}+\frac{10 \tan (e+f x) \left(a^3 \sec (e+f x)+a^3\right)}{3 f \left(c^2-c^2 \sec (e+f x)\right)}-\frac{2 a \tan (e+f x) (a \sec (e+f x)+a)^2}{3 f (c-c \sec (e+f x))^2}",1,"(5*a^3*ArcTanh[Sin[e + f*x]])/(c^2*f) + (5*a^3*Tan[e + f*x])/(c^2*f) - (2*a*(a + a*Sec[e + f*x])^2*Tan[e + f*x])/(3*f*(c - c*Sec[e + f*x])^2) + (10*(a^3 + a^3*Sec[e + f*x])*Tan[e + f*x])/(3*f*(c^2 - c^2*Sec[e + f*x]))","A",6,5,32,0.1562,1,"{3957, 3787, 3770, 3767, 8}"
29,1,132,0,0.2144204,"\int \frac{\sec (e+f x) (a+a \sec (e+f x))^3}{(c-c \sec (e+f x))^3} \, dx","Int[(Sec[e + f*x]*(a + a*Sec[e + f*x])^3)/(c - c*Sec[e + f*x])^3,x]","-\frac{a^3 \tanh ^{-1}(\sin (e+f x))}{c^3 f}-\frac{2 a^3 \tan (e+f x)}{f \left(c^3-c^3 \sec (e+f x)\right)}+\frac{2 \tan (e+f x) \left(a^3 \sec (e+f x)+a^3\right)}{3 c f (c-c \sec (e+f x))^2}-\frac{2 a \tan (e+f x) (a \sec (e+f x)+a)^2}{5 f (c-c \sec (e+f x))^3}","-\frac{a^3 \tanh ^{-1}(\sin (e+f x))}{c^3 f}-\frac{2 a^3 \tan (e+f x)}{f \left(c^3-c^3 \sec (e+f x)\right)}+\frac{2 \tan (e+f x) \left(a^3 \sec (e+f x)+a^3\right)}{3 c f (c-c \sec (e+f x))^2}-\frac{2 a \tan (e+f x) (a \sec (e+f x)+a)^2}{5 f (c-c \sec (e+f x))^3}",1,"-((a^3*ArcTanh[Sin[e + f*x]])/(c^3*f)) - (2*a*(a + a*Sec[e + f*x])^2*Tan[e + f*x])/(5*f*(c - c*Sec[e + f*x])^3) + (2*(a^3 + a^3*Sec[e + f*x])*Tan[e + f*x])/(3*c*f*(c - c*Sec[e + f*x])^2) - (2*a^3*Tan[e + f*x])/(f*(c^3 - c^3*Sec[e + f*x]))","A",4,2,32,0.06250,1,"{3957, 3770}"
30,1,38,0,0.0724353,"\int \frac{\sec (e+f x) (a+a \sec (e+f x))^3}{(c-c \sec (e+f x))^4} \, dx","Int[(Sec[e + f*x]*(a + a*Sec[e + f*x])^3)/(c - c*Sec[e + f*x])^4,x]","-\frac{\tan (e+f x) (a \sec (e+f x)+a)^3}{7 f (c-c \sec (e+f x))^4}","-\frac{\tan (e+f x) (a \sec (e+f x)+a)^3}{7 f (c-c \sec (e+f x))^4}",1,"-((a + a*Sec[e + f*x])^3*Tan[e + f*x])/(7*f*(c - c*Sec[e + f*x])^4)","A",1,1,32,0.03125,1,"{3950}"
31,1,80,0,0.152401,"\int \frac{\sec (e+f x) (a+a \sec (e+f x))^3}{(c-c \sec (e+f x))^5} \, dx","Int[(Sec[e + f*x]*(a + a*Sec[e + f*x])^3)/(c - c*Sec[e + f*x])^5,x]","-\frac{\tan (e+f x) (a \sec (e+f x)+a)^3}{63 c f (c-c \sec (e+f x))^4}-\frac{\tan (e+f x) (a \sec (e+f x)+a)^3}{9 f (c-c \sec (e+f x))^5}","-\frac{\tan (e+f x) (a \sec (e+f x)+a)^3}{63 c f (c-c \sec (e+f x))^4}-\frac{\tan (e+f x) (a \sec (e+f x)+a)^3}{9 f (c-c \sec (e+f x))^5}",1,"-((a + a*Sec[e + f*x])^3*Tan[e + f*x])/(9*f*(c - c*Sec[e + f*x])^5) - ((a + a*Sec[e + f*x])^3*Tan[e + f*x])/(63*c*f*(c - c*Sec[e + f*x])^4)","A",2,2,32,0.06250,1,"{3951, 3950}"
32,1,121,0,0.2303254,"\int \frac{\sec (e+f x) (a+a \sec (e+f x))^3}{(c-c \sec (e+f x))^6} \, dx","Int[(Sec[e + f*x]*(a + a*Sec[e + f*x])^3)/(c - c*Sec[e + f*x])^6,x]","-\frac{2 \tan (e+f x) (a \sec (e+f x)+a)^3}{693 c^2 f (c-c \sec (e+f x))^4}-\frac{2 \tan (e+f x) (a \sec (e+f x)+a)^3}{99 c f (c-c \sec (e+f x))^5}-\frac{\tan (e+f x) (a \sec (e+f x)+a)^3}{11 f (c-c \sec (e+f x))^6}","-\frac{2 \tan (e+f x) (a \sec (e+f x)+a)^3}{693 c^2 f (c-c \sec (e+f x))^4}-\frac{2 \tan (e+f x) (a \sec (e+f x)+a)^3}{99 c f (c-c \sec (e+f x))^5}-\frac{\tan (e+f x) (a \sec (e+f x)+a)^3}{11 f (c-c \sec (e+f x))^6}",1,"-((a + a*Sec[e + f*x])^3*Tan[e + f*x])/(11*f*(c - c*Sec[e + f*x])^6) - (2*(a + a*Sec[e + f*x])^3*Tan[e + f*x])/(99*c*f*(c - c*Sec[e + f*x])^5) - (2*(a + a*Sec[e + f*x])^3*Tan[e + f*x])/(693*c^2*f*(c - c*Sec[e + f*x])^4)","A",3,2,32,0.06250,1,"{3951, 3950}"
33,1,162,0,0.3167153,"\int \frac{\sec (e+f x) (a+a \sec (e+f x))^3}{(c-c \sec (e+f x))^7} \, dx","Int[(Sec[e + f*x]*(a + a*Sec[e + f*x])^3)/(c - c*Sec[e + f*x])^7,x]","-\frac{2 \tan (e+f x) (a \sec (e+f x)+a)^3}{3003 c^3 f (c-c \sec (e+f x))^4}-\frac{2 \tan (e+f x) (a \sec (e+f x)+a)^3}{429 c^2 f (c-c \sec (e+f x))^5}-\frac{3 \tan (e+f x) (a \sec (e+f x)+a)^3}{143 c f (c-c \sec (e+f x))^6}-\frac{\tan (e+f x) (a \sec (e+f x)+a)^3}{13 f (c-c \sec (e+f x))^7}","-\frac{2 \tan (e+f x) (a \sec (e+f x)+a)^3}{3003 c^3 f (c-c \sec (e+f x))^4}-\frac{2 \tan (e+f x) (a \sec (e+f x)+a)^3}{429 c^2 f (c-c \sec (e+f x))^5}-\frac{3 \tan (e+f x) (a \sec (e+f x)+a)^3}{143 c f (c-c \sec (e+f x))^6}-\frac{\tan (e+f x) (a \sec (e+f x)+a)^3}{13 f (c-c \sec (e+f x))^7}",1,"-((a + a*Sec[e + f*x])^3*Tan[e + f*x])/(13*f*(c - c*Sec[e + f*x])^7) - (3*(a + a*Sec[e + f*x])^3*Tan[e + f*x])/(143*c*f*(c - c*Sec[e + f*x])^6) - (2*(a + a*Sec[e + f*x])^3*Tan[e + f*x])/(429*c^2*f*(c - c*Sec[e + f*x])^5) - (2*(a + a*Sec[e + f*x])^3*Tan[e + f*x])/(3003*c^3*f*(c - c*Sec[e + f*x])^4)","A",4,2,32,0.06250,1,"{3951, 3950}"
34,1,121,0,0.1555139,"\int \frac{\sec (e+f x) (c-c \sec (e+f x))^4}{a+a \sec (e+f x)} \, dx","Int[(Sec[e + f*x]*(c - c*Sec[e + f*x])^4)/(a + a*Sec[e + f*x]),x]","\frac{7 c^4 \tan ^3(e+f x)}{3 a f}+\frac{28 c^4 \tan (e+f x)}{a f}-\frac{35 c^4 \tanh ^{-1}(\sin (e+f x))}{2 a f}-\frac{21 c^4 \tan (e+f x) \sec (e+f x)}{2 a f}+\frac{2 c \tan (e+f x) (c-c \sec (e+f x))^3}{f (a \sec (e+f x)+a)}","\frac{7 c^4 \tan ^3(e+f x)}{3 a f}+\frac{28 c^4 \tan (e+f x)}{a f}-\frac{35 c^4 \tanh ^{-1}(\sin (e+f x))}{2 a f}-\frac{21 c^4 \tan (e+f x) \sec (e+f x)}{2 a f}+\frac{2 c \tan (e+f x) (c-c \sec (e+f x))^3}{f (a \sec (e+f x)+a)}",1,"(-35*c^4*ArcTanh[Sin[e + f*x]])/(2*a*f) + (28*c^4*Tan[e + f*x])/(a*f) - (21*c^4*Sec[e + f*x]*Tan[e + f*x])/(2*a*f) + (2*c*(c - c*Sec[e + f*x])^3*Tan[e + f*x])/(f*(a + a*Sec[e + f*x])) + (7*c^4*Tan[e + f*x]^3)/(3*a*f)","A",10,6,32,0.1875,1,"{3957, 3791, 3770, 3767, 8, 3768}"
35,1,100,0,0.1300969,"\int \frac{\sec (e+f x) (c-c \sec (e+f x))^3}{a+a \sec (e+f x)} \, dx","Int[(Sec[e + f*x]*(c - c*Sec[e + f*x])^3)/(a + a*Sec[e + f*x]),x]","\frac{10 c^3 \tan (e+f x)}{a f}-\frac{15 c^3 \tanh ^{-1}(\sin (e+f x))}{2 a f}-\frac{5 c^3 \tan (e+f x) \sec (e+f x)}{2 a f}+\frac{2 c \tan (e+f x) (c-c \sec (e+f x))^2}{f (a \sec (e+f x)+a)}","\frac{10 c^3 \tan (e+f x)}{a f}-\frac{15 c^3 \tanh ^{-1}(\sin (e+f x))}{2 a f}-\frac{5 c^3 \tan (e+f x) \sec (e+f x)}{2 a f}+\frac{2 c \tan (e+f x) (c-c \sec (e+f x))^2}{f (a \sec (e+f x)+a)}",1,"(-15*c^3*ArcTanh[Sin[e + f*x]])/(2*a*f) + (10*c^3*Tan[e + f*x])/(a*f) - (5*c^3*Sec[e + f*x]*Tan[e + f*x])/(2*a*f) + (2*c*(c - c*Sec[e + f*x])^2*Tan[e + f*x])/(f*(a + a*Sec[e + f*x]))","A",6,6,32,0.1875,1,"{3957, 3788, 3767, 8, 4046, 3770}"
36,1,74,0,0.1029346,"\int \frac{\sec (e+f x) (c-c \sec (e+f x))^2}{a+a \sec (e+f x)} \, dx","Int[(Sec[e + f*x]*(c - c*Sec[e + f*x])^2)/(a + a*Sec[e + f*x]),x]","\frac{3 c^2 \tan (e+f x)}{a f}-\frac{3 c^2 \tanh ^{-1}(\sin (e+f x))}{a f}+\frac{2 \tan (e+f x) \left(c^2-c^2 \sec (e+f x)\right)}{f (a \sec (e+f x)+a)}","\frac{3 c^2 \tan (e+f x)}{a f}-\frac{3 c^2 \tanh ^{-1}(\sin (e+f x))}{a f}+\frac{2 \tan (e+f x) \left(c^2-c^2 \sec (e+f x)\right)}{f (a \sec (e+f x)+a)}",1,"(-3*c^2*ArcTanh[Sin[e + f*x]])/(a*f) + (3*c^2*Tan[e + f*x])/(a*f) + (2*(c^2 - c^2*Sec[e + f*x])*Tan[e + f*x])/(f*(a + a*Sec[e + f*x]))","A",5,5,32,0.1562,1,"{3957, 3787, 3770, 3767, 8}"
37,1,41,0,0.0533329,"\int \frac{\sec (e+f x) (c-c \sec (e+f x))}{a+a \sec (e+f x)} \, dx","Int[(Sec[e + f*x]*(c - c*Sec[e + f*x]))/(a + a*Sec[e + f*x]),x]","\frac{2 c \tan (e+f x)}{f (a \sec (e+f x)+a)}-\frac{c \tanh ^{-1}(\sin (e+f x))}{a f}","\frac{2 c \tan (e+f x)}{f (a \sec (e+f x)+a)}-\frac{c \tanh ^{-1}(\sin (e+f x))}{a f}",1,"-((c*ArcTanh[Sin[e + f*x]])/(a*f)) + (2*c*Tan[e + f*x])/(f*(a + a*Sec[e + f*x]))","A",2,2,30,0.06667,1,"{3957, 3770}"
38,1,16,0,0.0890242,"\int \frac{\sec (e+f x)}{(a+a \sec (e+f x)) (c-c \sec (e+f x))} \, dx","Int[Sec[e + f*x]/((a + a*Sec[e + f*x])*(c - c*Sec[e + f*x])),x]","\frac{\csc (e+f x)}{a c f}","\frac{\csc (e+f x)}{a c f}",1,"Csc[e + f*x]/(a*c*f)","A",3,3,32,0.09375,1,"{3958, 2606, 8}"
39,1,59,0,0.1366838,"\int \frac{\sec (e+f x)}{(a+a \sec (e+f x)) (c-c \sec (e+f x))^2} \, dx","Int[Sec[e + f*x]/((a + a*Sec[e + f*x])*(c - c*Sec[e + f*x])^2),x]","-\frac{\cot ^3(e+f x)}{3 a c^2 f}-\frac{\csc ^3(e+f x)}{3 a c^2 f}+\frac{\csc (e+f x)}{a c^2 f}","-\frac{\cot ^3(e+f x)}{3 a c^2 f}-\frac{\csc ^3(e+f x)}{3 a c^2 f}+\frac{\csc (e+f x)}{a c^2 f}",1,"-Cot[e + f*x]^3/(3*a*c^2*f) + Csc[e + f*x]/(a*c^2*f) - Csc[e + f*x]^3/(3*a*c^2*f)","A",6,4,32,0.1250,1,"{3958, 2606, 2607, 30}"
40,1,78,0,0.1793226,"\int \frac{\sec (e+f x)}{(a+a \sec (e+f x)) (c-c \sec (e+f x))^3} \, dx","Int[Sec[e + f*x]/((a + a*Sec[e + f*x])*(c - c*Sec[e + f*x])^3),x]","\frac{2 \cot ^5(e+f x)}{5 a c^3 f}+\frac{2 \csc ^5(e+f x)}{5 a c^3 f}-\frac{\csc ^3(e+f x)}{a c^3 f}+\frac{\csc (e+f x)}{a c^3 f}","\frac{2 \cot ^5(e+f x)}{5 a c^3 f}+\frac{2 \csc ^5(e+f x)}{5 a c^3 f}-\frac{\csc ^3(e+f x)}{a c^3 f}+\frac{\csc (e+f x)}{a c^3 f}",1,"(2*Cot[e + f*x]^5)/(5*a*c^3*f) + Csc[e + f*x]/(a*c^3*f) - Csc[e + f*x]^3/(a*c^3*f) + (2*Csc[e + f*x]^5)/(5*a*c^3*f)","A",10,6,32,0.1875,1,"{3958, 2606, 194, 2607, 30, 14}"
41,1,120,0,0.2290385,"\int \frac{\sec (e+f x)}{(a+a \sec (e+f x)) (c-c \sec (e+f x))^4} \, dx","Int[Sec[e + f*x]/((a + a*Sec[e + f*x])*(c - c*Sec[e + f*x])^4),x]","-\frac{4 \cot ^7(e+f x)}{7 a c^4 f}-\frac{\cot ^5(e+f x)}{5 a c^4 f}-\frac{4 \csc ^7(e+f x)}{7 a c^4 f}+\frac{9 \csc ^5(e+f x)}{5 a c^4 f}-\frac{2 \csc ^3(e+f x)}{a c^4 f}+\frac{\csc (e+f x)}{a c^4 f}","-\frac{4 \cot ^7(e+f x)}{7 a c^4 f}-\frac{\cot ^5(e+f x)}{5 a c^4 f}-\frac{4 \csc ^7(e+f x)}{7 a c^4 f}+\frac{9 \csc ^5(e+f x)}{5 a c^4 f}-\frac{2 \csc ^3(e+f x)}{a c^4 f}+\frac{\csc (e+f x)}{a c^4 f}",1,"-Cot[e + f*x]^5/(5*a*c^4*f) - (4*Cot[e + f*x]^7)/(7*a*c^4*f) + Csc[e + f*x]/(a*c^4*f) - (2*Csc[e + f*x]^3)/(a*c^4*f) + (9*Csc[e + f*x]^5)/(5*a*c^4*f) - (4*Csc[e + f*x]^7)/(7*a*c^4*f)","A",13,7,32,0.2188,1,"{3958, 2606, 194, 2607, 30, 270, 14}"
42,1,164,0,0.2469425,"\int \frac{\sec (e+f x) (c-c \sec (e+f x))^5}{(a+a \sec (e+f x))^2} \, dx","Int[(Sec[e + f*x]*(c - c*Sec[e + f*x])^5)/(a + a*Sec[e + f*x])^2,x]","-\frac{7 c^5 \tan ^3(e+f x)}{a^2 f}-\frac{84 c^5 \tan (e+f x)}{a^2 f}+\frac{105 c^5 \tanh ^{-1}(\sin (e+f x))}{2 a^2 f}+\frac{63 c^5 \tan (e+f x) \sec (e+f x)}{2 a^2 f}-\frac{6 c^2 \tan (e+f x) (c-c \sec (e+f x))^3}{f \left(a^2 \sec (e+f x)+a^2\right)}+\frac{2 c \tan (e+f x) (c-c \sec (e+f x))^4}{3 f (a \sec (e+f x)+a)^2}","-\frac{7 c^5 \tan ^3(e+f x)}{a^2 f}-\frac{84 c^5 \tan (e+f x)}{a^2 f}+\frac{105 c^5 \tanh ^{-1}(\sin (e+f x))}{2 a^2 f}+\frac{63 c^5 \tan (e+f x) \sec (e+f x)}{2 a^2 f}-\frac{6 c^2 \tan (e+f x) (c-c \sec (e+f x))^3}{f \left(a^2 \sec (e+f x)+a^2\right)}+\frac{2 c \tan (e+f x) (c-c \sec (e+f x))^4}{3 f (a \sec (e+f x)+a)^2}",1,"(105*c^5*ArcTanh[Sin[e + f*x]])/(2*a^2*f) - (84*c^5*Tan[e + f*x])/(a^2*f) + (63*c^5*Sec[e + f*x]*Tan[e + f*x])/(2*a^2*f) - (6*c^2*(c - c*Sec[e + f*x])^3*Tan[e + f*x])/(f*(a^2 + a^2*Sec[e + f*x])) + (2*c*(c - c*Sec[e + f*x])^4*Tan[e + f*x])/(3*f*(a + a*Sec[e + f*x])^2) - (7*c^5*Tan[e + f*x]^3)/(a^2*f)","A",11,6,32,0.1875,1,"{3957, 3791, 3770, 3767, 8, 3768}"
43,1,150,0,0.2150914,"\int \frac{\sec (e+f x) (c-c \sec (e+f x))^4}{(a+a \sec (e+f x))^2} \, dx","Int[(Sec[e + f*x]*(c - c*Sec[e + f*x])^4)/(a + a*Sec[e + f*x])^2,x]","-\frac{70 c^4 \tan (e+f x)}{3 a^2 f}+\frac{35 c^4 \tanh ^{-1}(\sin (e+f x))}{2 a^2 f}+\frac{35 c^4 \tan (e+f x) \sec (e+f x)}{6 a^2 f}-\frac{14 \tan (e+f x) \left(c^2-c^2 \sec (e+f x)\right)^2}{3 f \left(a^2 \sec (e+f x)+a^2\right)}+\frac{2 c \tan (e+f x) (c-c \sec (e+f x))^3}{3 f (a \sec (e+f x)+a)^2}","-\frac{70 c^4 \tan (e+f x)}{3 a^2 f}+\frac{35 c^4 \tanh ^{-1}(\sin (e+f x))}{2 a^2 f}+\frac{35 c^4 \tan (e+f x) \sec (e+f x)}{6 a^2 f}-\frac{14 \tan (e+f x) \left(c^2-c^2 \sec (e+f x)\right)^2}{3 f \left(a^2 \sec (e+f x)+a^2\right)}+\frac{2 c \tan (e+f x) (c-c \sec (e+f x))^3}{3 f (a \sec (e+f x)+a)^2}",1,"(35*c^4*ArcTanh[Sin[e + f*x]])/(2*a^2*f) - (70*c^4*Tan[e + f*x])/(3*a^2*f) + (35*c^4*Sec[e + f*x]*Tan[e + f*x])/(6*a^2*f) + (2*c*(c - c*Sec[e + f*x])^3*Tan[e + f*x])/(3*f*(a + a*Sec[e + f*x])^2) - (14*(c^2 - c^2*Sec[e + f*x])^2*Tan[e + f*x])/(3*f*(a^2 + a^2*Sec[e + f*x]))","A",7,6,32,0.1875,1,"{3957, 3788, 3767, 8, 4046, 3770}"
44,1,119,0,0.1858869,"\int \frac{\sec (e+f x) (c-c \sec (e+f x))^3}{(a+a \sec (e+f x))^2} \, dx","Int[(Sec[e + f*x]*(c - c*Sec[e + f*x])^3)/(a + a*Sec[e + f*x])^2,x]","-\frac{5 c^3 \tan (e+f x)}{a^2 f}+\frac{5 c^3 \tanh ^{-1}(\sin (e+f x))}{a^2 f}-\frac{10 \tan (e+f x) \left(c^3-c^3 \sec (e+f x)\right)}{3 f \left(a^2 \sec (e+f x)+a^2\right)}+\frac{2 c \tan (e+f x) (c-c \sec (e+f x))^2}{3 f (a \sec (e+f x)+a)^2}","-\frac{5 c^3 \tan (e+f x)}{a^2 f}+\frac{5 c^3 \tanh ^{-1}(\sin (e+f x))}{a^2 f}-\frac{10 \tan (e+f x) \left(c^3-c^3 \sec (e+f x)\right)}{3 f \left(a^2 \sec (e+f x)+a^2\right)}+\frac{2 c \tan (e+f x) (c-c \sec (e+f x))^2}{3 f (a \sec (e+f x)+a)^2}",1,"(5*c^3*ArcTanh[Sin[e + f*x]])/(a^2*f) - (5*c^3*Tan[e + f*x])/(a^2*f) + (2*c*(c - c*Sec[e + f*x])^2*Tan[e + f*x])/(3*f*(a + a*Sec[e + f*x])^2) - (10*(c^3 - c^3*Sec[e + f*x])*Tan[e + f*x])/(3*f*(a^2 + a^2*Sec[e + f*x]))","A",6,5,32,0.1562,1,"{3957, 3787, 3770, 3767, 8}"
45,1,88,0,0.1312766,"\int \frac{\sec (e+f x) (c-c \sec (e+f x))^2}{(a+a \sec (e+f x))^2} \, dx","Int[(Sec[e + f*x]*(c - c*Sec[e + f*x])^2)/(a + a*Sec[e + f*x])^2,x]","\frac{c^2 \tanh ^{-1}(\sin (e+f x))}{a^2 f}-\frac{2 c^2 \tan (e+f x)}{f \left(a^2 \sec (e+f x)+a^2\right)}+\frac{2 \tan (e+f x) \left(c^2-c^2 \sec (e+f x)\right)}{3 f (a \sec (e+f x)+a)^2}","\frac{c^2 \tanh ^{-1}(\sin (e+f x))}{a^2 f}-\frac{2 c^2 \tan (e+f x)}{f \left(a^2 \sec (e+f x)+a^2\right)}+\frac{2 \tan (e+f x) \left(c^2-c^2 \sec (e+f x)\right)}{3 f (a \sec (e+f x)+a)^2}",1,"(c^2*ArcTanh[Sin[e + f*x]])/(a^2*f) - (2*c^2*Tan[e + f*x])/(f*(a^2 + a^2*Sec[e + f*x])) + (2*(c^2 - c^2*Sec[e + f*x])*Tan[e + f*x])/(3*f*(a + a*Sec[e + f*x])^2)","A",3,2,32,0.06250,1,"{3957, 3770}"
46,1,36,0,0.047863,"\int \frac{\sec (e+f x) (c-c \sec (e+f x))}{(a+a \sec (e+f x))^2} \, dx","Int[(Sec[e + f*x]*(c - c*Sec[e + f*x]))/(a + a*Sec[e + f*x])^2,x]","\frac{\tan (e+f x) (c-c \sec (e+f x))}{3 f (a \sec (e+f x)+a)^2}","\frac{\tan (e+f x) (c-c \sec (e+f x))}{3 f (a \sec (e+f x)+a)^2}",1,"((c - c*Sec[e + f*x])*Tan[e + f*x])/(3*f*(a + a*Sec[e + f*x])^2)","A",1,1,30,0.03333,1,"{3950}"
47,1,59,0,0.1361555,"\int \frac{\sec (e+f x)}{(a+a \sec (e+f x))^2 (c-c \sec (e+f x))} \, dx","Int[Sec[e + f*x]/((a + a*Sec[e + f*x])^2*(c - c*Sec[e + f*x])),x]","\frac{\cot ^3(e+f x)}{3 a^2 c f}-\frac{\csc ^3(e+f x)}{3 a^2 c f}+\frac{\csc (e+f x)}{a^2 c f}","\frac{\cot ^3(e+f x)}{3 a^2 c f}-\frac{\csc ^3(e+f x)}{3 a^2 c f}+\frac{\csc (e+f x)}{a^2 c f}",1,"Cot[e + f*x]^3/(3*a^2*c*f) + Csc[e + f*x]/(a^2*c*f) - Csc[e + f*x]^3/(3*a^2*c*f)","A",6,4,32,0.1250,1,"{3958, 2606, 2607, 30}"
48,1,38,0,0.0981878,"\int \frac{\sec (e+f x)}{(a+a \sec (e+f x))^2 (c-c \sec (e+f x))^2} \, dx","Int[Sec[e + f*x]/((a + a*Sec[e + f*x])^2*(c - c*Sec[e + f*x])^2),x]","\frac{\csc (e+f x)}{a^2 c^2 f}-\frac{\csc ^3(e+f x)}{3 a^2 c^2 f}","\frac{\csc (e+f x)}{a^2 c^2 f}-\frac{\csc ^3(e+f x)}{3 a^2 c^2 f}",1,"Csc[e + f*x]/(a^2*c^2*f) - Csc[e + f*x]^3/(3*a^2*c^2*f)","A",3,2,32,0.06250,1,"{3958, 2606}"
49,1,80,0,0.146201,"\int \frac{\sec (e+f x)}{(a+a \sec (e+f x))^2 (c-c \sec (e+f x))^3} \, dx","Int[Sec[e + f*x]/((a + a*Sec[e + f*x])^2*(c - c*Sec[e + f*x])^3),x]","\frac{\cot ^5(e+f x)}{5 a^2 c^3 f}+\frac{\csc ^5(e+f x)}{5 a^2 c^3 f}-\frac{2 \csc ^3(e+f x)}{3 a^2 c^3 f}+\frac{\csc (e+f x)}{a^2 c^3 f}","\frac{\cot ^5(e+f x)}{5 a^2 c^3 f}+\frac{\csc ^5(e+f x)}{5 a^2 c^3 f}-\frac{2 \csc ^3(e+f x)}{3 a^2 c^3 f}+\frac{\csc (e+f x)}{a^2 c^3 f}",1,"Cot[e + f*x]^5/(5*a^2*c^3*f) + Csc[e + f*x]/(a^2*c^3*f) - (2*Csc[e + f*x]^3)/(3*a^2*c^3*f) + Csc[e + f*x]^5/(5*a^2*c^3*f)","A",7,5,32,0.1562,1,"{3958, 2606, 194, 2607, 30}"
50,1,98,0,0.1885725,"\int \frac{\sec (e+f x)}{(a+a \sec (e+f x))^2 (c-c \sec (e+f x))^4} \, dx","Int[Sec[e + f*x]/((a + a*Sec[e + f*x])^2*(c - c*Sec[e + f*x])^4),x]","-\frac{2 \cot ^7(e+f x)}{7 a^2 c^4 f}-\frac{2 \csc ^7(e+f x)}{7 a^2 c^4 f}+\frac{\csc ^5(e+f x)}{a^2 c^4 f}-\frac{4 \csc ^3(e+f x)}{3 a^2 c^4 f}+\frac{\csc (e+f x)}{a^2 c^4 f}","-\frac{2 \cot ^7(e+f x)}{7 a^2 c^4 f}-\frac{2 \csc ^7(e+f x)}{7 a^2 c^4 f}+\frac{\csc ^5(e+f x)}{a^2 c^4 f}-\frac{4 \csc ^3(e+f x)}{3 a^2 c^4 f}+\frac{\csc (e+f x)}{a^2 c^4 f}",1,"(-2*Cot[e + f*x]^7)/(7*a^2*c^4*f) + Csc[e + f*x]/(a^2*c^4*f) - (4*Csc[e + f*x]^3)/(3*a^2*c^4*f) + Csc[e + f*x]^5/(a^2*c^4*f) - (2*Csc[e + f*x]^7)/(7*a^2*c^4*f)","A",10,6,32,0.1875,1,"{3958, 2606, 194, 2607, 30, 270}"
51,1,141,0,0.2455912,"\int \frac{\sec (e+f x)}{(a+a \sec (e+f x))^2 (c-c \sec (e+f x))^5} \, dx","Int[Sec[e + f*x]/((a + a*Sec[e + f*x])^2*(c - c*Sec[e + f*x])^5),x]","\frac{4 \cot ^9(e+f x)}{9 a^2 c^5 f}+\frac{\cot ^7(e+f x)}{7 a^2 c^5 f}+\frac{4 \csc ^9(e+f x)}{9 a^2 c^5 f}-\frac{13 \csc ^7(e+f x)}{7 a^2 c^5 f}+\frac{3 \csc ^5(e+f x)}{a^2 c^5 f}-\frac{7 \csc ^3(e+f x)}{3 a^2 c^5 f}+\frac{\csc (e+f x)}{a^2 c^5 f}","\frac{4 \cot ^9(e+f x)}{9 a^2 c^5 f}+\frac{\cot ^7(e+f x)}{7 a^2 c^5 f}+\frac{4 \csc ^9(e+f x)}{9 a^2 c^5 f}-\frac{13 \csc ^7(e+f x)}{7 a^2 c^5 f}+\frac{3 \csc ^5(e+f x)}{a^2 c^5 f}-\frac{7 \csc ^3(e+f x)}{3 a^2 c^5 f}+\frac{\csc (e+f x)}{a^2 c^5 f}",1,"Cot[e + f*x]^7/(7*a^2*c^5*f) + (4*Cot[e + f*x]^9)/(9*a^2*c^5*f) + Csc[e + f*x]/(a^2*c^5*f) - (7*Csc[e + f*x]^3)/(3*a^2*c^5*f) + (3*Csc[e + f*x]^5)/(a^2*c^5*f) - (13*Csc[e + f*x]^7)/(7*a^2*c^5*f) + (4*Csc[e + f*x]^9)/(9*a^2*c^5*f)","A",13,7,32,0.2188,1,"{3958, 2606, 194, 2607, 30, 270, 14}"
52,1,215,0,0.3361451,"\int \frac{\sec (e+f x) (c-c \sec (e+f x))^6}{(a+a \sec (e+f x))^3} \, dx","Int[(Sec[e + f*x]*(c - c*Sec[e + f*x])^6)/(a + a*Sec[e + f*x])^3,x]","\frac{77 c^6 \tan ^3(e+f x)}{5 a^3 f}+\frac{924 c^6 \tan (e+f x)}{5 a^3 f}-\frac{231 c^6 \tanh ^{-1}(\sin (e+f x))}{2 a^3 f}-\frac{693 c^6 \tan (e+f x) \sec (e+f x)}{10 a^3 f}+\frac{66 \tan (e+f x) \left(c^2-c^2 \sec (e+f x)\right)^3}{5 f \left(a^3 \sec (e+f x)+a^3\right)}-\frac{22 c^2 \tan (e+f x) (c-c \sec (e+f x))^4}{15 a f (a \sec (e+f x)+a)^2}+\frac{2 c \tan (e+f x) (c-c \sec (e+f x))^5}{5 f (a \sec (e+f x)+a)^3}","\frac{77 c^6 \tan ^3(e+f x)}{5 a^3 f}+\frac{924 c^6 \tan (e+f x)}{5 a^3 f}-\frac{231 c^6 \tanh ^{-1}(\sin (e+f x))}{2 a^3 f}-\frac{693 c^6 \tan (e+f x) \sec (e+f x)}{10 a^3 f}+\frac{66 \tan (e+f x) \left(c^2-c^2 \sec (e+f x)\right)^3}{5 f \left(a^3 \sec (e+f x)+a^3\right)}-\frac{22 c^2 \tan (e+f x) (c-c \sec (e+f x))^4}{15 a f (a \sec (e+f x)+a)^2}+\frac{2 c \tan (e+f x) (c-c \sec (e+f x))^5}{5 f (a \sec (e+f x)+a)^3}",1,"(-231*c^6*ArcTanh[Sin[e + f*x]])/(2*a^3*f) + (924*c^6*Tan[e + f*x])/(5*a^3*f) - (693*c^6*Sec[e + f*x]*Tan[e + f*x])/(10*a^3*f) - (22*c^2*(c - c*Sec[e + f*x])^4*Tan[e + f*x])/(15*a*f*(a + a*Sec[e + f*x])^2) + (2*c*(c - c*Sec[e + f*x])^5*Tan[e + f*x])/(5*f*(a + a*Sec[e + f*x])^3) + (66*(c^2 - c^2*Sec[e + f*x])^3*Tan[e + f*x])/(5*f*(a^3 + a^3*Sec[e + f*x])) + (77*c^6*Tan[e + f*x]^3)/(5*a^3*f)","A",12,6,32,0.1875,1,"{3957, 3791, 3770, 3767, 8, 3768}"
53,1,193,0,0.309145,"\int \frac{\sec (e+f x) (c-c \sec (e+f x))^5}{(a+a \sec (e+f x))^3} \, dx","Int[(Sec[e + f*x]*(c - c*Sec[e + f*x])^5)/(a + a*Sec[e + f*x])^3,x]","\frac{42 c^5 \tan (e+f x)}{a^3 f}-\frac{63 c^5 \tanh ^{-1}(\sin (e+f x))}{2 a^3 f}-\frac{21 c^5 \tan (e+f x) \sec (e+f x)}{2 a^3 f}+\frac{42 c \tan (e+f x) \left(c^2-c^2 \sec (e+f x)\right)^2}{5 f \left(a^3 \sec (e+f x)+a^3\right)}-\frac{6 c^2 \tan (e+f x) (c-c \sec (e+f x))^3}{5 a f (a \sec (e+f x)+a)^2}+\frac{2 c \tan (e+f x) (c-c \sec (e+f x))^4}{5 f (a \sec (e+f x)+a)^3}","\frac{42 c^5 \tan (e+f x)}{a^3 f}-\frac{63 c^5 \tanh ^{-1}(\sin (e+f x))}{2 a^3 f}-\frac{21 c^5 \tan (e+f x) \sec (e+f x)}{2 a^3 f}+\frac{42 c \tan (e+f x) \left(c^2-c^2 \sec (e+f x)\right)^2}{5 f \left(a^3 \sec (e+f x)+a^3\right)}-\frac{6 c^2 \tan (e+f x) (c-c \sec (e+f x))^3}{5 a f (a \sec (e+f x)+a)^2}+\frac{2 c \tan (e+f x) (c-c \sec (e+f x))^4}{5 f (a \sec (e+f x)+a)^3}",1,"(-63*c^5*ArcTanh[Sin[e + f*x]])/(2*a^3*f) + (42*c^5*Tan[e + f*x])/(a^3*f) - (21*c^5*Sec[e + f*x]*Tan[e + f*x])/(2*a^3*f) - (6*c^2*(c - c*Sec[e + f*x])^3*Tan[e + f*x])/(5*a*f*(a + a*Sec[e + f*x])^2) + (2*c*(c - c*Sec[e + f*x])^4*Tan[e + f*x])/(5*f*(a + a*Sec[e + f*x])^3) + (42*c*(c^2 - c^2*Sec[e + f*x])^2*Tan[e + f*x])/(5*f*(a^3 + a^3*Sec[e + f*x]))","A",8,6,32,0.1875,1,"{3957, 3788, 3767, 8, 4046, 3770}"
54,1,164,0,0.2752213,"\int \frac{\sec (e+f x) (c-c \sec (e+f x))^4}{(a+a \sec (e+f x))^3} \, dx","Int[(Sec[e + f*x]*(c - c*Sec[e + f*x])^4)/(a + a*Sec[e + f*x])^3,x]","\frac{7 c^4 \tan (e+f x)}{a^3 f}-\frac{7 c^4 \tanh ^{-1}(\sin (e+f x))}{a^3 f}+\frac{14 \tan (e+f x) \left(c^4-c^4 \sec (e+f x)\right)}{3 f \left(a^3 \sec (e+f x)+a^3\right)}-\frac{14 \tan (e+f x) \left(c^2-c^2 \sec (e+f x)\right)^2}{15 a f (a \sec (e+f x)+a)^2}+\frac{2 c \tan (e+f x) (c-c \sec (e+f x))^3}{5 f (a \sec (e+f x)+a)^3}","\frac{7 c^4 \tan (e+f x)}{a^3 f}-\frac{7 c^4 \tanh ^{-1}(\sin (e+f x))}{a^3 f}+\frac{14 \tan (e+f x) \left(c^4-c^4 \sec (e+f x)\right)}{3 f \left(a^3 \sec (e+f x)+a^3\right)}-\frac{14 \tan (e+f x) \left(c^2-c^2 \sec (e+f x)\right)^2}{15 a f (a \sec (e+f x)+a)^2}+\frac{2 c \tan (e+f x) (c-c \sec (e+f x))^3}{5 f (a \sec (e+f x)+a)^3}",1,"(-7*c^4*ArcTanh[Sin[e + f*x]])/(a^3*f) + (7*c^4*Tan[e + f*x])/(a^3*f) + (2*c*(c - c*Sec[e + f*x])^3*Tan[e + f*x])/(5*f*(a + a*Sec[e + f*x])^3) - (14*(c^2 - c^2*Sec[e + f*x])^2*Tan[e + f*x])/(15*a*f*(a + a*Sec[e + f*x])^2) + (14*(c^4 - c^4*Sec[e + f*x])*Tan[e + f*x])/(3*f*(a^3 + a^3*Sec[e + f*x]))","A",7,5,32,0.1562,1,"{3957, 3787, 3770, 3767, 8}"
55,1,131,0,0.214818,"\int \frac{\sec (e+f x) (c-c \sec (e+f x))^3}{(a+a \sec (e+f x))^3} \, dx","Int[(Sec[e + f*x]*(c - c*Sec[e + f*x])^3)/(a + a*Sec[e + f*x])^3,x]","-\frac{c^3 \tanh ^{-1}(\sin (e+f x))}{a^3 f}+\frac{2 c^3 \tan (e+f x)}{f \left(a^3 \sec (e+f x)+a^3\right)}-\frac{2 \tan (e+f x) \left(c^3-c^3 \sec (e+f x)\right)}{3 a f (a \sec (e+f x)+a)^2}+\frac{2 c \tan (e+f x) (c-c \sec (e+f x))^2}{5 f (a \sec (e+f x)+a)^3}","-\frac{c^3 \tanh ^{-1}(\sin (e+f x))}{a^3 f}+\frac{2 c^3 \tan (e+f x)}{f \left(a^3 \sec (e+f x)+a^3\right)}-\frac{2 \tan (e+f x) \left(c^3-c^3 \sec (e+f x)\right)}{3 a f (a \sec (e+f x)+a)^2}+\frac{2 c \tan (e+f x) (c-c \sec (e+f x))^2}{5 f (a \sec (e+f x)+a)^3}",1,"-((c^3*ArcTanh[Sin[e + f*x]])/(a^3*f)) + (2*c^3*Tan[e + f*x])/(f*(a^3 + a^3*Sec[e + f*x])) + (2*c*(c - c*Sec[e + f*x])^2*Tan[e + f*x])/(5*f*(a + a*Sec[e + f*x])^3) - (2*(c^3 - c^3*Sec[e + f*x])*Tan[e + f*x])/(3*a*f*(a + a*Sec[e + f*x])^2)","A",4,2,32,0.06250,1,"{3957, 3770}"
56,1,38,0,0.0737364,"\int \frac{\sec (e+f x) (c-c \sec (e+f x))^2}{(a+a \sec (e+f x))^3} \, dx","Int[(Sec[e + f*x]*(c - c*Sec[e + f*x])^2)/(a + a*Sec[e + f*x])^3,x]","\frac{\tan (e+f x) (c-c \sec (e+f x))^2}{5 f (a \sec (e+f x)+a)^3}","\frac{\tan (e+f x) (c-c \sec (e+f x))^2}{5 f (a \sec (e+f x)+a)^3}",1,"((c - c*Sec[e + f*x])^2*Tan[e + f*x])/(5*f*(a + a*Sec[e + f*x])^3)","A",1,1,32,0.03125,1,"{3950}"
57,1,76,0,0.0987711,"\int \frac{\sec (e+f x) (c-c \sec (e+f x))}{(a+a \sec (e+f x))^3} \, dx","Int[(Sec[e + f*x]*(c - c*Sec[e + f*x]))/(a + a*Sec[e + f*x])^3,x]","\frac{\tan (e+f x) (c-c \sec (e+f x))}{15 a f (a \sec (e+f x)+a)^2}+\frac{\tan (e+f x) (c-c \sec (e+f x))}{5 f (a \sec (e+f x)+a)^3}","\frac{\tan (e+f x) (c-c \sec (e+f x))}{15 a f (a \sec (e+f x)+a)^2}+\frac{\tan (e+f x) (c-c \sec (e+f x))}{5 f (a \sec (e+f x)+a)^3}",1,"((c - c*Sec[e + f*x])*Tan[e + f*x])/(5*f*(a + a*Sec[e + f*x])^3) + ((c - c*Sec[e + f*x])*Tan[e + f*x])/(15*a*f*(a + a*Sec[e + f*x])^2)","A",2,2,30,0.06667,1,"{3951, 3950}"
58,1,78,0,0.1809931,"\int \frac{\sec (e+f x)}{(a+a \sec (e+f x))^3 (c-c \sec (e+f x))} \, dx","Int[Sec[e + f*x]/((a + a*Sec[e + f*x])^3*(c - c*Sec[e + f*x])),x]","-\frac{2 \cot ^5(e+f x)}{5 a^3 c f}+\frac{2 \csc ^5(e+f x)}{5 a^3 c f}-\frac{\csc ^3(e+f x)}{a^3 c f}+\frac{\csc (e+f x)}{a^3 c f}","-\frac{2 \cot ^5(e+f x)}{5 a^3 c f}+\frac{2 \csc ^5(e+f x)}{5 a^3 c f}-\frac{\csc ^3(e+f x)}{a^3 c f}+\frac{\csc (e+f x)}{a^3 c f}",1,"(-2*Cot[e + f*x]^5)/(5*a^3*c*f) + Csc[e + f*x]/(a^3*c*f) - Csc[e + f*x]^3/(a^3*c*f) + (2*Csc[e + f*x]^5)/(5*a^3*c*f)","A",10,6,32,0.1875,1,"{3958, 2606, 194, 2607, 30, 14}"
59,1,80,0,0.1416156,"\int \frac{\sec (e+f x)}{(a+a \sec (e+f x))^3 (c-c \sec (e+f x))^2} \, dx","Int[Sec[e + f*x]/((a + a*Sec[e + f*x])^3*(c - c*Sec[e + f*x])^2),x]","-\frac{\cot ^5(e+f x)}{5 a^3 c^2 f}+\frac{\csc ^5(e+f x)}{5 a^3 c^2 f}-\frac{2 \csc ^3(e+f x)}{3 a^3 c^2 f}+\frac{\csc (e+f x)}{a^3 c^2 f}","-\frac{\cot ^5(e+f x)}{5 a^3 c^2 f}+\frac{\csc ^5(e+f x)}{5 a^3 c^2 f}-\frac{2 \csc ^3(e+f x)}{3 a^3 c^2 f}+\frac{\csc (e+f x)}{a^3 c^2 f}",1,"-Cot[e + f*x]^5/(5*a^3*c^2*f) + Csc[e + f*x]/(a^3*c^2*f) - (2*Csc[e + f*x]^3)/(3*a^3*c^2*f) + Csc[e + f*x]^5/(5*a^3*c^2*f)","A",7,5,32,0.1562,1,"{3958, 2606, 194, 2607, 30}"
60,1,59,0,0.1086732,"\int \frac{\sec (e+f x)}{(a+a \sec (e+f x))^3 (c-c \sec (e+f x))^3} \, dx","Int[Sec[e + f*x]/((a + a*Sec[e + f*x])^3*(c - c*Sec[e + f*x])^3),x]","\frac{\csc ^5(e+f x)}{5 a^3 c^3 f}-\frac{2 \csc ^3(e+f x)}{3 a^3 c^3 f}+\frac{\csc (e+f x)}{a^3 c^3 f}","\frac{\csc ^5(e+f x)}{5 a^3 c^3 f}-\frac{2 \csc ^3(e+f x)}{3 a^3 c^3 f}+\frac{\csc (e+f x)}{a^3 c^3 f}",1,"Csc[e + f*x]/(a^3*c^3*f) - (2*Csc[e + f*x]^3)/(3*a^3*c^3*f) + Csc[e + f*x]^5/(5*a^3*c^3*f)","A",4,3,32,0.09375,1,"{3958, 2606, 194}"
61,1,99,0,0.1489941,"\int \frac{\sec (e+f x)}{(a+a \sec (e+f x))^3 (c-c \sec (e+f x))^4} \, dx","Int[Sec[e + f*x]/((a + a*Sec[e + f*x])^3*(c - c*Sec[e + f*x])^4),x]","-\frac{\cot ^7(e+f x)}{7 a^3 c^4 f}-\frac{\csc ^7(e+f x)}{7 a^3 c^4 f}+\frac{3 \csc ^5(e+f x)}{5 a^3 c^4 f}-\frac{\csc ^3(e+f x)}{a^3 c^4 f}+\frac{\csc (e+f x)}{a^3 c^4 f}","-\frac{\cot ^7(e+f x)}{7 a^3 c^4 f}-\frac{\csc ^7(e+f x)}{7 a^3 c^4 f}+\frac{3 \csc ^5(e+f x)}{5 a^3 c^4 f}-\frac{\csc ^3(e+f x)}{a^3 c^4 f}+\frac{\csc (e+f x)}{a^3 c^4 f}",1,"-Cot[e + f*x]^7/(7*a^3*c^4*f) + Csc[e + f*x]/(a^3*c^4*f) - Csc[e + f*x]^3/(a^3*c^4*f) + (3*Csc[e + f*x]^5)/(5*a^3*c^4*f) - Csc[e + f*x]^7/(7*a^3*c^4*f)","A",7,5,32,0.1562,1,"{3958, 2606, 194, 2607, 30}"
62,1,120,0,0.2041631,"\int \frac{\sec (e+f x)}{(a+a \sec (e+f x))^3 (c-c \sec (e+f x))^5} \, dx","Int[Sec[e + f*x]/((a + a*Sec[e + f*x])^3*(c - c*Sec[e + f*x])^5),x]","\frac{2 \cot ^9(e+f x)}{9 a^3 c^5 f}+\frac{2 \csc ^9(e+f x)}{9 a^3 c^5 f}-\frac{\csc ^7(e+f x)}{a^3 c^5 f}+\frac{9 \csc ^5(e+f x)}{5 a^3 c^5 f}-\frac{5 \csc ^3(e+f x)}{3 a^3 c^5 f}+\frac{\csc (e+f x)}{a^3 c^5 f}","\frac{2 \cot ^9(e+f x)}{9 a^3 c^5 f}+\frac{2 \csc ^9(e+f x)}{9 a^3 c^5 f}-\frac{\csc ^7(e+f x)}{a^3 c^5 f}+\frac{9 \csc ^5(e+f x)}{5 a^3 c^5 f}-\frac{5 \csc ^3(e+f x)}{3 a^3 c^5 f}+\frac{\csc (e+f x)}{a^3 c^5 f}",1,"(2*Cot[e + f*x]^9)/(9*a^3*c^5*f) + Csc[e + f*x]/(a^3*c^5*f) - (5*Csc[e + f*x]^3)/(3*a^3*c^5*f) + (9*Csc[e + f*x]^5)/(5*a^3*c^5*f) - Csc[e + f*x]^7/(a^3*c^5*f) + (2*Csc[e + f*x]^9)/(9*a^3*c^5*f)","A",10,6,32,0.1875,1,"{3958, 2606, 194, 2607, 30, 270}"
63,1,162,0,0.2598664,"\int \frac{\sec (e+f x)}{(a+a \sec (e+f x))^3 (c-c \sec (e+f x))^6} \, dx","Int[Sec[e + f*x]/((a + a*Sec[e + f*x])^3*(c - c*Sec[e + f*x])^6),x]","-\frac{4 \cot ^{11}(e+f x)}{11 a^3 c^6 f}-\frac{\cot ^9(e+f x)}{9 a^3 c^6 f}-\frac{4 \csc ^{11}(e+f x)}{11 a^3 c^6 f}+\frac{17 \csc ^9(e+f x)}{9 a^3 c^6 f}-\frac{4 \csc ^7(e+f x)}{a^3 c^6 f}+\frac{22 \csc ^5(e+f x)}{5 a^3 c^6 f}-\frac{8 \csc ^3(e+f x)}{3 a^3 c^6 f}+\frac{\csc (e+f x)}{a^3 c^6 f}","-\frac{4 \cot ^{11}(e+f x)}{11 a^3 c^6 f}-\frac{\cot ^9(e+f x)}{9 a^3 c^6 f}-\frac{4 \csc ^{11}(e+f x)}{11 a^3 c^6 f}+\frac{17 \csc ^9(e+f x)}{9 a^3 c^6 f}-\frac{4 \csc ^7(e+f x)}{a^3 c^6 f}+\frac{22 \csc ^5(e+f x)}{5 a^3 c^6 f}-\frac{8 \csc ^3(e+f x)}{3 a^3 c^6 f}+\frac{\csc (e+f x)}{a^3 c^6 f}",1,"-Cot[e + f*x]^9/(9*a^3*c^6*f) - (4*Cot[e + f*x]^11)/(11*a^3*c^6*f) + Csc[e + f*x]/(a^3*c^6*f) - (8*Csc[e + f*x]^3)/(3*a^3*c^6*f) + (22*Csc[e + f*x]^5)/(5*a^3*c^6*f) - (4*Csc[e + f*x]^7)/(a^3*c^6*f) + (17*Csc[e + f*x]^9)/(9*a^3*c^6*f) - (4*Csc[e + f*x]^11)/(11*a^3*c^6*f)","A",13,7,32,0.2188,1,"{3958, 2606, 194, 2607, 30, 270, 14}"
64,1,163,0,0.2776567,"\int \sec (e+f x) (a+a \sec (e+f x)) (c-c \sec (e+f x))^{7/2} \, dx","Int[Sec[e + f*x]*(a + a*Sec[e + f*x])*(c - c*Sec[e + f*x])^(7/2),x]","-\frac{256 c^4 \tan (e+f x) (a \sec (e+f x)+a)}{315 f \sqrt{c-c \sec (e+f x)}}-\frac{64 c^3 \tan (e+f x) (a \sec (e+f x)+a) \sqrt{c-c \sec (e+f x)}}{105 f}-\frac{8 c^2 \tan (e+f x) (a \sec (e+f x)+a) (c-c \sec (e+f x))^{3/2}}{21 f}-\frac{2 c \tan (e+f x) (a \sec (e+f x)+a) (c-c \sec (e+f x))^{5/2}}{9 f}","-\frac{256 c^4 \tan (e+f x) (a \sec (e+f x)+a)}{315 f \sqrt{c-c \sec (e+f x)}}-\frac{64 c^3 \tan (e+f x) (a \sec (e+f x)+a) \sqrt{c-c \sec (e+f x)}}{105 f}-\frac{8 c^2 \tan (e+f x) (a \sec (e+f x)+a) (c-c \sec (e+f x))^{3/2}}{21 f}-\frac{2 c \tan (e+f x) (a \sec (e+f x)+a) (c-c \sec (e+f x))^{5/2}}{9 f}",1,"(-256*c^4*(a + a*Sec[e + f*x])*Tan[e + f*x])/(315*f*Sqrt[c - c*Sec[e + f*x]]) - (64*c^3*(a + a*Sec[e + f*x])*Sqrt[c - c*Sec[e + f*x]]*Tan[e + f*x])/(105*f) - (8*c^2*(a + a*Sec[e + f*x])*(c - c*Sec[e + f*x])^(3/2)*Tan[e + f*x])/(21*f) - (2*c*(a + a*Sec[e + f*x])*(c - c*Sec[e + f*x])^(5/2)*Tan[e + f*x])/(9*f)","A",4,2,32,0.06250,1,"{3955, 3953}"
65,1,122,0,0.2003548,"\int \sec (e+f x) (a+a \sec (e+f x)) (c-c \sec (e+f x))^{5/2} \, dx","Int[Sec[e + f*x]*(a + a*Sec[e + f*x])*(c - c*Sec[e + f*x])^(5/2),x]","-\frac{64 c^3 \tan (e+f x) (a \sec (e+f x)+a)}{105 f \sqrt{c-c \sec (e+f x)}}-\frac{16 c^2 \tan (e+f x) (a \sec (e+f x)+a) \sqrt{c-c \sec (e+f x)}}{35 f}-\frac{2 c \tan (e+f x) (a \sec (e+f x)+a) (c-c \sec (e+f x))^{3/2}}{7 f}","-\frac{64 c^3 \tan (e+f x) (a \sec (e+f x)+a)}{105 f \sqrt{c-c \sec (e+f x)}}-\frac{16 c^2 \tan (e+f x) (a \sec (e+f x)+a) \sqrt{c-c \sec (e+f x)}}{35 f}-\frac{2 c \tan (e+f x) (a \sec (e+f x)+a) (c-c \sec (e+f x))^{3/2}}{7 f}",1,"(-64*c^3*(a + a*Sec[e + f*x])*Tan[e + f*x])/(105*f*Sqrt[c - c*Sec[e + f*x]]) - (16*c^2*(a + a*Sec[e + f*x])*Sqrt[c - c*Sec[e + f*x]]*Tan[e + f*x])/(35*f) - (2*c*(a + a*Sec[e + f*x])*(c - c*Sec[e + f*x])^(3/2)*Tan[e + f*x])/(7*f)","A",3,2,32,0.06250,1,"{3955, 3953}"
66,1,81,0,0.1278021,"\int \sec (e+f x) (a+a \sec (e+f x)) (c-c \sec (e+f x))^{3/2} \, dx","Int[Sec[e + f*x]*(a + a*Sec[e + f*x])*(c - c*Sec[e + f*x])^(3/2),x]","-\frac{8 c^2 \tan (e+f x) (a \sec (e+f x)+a)}{15 f \sqrt{c-c \sec (e+f x)}}-\frac{2 c \tan (e+f x) (a \sec (e+f x)+a) \sqrt{c-c \sec (e+f x)}}{5 f}","-\frac{8 c^2 \tan (e+f x) (a \sec (e+f x)+a)}{15 f \sqrt{c-c \sec (e+f x)}}-\frac{2 c \tan (e+f x) (a \sec (e+f x)+a) \sqrt{c-c \sec (e+f x)}}{5 f}",1,"(-8*c^2*(a + a*Sec[e + f*x])*Tan[e + f*x])/(15*f*Sqrt[c - c*Sec[e + f*x]]) - (2*c*(a + a*Sec[e + f*x])*Sqrt[c - c*Sec[e + f*x]]*Tan[e + f*x])/(5*f)","A",2,2,32,0.06250,1,"{3955, 3953}"
67,1,39,0,0.0591537,"\int \sec (e+f x) (a+a \sec (e+f x)) \sqrt{c-c \sec (e+f x)} \, dx","Int[Sec[e + f*x]*(a + a*Sec[e + f*x])*Sqrt[c - c*Sec[e + f*x]],x]","-\frac{2 c \tan (e+f x) (a \sec (e+f x)+a)}{3 f \sqrt{c-c \sec (e+f x)}}","-\frac{2 c \tan (e+f x) (a \sec (e+f x)+a)}{3 f \sqrt{c-c \sec (e+f x)}}",1,"(-2*c*(a + a*Sec[e + f*x])*Tan[e + f*x])/(3*f*Sqrt[c - c*Sec[e + f*x]])","A",1,1,32,0.03125,1,"{3953}"
68,1,77,0,0.1068491,"\int \frac{\sec (e+f x) (a+a \sec (e+f x))}{\sqrt{c-c \sec (e+f x)}} \, dx","Int[(Sec[e + f*x]*(a + a*Sec[e + f*x]))/Sqrt[c - c*Sec[e + f*x]],x]","\frac{2 a \tan (e+f x)}{f \sqrt{c-c \sec (e+f x)}}-\frac{2 \sqrt{2} a \tan ^{-1}\left(\frac{\sqrt{c} \tan (e+f x)}{\sqrt{2} \sqrt{c-c \sec (e+f x)}}\right)}{\sqrt{c} f}","\frac{2 a \tan (e+f x)}{f \sqrt{c-c \sec (e+f x)}}-\frac{2 \sqrt{2} a \tan ^{-1}\left(\frac{\sqrt{c} \tan (e+f x)}{\sqrt{2} \sqrt{c-c \sec (e+f x)}}\right)}{\sqrt{c} f}",1,"(-2*Sqrt[2]*a*ArcTan[(Sqrt[c]*Tan[e + f*x])/(Sqrt[2]*Sqrt[c - c*Sec[e + f*x]])])/(Sqrt[c]*f) + (2*a*Tan[e + f*x])/(f*Sqrt[c - c*Sec[e + f*x]])","A",3,3,32,0.09375,1,"{3956, 3795, 203}"
69,1,76,0,0.1144231,"\int \frac{\sec (e+f x) (a+a \sec (e+f x))}{(c-c \sec (e+f x))^{3/2}} \, dx","Int[(Sec[e + f*x]*(a + a*Sec[e + f*x]))/(c - c*Sec[e + f*x])^(3/2),x]","\frac{a \tan ^{-1}\left(\frac{\sqrt{c} \tan (e+f x)}{\sqrt{2} \sqrt{c-c \sec (e+f x)}}\right)}{\sqrt{2} c^{3/2} f}-\frac{a \tan (e+f x)}{f (c-c \sec (e+f x))^{3/2}}","\frac{a \tan ^{-1}\left(\frac{\sqrt{c} \tan (e+f x)}{\sqrt{2} \sqrt{c-c \sec (e+f x)}}\right)}{\sqrt{2} c^{3/2} f}-\frac{a \tan (e+f x)}{f (c-c \sec (e+f x))^{3/2}}",1,"(a*ArcTan[(Sqrt[c]*Tan[e + f*x])/(Sqrt[2]*Sqrt[c - c*Sec[e + f*x]])])/(Sqrt[2]*c^(3/2)*f) - (a*Tan[e + f*x])/(f*(c - c*Sec[e + f*x])^(3/2))","A",3,3,32,0.09375,1,"{3957, 3795, 203}"
70,1,113,0,0.1548825,"\int \frac{\sec (e+f x) (a+a \sec (e+f x))}{(c-c \sec (e+f x))^{5/2}} \, dx","Int[(Sec[e + f*x]*(a + a*Sec[e + f*x]))/(c - c*Sec[e + f*x])^(5/2),x]","\frac{a \tan ^{-1}\left(\frac{\sqrt{c} \tan (e+f x)}{\sqrt{2} \sqrt{c-c \sec (e+f x)}}\right)}{8 \sqrt{2} c^{5/2} f}+\frac{a \tan (e+f x)}{8 c f (c-c \sec (e+f x))^{3/2}}-\frac{a \tan (e+f x)}{2 f (c-c \sec (e+f x))^{5/2}}","\frac{a \tan ^{-1}\left(\frac{\sqrt{c} \tan (e+f x)}{\sqrt{2} \sqrt{c-c \sec (e+f x)}}\right)}{8 \sqrt{2} c^{5/2} f}+\frac{a \tan (e+f x)}{8 c f (c-c \sec (e+f x))^{3/2}}-\frac{a \tan (e+f x)}{2 f (c-c \sec (e+f x))^{5/2}}",1,"(a*ArcTan[(Sqrt[c]*Tan[e + f*x])/(Sqrt[2]*Sqrt[c - c*Sec[e + f*x]])])/(8*Sqrt[2]*c^(5/2)*f) - (a*Tan[e + f*x])/(2*f*(c - c*Sec[e + f*x])^(5/2)) + (a*Tan[e + f*x])/(8*c*f*(c - c*Sec[e + f*x])^(3/2))","A",4,4,32,0.1250,1,"{3957, 3796, 3795, 203}"
71,1,171,0,0.4479412,"\int \sec (e+f x) (a+a \sec (e+f x))^2 (c-c \sec (e+f x))^{7/2} \, dx","Int[Sec[e + f*x]*(a + a*Sec[e + f*x])^2*(c - c*Sec[e + f*x])^(7/2),x]","-\frac{256 c^4 \tan (e+f x) (a \sec (e+f x)+a)^2}{1155 f \sqrt{c-c \sec (e+f x)}}-\frac{64 c^3 \tan (e+f x) (a \sec (e+f x)+a)^2 \sqrt{c-c \sec (e+f x)}}{231 f}-\frac{8 c^2 \tan (e+f x) (a \sec (e+f x)+a)^2 (c-c \sec (e+f x))^{3/2}}{33 f}-\frac{2 c \tan (e+f x) (a \sec (e+f x)+a)^2 (c-c \sec (e+f x))^{5/2}}{11 f}","-\frac{256 c^4 \tan (e+f x) (a \sec (e+f x)+a)^2}{1155 f \sqrt{c-c \sec (e+f x)}}-\frac{64 c^3 \tan (e+f x) (a \sec (e+f x)+a)^2 \sqrt{c-c \sec (e+f x)}}{231 f}-\frac{8 c^2 \tan (e+f x) (a \sec (e+f x)+a)^2 (c-c \sec (e+f x))^{3/2}}{33 f}-\frac{2 c \tan (e+f x) (a \sec (e+f x)+a)^2 (c-c \sec (e+f x))^{5/2}}{11 f}",1,"(-256*c^4*(a + a*Sec[e + f*x])^2*Tan[e + f*x])/(1155*f*Sqrt[c - c*Sec[e + f*x]]) - (64*c^3*(a + a*Sec[e + f*x])^2*Sqrt[c - c*Sec[e + f*x]]*Tan[e + f*x])/(231*f) - (8*c^2*(a + a*Sec[e + f*x])^2*(c - c*Sec[e + f*x])^(3/2)*Tan[e + f*x])/(33*f) - (2*c*(a + a*Sec[e + f*x])^2*(c - c*Sec[e + f*x])^(5/2)*Tan[e + f*x])/(11*f)","A",4,2,34,0.05882,1,"{3955, 3953}"
72,1,128,0,0.3273049,"\int \sec (e+f x) (a+a \sec (e+f x))^2 (c-c \sec (e+f x))^{5/2} \, dx","Int[Sec[e + f*x]*(a + a*Sec[e + f*x])^2*(c - c*Sec[e + f*x])^(5/2),x]","-\frac{64 c^3 \tan (e+f x) (a \sec (e+f x)+a)^2}{315 f \sqrt{c-c \sec (e+f x)}}-\frac{16 c^2 \tan (e+f x) (a \sec (e+f x)+a)^2 \sqrt{c-c \sec (e+f x)}}{63 f}-\frac{2 c \tan (e+f x) (a \sec (e+f x)+a)^2 (c-c \sec (e+f x))^{3/2}}{9 f}","-\frac{64 c^3 \tan (e+f x) (a \sec (e+f x)+a)^2}{315 f \sqrt{c-c \sec (e+f x)}}-\frac{16 c^2 \tan (e+f x) (a \sec (e+f x)+a)^2 \sqrt{c-c \sec (e+f x)}}{63 f}-\frac{2 c \tan (e+f x) (a \sec (e+f x)+a)^2 (c-c \sec (e+f x))^{3/2}}{9 f}",1,"(-64*c^3*(a + a*Sec[e + f*x])^2*Tan[e + f*x])/(315*f*Sqrt[c - c*Sec[e + f*x]]) - (16*c^2*(a + a*Sec[e + f*x])^2*Sqrt[c - c*Sec[e + f*x]]*Tan[e + f*x])/(63*f) - (2*c*(a + a*Sec[e + f*x])^2*(c - c*Sec[e + f*x])^(3/2)*Tan[e + f*x])/(9*f)","A",3,2,34,0.05882,1,"{3955, 3953}"
73,1,85,0,0.2077929,"\int \sec (e+f x) (a+a \sec (e+f x))^2 (c-c \sec (e+f x))^{3/2} \, dx","Int[Sec[e + f*x]*(a + a*Sec[e + f*x])^2*(c - c*Sec[e + f*x])^(3/2),x]","-\frac{8 c^2 \tan (e+f x) (a \sec (e+f x)+a)^2}{35 f \sqrt{c-c \sec (e+f x)}}-\frac{2 c \tan (e+f x) (a \sec (e+f x)+a)^2 \sqrt{c-c \sec (e+f x)}}{7 f}","-\frac{8 c^2 \tan (e+f x) (a \sec (e+f x)+a)^2}{35 f \sqrt{c-c \sec (e+f x)}}-\frac{2 c \tan (e+f x) (a \sec (e+f x)+a)^2 \sqrt{c-c \sec (e+f x)}}{7 f}",1,"(-8*c^2*(a + a*Sec[e + f*x])^2*Tan[e + f*x])/(35*f*Sqrt[c - c*Sec[e + f*x]]) - (2*c*(a + a*Sec[e + f*x])^2*Sqrt[c - c*Sec[e + f*x]]*Tan[e + f*x])/(7*f)","A",2,2,34,0.05882,1,"{3955, 3953}"
74,1,41,0,0.0967487,"\int \sec (e+f x) (a+a \sec (e+f x))^2 \sqrt{c-c \sec (e+f x)} \, dx","Int[Sec[e + f*x]*(a + a*Sec[e + f*x])^2*Sqrt[c - c*Sec[e + f*x]],x]","-\frac{2 c \tan (e+f x) (a \sec (e+f x)+a)^2}{5 f \sqrt{c-c \sec (e+f x)}}","-\frac{2 c \tan (e+f x) (a \sec (e+f x)+a)^2}{5 f \sqrt{c-c \sec (e+f x)}}",1,"(-2*c*(a + a*Sec[e + f*x])^2*Tan[e + f*x])/(5*f*Sqrt[c - c*Sec[e + f*x]])","A",1,1,34,0.02941,1,"{3953}"
75,1,123,0,0.213263,"\int \frac{\sec (e+f x) (a+a \sec (e+f x))^2}{\sqrt{c-c \sec (e+f x)}} \, dx","Int[(Sec[e + f*x]*(a + a*Sec[e + f*x])^2)/Sqrt[c - c*Sec[e + f*x]],x]","-\frac{4 \sqrt{2} a^2 \tan ^{-1}\left(\frac{\sqrt{c} \tan (e+f x)}{\sqrt{2} \sqrt{c-c \sec (e+f x)}}\right)}{\sqrt{c} f}+\frac{4 a^2 \tan (e+f x)}{f \sqrt{c-c \sec (e+f x)}}+\frac{2 \tan (e+f x) \left(a^2 \sec (e+f x)+a^2\right)}{3 f \sqrt{c-c \sec (e+f x)}}","-\frac{4 \sqrt{2} a^2 \tan ^{-1}\left(\frac{\sqrt{c} \tan (e+f x)}{\sqrt{2} \sqrt{c-c \sec (e+f x)}}\right)}{\sqrt{c} f}-\frac{2 a^2 \tan (e+f x) \sqrt{c-c \sec (e+f x)}}{3 c f}+\frac{16 a^2 \tan (e+f x)}{3 f \sqrt{c-c \sec (e+f x)}}",1,"(-4*Sqrt[2]*a^2*ArcTan[(Sqrt[c]*Tan[e + f*x])/(Sqrt[2]*Sqrt[c - c*Sec[e + f*x]])])/(Sqrt[c]*f) + (4*a^2*Tan[e + f*x])/(f*Sqrt[c - c*Sec[e + f*x]]) + (2*(a^2 + a^2*Sec[e + f*x])*Tan[e + f*x])/(3*f*Sqrt[c - c*Sec[e + f*x]])","A",4,3,34,0.08824,1,"{3956, 3795, 203}"
76,1,124,0,0.2281095,"\int \frac{\sec (e+f x) (a+a \sec (e+f x))^2}{(c-c \sec (e+f x))^{3/2}} \, dx","Int[(Sec[e + f*x]*(a + a*Sec[e + f*x])^2)/(c - c*Sec[e + f*x])^(3/2),x]","\frac{3 \sqrt{2} a^2 \tan ^{-1}\left(\frac{\sqrt{c} \tan (e+f x)}{\sqrt{2} \sqrt{c-c \sec (e+f x)}}\right)}{c^{3/2} f}-\frac{3 a^2 \tan (e+f x)}{c f \sqrt{c-c \sec (e+f x)}}-\frac{\tan (e+f x) \left(a^2 \sec (e+f x)+a^2\right)}{f (c-c \sec (e+f x))^{3/2}}","\frac{3 \sqrt{2} a^2 \tan ^{-1}\left(\frac{\sqrt{c} \tan (e+f x)}{\sqrt{2} \sqrt{c-c \sec (e+f x)}}\right)}{c^{3/2} f}-\frac{2 a^2 \tan (e+f x)}{c f \sqrt{c-c \sec (e+f x)}}-\frac{2 a^2 \tan (e+f x)}{f (c-c \sec (e+f x))^{3/2}}",1,"(3*Sqrt[2]*a^2*ArcTan[(Sqrt[c]*Tan[e + f*x])/(Sqrt[2]*Sqrt[c - c*Sec[e + f*x]])])/(c^(3/2)*f) - ((a^2 + a^2*Sec[e + f*x])*Tan[e + f*x])/(f*(c - c*Sec[e + f*x])^(3/2)) - (3*a^2*Tan[e + f*x])/(c*f*Sqrt[c - c*Sec[e + f*x]])","A",4,4,34,0.1176,1,"{3957, 3956, 3795, 203}"
77,1,130,0,0.2375837,"\int \frac{\sec (e+f x) (a+a \sec (e+f x))^2}{(c-c \sec (e+f x))^{5/2}} \, dx","Int[(Sec[e + f*x]*(a + a*Sec[e + f*x])^2)/(c - c*Sec[e + f*x])^(5/2),x]","-\frac{3 a^2 \tan ^{-1}\left(\frac{\sqrt{c} \tan (e+f x)}{\sqrt{2} \sqrt{c-c \sec (e+f x)}}\right)}{4 \sqrt{2} c^{5/2} f}+\frac{3 a^2 \tan (e+f x)}{4 c f (c-c \sec (e+f x))^{3/2}}-\frac{\tan (e+f x) \left(a^2 \sec (e+f x)+a^2\right)}{2 f (c-c \sec (e+f x))^{5/2}}","-\frac{3 a^2 \tan ^{-1}\left(\frac{\sqrt{c} \tan (e+f x)}{\sqrt{2} \sqrt{c-c \sec (e+f x)}}\right)}{4 \sqrt{2} c^{5/2} f}+\frac{5 a^2 \tan (e+f x)}{4 c f (c-c \sec (e+f x))^{3/2}}-\frac{a^2 \tan (e+f x)}{f (c-c \sec (e+f x))^{5/2}}",1,"(-3*a^2*ArcTan[(Sqrt[c]*Tan[e + f*x])/(Sqrt[2]*Sqrt[c - c*Sec[e + f*x]])])/(4*Sqrt[2]*c^(5/2)*f) - ((a^2 + a^2*Sec[e + f*x])*Tan[e + f*x])/(2*f*(c - c*Sec[e + f*x])^(5/2)) + (3*a^2*Tan[e + f*x])/(4*c*f*(c - c*Sec[e + f*x])^(3/2))","A",4,3,34,0.08824,1,"{3957, 3795, 203}"
78,1,164,0,0.2818708,"\int \frac{\sec (e+f x) (a+a \sec (e+f x))^2}{(c-c \sec (e+f x))^{7/2}} \, dx","Int[(Sec[e + f*x]*(a + a*Sec[e + f*x])^2)/(c - c*Sec[e + f*x])^(7/2),x]","-\frac{a^2 \tan ^{-1}\left(\frac{\sqrt{c} \tan (e+f x)}{\sqrt{2} \sqrt{c-c \sec (e+f x)}}\right)}{16 \sqrt{2} c^{7/2} f}-\frac{a^2 \tan (e+f x)}{16 c^2 f (c-c \sec (e+f x))^{3/2}}+\frac{a^2 \tan (e+f x)}{4 c f (c-c \sec (e+f x))^{5/2}}-\frac{\tan (e+f x) \left(a^2 \sec (e+f x)+a^2\right)}{3 f (c-c \sec (e+f x))^{7/2}}","-\frac{a^2 \tan ^{-1}\left(\frac{\sqrt{c} \tan (e+f x)}{\sqrt{2} \sqrt{c-c \sec (e+f x)}}\right)}{16 \sqrt{2} c^{7/2} f}-\frac{a^2 \tan (e+f x)}{16 c^2 f (c-c \sec (e+f x))^{3/2}}+\frac{a^2 \tan (e+f x)}{4 c f (c-c \sec (e+f x))^{5/2}}-\frac{\tan (e+f x) \left(a^2 \sec (e+f x)+a^2\right)}{3 f (c-c \sec (e+f x))^{7/2}}",1,"-(a^2*ArcTan[(Sqrt[c]*Tan[e + f*x])/(Sqrt[2]*Sqrt[c - c*Sec[e + f*x]])])/(16*Sqrt[2]*c^(7/2)*f) - ((a^2 + a^2*Sec[e + f*x])*Tan[e + f*x])/(3*f*(c - c*Sec[e + f*x])^(7/2)) + (a^2*Tan[e + f*x])/(4*c*f*(c - c*Sec[e + f*x])^(5/2)) - (a^2*Tan[e + f*x])/(16*c^2*f*(c - c*Sec[e + f*x])^(3/2))","A",5,4,34,0.1176,1,"{3957, 3796, 3795, 203}"
79,1,171,0,0.4438585,"\int \sec (e+f x) (a+a \sec (e+f x))^3 (c-c \sec (e+f x))^{7/2} \, dx","Int[Sec[e + f*x]*(a + a*Sec[e + f*x])^3*(c - c*Sec[e + f*x])^(7/2),x]","-\frac{256 c^4 \tan (e+f x) (a \sec (e+f x)+a)^3}{3003 f \sqrt{c-c \sec (e+f x)}}-\frac{64 c^3 \tan (e+f x) (a \sec (e+f x)+a)^3 \sqrt{c-c \sec (e+f x)}}{429 f}-\frac{24 c^2 \tan (e+f x) (a \sec (e+f x)+a)^3 (c-c \sec (e+f x))^{3/2}}{143 f}-\frac{2 c \tan (e+f x) (a \sec (e+f x)+a)^3 (c-c \sec (e+f x))^{5/2}}{13 f}","-\frac{256 c^4 \tan (e+f x) (a \sec (e+f x)+a)^3}{3003 f \sqrt{c-c \sec (e+f x)}}-\frac{64 c^3 \tan (e+f x) (a \sec (e+f x)+a)^3 \sqrt{c-c \sec (e+f x)}}{429 f}-\frac{24 c^2 \tan (e+f x) (a \sec (e+f x)+a)^3 (c-c \sec (e+f x))^{3/2}}{143 f}-\frac{2 c \tan (e+f x) (a \sec (e+f x)+a)^3 (c-c \sec (e+f x))^{5/2}}{13 f}",1,"(-256*c^4*(a + a*Sec[e + f*x])^3*Tan[e + f*x])/(3003*f*Sqrt[c - c*Sec[e + f*x]]) - (64*c^3*(a + a*Sec[e + f*x])^3*Sqrt[c - c*Sec[e + f*x]]*Tan[e + f*x])/(429*f) - (24*c^2*(a + a*Sec[e + f*x])^3*(c - c*Sec[e + f*x])^(3/2)*Tan[e + f*x])/(143*f) - (2*c*(a + a*Sec[e + f*x])^3*(c - c*Sec[e + f*x])^(5/2)*Tan[e + f*x])/(13*f)","A",4,2,34,0.05882,1,"{3955, 3953}"
80,1,128,0,0.3234417,"\int \sec (e+f x) (a+a \sec (e+f x))^3 (c-c \sec (e+f x))^{5/2} \, dx","Int[Sec[e + f*x]*(a + a*Sec[e + f*x])^3*(c - c*Sec[e + f*x])^(5/2),x]","-\frac{16 c^2 \tan (e+f x) (a \sec (e+f x)+a)^3 \sqrt{c-c \sec (e+f x)}}{99 f}-\frac{64 c^3 \tan (e+f x) (a \sec (e+f x)+a)^3}{693 f \sqrt{c-c \sec (e+f x)}}-\frac{2 c \tan (e+f x) (a \sec (e+f x)+a)^3 (c-c \sec (e+f x))^{3/2}}{11 f}","-\frac{16 c^2 \tan (e+f x) (a \sec (e+f x)+a)^3 \sqrt{c-c \sec (e+f x)}}{99 f}-\frac{64 c^3 \tan (e+f x) (a \sec (e+f x)+a)^3}{693 f \sqrt{c-c \sec (e+f x)}}-\frac{2 c \tan (e+f x) (a \sec (e+f x)+a)^3 (c-c \sec (e+f x))^{3/2}}{11 f}",1,"(-64*c^3*(a + a*Sec[e + f*x])^3*Tan[e + f*x])/(693*f*Sqrt[c - c*Sec[e + f*x]]) - (16*c^2*(a + a*Sec[e + f*x])^3*Sqrt[c - c*Sec[e + f*x]]*Tan[e + f*x])/(99*f) - (2*c*(a + a*Sec[e + f*x])^3*(c - c*Sec[e + f*x])^(3/2)*Tan[e + f*x])/(11*f)","A",3,2,34,0.05882,1,"{3955, 3953}"
81,1,85,0,0.2088525,"\int \sec (e+f x) (a+a \sec (e+f x))^3 (c-c \sec (e+f x))^{3/2} \, dx","Int[Sec[e + f*x]*(a + a*Sec[e + f*x])^3*(c - c*Sec[e + f*x])^(3/2),x]","-\frac{8 c^2 \tan (e+f x) (a \sec (e+f x)+a)^3}{63 f \sqrt{c-c \sec (e+f x)}}-\frac{2 c \tan (e+f x) (a \sec (e+f x)+a)^3 \sqrt{c-c \sec (e+f x)}}{9 f}","-\frac{8 c^2 \tan (e+f x) (a \sec (e+f x)+a)^3}{63 f \sqrt{c-c \sec (e+f x)}}-\frac{2 c \tan (e+f x) (a \sec (e+f x)+a)^3 \sqrt{c-c \sec (e+f x)}}{9 f}",1,"(-8*c^2*(a + a*Sec[e + f*x])^3*Tan[e + f*x])/(63*f*Sqrt[c - c*Sec[e + f*x]]) - (2*c*(a + a*Sec[e + f*x])^3*Sqrt[c - c*Sec[e + f*x]]*Tan[e + f*x])/(9*f)","A",2,2,34,0.05882,1,"{3955, 3953}"
82,1,41,0,0.09561,"\int \sec (e+f x) (a+a \sec (e+f x))^3 \sqrt{c-c \sec (e+f x)} \, dx","Int[Sec[e + f*x]*(a + a*Sec[e + f*x])^3*Sqrt[c - c*Sec[e + f*x]],x]","-\frac{2 c \tan (e+f x) (a \sec (e+f x)+a)^3}{7 f \sqrt{c-c \sec (e+f x)}}","-\frac{2 c \tan (e+f x) (a \sec (e+f x)+a)^3}{7 f \sqrt{c-c \sec (e+f x)}}",1,"(-2*c*(a + a*Sec[e + f*x])^3*Tan[e + f*x])/(7*f*Sqrt[c - c*Sec[e + f*x]])","A",1,1,34,0.02941,1,"{3953}"
83,1,164,0,0.3254022,"\int \frac{\sec (e+f x) (a+a \sec (e+f x))^3}{\sqrt{c-c \sec (e+f x)}} \, dx","Int[(Sec[e + f*x]*(a + a*Sec[e + f*x])^3)/Sqrt[c - c*Sec[e + f*x]],x]","-\frac{8 \sqrt{2} a^3 \tan ^{-1}\left(\frac{\sqrt{c} \tan (e+f x)}{\sqrt{2} \sqrt{c-c \sec (e+f x)}}\right)}{\sqrt{c} f}+\frac{8 a^3 \tan (e+f x)}{f \sqrt{c-c \sec (e+f x)}}+\frac{4 \tan (e+f x) \left(a^3 \sec (e+f x)+a^3\right)}{3 f \sqrt{c-c \sec (e+f x)}}+\frac{2 a \tan (e+f x) (a \sec (e+f x)+a)^2}{5 f \sqrt{c-c \sec (e+f x)}}","-\frac{8 \sqrt{2} a^3 \tan ^{-1}\left(\frac{\sqrt{c} \tan (e+f x)}{\sqrt{2} \sqrt{c-c \sec (e+f x)}}\right)}{\sqrt{c} f}+\frac{8 a^3 \tan (e+f x)}{f \sqrt{c-c \sec (e+f x)}}+\frac{4 \tan (e+f x) \left(a^3 \sec (e+f x)+a^3\right)}{3 f \sqrt{c-c \sec (e+f x)}}+\frac{2 a \tan (e+f x) (a \sec (e+f x)+a)^2}{5 f \sqrt{c-c \sec (e+f x)}}",1,"(-8*Sqrt[2]*a^3*ArcTan[(Sqrt[c]*Tan[e + f*x])/(Sqrt[2]*Sqrt[c - c*Sec[e + f*x]])])/(Sqrt[c]*f) + (8*a^3*Tan[e + f*x])/(f*Sqrt[c - c*Sec[e + f*x]]) + (2*a*(a + a*Sec[e + f*x])^2*Tan[e + f*x])/(5*f*Sqrt[c - c*Sec[e + f*x]]) + (4*(a^3 + a^3*Sec[e + f*x])*Tan[e + f*x])/(3*f*Sqrt[c - c*Sec[e + f*x]])","A",5,3,34,0.08824,1,"{3956, 3795, 203}"
84,1,168,0,0.3364869,"\int \frac{\sec (e+f x) (a+a \sec (e+f x))^3}{(c-c \sec (e+f x))^{3/2}} \, dx","Int[(Sec[e + f*x]*(a + a*Sec[e + f*x])^3)/(c - c*Sec[e + f*x])^(3/2),x]","\frac{10 \sqrt{2} a^3 \tan ^{-1}\left(\frac{\sqrt{c} \tan (e+f x)}{\sqrt{2} \sqrt{c-c \sec (e+f x)}}\right)}{c^{3/2} f}-\frac{10 a^3 \tan (e+f x)}{c f \sqrt{c-c \sec (e+f x)}}-\frac{5 \tan (e+f x) \left(a^3 \sec (e+f x)+a^3\right)}{3 c f \sqrt{c-c \sec (e+f x)}}-\frac{a \tan (e+f x) (a \sec (e+f x)+a)^2}{f (c-c \sec (e+f x))^{3/2}}","\frac{10 \sqrt{2} a^3 \tan ^{-1}\left(\frac{\sqrt{c} \tan (e+f x)}{\sqrt{2} \sqrt{c-c \sec (e+f x)}}\right)}{c^{3/2} f}-\frac{10 a^3 \tan (e+f x)}{c f \sqrt{c-c \sec (e+f x)}}-\frac{5 \tan (e+f x) \left(a^3 \sec (e+f x)+a^3\right)}{3 c f \sqrt{c-c \sec (e+f x)}}-\frac{a \tan (e+f x) (a \sec (e+f x)+a)^2}{f (c-c \sec (e+f x))^{3/2}}",1,"(10*Sqrt[2]*a^3*ArcTan[(Sqrt[c]*Tan[e + f*x])/(Sqrt[2]*Sqrt[c - c*Sec[e + f*x]])])/(c^(3/2)*f) - (a*(a + a*Sec[e + f*x])^2*Tan[e + f*x])/(f*(c - c*Sec[e + f*x])^(3/2)) - (10*a^3*Tan[e + f*x])/(c*f*Sqrt[c - c*Sec[e + f*x]]) - (5*(a^3 + a^3*Sec[e + f*x])*Tan[e + f*x])/(3*c*f*Sqrt[c - c*Sec[e + f*x]])","A",5,4,34,0.1176,1,"{3957, 3956, 3795, 203}"
85,1,174,0,0.3519807,"\int \frac{\sec (e+f x) (a+a \sec (e+f x))^3}{(c-c \sec (e+f x))^{5/2}} \, dx","Int[(Sec[e + f*x]*(a + a*Sec[e + f*x])^3)/(c - c*Sec[e + f*x])^(5/2),x]","-\frac{15 a^3 \tan ^{-1}\left(\frac{\sqrt{c} \tan (e+f x)}{\sqrt{2} \sqrt{c-c \sec (e+f x)}}\right)}{2 \sqrt{2} c^{5/2} f}+\frac{15 a^3 \tan (e+f x)}{4 c^2 f \sqrt{c-c \sec (e+f x)}}+\frac{5 \tan (e+f x) \left(a^3 \sec (e+f x)+a^3\right)}{4 c f (c-c \sec (e+f x))^{3/2}}-\frac{a \tan (e+f x) (a \sec (e+f x)+a)^2}{2 f (c-c \sec (e+f x))^{5/2}}","-\frac{15 a^3 \tan ^{-1}\left(\frac{\sqrt{c} \tan (e+f x)}{\sqrt{2} \sqrt{c-c \sec (e+f x)}}\right)}{2 \sqrt{2} c^{5/2} f}+\frac{15 a^3 \tan (e+f x)}{4 c^2 f \sqrt{c-c \sec (e+f x)}}+\frac{5 \tan (e+f x) \left(a^3 \sec (e+f x)+a^3\right)}{4 c f (c-c \sec (e+f x))^{3/2}}-\frac{a \tan (e+f x) (a \sec (e+f x)+a)^2}{2 f (c-c \sec (e+f x))^{5/2}}",1,"(-15*a^3*ArcTan[(Sqrt[c]*Tan[e + f*x])/(Sqrt[2]*Sqrt[c - c*Sec[e + f*x]])])/(2*Sqrt[2]*c^(5/2)*f) - (a*(a + a*Sec[e + f*x])^2*Tan[e + f*x])/(2*f*(c - c*Sec[e + f*x])^(5/2)) + (5*(a^3 + a^3*Sec[e + f*x])*Tan[e + f*x])/(4*c*f*(c - c*Sec[e + f*x])^(3/2)) + (15*a^3*Tan[e + f*x])/(4*c^2*f*Sqrt[c - c*Sec[e + f*x]])","A",5,4,34,0.1176,1,"{3957, 3956, 3795, 203}"
86,1,142,0,0.2336666,"\int \frac{\sec (e+f x) (c-c \sec (e+f x))^{7/2}}{a+a \sec (e+f x)} \, dx","Int[(Sec[e + f*x]*(c - c*Sec[e + f*x])^(7/2))/(a + a*Sec[e + f*x]),x]","\frac{128 c^4 \tan (e+f x)}{5 a f \sqrt{c-c \sec (e+f x)}}+\frac{32 c^3 \tan (e+f x) \sqrt{c-c \sec (e+f x)}}{5 a f}+\frac{12 c^2 \tan (e+f x) (c-c \sec (e+f x))^{3/2}}{5 a f}+\frac{2 c \tan (e+f x) (c-c \sec (e+f x))^{5/2}}{f (a \sec (e+f x)+a)}","\frac{128 c^4 \tan (e+f x)}{5 a f \sqrt{c-c \sec (e+f x)}}+\frac{32 c^3 \tan (e+f x) \sqrt{c-c \sec (e+f x)}}{5 a f}+\frac{12 c^2 \tan (e+f x) (c-c \sec (e+f x))^{3/2}}{5 a f}+\frac{2 c \tan (e+f x) (c-c \sec (e+f x))^{5/2}}{f (a \sec (e+f x)+a)}",1,"(128*c^4*Tan[e + f*x])/(5*a*f*Sqrt[c - c*Sec[e + f*x]]) + (32*c^3*Sqrt[c - c*Sec[e + f*x]]*Tan[e + f*x])/(5*a*f) + (12*c^2*(c - c*Sec[e + f*x])^(3/2)*Tan[e + f*x])/(5*a*f) + (2*c*(c - c*Sec[e + f*x])^(5/2)*Tan[e + f*x])/(f*(a + a*Sec[e + f*x]))","A",4,3,34,0.08824,1,"{3954, 3793, 3792}"
87,1,108,0,0.1905157,"\int \frac{\sec (e+f x) (c-c \sec (e+f x))^{5/2}}{a+a \sec (e+f x)} \, dx","Int[(Sec[e + f*x]*(c - c*Sec[e + f*x])^(5/2))/(a + a*Sec[e + f*x]),x]","\frac{32 c^3 \tan (e+f x)}{3 a f \sqrt{c-c \sec (e+f x)}}+\frac{8 c^2 \tan (e+f x) \sqrt{c-c \sec (e+f x)}}{3 a f}+\frac{2 c \tan (e+f x) (c-c \sec (e+f x))^{3/2}}{f (a \sec (e+f x)+a)}","\frac{32 c^3 \tan (e+f x)}{3 a f \sqrt{c-c \sec (e+f x)}}+\frac{8 c^2 \tan (e+f x) \sqrt{c-c \sec (e+f x)}}{3 a f}+\frac{2 c \tan (e+f x) (c-c \sec (e+f x))^{3/2}}{f (a \sec (e+f x)+a)}",1,"(32*c^3*Tan[e + f*x])/(3*a*f*Sqrt[c - c*Sec[e + f*x]]) + (8*c^2*Sqrt[c - c*Sec[e + f*x]]*Tan[e + f*x])/(3*a*f) + (2*c*(c - c*Sec[e + f*x])^(3/2)*Tan[e + f*x])/(f*(a + a*Sec[e + f*x]))","A",3,3,34,0.08824,1,"{3954, 3793, 3792}"
88,1,72,0,0.1529222,"\int \frac{\sec (e+f x) (c-c \sec (e+f x))^{3/2}}{a+a \sec (e+f x)} \, dx","Int[(Sec[e + f*x]*(c - c*Sec[e + f*x])^(3/2))/(a + a*Sec[e + f*x]),x]","\frac{4 c^2 \tan (e+f x)}{a f \sqrt{c-c \sec (e+f x)}}+\frac{2 c \tan (e+f x) \sqrt{c-c \sec (e+f x)}}{f (a \sec (e+f x)+a)}","\frac{4 c^2 \tan (e+f x)}{a f \sqrt{c-c \sec (e+f x)}}+\frac{2 c \tan (e+f x) \sqrt{c-c \sec (e+f x)}}{f (a \sec (e+f x)+a)}",1,"(4*c^2*Tan[e + f*x])/(a*f*Sqrt[c - c*Sec[e + f*x]]) + (2*c*Sqrt[c - c*Sec[e + f*x]]*Tan[e + f*x])/(f*(a + a*Sec[e + f*x]))","A",2,2,34,0.05882,1,"{3954, 3792}"
89,1,39,0,0.1065479,"\int \frac{\sec (e+f x) \sqrt{c-c \sec (e+f x)}}{a+a \sec (e+f x)} \, dx","Int[(Sec[e + f*x]*Sqrt[c - c*Sec[e + f*x]])/(a + a*Sec[e + f*x]),x]","\frac{2 c \tan (e+f x)}{f (a \sec (e+f x)+a) \sqrt{c-c \sec (e+f x)}}","\frac{2 c \tan (e+f x)}{f (a \sec (e+f x)+a) \sqrt{c-c \sec (e+f x)}}",1,"(2*c*Tan[e + f*x])/(f*(a + a*Sec[e + f*x])*Sqrt[c - c*Sec[e + f*x]])","A",1,1,34,0.02941,1,"{3953}"
90,1,89,0,0.1571633,"\int \frac{\sec (e+f x)}{(a+a \sec (e+f x)) \sqrt{c-c \sec (e+f x)}} \, dx","Int[Sec[e + f*x]/((a + a*Sec[e + f*x])*Sqrt[c - c*Sec[e + f*x]]),x]","\frac{\tan (e+f x)}{f (a \sec (e+f x)+a) \sqrt{c-c \sec (e+f x)}}-\frac{\tan ^{-1}\left(\frac{\sqrt{c} \tan (e+f x)}{\sqrt{2} \sqrt{c-c \sec (e+f x)}}\right)}{\sqrt{2} a \sqrt{c} f}","\frac{\tan (e+f x)}{f (a \sec (e+f x)+a) \sqrt{c-c \sec (e+f x)}}-\frac{\tan ^{-1}\left(\frac{\sqrt{c} \tan (e+f x)}{\sqrt{2} \sqrt{c-c \sec (e+f x)}}\right)}{\sqrt{2} a \sqrt{c} f}",1,"-(ArcTan[(Sqrt[c]*Tan[e + f*x])/(Sqrt[2]*Sqrt[c - c*Sec[e + f*x]])]/(Sqrt[2]*a*Sqrt[c]*f)) + Tan[e + f*x]/(f*(a + a*Sec[e + f*x])*Sqrt[c - c*Sec[e + f*x]])","A",3,3,34,0.08824,1,"{3960, 3795, 203}"
91,1,122,0,0.2105109,"\int \frac{\sec (e+f x)}{(a+a \sec (e+f x)) (c-c \sec (e+f x))^{3/2}} \, dx","Int[Sec[e + f*x]/((a + a*Sec[e + f*x])*(c - c*Sec[e + f*x])^(3/2)),x]","-\frac{3 \tan ^{-1}\left(\frac{\sqrt{c} \tan (e+f x)}{\sqrt{2} \sqrt{c-c \sec (e+f x)}}\right)}{4 \sqrt{2} a c^{3/2} f}-\frac{3 \tan (e+f x)}{4 a f (c-c \sec (e+f x))^{3/2}}+\frac{\tan (e+f x)}{f (a \sec (e+f x)+a) (c-c \sec (e+f x))^{3/2}}","-\frac{3 \tan ^{-1}\left(\frac{\sqrt{c} \tan (e+f x)}{\sqrt{2} \sqrt{c-c \sec (e+f x)}}\right)}{4 \sqrt{2} a c^{3/2} f}-\frac{3 \tan (e+f x)}{4 a f (c-c \sec (e+f x))^{3/2}}+\frac{\tan (e+f x)}{f (a \sec (e+f x)+a) (c-c \sec (e+f x))^{3/2}}",1,"(-3*ArcTan[(Sqrt[c]*Tan[e + f*x])/(Sqrt[2]*Sqrt[c - c*Sec[e + f*x]])])/(4*Sqrt[2]*a*c^(3/2)*f) - (3*Tan[e + f*x])/(4*a*f*(c - c*Sec[e + f*x])^(3/2)) + Tan[e + f*x]/(f*(a + a*Sec[e + f*x])*(c - c*Sec[e + f*x])^(3/2))","A",4,4,34,0.1176,1,"{3960, 3796, 3795, 203}"
92,1,156,0,0.2552638,"\int \frac{\sec (e+f x)}{(a+a \sec (e+f x)) (c-c \sec (e+f x))^{5/2}} \, dx","Int[Sec[e + f*x]/((a + a*Sec[e + f*x])*(c - c*Sec[e + f*x])^(5/2)),x]","-\frac{15 \tan ^{-1}\left(\frac{\sqrt{c} \tan (e+f x)}{\sqrt{2} \sqrt{c-c \sec (e+f x)}}\right)}{32 \sqrt{2} a c^{5/2} f}-\frac{15 \tan (e+f x)}{32 a c f (c-c \sec (e+f x))^{3/2}}-\frac{5 \tan (e+f x)}{8 a f (c-c \sec (e+f x))^{5/2}}+\frac{\tan (e+f x)}{f (a \sec (e+f x)+a) (c-c \sec (e+f x))^{5/2}}","-\frac{15 \tan ^{-1}\left(\frac{\sqrt{c} \tan (e+f x)}{\sqrt{2} \sqrt{c-c \sec (e+f x)}}\right)}{32 \sqrt{2} a c^{5/2} f}-\frac{15 \tan (e+f x)}{32 a c f (c-c \sec (e+f x))^{3/2}}-\frac{5 \tan (e+f x)}{8 a f (c-c \sec (e+f x))^{5/2}}+\frac{\tan (e+f x)}{f (a \sec (e+f x)+a) (c-c \sec (e+f x))^{5/2}}",1,"(-15*ArcTan[(Sqrt[c]*Tan[e + f*x])/(Sqrt[2]*Sqrt[c - c*Sec[e + f*x]])])/(32*Sqrt[2]*a*c^(5/2)*f) - (5*Tan[e + f*x])/(8*a*f*(c - c*Sec[e + f*x])^(5/2)) + Tan[e + f*x]/(f*(a + a*Sec[e + f*x])*(c - c*Sec[e + f*x])^(5/2)) - (15*Tan[e + f*x])/(32*a*c*f*(c - c*Sec[e + f*x])^(3/2))","A",5,4,34,0.1176,1,"{3960, 3796, 3795, 203}"
93,1,155,0,0.3174463,"\int \frac{\sec (e+f x) (c-c \sec (e+f x))^{7/2}}{(a+a \sec (e+f x))^2} \, dx","Int[(Sec[e + f*x]*(c - c*Sec[e + f*x])^(7/2))/(a + a*Sec[e + f*x])^2,x]","-\frac{64 c^4 \tan (e+f x)}{3 a^2 f \sqrt{c-c \sec (e+f x)}}-\frac{16 c^3 \tan (e+f x) \sqrt{c-c \sec (e+f x)}}{3 a^2 f}-\frac{4 c^2 \tan (e+f x) (c-c \sec (e+f x))^{3/2}}{f \left(a^2 \sec (e+f x)+a^2\right)}+\frac{2 c \tan (e+f x) (c-c \sec (e+f x))^{5/2}}{3 f (a \sec (e+f x)+a)^2}","-\frac{64 c^4 \tan (e+f x)}{3 a^2 f \sqrt{c-c \sec (e+f x)}}-\frac{16 c^3 \tan (e+f x) \sqrt{c-c \sec (e+f x)}}{3 a^2 f}-\frac{4 c^2 \tan (e+f x) (c-c \sec (e+f x))^{3/2}}{f \left(a^2 \sec (e+f x)+a^2\right)}+\frac{2 c \tan (e+f x) (c-c \sec (e+f x))^{5/2}}{3 f (a \sec (e+f x)+a)^2}",1,"(-64*c^4*Tan[e + f*x])/(3*a^2*f*Sqrt[c - c*Sec[e + f*x]]) - (16*c^3*Sqrt[c - c*Sec[e + f*x]]*Tan[e + f*x])/(3*a^2*f) - (4*c^2*(c - c*Sec[e + f*x])^(3/2)*Tan[e + f*x])/(f*(a^2 + a^2*Sec[e + f*x])) + (2*c*(c - c*Sec[e + f*x])^(5/2)*Tan[e + f*x])/(3*f*(a + a*Sec[e + f*x])^2)","A",4,3,34,0.08824,1,"{3954, 3793, 3792}"
94,1,123,0,0.2740392,"\int \frac{\sec (e+f x) (c-c \sec (e+f x))^{5/2}}{(a+a \sec (e+f x))^2} \, dx","Int[(Sec[e + f*x]*(c - c*Sec[e + f*x])^(5/2))/(a + a*Sec[e + f*x])^2,x]","-\frac{16 c^3 \tan (e+f x)}{3 a^2 f \sqrt{c-c \sec (e+f x)}}-\frac{8 c^2 \tan (e+f x) \sqrt{c-c \sec (e+f x)}}{3 f \left(a^2 \sec (e+f x)+a^2\right)}+\frac{2 c \tan (e+f x) (c-c \sec (e+f x))^{3/2}}{3 f (a \sec (e+f x)+a)^2}","-\frac{16 c^3 \tan (e+f x)}{3 a^2 f \sqrt{c-c \sec (e+f x)}}-\frac{8 c^2 \tan (e+f x) \sqrt{c-c \sec (e+f x)}}{3 f \left(a^2 \sec (e+f x)+a^2\right)}+\frac{2 c \tan (e+f x) (c-c \sec (e+f x))^{3/2}}{3 f (a \sec (e+f x)+a)^2}",1,"(-16*c^3*Tan[e + f*x])/(3*a^2*f*Sqrt[c - c*Sec[e + f*x]]) - (8*c^2*Sqrt[c - c*Sec[e + f*x]]*Tan[e + f*x])/(3*f*(a^2 + a^2*Sec[e + f*x])) + (2*c*(c - c*Sec[e + f*x])^(3/2)*Tan[e + f*x])/(3*f*(a + a*Sec[e + f*x])^2)","A",3,2,34,0.05882,1,"{3954, 3792}"
95,1,89,0,0.2192715,"\int \frac{\sec (e+f x) (c-c \sec (e+f x))^{3/2}}{(a+a \sec (e+f x))^2} \, dx","Int[(Sec[e + f*x]*(c - c*Sec[e + f*x])^(3/2))/(a + a*Sec[e + f*x])^2,x]","\frac{2 c \tan (e+f x) \sqrt{c-c \sec (e+f x)}}{3 f (a \sec (e+f x)+a)^2}-\frac{4 c^2 \tan (e+f x)}{3 f \left(a^2 \sec (e+f x)+a^2\right) \sqrt{c-c \sec (e+f x)}}","\frac{2 c \tan (e+f x) \sqrt{c-c \sec (e+f x)}}{3 f (a \sec (e+f x)+a)^2}-\frac{4 c^2 \tan (e+f x)}{3 f \left(a^2 \sec (e+f x)+a^2\right) \sqrt{c-c \sec (e+f x)}}",1,"(-4*c^2*Tan[e + f*x])/(3*f*(a^2 + a^2*Sec[e + f*x])*Sqrt[c - c*Sec[e + f*x]]) + (2*c*Sqrt[c - c*Sec[e + f*x]]*Tan[e + f*x])/(3*f*(a + a*Sec[e + f*x])^2)","A",2,2,34,0.05882,1,"{3954, 3953}"
96,1,41,0,0.1004313,"\int \frac{\sec (e+f x) \sqrt{c-c \sec (e+f x)}}{(a+a \sec (e+f x))^2} \, dx","Int[(Sec[e + f*x]*Sqrt[c - c*Sec[e + f*x]])/(a + a*Sec[e + f*x])^2,x]","\frac{2 c \tan (e+f x)}{3 f (a \sec (e+f x)+a)^2 \sqrt{c-c \sec (e+f x)}}","\frac{2 c \tan (e+f x)}{3 f (a \sec (e+f x)+a)^2 \sqrt{c-c \sec (e+f x)}}",1,"(2*c*Tan[e + f*x])/(3*f*(a + a*Sec[e + f*x])^2*Sqrt[c - c*Sec[e + f*x]])","A",1,1,34,0.02941,1,"{3953}"
97,1,138,0,0.2710978,"\int \frac{\sec (e+f x)}{(a+a \sec (e+f x))^2 \sqrt{c-c \sec (e+f x)}} \, dx","Int[Sec[e + f*x]/((a + a*Sec[e + f*x])^2*Sqrt[c - c*Sec[e + f*x]]),x]","-\frac{\tan ^{-1}\left(\frac{\sqrt{c} \tan (e+f x)}{\sqrt{2} \sqrt{c-c \sec (e+f x)}}\right)}{2 \sqrt{2} a^2 \sqrt{c} f}+\frac{\tan (e+f x)}{2 f \left(a^2 \sec (e+f x)+a^2\right) \sqrt{c-c \sec (e+f x)}}+\frac{\tan (e+f x)}{3 f (a \sec (e+f x)+a)^2 \sqrt{c-c \sec (e+f x)}}","-\frac{\tan ^{-1}\left(\frac{\sqrt{c} \tan (e+f x)}{\sqrt{2} \sqrt{c-c \sec (e+f x)}}\right)}{2 \sqrt{2} a^2 \sqrt{c} f}+\frac{\tan (e+f x)}{2 f \left(a^2 \sec (e+f x)+a^2\right) \sqrt{c-c \sec (e+f x)}}+\frac{\tan (e+f x)}{3 f (a \sec (e+f x)+a)^2 \sqrt{c-c \sec (e+f x)}}",1,"-ArcTan[(Sqrt[c]*Tan[e + f*x])/(Sqrt[2]*Sqrt[c - c*Sec[e + f*x]])]/(2*Sqrt[2]*a^2*Sqrt[c]*f) + Tan[e + f*x]/(3*f*(a + a*Sec[e + f*x])^2*Sqrt[c - c*Sec[e + f*x]]) + Tan[e + f*x]/(2*f*(a^2 + a^2*Sec[e + f*x])*Sqrt[c - c*Sec[e + f*x]])","A",4,3,34,0.08824,1,"{3960, 3795, 203}"
98,1,169,0,0.3434589,"\int \frac{\sec (e+f x)}{(a+a \sec (e+f x))^2 (c-c \sec (e+f x))^{3/2}} \, dx","Int[Sec[e + f*x]/((a + a*Sec[e + f*x])^2*(c - c*Sec[e + f*x])^(3/2)),x]","-\frac{5 \tan ^{-1}\left(\frac{\sqrt{c} \tan (e+f x)}{\sqrt{2} \sqrt{c-c \sec (e+f x)}}\right)}{8 \sqrt{2} a^2 c^{3/2} f}-\frac{5 \tan (e+f x)}{8 a^2 f (c-c \sec (e+f x))^{3/2}}+\frac{5 \tan (e+f x)}{6 f \left(a^2 \sec (e+f x)+a^2\right) (c-c \sec (e+f x))^{3/2}}+\frac{\tan (e+f x)}{3 f (a \sec (e+f x)+a)^2 (c-c \sec (e+f x))^{3/2}}","-\frac{5 \tan ^{-1}\left(\frac{\sqrt{c} \tan (e+f x)}{\sqrt{2} \sqrt{c-c \sec (e+f x)}}\right)}{8 \sqrt{2} a^2 c^{3/2} f}-\frac{5 \tan (e+f x)}{8 a^2 f (c-c \sec (e+f x))^{3/2}}+\frac{5 \tan (e+f x)}{6 f \left(a^2 \sec (e+f x)+a^2\right) (c-c \sec (e+f x))^{3/2}}+\frac{\tan (e+f x)}{3 f (a \sec (e+f x)+a)^2 (c-c \sec (e+f x))^{3/2}}",1,"(-5*ArcTan[(Sqrt[c]*Tan[e + f*x])/(Sqrt[2]*Sqrt[c - c*Sec[e + f*x]])])/(8*Sqrt[2]*a^2*c^(3/2)*f) - (5*Tan[e + f*x])/(8*a^2*f*(c - c*Sec[e + f*x])^(3/2)) + Tan[e + f*x]/(3*f*(a + a*Sec[e + f*x])^2*(c - c*Sec[e + f*x])^(3/2)) + (5*Tan[e + f*x])/(6*f*(a^2 + a^2*Sec[e + f*x])*(c - c*Sec[e + f*x])^(3/2))","A",5,4,34,0.1176,1,"{3960, 3796, 3795, 203}"
99,1,203,0,0.3889745,"\int \frac{\sec (e+f x)}{(a+a \sec (e+f x))^2 (c-c \sec (e+f x))^{5/2}} \, dx","Int[Sec[e + f*x]/((a + a*Sec[e + f*x])^2*(c - c*Sec[e + f*x])^(5/2)),x]","-\frac{35 \tan ^{-1}\left(\frac{\sqrt{c} \tan (e+f x)}{\sqrt{2} \sqrt{c-c \sec (e+f x)}}\right)}{64 \sqrt{2} a^2 c^{5/2} f}-\frac{35 \tan (e+f x)}{64 a^2 c f (c-c \sec (e+f x))^{3/2}}-\frac{35 \tan (e+f x)}{48 a^2 f (c-c \sec (e+f x))^{5/2}}+\frac{7 \tan (e+f x)}{6 f \left(a^2 \sec (e+f x)+a^2\right) (c-c \sec (e+f x))^{5/2}}+\frac{\tan (e+f x)}{3 f (a \sec (e+f x)+a)^2 (c-c \sec (e+f x))^{5/2}}","-\frac{35 \tan ^{-1}\left(\frac{\sqrt{c} \tan (e+f x)}{\sqrt{2} \sqrt{c-c \sec (e+f x)}}\right)}{64 \sqrt{2} a^2 c^{5/2} f}-\frac{35 \tan (e+f x)}{64 a^2 c f (c-c \sec (e+f x))^{3/2}}-\frac{35 \tan (e+f x)}{48 a^2 f (c-c \sec (e+f x))^{5/2}}+\frac{7 \tan (e+f x)}{6 f \left(a^2 \sec (e+f x)+a^2\right) (c-c \sec (e+f x))^{5/2}}+\frac{\tan (e+f x)}{3 f (a \sec (e+f x)+a)^2 (c-c \sec (e+f x))^{5/2}}",1,"(-35*ArcTan[(Sqrt[c]*Tan[e + f*x])/(Sqrt[2]*Sqrt[c - c*Sec[e + f*x]])])/(64*Sqrt[2]*a^2*c^(5/2)*f) - (35*Tan[e + f*x])/(48*a^2*f*(c - c*Sec[e + f*x])^(5/2)) + Tan[e + f*x]/(3*f*(a + a*Sec[e + f*x])^2*(c - c*Sec[e + f*x])^(5/2)) + (7*Tan[e + f*x])/(6*f*(a^2 + a^2*Sec[e + f*x])*(c - c*Sec[e + f*x])^(5/2)) - (35*Tan[e + f*x])/(64*a^2*c*f*(c - c*Sec[e + f*x])^(3/2))","A",6,4,34,0.1176,1,"{3960, 3796, 3795, 203}"
100,1,169,0,0.4020539,"\int \frac{\sec (e+f x) (c-c \sec (e+f x))^{7/2}}{(a+a \sec (e+f x))^3} \, dx","Int[(Sec[e + f*x]*(c - c*Sec[e + f*x])^(7/2))/(a + a*Sec[e + f*x])^3,x]","\frac{32 c^4 \tan (e+f x)}{5 a^3 f \sqrt{c-c \sec (e+f x)}}+\frac{16 c^3 \tan (e+f x) \sqrt{c-c \sec (e+f x)}}{5 f \left(a^3 \sec (e+f x)+a^3\right)}-\frac{4 c^2 \tan (e+f x) (c-c \sec (e+f x))^{3/2}}{5 a f (a \sec (e+f x)+a)^2}+\frac{2 c \tan (e+f x) (c-c \sec (e+f x))^{5/2}}{5 f (a \sec (e+f x)+a)^3}","\frac{32 c^4 \tan (e+f x)}{5 a^3 f \sqrt{c-c \sec (e+f x)}}+\frac{16 c^3 \tan (e+f x) \sqrt{c-c \sec (e+f x)}}{5 f \left(a^3 \sec (e+f x)+a^3\right)}-\frac{4 c^2 \tan (e+f x) (c-c \sec (e+f x))^{3/2}}{5 a f (a \sec (e+f x)+a)^2}+\frac{2 c \tan (e+f x) (c-c \sec (e+f x))^{5/2}}{5 f (a \sec (e+f x)+a)^3}",1,"(32*c^4*Tan[e + f*x])/(5*a^3*f*Sqrt[c - c*Sec[e + f*x]]) + (16*c^3*Sqrt[c - c*Sec[e + f*x]]*Tan[e + f*x])/(5*f*(a^3 + a^3*Sec[e + f*x])) - (4*c^2*(c - c*Sec[e + f*x])^(3/2)*Tan[e + f*x])/(5*a*f*(a + a*Sec[e + f*x])^2) + (2*c*(c - c*Sec[e + f*x])^(5/2)*Tan[e + f*x])/(5*f*(a + a*Sec[e + f*x])^3)","A",4,2,34,0.05882,1,"{3954, 3792}"
101,1,135,0,0.3483453,"\int \frac{\sec (e+f x) (c-c \sec (e+f x))^{5/2}}{(a+a \sec (e+f x))^3} \, dx","Int[(Sec[e + f*x]*(c - c*Sec[e + f*x])^(5/2))/(a + a*Sec[e + f*x])^3,x]","\frac{16 c^3 \tan (e+f x)}{15 f \left(a^3 \sec (e+f x)+a^3\right) \sqrt{c-c \sec (e+f x)}}-\frac{8 c^2 \tan (e+f x) \sqrt{c-c \sec (e+f x)}}{15 a f (a \sec (e+f x)+a)^2}+\frac{2 c \tan (e+f x) (c-c \sec (e+f x))^{3/2}}{5 f (a \sec (e+f x)+a)^3}","\frac{16 c^3 \tan (e+f x)}{15 f \left(a^3 \sec (e+f x)+a^3\right) \sqrt{c-c \sec (e+f x)}}-\frac{8 c^2 \tan (e+f x) \sqrt{c-c \sec (e+f x)}}{15 a f (a \sec (e+f x)+a)^2}+\frac{2 c \tan (e+f x) (c-c \sec (e+f x))^{3/2}}{5 f (a \sec (e+f x)+a)^3}",1,"(16*c^3*Tan[e + f*x])/(15*f*(a^3 + a^3*Sec[e + f*x])*Sqrt[c - c*Sec[e + f*x]]) - (8*c^2*Sqrt[c - c*Sec[e + f*x]]*Tan[e + f*x])/(15*a*f*(a + a*Sec[e + f*x])^2) + (2*c*(c - c*Sec[e + f*x])^(3/2)*Tan[e + f*x])/(5*f*(a + a*Sec[e + f*x])^3)","A",3,2,34,0.05882,1,"{3954, 3953}"
102,1,88,0,0.2222019,"\int \frac{\sec (e+f x) (c-c \sec (e+f x))^{3/2}}{(a+a \sec (e+f x))^3} \, dx","Int[(Sec[e + f*x]*(c - c*Sec[e + f*x])^(3/2))/(a + a*Sec[e + f*x])^3,x]","\frac{2 c \tan (e+f x) \sqrt{c-c \sec (e+f x)}}{5 f (a \sec (e+f x)+a)^3}-\frac{4 c^2 \tan (e+f x)}{15 a f (a \sec (e+f x)+a)^2 \sqrt{c-c \sec (e+f x)}}","\frac{2 c \tan (e+f x) \sqrt{c-c \sec (e+f x)}}{5 f (a \sec (e+f x)+a)^3}-\frac{4 c^2 \tan (e+f x)}{15 a f (a \sec (e+f x)+a)^2 \sqrt{c-c \sec (e+f x)}}",1,"(-4*c^2*Tan[e + f*x])/(15*a*f*(a + a*Sec[e + f*x])^2*Sqrt[c - c*Sec[e + f*x]]) + (2*c*Sqrt[c - c*Sec[e + f*x]]*Tan[e + f*x])/(5*f*(a + a*Sec[e + f*x])^3)","A",2,2,34,0.05882,1,"{3954, 3953}"
103,1,41,0,0.1015932,"\int \frac{\sec (e+f x) \sqrt{c-c \sec (e+f x)}}{(a+a \sec (e+f x))^3} \, dx","Int[(Sec[e + f*x]*Sqrt[c - c*Sec[e + f*x]])/(a + a*Sec[e + f*x])^3,x]","\frac{2 c \tan (e+f x)}{5 f (a \sec (e+f x)+a)^3 \sqrt{c-c \sec (e+f x)}}","\frac{2 c \tan (e+f x)}{5 f (a \sec (e+f x)+a)^3 \sqrt{c-c \sec (e+f x)}}",1,"(2*c*Tan[e + f*x])/(5*f*(a + a*Sec[e + f*x])^3*Sqrt[c - c*Sec[e + f*x]])","A",1,1,34,0.02941,1,"{3953}"
104,1,181,0,0.3941113,"\int \frac{\sec (e+f x)}{(a+a \sec (e+f x))^3 \sqrt{c-c \sec (e+f x)}} \, dx","Int[Sec[e + f*x]/((a + a*Sec[e + f*x])^3*Sqrt[c - c*Sec[e + f*x]]),x]","-\frac{\tan ^{-1}\left(\frac{\sqrt{c} \tan (e+f x)}{\sqrt{2} \sqrt{c-c \sec (e+f x)}}\right)}{4 \sqrt{2} a^3 \sqrt{c} f}+\frac{\tan (e+f x)}{4 f \left(a^3 \sec (e+f x)+a^3\right) \sqrt{c-c \sec (e+f x)}}+\frac{\tan (e+f x)}{6 a f (a \sec (e+f x)+a)^2 \sqrt{c-c \sec (e+f x)}}+\frac{\tan (e+f x)}{5 f (a \sec (e+f x)+a)^3 \sqrt{c-c \sec (e+f x)}}","-\frac{\tan ^{-1}\left(\frac{\sqrt{c} \tan (e+f x)}{\sqrt{2} \sqrt{c-c \sec (e+f x)}}\right)}{4 \sqrt{2} a^3 \sqrt{c} f}+\frac{\tan (e+f x)}{4 f \left(a^3 \sec (e+f x)+a^3\right) \sqrt{c-c \sec (e+f x)}}+\frac{\tan (e+f x)}{6 a f (a \sec (e+f x)+a)^2 \sqrt{c-c \sec (e+f x)}}+\frac{\tan (e+f x)}{5 f (a \sec (e+f x)+a)^3 \sqrt{c-c \sec (e+f x)}}",1,"-ArcTan[(Sqrt[c]*Tan[e + f*x])/(Sqrt[2]*Sqrt[c - c*Sec[e + f*x]])]/(4*Sqrt[2]*a^3*Sqrt[c]*f) + Tan[e + f*x]/(5*f*(a + a*Sec[e + f*x])^3*Sqrt[c - c*Sec[e + f*x]]) + Tan[e + f*x]/(6*a*f*(a + a*Sec[e + f*x])^2*Sqrt[c - c*Sec[e + f*x]]) + Tan[e + f*x]/(4*f*(a^3 + a^3*Sec[e + f*x])*Sqrt[c - c*Sec[e + f*x]])","A",5,3,34,0.08824,1,"{3960, 3795, 203}"
105,1,212,0,0.477317,"\int \frac{\sec (e+f x)}{(a+a \sec (e+f x))^3 (c-c \sec (e+f x))^{3/2}} \, dx","Int[Sec[e + f*x]/((a + a*Sec[e + f*x])^3*(c - c*Sec[e + f*x])^(3/2)),x]","-\frac{7 \tan ^{-1}\left(\frac{\sqrt{c} \tan (e+f x)}{\sqrt{2} \sqrt{c-c \sec (e+f x)}}\right)}{16 \sqrt{2} a^3 c^{3/2} f}-\frac{7 \tan (e+f x)}{16 a^3 f (c-c \sec (e+f x))^{3/2}}+\frac{7 \tan (e+f x)}{12 f \left(a^3 \sec (e+f x)+a^3\right) (c-c \sec (e+f x))^{3/2}}+\frac{7 \tan (e+f x)}{30 a f (a \sec (e+f x)+a)^2 (c-c \sec (e+f x))^{3/2}}+\frac{\tan (e+f x)}{5 f (a \sec (e+f x)+a)^3 (c-c \sec (e+f x))^{3/2}}","-\frac{7 \tan ^{-1}\left(\frac{\sqrt{c} \tan (e+f x)}{\sqrt{2} \sqrt{c-c \sec (e+f x)}}\right)}{16 \sqrt{2} a^3 c^{3/2} f}-\frac{7 \tan (e+f x)}{16 a^3 f (c-c \sec (e+f x))^{3/2}}+\frac{7 \tan (e+f x)}{12 f \left(a^3 \sec (e+f x)+a^3\right) (c-c \sec (e+f x))^{3/2}}+\frac{7 \tan (e+f x)}{30 a f (a \sec (e+f x)+a)^2 (c-c \sec (e+f x))^{3/2}}+\frac{\tan (e+f x)}{5 f (a \sec (e+f x)+a)^3 (c-c \sec (e+f x))^{3/2}}",1,"(-7*ArcTan[(Sqrt[c]*Tan[e + f*x])/(Sqrt[2]*Sqrt[c - c*Sec[e + f*x]])])/(16*Sqrt[2]*a^3*c^(3/2)*f) - (7*Tan[e + f*x])/(16*a^3*f*(c - c*Sec[e + f*x])^(3/2)) + Tan[e + f*x]/(5*f*(a + a*Sec[e + f*x])^3*(c - c*Sec[e + f*x])^(3/2)) + (7*Tan[e + f*x])/(30*a*f*(a + a*Sec[e + f*x])^2*(c - c*Sec[e + f*x])^(3/2)) + (7*Tan[e + f*x])/(12*f*(a^3 + a^3*Sec[e + f*x])*(c - c*Sec[e + f*x])^(3/2))","A",6,4,34,0.1176,1,"{3960, 3796, 3795, 203}"
106,1,246,0,0.5320181,"\int \frac{\sec (e+f x)}{(a+a \sec (e+f x))^3 (c-c \sec (e+f x))^{5/2}} \, dx","Int[Sec[e + f*x]/((a + a*Sec[e + f*x])^3*(c - c*Sec[e + f*x])^(5/2)),x]","-\frac{63 \tan ^{-1}\left(\frac{\sqrt{c} \tan (e+f x)}{\sqrt{2} \sqrt{c-c \sec (e+f x)}}\right)}{128 \sqrt{2} a^3 c^{5/2} f}-\frac{63 \tan (e+f x)}{128 a^3 c f (c-c \sec (e+f x))^{3/2}}-\frac{21 \tan (e+f x)}{32 a^3 f (c-c \sec (e+f x))^{5/2}}+\frac{21 \tan (e+f x)}{20 f \left(a^3 \sec (e+f x)+a^3\right) (c-c \sec (e+f x))^{5/2}}+\frac{3 \tan (e+f x)}{10 a f (a \sec (e+f x)+a)^2 (c-c \sec (e+f x))^{5/2}}+\frac{\tan (e+f x)}{5 f (a \sec (e+f x)+a)^3 (c-c \sec (e+f x))^{5/2}}","-\frac{63 \tan ^{-1}\left(\frac{\sqrt{c} \tan (e+f x)}{\sqrt{2} \sqrt{c-c \sec (e+f x)}}\right)}{128 \sqrt{2} a^3 c^{5/2} f}-\frac{63 \tan (e+f x)}{128 a^3 c f (c-c \sec (e+f x))^{3/2}}-\frac{21 \tan (e+f x)}{32 a^3 f (c-c \sec (e+f x))^{5/2}}+\frac{21 \tan (e+f x)}{20 f \left(a^3 \sec (e+f x)+a^3\right) (c-c \sec (e+f x))^{5/2}}+\frac{3 \tan (e+f x)}{10 a f (a \sec (e+f x)+a)^2 (c-c \sec (e+f x))^{5/2}}+\frac{\tan (e+f x)}{5 f (a \sec (e+f x)+a)^3 (c-c \sec (e+f x))^{5/2}}",1,"(-63*ArcTan[(Sqrt[c]*Tan[e + f*x])/(Sqrt[2]*Sqrt[c - c*Sec[e + f*x]])])/(128*Sqrt[2]*a^3*c^(5/2)*f) - (21*Tan[e + f*x])/(32*a^3*f*(c - c*Sec[e + f*x])^(5/2)) + Tan[e + f*x]/(5*f*(a + a*Sec[e + f*x])^3*(c - c*Sec[e + f*x])^(5/2)) + (3*Tan[e + f*x])/(10*a*f*(a + a*Sec[e + f*x])^2*(c - c*Sec[e + f*x])^(5/2)) + (21*Tan[e + f*x])/(20*f*(a^3 + a^3*Sec[e + f*x])*(c - c*Sec[e + f*x])^(5/2)) - (63*Tan[e + f*x])/(128*a^3*c*f*(c - c*Sec[e + f*x])^(3/2))","A",7,4,34,0.1176,1,"{3960, 3796, 3795, 203}"
107,1,43,0,0.1325947,"\int \sec (e+f x) \sqrt{a+a \sec (e+f x)} (c-c \sec (e+f x))^{5/2} \, dx","Int[Sec[e + f*x]*Sqrt[a + a*Sec[e + f*x]]*(c - c*Sec[e + f*x])^(5/2),x]","\frac{a \tan (e+f x) (c-c \sec (e+f x))^{5/2}}{3 f \sqrt{a \sec (e+f x)+a}}","\frac{a \tan (e+f x) (c-c \sec (e+f x))^{5/2}}{3 f \sqrt{a \sec (e+f x)+a}}",1,"(a*(c - c*Sec[e + f*x])^(5/2)*Tan[e + f*x])/(3*f*Sqrt[a + a*Sec[e + f*x]])","A",1,1,36,0.02778,1,"{3953}"
108,1,43,0,0.1326175,"\int \sec (e+f x) \sqrt{a+a \sec (e+f x)} (c-c \sec (e+f x))^{3/2} \, dx","Int[Sec[e + f*x]*Sqrt[a + a*Sec[e + f*x]]*(c - c*Sec[e + f*x])^(3/2),x]","\frac{a \tan (e+f x) (c-c \sec (e+f x))^{3/2}}{2 f \sqrt{a \sec (e+f x)+a}}","\frac{a \tan (e+f x) (c-c \sec (e+f x))^{3/2}}{2 f \sqrt{a \sec (e+f x)+a}}",1,"(a*(c - c*Sec[e + f*x])^(3/2)*Tan[e + f*x])/(2*f*Sqrt[a + a*Sec[e + f*x]])","A",1,1,36,0.02778,1,"{3953}"
109,1,41,0,0.1203713,"\int \sec (e+f x) \sqrt{a+a \sec (e+f x)} \sqrt{c-c \sec (e+f x)} \, dx","Int[Sec[e + f*x]*Sqrt[a + a*Sec[e + f*x]]*Sqrt[c - c*Sec[e + f*x]],x]","-\frac{c \tan (e+f x) \sqrt{a \sec (e+f x)+a}}{f \sqrt{c-c \sec (e+f x)}}","-\frac{c \tan (e+f x) \sqrt{a \sec (e+f x)+a}}{f \sqrt{c-c \sec (e+f x)}}",1,"-((c*Sqrt[a + a*Sec[e + f*x]]*Tan[e + f*x])/(f*Sqrt[c - c*Sec[e + f*x]]))","A",1,1,36,0.02778,1,"{3953}"
110,1,51,0,0.1252574,"\int \frac{\sec (e+f x) \sqrt{a+a \sec (e+f x)}}{\sqrt{c-c \sec (e+f x)}} \, dx","Int[(Sec[e + f*x]*Sqrt[a + a*Sec[e + f*x]])/Sqrt[c - c*Sec[e + f*x]],x]","\frac{a \tan (e+f x) \log (1-\sec (e+f x))}{f \sqrt{a \sec (e+f x)+a} \sqrt{c-c \sec (e+f x)}}","\frac{a \tan (e+f x) \log (1-\sec (e+f x))}{f \sqrt{a \sec (e+f x)+a} \sqrt{c-c \sec (e+f x)}}",1,"(a*Log[1 - Sec[e + f*x]]*Tan[e + f*x])/(f*Sqrt[a + a*Sec[e + f*x]]*Sqrt[c - c*Sec[e + f*x]])","A",1,1,36,0.02778,1,"{3952}"
111,1,42,0,0.1391669,"\int \frac{\sec (e+f x) \sqrt{a+a \sec (e+f x)}}{(c-c \sec (e+f x))^{3/2}} \, dx","Int[(Sec[e + f*x]*Sqrt[a + a*Sec[e + f*x]])/(c - c*Sec[e + f*x])^(3/2),x]","-\frac{\tan (e+f x) \sqrt{a \sec (e+f x)+a}}{2 f (c-c \sec (e+f x))^{3/2}}","-\frac{\tan (e+f x) \sqrt{a \sec (e+f x)+a}}{2 f (c-c \sec (e+f x))^{3/2}}",1,"-(Sqrt[a + a*Sec[e + f*x]]*Tan[e + f*x])/(2*f*(c - c*Sec[e + f*x])^(3/2))","A",1,1,36,0.02778,1,"{3950}"
112,1,43,0,0.1368121,"\int \frac{\sec (e+f x) \sqrt{a+a \sec (e+f x)}}{(c-c \sec (e+f x))^{5/2}} \, dx","Int[(Sec[e + f*x]*Sqrt[a + a*Sec[e + f*x]])/(c - c*Sec[e + f*x])^(5/2),x]","-\frac{a \tan (e+f x)}{2 f \sqrt{a \sec (e+f x)+a} (c-c \sec (e+f x))^{5/2}}","-\frac{a \tan (e+f x)}{2 f \sqrt{a \sec (e+f x)+a} (c-c \sec (e+f x))^{5/2}}",1,"-(a*Tan[e + f*x])/(2*f*Sqrt[a + a*Sec[e + f*x]]*(c - c*Sec[e + f*x])^(5/2))","A",1,1,36,0.02778,1,"{3953}"
113,1,89,0,0.2750517,"\int \sec (e+f x) (a+a \sec (e+f x))^{3/2} (c-c \sec (e+f x))^{7/2} \, dx","Int[Sec[e + f*x]*(a + a*Sec[e + f*x])^(3/2)*(c - c*Sec[e + f*x])^(7/2),x]","\frac{a^2 \tan (e+f x) (c-c \sec (e+f x))^{7/2}}{10 f \sqrt{a \sec (e+f x)+a}}+\frac{a \tan (e+f x) \sqrt{a \sec (e+f x)+a} (c-c \sec (e+f x))^{7/2}}{5 f}","\frac{a^2 \tan (e+f x) (c-c \sec (e+f x))^{7/2}}{10 f \sqrt{a \sec (e+f x)+a}}+\frac{a \tan (e+f x) \sqrt{a \sec (e+f x)+a} (c-c \sec (e+f x))^{7/2}}{5 f}",1,"(a^2*(c - c*Sec[e + f*x])^(7/2)*Tan[e + f*x])/(10*f*Sqrt[a + a*Sec[e + f*x]]) + (a*Sqrt[a + a*Sec[e + f*x]]*(c - c*Sec[e + f*x])^(7/2)*Tan[e + f*x])/(5*f)","A",2,2,36,0.05556,1,"{3955, 3953}"
114,1,89,0,0.2757891,"\int \sec (e+f x) (a+a \sec (e+f x))^{3/2} (c-c \sec (e+f x))^{5/2} \, dx","Int[Sec[e + f*x]*(a + a*Sec[e + f*x])^(3/2)*(c - c*Sec[e + f*x])^(5/2),x]","\frac{a^2 \tan (e+f x) (c-c \sec (e+f x))^{5/2}}{6 f \sqrt{a \sec (e+f x)+a}}+\frac{a \tan (e+f x) \sqrt{a \sec (e+f x)+a} (c-c \sec (e+f x))^{5/2}}{4 f}","\frac{a^2 \tan (e+f x) (c-c \sec (e+f x))^{5/2}}{6 f \sqrt{a \sec (e+f x)+a}}+\frac{a \tan (e+f x) \sqrt{a \sec (e+f x)+a} (c-c \sec (e+f x))^{5/2}}{4 f}",1,"(a^2*(c - c*Sec[e + f*x])^(5/2)*Tan[e + f*x])/(6*f*Sqrt[a + a*Sec[e + f*x]]) + (a*Sqrt[a + a*Sec[e + f*x]]*(c - c*Sec[e + f*x])^(5/2)*Tan[e + f*x])/(4*f)","A",2,2,36,0.05556,1,"{3955, 3953}"
115,1,89,0,0.2743891,"\int \sec (e+f x) (a+a \sec (e+f x))^{3/2} (c-c \sec (e+f x))^{3/2} \, dx","Int[Sec[e + f*x]*(a + a*Sec[e + f*x])^(3/2)*(c - c*Sec[e + f*x])^(3/2),x]","-\frac{c^2 \tan (e+f x) (a \sec (e+f x)+a)^{3/2}}{3 f \sqrt{c-c \sec (e+f x)}}-\frac{c \tan (e+f x) (a \sec (e+f x)+a)^{3/2} \sqrt{c-c \sec (e+f x)}}{3 f}","-\frac{c^2 \tan (e+f x) (a \sec (e+f x)+a)^{3/2}}{3 f \sqrt{c-c \sec (e+f x)}}-\frac{c \tan (e+f x) (a \sec (e+f x)+a)^{3/2} \sqrt{c-c \sec (e+f x)}}{3 f}",1,"-(c^2*(a + a*Sec[e + f*x])^(3/2)*Tan[e + f*x])/(3*f*Sqrt[c - c*Sec[e + f*x]]) - (c*(a + a*Sec[e + f*x])^(3/2)*Sqrt[c - c*Sec[e + f*x]]*Tan[e + f*x])/(3*f)","A",2,2,36,0.05556,1,"{3955, 3953}"
116,1,43,0,0.1299044,"\int \sec (e+f x) (a+a \sec (e+f x))^{3/2} \sqrt{c-c \sec (e+f x)} \, dx","Int[Sec[e + f*x]*(a + a*Sec[e + f*x])^(3/2)*Sqrt[c - c*Sec[e + f*x]],x]","-\frac{c \tan (e+f x) (a \sec (e+f x)+a)^{3/2}}{2 f \sqrt{c-c \sec (e+f x)}}","-\frac{c \tan (e+f x) (a \sec (e+f x)+a)^{3/2}}{2 f \sqrt{c-c \sec (e+f x)}}",1,"-(c*(a + a*Sec[e + f*x])^(3/2)*Tan[e + f*x])/(2*f*Sqrt[c - c*Sec[e + f*x]])","A",1,1,36,0.02778,1,"{3953}"
117,1,95,0,0.263783,"\int \frac{\sec (e+f x) (a+a \sec (e+f x))^{3/2}}{\sqrt{c-c \sec (e+f x)}} \, dx","Int[(Sec[e + f*x]*(a + a*Sec[e + f*x])^(3/2))/Sqrt[c - c*Sec[e + f*x]],x]","\frac{2 a^2 \tan (e+f x) \log (1-\sec (e+f x))}{f \sqrt{a \sec (e+f x)+a} \sqrt{c-c \sec (e+f x)}}+\frac{a \tan (e+f x) \sqrt{a \sec (e+f x)+a}}{f \sqrt{c-c \sec (e+f x)}}","\frac{2 a^2 \tan (e+f x) \log (1-\sec (e+f x))}{f \sqrt{a \sec (e+f x)+a} \sqrt{c-c \sec (e+f x)}}+\frac{a \tan (e+f x) \sqrt{a \sec (e+f x)+a}}{f \sqrt{c-c \sec (e+f x)}}",1,"(2*a^2*Log[1 - Sec[e + f*x]]*Tan[e + f*x])/(f*Sqrt[a + a*Sec[e + f*x]]*Sqrt[c - c*Sec[e + f*x]]) + (a*Sqrt[a + a*Sec[e + f*x]]*Tan[e + f*x])/(f*Sqrt[c - c*Sec[e + f*x]])","A",2,2,36,0.05556,1,"{3955, 3952}"
118,1,99,0,0.2754838,"\int \frac{\sec (e+f x) (a+a \sec (e+f x))^{3/2}}{(c-c \sec (e+f x))^{3/2}} \, dx","Int[(Sec[e + f*x]*(a + a*Sec[e + f*x])^(3/2))/(c - c*Sec[e + f*x])^(3/2),x]","-\frac{a^2 \tan (e+f x) \log (1-\sec (e+f x))}{c f \sqrt{a \sec (e+f x)+a} \sqrt{c-c \sec (e+f x)}}-\frac{a \tan (e+f x) \sqrt{a \sec (e+f x)+a}}{f (c-c \sec (e+f x))^{3/2}}","-\frac{a^2 \tan (e+f x) \log (1-\sec (e+f x))}{c f \sqrt{a \sec (e+f x)+a} \sqrt{c-c \sec (e+f x)}}-\frac{a \tan (e+f x) \sqrt{a \sec (e+f x)+a}}{f (c-c \sec (e+f x))^{3/2}}",1,"-((a*Sqrt[a + a*Sec[e + f*x]]*Tan[e + f*x])/(f*(c - c*Sec[e + f*x])^(3/2))) - (a^2*Log[1 - Sec[e + f*x]]*Tan[e + f*x])/(c*f*Sqrt[a + a*Sec[e + f*x]]*Sqrt[c - c*Sec[e + f*x]])","A",2,2,36,0.05556,1,"{3954, 3952}"
119,1,42,0,0.1491076,"\int \frac{\sec (e+f x) (a+a \sec (e+f x))^{3/2}}{(c-c \sec (e+f x))^{5/2}} \, dx","Int[(Sec[e + f*x]*(a + a*Sec[e + f*x])^(3/2))/(c - c*Sec[e + f*x])^(5/2),x]","-\frac{\tan (e+f x) (a \sec (e+f x)+a)^{3/2}}{4 f (c-c \sec (e+f x))^{5/2}}","-\frac{\tan (e+f x) (a \sec (e+f x)+a)^{3/2}}{4 f (c-c \sec (e+f x))^{5/2}}",1,"-((a + a*Sec[e + f*x])^(3/2)*Tan[e + f*x])/(4*f*(c - c*Sec[e + f*x])^(5/2))","A",1,1,36,0.02778,1,"{3950}"
120,1,88,0,0.3009413,"\int \frac{\sec (e+f x) (a+a \sec (e+f x))^{3/2}}{(c-c \sec (e+f x))^{7/2}} \, dx","Int[(Sec[e + f*x]*(a + a*Sec[e + f*x])^(3/2))/(c - c*Sec[e + f*x])^(7/2),x]","-\frac{\tan (e+f x) (a \sec (e+f x)+a)^{3/2}}{24 c f (c-c \sec (e+f x))^{5/2}}-\frac{\tan (e+f x) (a \sec (e+f x)+a)^{3/2}}{6 f (c-c \sec (e+f x))^{7/2}}","-\frac{\tan (e+f x) (a \sec (e+f x)+a)^{3/2}}{24 c f (c-c \sec (e+f x))^{5/2}}-\frac{\tan (e+f x) (a \sec (e+f x)+a)^{3/2}}{6 f (c-c \sec (e+f x))^{7/2}}",1,"-((a + a*Sec[e + f*x])^(3/2)*Tan[e + f*x])/(6*f*(c - c*Sec[e + f*x])^(7/2)) - ((a + a*Sec[e + f*x])^(3/2)*Tan[e + f*x])/(24*c*f*(c - c*Sec[e + f*x])^(5/2))","A",2,2,36,0.05556,1,"{3951, 3950}"
121,1,92,0,0.2847655,"\int \frac{\sec (e+f x) (a+a \sec (e+f x))^{3/2}}{(c-c \sec (e+f x))^{9/2}} \, dx","Int[(Sec[e + f*x]*(a + a*Sec[e + f*x])^(3/2))/(c - c*Sec[e + f*x])^(9/2),x]","\frac{a^2 \tan (e+f x)}{12 c f \sqrt{a \sec (e+f x)+a} (c-c \sec (e+f x))^{7/2}}-\frac{a \tan (e+f x) \sqrt{a \sec (e+f x)+a}}{4 f (c-c \sec (e+f x))^{9/2}}","\frac{a^2 \tan (e+f x)}{12 c f \sqrt{a \sec (e+f x)+a} (c-c \sec (e+f x))^{7/2}}-\frac{a \tan (e+f x) \sqrt{a \sec (e+f x)+a}}{4 f (c-c \sec (e+f x))^{9/2}}",1,"-(a*Sqrt[a + a*Sec[e + f*x]]*Tan[e + f*x])/(4*f*(c - c*Sec[e + f*x])^(9/2)) + (a^2*Tan[e + f*x])/(12*c*f*Sqrt[a + a*Sec[e + f*x]]*(c - c*Sec[e + f*x])^(7/2))","A",2,2,36,0.05556,1,"{3954, 3953}"
122,1,92,0,0.2867128,"\int \frac{\sec (e+f x) (a+a \sec (e+f x))^{3/2}}{(c-c \sec (e+f x))^{11/2}} \, dx","Int[(Sec[e + f*x]*(a + a*Sec[e + f*x])^(3/2))/(c - c*Sec[e + f*x])^(11/2),x]","\frac{a^2 \tan (e+f x)}{20 c f \sqrt{a \sec (e+f x)+a} (c-c \sec (e+f x))^{9/2}}-\frac{a \tan (e+f x) \sqrt{a \sec (e+f x)+a}}{5 f (c-c \sec (e+f x))^{11/2}}","\frac{a^2 \tan (e+f x)}{20 c f \sqrt{a \sec (e+f x)+a} (c-c \sec (e+f x))^{9/2}}-\frac{a \tan (e+f x) \sqrt{a \sec (e+f x)+a}}{5 f (c-c \sec (e+f x))^{11/2}}",1,"-(a*Sqrt[a + a*Sec[e + f*x]]*Tan[e + f*x])/(5*f*(c - c*Sec[e + f*x])^(11/2)) + (a^2*Tan[e + f*x])/(20*c*f*Sqrt[a + a*Sec[e + f*x]]*(c - c*Sec[e + f*x])^(9/2))","A",2,2,36,0.05556,1,"{3954, 3953}"
123,1,134,0,0.4214191,"\int \sec (e+f x) (a+a \sec (e+f x))^{5/2} (c-c \sec (e+f x))^{7/2} \, dx","Int[Sec[e + f*x]*(a + a*Sec[e + f*x])^(5/2)*(c - c*Sec[e + f*x])^(7/2),x]","\frac{2 a^2 \tan (e+f x) \sqrt{a \sec (e+f x)+a} (c-c \sec (e+f x))^{7/2}}{15 f}+\frac{a^3 \tan (e+f x) (c-c \sec (e+f x))^{7/2}}{15 f \sqrt{a \sec (e+f x)+a}}+\frac{a \tan (e+f x) (a \sec (e+f x)+a)^{3/2} (c-c \sec (e+f x))^{7/2}}{6 f}","\frac{2 a^2 \tan (e+f x) \sqrt{a \sec (e+f x)+a} (c-c \sec (e+f x))^{7/2}}{15 f}+\frac{a^3 \tan (e+f x) (c-c \sec (e+f x))^{7/2}}{15 f \sqrt{a \sec (e+f x)+a}}+\frac{a \tan (e+f x) (a \sec (e+f x)+a)^{3/2} (c-c \sec (e+f x))^{7/2}}{6 f}",1,"(a^3*(c - c*Sec[e + f*x])^(7/2)*Tan[e + f*x])/(15*f*Sqrt[a + a*Sec[e + f*x]]) + (2*a^2*Sqrt[a + a*Sec[e + f*x]]*(c - c*Sec[e + f*x])^(7/2)*Tan[e + f*x])/(15*f) + (a*(a + a*Sec[e + f*x])^(3/2)*(c - c*Sec[e + f*x])^(7/2)*Tan[e + f*x])/(6*f)","A",3,2,36,0.05556,1,"{3955, 3953}"
124,1,134,0,0.4240527,"\int \sec (e+f x) (a+a \sec (e+f x))^{5/2} (c-c \sec (e+f x))^{5/2} \, dx","Int[Sec[e + f*x]*(a + a*Sec[e + f*x])^(5/2)*(c - c*Sec[e + f*x])^(5/2),x]","-\frac{2 c^3 \tan (e+f x) (a \sec (e+f x)+a)^{5/2}}{15 f \sqrt{c-c \sec (e+f x)}}-\frac{c^2 \tan (e+f x) (a \sec (e+f x)+a)^{5/2} \sqrt{c-c \sec (e+f x)}}{5 f}-\frac{c \tan (e+f x) (a \sec (e+f x)+a)^{5/2} (c-c \sec (e+f x))^{3/2}}{5 f}","-\frac{2 c^3 \tan (e+f x) (a \sec (e+f x)+a)^{5/2}}{15 f \sqrt{c-c \sec (e+f x)}}-\frac{c^2 \tan (e+f x) (a \sec (e+f x)+a)^{5/2} \sqrt{c-c \sec (e+f x)}}{5 f}-\frac{c \tan (e+f x) (a \sec (e+f x)+a)^{5/2} (c-c \sec (e+f x))^{3/2}}{5 f}",1,"(-2*c^3*(a + a*Sec[e + f*x])^(5/2)*Tan[e + f*x])/(15*f*Sqrt[c - c*Sec[e + f*x]]) - (c^2*(a + a*Sec[e + f*x])^(5/2)*Sqrt[c - c*Sec[e + f*x]]*Tan[e + f*x])/(5*f) - (c*(a + a*Sec[e + f*x])^(5/2)*(c - c*Sec[e + f*x])^(3/2)*Tan[e + f*x])/(5*f)","A",3,2,36,0.05556,1,"{3955, 3953}"
125,1,89,0,0.2749399,"\int \sec (e+f x) (a+a \sec (e+f x))^{5/2} (c-c \sec (e+f x))^{3/2} \, dx","Int[Sec[e + f*x]*(a + a*Sec[e + f*x])^(5/2)*(c - c*Sec[e + f*x])^(3/2),x]","-\frac{c^2 \tan (e+f x) (a \sec (e+f x)+a)^{5/2}}{6 f \sqrt{c-c \sec (e+f x)}}-\frac{c \tan (e+f x) (a \sec (e+f x)+a)^{5/2} \sqrt{c-c \sec (e+f x)}}{4 f}","-\frac{c^2 \tan (e+f x) (a \sec (e+f x)+a)^{5/2}}{6 f \sqrt{c-c \sec (e+f x)}}-\frac{c \tan (e+f x) (a \sec (e+f x)+a)^{5/2} \sqrt{c-c \sec (e+f x)}}{4 f}",1,"-(c^2*(a + a*Sec[e + f*x])^(5/2)*Tan[e + f*x])/(6*f*Sqrt[c - c*Sec[e + f*x]]) - (c*(a + a*Sec[e + f*x])^(5/2)*Sqrt[c - c*Sec[e + f*x]]*Tan[e + f*x])/(4*f)","A",2,2,36,0.05556,1,"{3955, 3953}"
126,1,43,0,0.1283068,"\int \sec (e+f x) (a+a \sec (e+f x))^{5/2} \sqrt{c-c \sec (e+f x)} \, dx","Int[Sec[e + f*x]*(a + a*Sec[e + f*x])^(5/2)*Sqrt[c - c*Sec[e + f*x]],x]","-\frac{c \tan (e+f x) (a \sec (e+f x)+a)^{5/2}}{3 f \sqrt{c-c \sec (e+f x)}}","-\frac{c \tan (e+f x) (a \sec (e+f x)+a)^{5/2}}{3 f \sqrt{c-c \sec (e+f x)}}",1,"-(c*(a + a*Sec[e + f*x])^(5/2)*Tan[e + f*x])/(3*f*Sqrt[c - c*Sec[e + f*x]])","A",1,1,36,0.02778,1,"{3953}"
127,1,141,0,0.4045259,"\int \frac{\sec (e+f x) (a+a \sec (e+f x))^{5/2}}{\sqrt{c-c \sec (e+f x)}} \, dx","Int[(Sec[e + f*x]*(a + a*Sec[e + f*x])^(5/2))/Sqrt[c - c*Sec[e + f*x]],x]","\frac{2 a^2 \tan (e+f x) \sqrt{a \sec (e+f x)+a}}{f \sqrt{c-c \sec (e+f x)}}+\frac{4 a^3 \tan (e+f x) \log (1-\sec (e+f x))}{f \sqrt{a \sec (e+f x)+a} \sqrt{c-c \sec (e+f x)}}+\frac{a \tan (e+f x) (a \sec (e+f x)+a)^{3/2}}{2 f \sqrt{c-c \sec (e+f x)}}","\frac{2 a^2 \tan (e+f x) \sqrt{a \sec (e+f x)+a}}{f \sqrt{c-c \sec (e+f x)}}+\frac{4 a^3 \tan (e+f x) \log (1-\sec (e+f x))}{f \sqrt{a \sec (e+f x)+a} \sqrt{c-c \sec (e+f x)}}+\frac{a \tan (e+f x) (a \sec (e+f x)+a)^{3/2}}{2 f \sqrt{c-c \sec (e+f x)}}",1,"(4*a^3*Log[1 - Sec[e + f*x]]*Tan[e + f*x])/(f*Sqrt[a + a*Sec[e + f*x]]*Sqrt[c - c*Sec[e + f*x]]) + (2*a^2*Sqrt[a + a*Sec[e + f*x]]*Tan[e + f*x])/(f*Sqrt[c - c*Sec[e + f*x]]) + (a*(a + a*Sec[e + f*x])^(3/2)*Tan[e + f*x])/(2*f*Sqrt[c - c*Sec[e + f*x]])","A",3,2,36,0.05556,1,"{3955, 3952}"
128,1,145,0,0.4199419,"\int \frac{\sec (e+f x) (a+a \sec (e+f x))^{5/2}}{(c-c \sec (e+f x))^{3/2}} \, dx","Int[(Sec[e + f*x]*(a + a*Sec[e + f*x])^(5/2))/(c - c*Sec[e + f*x])^(3/2),x]","-\frac{2 a^2 \tan (e+f x) \sqrt{a \sec (e+f x)+a}}{c f \sqrt{c-c \sec (e+f x)}}-\frac{4 a^3 \tan (e+f x) \log (1-\sec (e+f x))}{c f \sqrt{a \sec (e+f x)+a} \sqrt{c-c \sec (e+f x)}}-\frac{a \tan (e+f x) (a \sec (e+f x)+a)^{3/2}}{f (c-c \sec (e+f x))^{3/2}}","-\frac{2 a^2 \tan (e+f x) \sqrt{a \sec (e+f x)+a}}{c f \sqrt{c-c \sec (e+f x)}}-\frac{4 a^3 \tan (e+f x) \log (1-\sec (e+f x))}{c f \sqrt{a \sec (e+f x)+a} \sqrt{c-c \sec (e+f x)}}-\frac{a \tan (e+f x) (a \sec (e+f x)+a)^{3/2}}{f (c-c \sec (e+f x))^{3/2}}",1,"-((a*(a + a*Sec[e + f*x])^(3/2)*Tan[e + f*x])/(f*(c - c*Sec[e + f*x])^(3/2))) - (4*a^3*Log[1 - Sec[e + f*x]]*Tan[e + f*x])/(c*f*Sqrt[a + a*Sec[e + f*x]]*Sqrt[c - c*Sec[e + f*x]]) - (2*a^2*Sqrt[a + a*Sec[e + f*x]]*Tan[e + f*x])/(c*f*Sqrt[c - c*Sec[e + f*x]])","A",3,3,36,0.08333,1,"{3954, 3955, 3952}"
129,1,145,0,0.4310878,"\int \frac{\sec (e+f x) (a+a \sec (e+f x))^{5/2}}{(c-c \sec (e+f x))^{5/2}} \, dx","Int[(Sec[e + f*x]*(a + a*Sec[e + f*x])^(5/2))/(c - c*Sec[e + f*x])^(5/2),x]","\frac{a^3 \tan (e+f x) \log (1-\sec (e+f x))}{c^2 f \sqrt{a \sec (e+f x)+a} \sqrt{c-c \sec (e+f x)}}+\frac{a^2 \tan (e+f x) \sqrt{a \sec (e+f x)+a}}{c f (c-c \sec (e+f x))^{3/2}}-\frac{a \tan (e+f x) (a \sec (e+f x)+a)^{3/2}}{2 f (c-c \sec (e+f x))^{5/2}}","\frac{a^3 \tan (e+f x) \log (1-\sec (e+f x))}{c^2 f \sqrt{a \sec (e+f x)+a} \sqrt{c-c \sec (e+f x)}}+\frac{a^2 \tan (e+f x) \sqrt{a \sec (e+f x)+a}}{c f (c-c \sec (e+f x))^{3/2}}-\frac{a \tan (e+f x) (a \sec (e+f x)+a)^{3/2}}{2 f (c-c \sec (e+f x))^{5/2}}",1,"-(a*(a + a*Sec[e + f*x])^(3/2)*Tan[e + f*x])/(2*f*(c - c*Sec[e + f*x])^(5/2)) + (a^2*Sqrt[a + a*Sec[e + f*x]]*Tan[e + f*x])/(c*f*(c - c*Sec[e + f*x])^(3/2)) + (a^3*Log[1 - Sec[e + f*x]]*Tan[e + f*x])/(c^2*f*Sqrt[a + a*Sec[e + f*x]]*Sqrt[c - c*Sec[e + f*x]])","A",3,2,36,0.05556,1,"{3954, 3952}"
130,1,42,0,0.1455825,"\int \frac{\sec (e+f x) (a+a \sec (e+f x))^{5/2}}{(c-c \sec (e+f x))^{7/2}} \, dx","Int[(Sec[e + f*x]*(a + a*Sec[e + f*x])^(5/2))/(c - c*Sec[e + f*x])^(7/2),x]","-\frac{\tan (e+f x) (a \sec (e+f x)+a)^{5/2}}{6 f (c-c \sec (e+f x))^{7/2}}","-\frac{\tan (e+f x) (a \sec (e+f x)+a)^{5/2}}{6 f (c-c \sec (e+f x))^{7/2}}",1,"-((a + a*Sec[e + f*x])^(5/2)*Tan[e + f*x])/(6*f*(c - c*Sec[e + f*x])^(7/2))","A",1,1,36,0.02778,1,"{3950}"
131,1,88,0,0.2976333,"\int \frac{\sec (e+f x) (a+a \sec (e+f x))^{5/2}}{(c-c \sec (e+f x))^{9/2}} \, dx","Int[(Sec[e + f*x]*(a + a*Sec[e + f*x])^(5/2))/(c - c*Sec[e + f*x])^(9/2),x]","-\frac{\tan (e+f x) (a \sec (e+f x)+a)^{5/2}}{48 c f (c-c \sec (e+f x))^{7/2}}-\frac{\tan (e+f x) (a \sec (e+f x)+a)^{5/2}}{8 f (c-c \sec (e+f x))^{9/2}}","-\frac{\tan (e+f x) (a \sec (e+f x)+a)^{5/2}}{48 c f (c-c \sec (e+f x))^{7/2}}-\frac{\tan (e+f x) (a \sec (e+f x)+a)^{5/2}}{8 f (c-c \sec (e+f x))^{9/2}}",1,"-((a + a*Sec[e + f*x])^(5/2)*Tan[e + f*x])/(8*f*(c - c*Sec[e + f*x])^(9/2)) - ((a + a*Sec[e + f*x])^(5/2)*Tan[e + f*x])/(48*c*f*(c - c*Sec[e + f*x])^(7/2))","A",2,2,36,0.05556,1,"{3951, 3950}"
132,1,133,0,0.4555793,"\int \frac{\sec (e+f x) (a+a \sec (e+f x))^{5/2}}{(c-c \sec (e+f x))^{11/2}} \, dx","Int[(Sec[e + f*x]*(a + a*Sec[e + f*x])^(5/2))/(c - c*Sec[e + f*x])^(11/2),x]","-\frac{\tan (e+f x) (a \sec (e+f x)+a)^{5/2}}{240 c^2 f (c-c \sec (e+f x))^{7/2}}-\frac{\tan (e+f x) (a \sec (e+f x)+a)^{5/2}}{40 c f (c-c \sec (e+f x))^{9/2}}-\frac{\tan (e+f x) (a \sec (e+f x)+a)^{5/2}}{10 f (c-c \sec (e+f x))^{11/2}}","-\frac{\tan (e+f x) (a \sec (e+f x)+a)^{5/2}}{240 c^2 f (c-c \sec (e+f x))^{7/2}}-\frac{\tan (e+f x) (a \sec (e+f x)+a)^{5/2}}{40 c f (c-c \sec (e+f x))^{9/2}}-\frac{\tan (e+f x) (a \sec (e+f x)+a)^{5/2}}{10 f (c-c \sec (e+f x))^{11/2}}",1,"-((a + a*Sec[e + f*x])^(5/2)*Tan[e + f*x])/(10*f*(c - c*Sec[e + f*x])^(11/2)) - ((a + a*Sec[e + f*x])^(5/2)*Tan[e + f*x])/(40*c*f*(c - c*Sec[e + f*x])^(9/2)) - ((a + a*Sec[e + f*x])^(5/2)*Tan[e + f*x])/(240*c^2*f*(c - c*Sec[e + f*x])^(7/2))","A",3,2,36,0.05556,1,"{3951, 3950}"
133,1,139,0,0.4092184,"\int \frac{\sec (e+f x) (c-c \sec (e+f x))^{5/2}}{\sqrt{a+a \sec (e+f x)}} \, dx","Int[(Sec[e + f*x]*(c - c*Sec[e + f*x])^(5/2))/Sqrt[a + a*Sec[e + f*x]],x]","-\frac{2 c^2 \tan (e+f x) \sqrt{c-c \sec (e+f x)}}{f \sqrt{a \sec (e+f x)+a}}-\frac{4 c^3 \tan (e+f x) \log (\sec (e+f x)+1)}{f \sqrt{a \sec (e+f x)+a} \sqrt{c-c \sec (e+f x)}}-\frac{c \tan (e+f x) (c-c \sec (e+f x))^{3/2}}{2 f \sqrt{a \sec (e+f x)+a}}","-\frac{2 c^2 \tan (e+f x) \sqrt{c-c \sec (e+f x)}}{f \sqrt{a \sec (e+f x)+a}}-\frac{4 c^3 \tan (e+f x) \log (\sec (e+f x)+1)}{f \sqrt{a \sec (e+f x)+a} \sqrt{c-c \sec (e+f x)}}-\frac{c \tan (e+f x) (c-c \sec (e+f x))^{3/2}}{2 f \sqrt{a \sec (e+f x)+a}}",1,"(-4*c^3*Log[1 + Sec[e + f*x]]*Tan[e + f*x])/(f*Sqrt[a + a*Sec[e + f*x]]*Sqrt[c - c*Sec[e + f*x]]) - (2*c^2*Sqrt[c - c*Sec[e + f*x]]*Tan[e + f*x])/(f*Sqrt[a + a*Sec[e + f*x]]) - (c*(c - c*Sec[e + f*x])^(3/2)*Tan[e + f*x])/(2*f*Sqrt[a + a*Sec[e + f*x]])","A",3,2,36,0.05556,1,"{3955, 3952}"
134,1,94,0,0.2658124,"\int \frac{\sec (e+f x) (c-c \sec (e+f x))^{3/2}}{\sqrt{a+a \sec (e+f x)}} \, dx","Int[(Sec[e + f*x]*(c - c*Sec[e + f*x])^(3/2))/Sqrt[a + a*Sec[e + f*x]],x]","-\frac{2 c^2 \tan (e+f x) \log (\sec (e+f x)+1)}{f \sqrt{a \sec (e+f x)+a} \sqrt{c-c \sec (e+f x)}}-\frac{c \tan (e+f x) \sqrt{c-c \sec (e+f x)}}{f \sqrt{a \sec (e+f x)+a}}","-\frac{2 c^2 \tan (e+f x) \log (\sec (e+f x)+1)}{f \sqrt{a \sec (e+f x)+a} \sqrt{c-c \sec (e+f x)}}-\frac{c \tan (e+f x) \sqrt{c-c \sec (e+f x)}}{f \sqrt{a \sec (e+f x)+a}}",1,"(-2*c^2*Log[1 + Sec[e + f*x]]*Tan[e + f*x])/(f*Sqrt[a + a*Sec[e + f*x]]*Sqrt[c - c*Sec[e + f*x]]) - (c*Sqrt[c - c*Sec[e + f*x]]*Tan[e + f*x])/(f*Sqrt[a + a*Sec[e + f*x]])","A",2,2,36,0.05556,1,"{3955, 3952}"
135,1,50,0,0.1222319,"\int \frac{\sec (e+f x) \sqrt{c-c \sec (e+f x)}}{\sqrt{a+a \sec (e+f x)}} \, dx","Int[(Sec[e + f*x]*Sqrt[c - c*Sec[e + f*x]])/Sqrt[a + a*Sec[e + f*x]],x]","-\frac{c \tan (e+f x) \log (\sec (e+f x)+1)}{f \sqrt{a \sec (e+f x)+a} \sqrt{c-c \sec (e+f x)}}","-\frac{c \tan (e+f x) \log (\sec (e+f x)+1)}{f \sqrt{a \sec (e+f x)+a} \sqrt{c-c \sec (e+f x)}}",1,"-((c*Log[1 + Sec[e + f*x]]*Tan[e + f*x])/(f*Sqrt[a + a*Sec[e + f*x]]*Sqrt[c - c*Sec[e + f*x]]))","A",1,1,36,0.02778,1,"{3952}"
136,1,47,0,0.1349703,"\int \frac{\sec (e+f x)}{\sqrt{a+a \sec (e+f x)} \sqrt{c-c \sec (e+f x)}} \, dx","Int[Sec[e + f*x]/(Sqrt[a + a*Sec[e + f*x]]*Sqrt[c - c*Sec[e + f*x]]),x]","-\frac{\tan (e+f x) \tanh ^{-1}(\cos (e+f x))}{f \sqrt{a \sec (e+f x)+a} \sqrt{c-c \sec (e+f x)}}","-\frac{\tan (e+f x) \tanh ^{-1}(\cos (e+f x))}{f \sqrt{a \sec (e+f x)+a} \sqrt{c-c \sec (e+f x)}}",1,"-((ArcTanh[Cos[e + f*x]]*Tan[e + f*x])/(f*Sqrt[a + a*Sec[e + f*x]]*Sqrt[c - c*Sec[e + f*x]]))","A",2,2,36,0.05556,1,"{3959, 3770}"
137,1,95,0,0.2800259,"\int \frac{\sec (e+f x)}{\sqrt{a+a \sec (e+f x)} (c-c \sec (e+f x))^{3/2}} \, dx","Int[Sec[e + f*x]/(Sqrt[a + a*Sec[e + f*x]]*(c - c*Sec[e + f*x])^(3/2)),x]","-\frac{\tan (e+f x)}{2 f \sqrt{a \sec (e+f x)+a} (c-c \sec (e+f x))^{3/2}}-\frac{\tan (e+f x) \tanh ^{-1}(\cos (e+f x))}{2 c f \sqrt{a \sec (e+f x)+a} \sqrt{c-c \sec (e+f x)}}","-\frac{\tan (e+f x)}{2 f \sqrt{a \sec (e+f x)+a} (c-c \sec (e+f x))^{3/2}}-\frac{\tan (e+f x) \tanh ^{-1}(\cos (e+f x))}{2 c f \sqrt{a \sec (e+f x)+a} \sqrt{c-c \sec (e+f x)}}",1,"-Tan[e + f*x]/(2*f*Sqrt[a + a*Sec[e + f*x]]*(c - c*Sec[e + f*x])^(3/2)) - (ArcTanh[Cos[e + f*x]]*Tan[e + f*x])/(2*c*f*Sqrt[a + a*Sec[e + f*x]]*Sqrt[c - c*Sec[e + f*x]])","A",3,3,36,0.08333,1,"{3960, 3959, 3770}"
138,1,140,0,0.4298637,"\int \frac{\sec (e+f x)}{\sqrt{a+a \sec (e+f x)} (c-c \sec (e+f x))^{5/2}} \, dx","Int[Sec[e + f*x]/(Sqrt[a + a*Sec[e + f*x]]*(c - c*Sec[e + f*x])^(5/2)),x]","-\frac{\tan (e+f x) \tanh ^{-1}(\cos (e+f x))}{4 c^2 f \sqrt{a \sec (e+f x)+a} \sqrt{c-c \sec (e+f x)}}-\frac{\tan (e+f x)}{4 c f \sqrt{a \sec (e+f x)+a} (c-c \sec (e+f x))^{3/2}}-\frac{\tan (e+f x)}{4 f \sqrt{a \sec (e+f x)+a} (c-c \sec (e+f x))^{5/2}}","-\frac{\tan (e+f x) \tanh ^{-1}(\cos (e+f x))}{4 c^2 f \sqrt{a \sec (e+f x)+a} \sqrt{c-c \sec (e+f x)}}-\frac{\tan (e+f x)}{4 c f \sqrt{a \sec (e+f x)+a} (c-c \sec (e+f x))^{3/2}}-\frac{\tan (e+f x)}{4 f \sqrt{a \sec (e+f x)+a} (c-c \sec (e+f x))^{5/2}}",1,"-Tan[e + f*x]/(4*f*Sqrt[a + a*Sec[e + f*x]]*(c - c*Sec[e + f*x])^(5/2)) - Tan[e + f*x]/(4*c*f*Sqrt[a + a*Sec[e + f*x]]*(c - c*Sec[e + f*x])^(3/2)) - (ArcTanh[Cos[e + f*x]]*Tan[e + f*x])/(4*c^2*f*Sqrt[a + a*Sec[e + f*x]]*Sqrt[c - c*Sec[e + f*x]])","A",4,3,36,0.08333,1,"{3960, 3959, 3770}"
139,1,142,0,0.4236436,"\int \frac{\sec (e+f x) (c-c \sec (e+f x))^{5/2}}{(a+a \sec (e+f x))^{3/2}} \, dx","Int[(Sec[e + f*x]*(c - c*Sec[e + f*x])^(5/2))/(a + a*Sec[e + f*x])^(3/2),x]","\frac{2 c^2 \tan (e+f x) \sqrt{c-c \sec (e+f x)}}{a f \sqrt{a \sec (e+f x)+a}}+\frac{4 c^3 \tan (e+f x) \log (\sec (e+f x)+1)}{a f \sqrt{a \sec (e+f x)+a} \sqrt{c-c \sec (e+f x)}}+\frac{c \tan (e+f x) (c-c \sec (e+f x))^{3/2}}{f (a \sec (e+f x)+a)^{3/2}}","\frac{2 c^2 \tan (e+f x) \sqrt{c-c \sec (e+f x)}}{a f \sqrt{a \sec (e+f x)+a}}+\frac{4 c^3 \tan (e+f x) \log (\sec (e+f x)+1)}{a f \sqrt{a \sec (e+f x)+a} \sqrt{c-c \sec (e+f x)}}+\frac{c \tan (e+f x) (c-c \sec (e+f x))^{3/2}}{f (a \sec (e+f x)+a)^{3/2}}",1,"(4*c^3*Log[1 + Sec[e + f*x]]*Tan[e + f*x])/(a*f*Sqrt[a + a*Sec[e + f*x]]*Sqrt[c - c*Sec[e + f*x]]) + (2*c^2*Sqrt[c - c*Sec[e + f*x]]*Tan[e + f*x])/(a*f*Sqrt[a + a*Sec[e + f*x]]) + (c*(c - c*Sec[e + f*x])^(3/2)*Tan[e + f*x])/(f*(a + a*Sec[e + f*x])^(3/2))","A",3,3,36,0.08333,1,"{3954, 3955, 3952}"
140,1,95,0,0.2784871,"\int \frac{\sec (e+f x) (c-c \sec (e+f x))^{3/2}}{(a+a \sec (e+f x))^{3/2}} \, dx","Int[(Sec[e + f*x]*(c - c*Sec[e + f*x])^(3/2))/(a + a*Sec[e + f*x])^(3/2),x]","\frac{c^2 \tan (e+f x) \log (\sec (e+f x)+1)}{a f \sqrt{a \sec (e+f x)+a} \sqrt{c-c \sec (e+f x)}}+\frac{c \tan (e+f x) \sqrt{c-c \sec (e+f x)}}{f (a \sec (e+f x)+a)^{3/2}}","\frac{c^2 \tan (e+f x) \log (\sec (e+f x)+1)}{a f \sqrt{a \sec (e+f x)+a} \sqrt{c-c \sec (e+f x)}}+\frac{c \tan (e+f x) \sqrt{c-c \sec (e+f x)}}{f (a \sec (e+f x)+a)^{3/2}}",1,"(c^2*Log[1 + Sec[e + f*x]]*Tan[e + f*x])/(a*f*Sqrt[a + a*Sec[e + f*x]]*Sqrt[c - c*Sec[e + f*x]]) + (c*Sqrt[c - c*Sec[e + f*x]]*Tan[e + f*x])/(f*(a + a*Sec[e + f*x])^(3/2))","A",2,2,36,0.05556,1,"{3954, 3952}"
141,1,42,0,0.1343053,"\int \frac{\sec (e+f x) \sqrt{c-c \sec (e+f x)}}{(a+a \sec (e+f x))^{3/2}} \, dx","Int[(Sec[e + f*x]*Sqrt[c - c*Sec[e + f*x]])/(a + a*Sec[e + f*x])^(3/2),x]","\frac{\tan (e+f x) \sqrt{c-c \sec (e+f x)}}{2 f (a \sec (e+f x)+a)^{3/2}}","\frac{\tan (e+f x) \sqrt{c-c \sec (e+f x)}}{2 f (a \sec (e+f x)+a)^{3/2}}",1,"(Sqrt[c - c*Sec[e + f*x]]*Tan[e + f*x])/(2*f*(a + a*Sec[e + f*x])^(3/2))","A",1,1,36,0.02778,1,"{3950}"
142,1,95,0,0.2789766,"\int \frac{\sec (e+f x)}{(a+a \sec (e+f x))^{3/2} \sqrt{c-c \sec (e+f x)}} \, dx","Int[Sec[e + f*x]/((a + a*Sec[e + f*x])^(3/2)*Sqrt[c - c*Sec[e + f*x]]),x]","\frac{\tan (e+f x)}{2 f (a \sec (e+f x)+a)^{3/2} \sqrt{c-c \sec (e+f x)}}-\frac{\tan (e+f x) \tanh ^{-1}(\cos (e+f x))}{2 a f \sqrt{a \sec (e+f x)+a} \sqrt{c-c \sec (e+f x)}}","\frac{\tan (e+f x)}{2 f (a \sec (e+f x)+a)^{3/2} \sqrt{c-c \sec (e+f x)}}-\frac{\tan (e+f x) \tanh ^{-1}(\cos (e+f x))}{2 a f \sqrt{a \sec (e+f x)+a} \sqrt{c-c \sec (e+f x)}}",1,"Tan[e + f*x]/(2*f*(a + a*Sec[e + f*x])^(3/2)*Sqrt[c - c*Sec[e + f*x]]) - (ArcTanh[Cos[e + f*x]]*Tan[e + f*x])/(2*a*f*Sqrt[a + a*Sec[e + f*x]]*Sqrt[c - c*Sec[e + f*x]])","A",3,3,36,0.08333,1,"{3960, 3959, 3770}"
143,1,104,0,0.1818767,"\int \frac{\sec (e+f x)}{(a+a \sec (e+f x))^{3/2} (c-c \sec (e+f x))^{3/2}} \, dx","Int[Sec[e + f*x]/((a + a*Sec[e + f*x])^(3/2)*(c - c*Sec[e + f*x])^(3/2)),x]","\frac{\csc (e+f x)}{2 a c f \sqrt{a \sec (e+f x)+a} \sqrt{c-c \sec (e+f x)}}-\frac{\tan (e+f x) \tanh ^{-1}(\cos (e+f x))}{2 a c f \sqrt{a \sec (e+f x)+a} \sqrt{c-c \sec (e+f x)}}","\frac{\csc (e+f x)}{2 a c f \sqrt{a \sec (e+f x)+a} \sqrt{c-c \sec (e+f x)}}-\frac{\tan (e+f x) \tanh ^{-1}(\cos (e+f x))}{2 a c f \sqrt{a \sec (e+f x)+a} \sqrt{c-c \sec (e+f x)}}",1,"Csc[e + f*x]/(2*a*c*f*Sqrt[a + a*Sec[e + f*x]]*Sqrt[c - c*Sec[e + f*x]]) - (ArcTanh[Cos[e + f*x]]*Tan[e + f*x])/(2*a*c*f*Sqrt[a + a*Sec[e + f*x]]*Sqrt[c - c*Sec[e + f*x]])","A",3,3,36,0.08333,1,"{3959, 2611, 3770}"
144,1,146,0,0.3406452,"\int \frac{\sec (e+f x)}{(a+a \sec (e+f x))^{3/2} (c-c \sec (e+f x))^{5/2}} \, dx","Int[Sec[e + f*x]/((a + a*Sec[e + f*x])^(3/2)*(c - c*Sec[e + f*x])^(5/2)),x]","\frac{3 \csc (e+f x)}{8 a c^2 f \sqrt{a \sec (e+f x)+a} \sqrt{c-c \sec (e+f x)}}-\frac{3 \tan (e+f x) \tanh ^{-1}(\cos (e+f x))}{8 a c^2 f \sqrt{a \sec (e+f x)+a} \sqrt{c-c \sec (e+f x)}}-\frac{\tan (e+f x)}{4 f (a \sec (e+f x)+a)^{3/2} (c-c \sec (e+f x))^{5/2}}","\frac{3 \csc (e+f x)}{8 a c^2 f \sqrt{a \sec (e+f x)+a} \sqrt{c-c \sec (e+f x)}}-\frac{3 \tan (e+f x) \tanh ^{-1}(\cos (e+f x))}{8 a c^2 f \sqrt{a \sec (e+f x)+a} \sqrt{c-c \sec (e+f x)}}-\frac{\tan (e+f x)}{4 f (a \sec (e+f x)+a)^{3/2} (c-c \sec (e+f x))^{5/2}}",1,"(3*Csc[e + f*x])/(8*a*c^2*f*Sqrt[a + a*Sec[e + f*x]]*Sqrt[c - c*Sec[e + f*x]]) - Tan[e + f*x]/(4*f*(a + a*Sec[e + f*x])^(3/2)*(c - c*Sec[e + f*x])^(5/2)) - (3*ArcTanh[Cos[e + f*x]]*Tan[e + f*x])/(8*a*c^2*f*Sqrt[a + a*Sec[e + f*x]]*Sqrt[c - c*Sec[e + f*x]])","A",4,4,36,0.1111,1,"{3960, 3959, 2611, 3770}"
145,1,145,0,0.4357581,"\int \frac{\sec (e+f x) (c-c \sec (e+f x))^{5/2}}{(a+a \sec (e+f x))^{5/2}} \, dx","Int[(Sec[e + f*x]*(c - c*Sec[e + f*x])^(5/2))/(a + a*Sec[e + f*x])^(5/2),x]","-\frac{c^3 \tan (e+f x) \log (\sec (e+f x)+1)}{a^2 f \sqrt{a \sec (e+f x)+a} \sqrt{c-c \sec (e+f x)}}-\frac{c^2 \tan (e+f x) \sqrt{c-c \sec (e+f x)}}{a f (a \sec (e+f x)+a)^{3/2}}+\frac{c \tan (e+f x) (c-c \sec (e+f x))^{3/2}}{2 f (a \sec (e+f x)+a)^{5/2}}","-\frac{c^3 \tan (e+f x) \log (\sec (e+f x)+1)}{a^2 f \sqrt{a \sec (e+f x)+a} \sqrt{c-c \sec (e+f x)}}-\frac{c^2 \tan (e+f x) \sqrt{c-c \sec (e+f x)}}{a f (a \sec (e+f x)+a)^{3/2}}+\frac{c \tan (e+f x) (c-c \sec (e+f x))^{3/2}}{2 f (a \sec (e+f x)+a)^{5/2}}",1,"-((c^3*Log[1 + Sec[e + f*x]]*Tan[e + f*x])/(a^2*f*Sqrt[a + a*Sec[e + f*x]]*Sqrt[c - c*Sec[e + f*x]])) - (c^2*Sqrt[c - c*Sec[e + f*x]]*Tan[e + f*x])/(a*f*(a + a*Sec[e + f*x])^(3/2)) + (c*(c - c*Sec[e + f*x])^(3/2)*Tan[e + f*x])/(2*f*(a + a*Sec[e + f*x])^(5/2))","A",3,2,36,0.05556,1,"{3954, 3952}"
146,1,42,0,0.1469476,"\int \frac{\sec (e+f x) (c-c \sec (e+f x))^{3/2}}{(a+a \sec (e+f x))^{5/2}} \, dx","Int[(Sec[e + f*x]*(c - c*Sec[e + f*x])^(3/2))/(a + a*Sec[e + f*x])^(5/2),x]","\frac{\tan (e+f x) (c-c \sec (e+f x))^{3/2}}{4 f (a \sec (e+f x)+a)^{5/2}}","\frac{\tan (e+f x) (c-c \sec (e+f x))^{3/2}}{4 f (a \sec (e+f x)+a)^{5/2}}",1,"((c - c*Sec[e + f*x])^(3/2)*Tan[e + f*x])/(4*f*(a + a*Sec[e + f*x])^(5/2))","A",1,1,36,0.02778,1,"{3950}"
147,1,43,0,0.1343251,"\int \frac{\sec (e+f x) \sqrt{c-c \sec (e+f x)}}{(a+a \sec (e+f x))^{5/2}} \, dx","Int[(Sec[e + f*x]*Sqrt[c - c*Sec[e + f*x]])/(a + a*Sec[e + f*x])^(5/2),x]","\frac{c \tan (e+f x)}{2 f (a \sec (e+f x)+a)^{5/2} \sqrt{c-c \sec (e+f x)}}","\frac{c \tan (e+f x)}{2 f (a \sec (e+f x)+a)^{5/2} \sqrt{c-c \sec (e+f x)}}",1,"(c*Tan[e + f*x])/(2*f*(a + a*Sec[e + f*x])^(5/2)*Sqrt[c - c*Sec[e + f*x]])","A",1,1,36,0.02778,1,"{3953}"
148,1,140,0,0.4240063,"\int \frac{\sec (e+f x)}{(a+a \sec (e+f x))^{5/2} \sqrt{c-c \sec (e+f x)}} \, dx","Int[Sec[e + f*x]/((a + a*Sec[e + f*x])^(5/2)*Sqrt[c - c*Sec[e + f*x]]),x]","-\frac{\tan (e+f x) \tanh ^{-1}(\cos (e+f x))}{4 a^2 f \sqrt{a \sec (e+f x)+a} \sqrt{c-c \sec (e+f x)}}+\frac{\tan (e+f x)}{4 a f (a \sec (e+f x)+a)^{3/2} \sqrt{c-c \sec (e+f x)}}+\frac{\tan (e+f x)}{4 f (a \sec (e+f x)+a)^{5/2} \sqrt{c-c \sec (e+f x)}}","-\frac{\tan (e+f x) \tanh ^{-1}(\cos (e+f x))}{4 a^2 f \sqrt{a \sec (e+f x)+a} \sqrt{c-c \sec (e+f x)}}+\frac{\tan (e+f x)}{4 a f (a \sec (e+f x)+a)^{3/2} \sqrt{c-c \sec (e+f x)}}+\frac{\tan (e+f x)}{4 f (a \sec (e+f x)+a)^{5/2} \sqrt{c-c \sec (e+f x)}}",1,"Tan[e + f*x]/(4*f*(a + a*Sec[e + f*x])^(5/2)*Sqrt[c - c*Sec[e + f*x]]) + Tan[e + f*x]/(4*a*f*(a + a*Sec[e + f*x])^(3/2)*Sqrt[c - c*Sec[e + f*x]]) - (ArcTanh[Cos[e + f*x]]*Tan[e + f*x])/(4*a^2*f*Sqrt[a + a*Sec[e + f*x]]*Sqrt[c - c*Sec[e + f*x]])","A",4,3,36,0.08333,1,"{3960, 3959, 3770}"
149,1,146,0,0.3440922,"\int \frac{\sec (e+f x)}{(a+a \sec (e+f x))^{5/2} (c-c \sec (e+f x))^{3/2}} \, dx","Int[Sec[e + f*x]/((a + a*Sec[e + f*x])^(5/2)*(c - c*Sec[e + f*x])^(3/2)),x]","\frac{3 \csc (e+f x)}{8 a^2 c f \sqrt{a \sec (e+f x)+a} \sqrt{c-c \sec (e+f x)}}-\frac{3 \tan (e+f x) \tanh ^{-1}(\cos (e+f x))}{8 a^2 c f \sqrt{a \sec (e+f x)+a} \sqrt{c-c \sec (e+f x)}}+\frac{\tan (e+f x)}{4 f (a \sec (e+f x)+a)^{5/2} (c-c \sec (e+f x))^{3/2}}","\frac{3 \csc (e+f x)}{8 a^2 c f \sqrt{a \sec (e+f x)+a} \sqrt{c-c \sec (e+f x)}}-\frac{3 \tan (e+f x) \tanh ^{-1}(\cos (e+f x))}{8 a^2 c f \sqrt{a \sec (e+f x)+a} \sqrt{c-c \sec (e+f x)}}+\frac{\tan (e+f x)}{4 f (a \sec (e+f x)+a)^{5/2} (c-c \sec (e+f x))^{3/2}}",1,"(3*Csc[e + f*x])/(8*a^2*c*f*Sqrt[a + a*Sec[e + f*x]]*Sqrt[c - c*Sec[e + f*x]]) + Tan[e + f*x]/(4*f*(a + a*Sec[e + f*x])^(5/2)*(c - c*Sec[e + f*x])^(3/2)) - (3*ArcTanh[Cos[e + f*x]]*Tan[e + f*x])/(8*a^2*c*f*Sqrt[a + a*Sec[e + f*x]]*Sqrt[c - c*Sec[e + f*x]])","A",4,4,36,0.1111,1,"{3960, 3959, 2611, 3770}"
150,1,160,0,0.2019457,"\int \frac{\sec (e+f x)}{(a+a \sec (e+f x))^{5/2} (c-c \sec (e+f x))^{5/2}} \, dx","Int[Sec[e + f*x]/((a + a*Sec[e + f*x])^(5/2)*(c - c*Sec[e + f*x])^(5/2)),x]","\frac{3 \csc (e+f x)}{8 a^2 c^2 f \sqrt{a \sec (e+f x)+a} \sqrt{c-c \sec (e+f x)}}-\frac{\cot ^2(e+f x) \csc (e+f x)}{4 a^2 c^2 f \sqrt{a \sec (e+f x)+a} \sqrt{c-c \sec (e+f x)}}-\frac{3 \tan (e+f x) \tanh ^{-1}(\cos (e+f x))}{8 a^2 c^2 f \sqrt{a \sec (e+f x)+a} \sqrt{c-c \sec (e+f x)}}","\frac{3 \csc (e+f x)}{8 a^2 c^2 f \sqrt{a \sec (e+f x)+a} \sqrt{c-c \sec (e+f x)}}-\frac{\cot ^2(e+f x) \csc (e+f x)}{4 a^2 c^2 f \sqrt{a \sec (e+f x)+a} \sqrt{c-c \sec (e+f x)}}-\frac{3 \tan (e+f x) \tanh ^{-1}(\cos (e+f x))}{8 a^2 c^2 f \sqrt{a \sec (e+f x)+a} \sqrt{c-c \sec (e+f x)}}",1,"(3*Csc[e + f*x])/(8*a^2*c^2*f*Sqrt[a + a*Sec[e + f*x]]*Sqrt[c - c*Sec[e + f*x]]) - (Cot[e + f*x]^2*Csc[e + f*x])/(4*a^2*c^2*f*Sqrt[a + a*Sec[e + f*x]]*Sqrt[c - c*Sec[e + f*x]]) - (3*ArcTanh[Cos[e + f*x]]*Tan[e + f*x])/(8*a^2*c^2*f*Sqrt[a + a*Sec[e + f*x]]*Sqrt[c - c*Sec[e + f*x]])","A",4,3,36,0.08333,1,"{3959, 2611, 3770}"
151,1,101,0,0.1202124,"\int \sec (e+f x) (a+a \sec (e+f x))^m (c-c \sec (e+f x))^n \, dx","Int[Sec[e + f*x]*(a + a*Sec[e + f*x])^m*(c - c*Sec[e + f*x])^n,x]","-\frac{c 2^{n+\frac{1}{2}} \tan (e+f x) (1-\sec (e+f x))^{\frac{1}{2}-n} (a \sec (e+f x)+a)^m (c-c \sec (e+f x))^{n-1} \, _2F_1\left(m+\frac{1}{2},\frac{1}{2}-n;m+\frac{3}{2};\frac{1}{2} (\sec (e+f x)+1)\right)}{f (2 m+1)}","-\frac{c 2^{n+\frac{1}{2}} \tan (e+f x) (1-\sec (e+f x))^{\frac{1}{2}-n} (a \sec (e+f x)+a)^m (c-c \sec (e+f x))^{n-1} \, _2F_1\left(m+\frac{1}{2},\frac{1}{2}-n;m+\frac{3}{2};\frac{1}{2} (\sec (e+f x)+1)\right)}{f (2 m+1)}",1,"-((2^(1/2 + n)*c*Hypergeometric2F1[1/2 + m, 1/2 - n, 3/2 + m, (1 + Sec[e + f*x])/2]*(1 - Sec[e + f*x])^(1/2 - n)*(a + a*Sec[e + f*x])^m*(c - c*Sec[e + f*x])^(-1 + n)*Tan[e + f*x])/(f*(1 + 2*m)))","A",3,3,32,0.09375,1,"{3961, 70, 69}"
152,1,92,0,0.108356,"\int \sec (e+f x) (a+a \sec (e+f x))^m (c-c \sec (e+f x))^2 \, dx","Int[Sec[e + f*x]*(a + a*Sec[e + f*x])^m*(c - c*Sec[e + f*x])^2,x]","\frac{a 2^{m+\frac{1}{2}} \tan (e+f x) (c-c \sec (e+f x))^2 (\sec (e+f x)+1)^{\frac{1}{2}-m} (a \sec (e+f x)+a)^{m-1} \, _2F_1\left(\frac{5}{2},\frac{1}{2}-m;\frac{7}{2};\frac{1}{2} (1-\sec (e+f x))\right)}{5 f}","\frac{a 2^{m+\frac{1}{2}} \tan (e+f x) (c-c \sec (e+f x))^2 (\sec (e+f x)+1)^{\frac{1}{2}-m} (a \sec (e+f x)+a)^{m-1} \, _2F_1\left(\frac{5}{2},\frac{1}{2}-m;\frac{7}{2};\frac{1}{2} (1-\sec (e+f x))\right)}{5 f}",1,"(2^(1/2 + m)*a*Hypergeometric2F1[5/2, 1/2 - m, 7/2, (1 - Sec[e + f*x])/2]*(1 + Sec[e + f*x])^(1/2 - m)*(a + a*Sec[e + f*x])^(-1 + m)*(c - c*Sec[e + f*x])^2*Tan[e + f*x])/(5*f)","A",3,3,32,0.09375,1,"{3961, 70, 69}"
153,1,90,0,0.0781782,"\int \sec (e+f x) (a+a \sec (e+f x))^m (c-c \sec (e+f x)) \, dx","Int[Sec[e + f*x]*(a + a*Sec[e + f*x])^m*(c - c*Sec[e + f*x]),x]","\frac{a 2^{m+\frac{1}{2}} \tan (e+f x) (c-c \sec (e+f x)) (\sec (e+f x)+1)^{\frac{1}{2}-m} (a \sec (e+f x)+a)^{m-1} \, _2F_1\left(\frac{3}{2},\frac{1}{2}-m;\frac{5}{2};\frac{1}{2} (1-\sec (e+f x))\right)}{3 f}","\frac{a 2^{m+\frac{1}{2}} \tan (e+f x) (c-c \sec (e+f x)) (\sec (e+f x)+1)^{\frac{1}{2}-m} (a \sec (e+f x)+a)^{m-1} \, _2F_1\left(\frac{3}{2},\frac{1}{2}-m;\frac{5}{2};\frac{1}{2} (1-\sec (e+f x))\right)}{3 f}",1,"(2^(1/2 + m)*a*Hypergeometric2F1[3/2, 1/2 - m, 5/2, (1 - Sec[e + f*x])/2]*(1 + Sec[e + f*x])^(1/2 - m)*(a + a*Sec[e + f*x])^(-1 + m)*(c - c*Sec[e + f*x])*Tan[e + f*x])/(3*f)","A",3,3,30,0.1000,1,"{3961, 70, 69}"
154,1,90,0,0.1115108,"\int \frac{\sec (e+f x) (a+a \sec (e+f x))^m}{c-c \sec (e+f x)} \, dx","Int[(Sec[e + f*x]*(a + a*Sec[e + f*x])^m)/(c - c*Sec[e + f*x]),x]","-\frac{a 2^{m+\frac{1}{2}} \tan (e+f x) (\sec (e+f x)+1)^{\frac{1}{2}-m} (a \sec (e+f x)+a)^{m-1} \, _2F_1\left(-\frac{1}{2},\frac{1}{2}-m;\frac{1}{2};\frac{1}{2} (1-\sec (e+f x))\right)}{f (c-c \sec (e+f x))}","-\frac{a 2^{m+\frac{1}{2}} \tan (e+f x) (\sec (e+f x)+1)^{\frac{1}{2}-m} (a \sec (e+f x)+a)^{m-1} \, _2F_1\left(-\frac{1}{2},\frac{1}{2}-m;\frac{1}{2};\frac{1}{2} (1-\sec (e+f x))\right)}{f (c-c \sec (e+f x))}",1,"-((2^(1/2 + m)*a*Hypergeometric2F1[-1/2, 1/2 - m, 1/2, (1 - Sec[e + f*x])/2]*(1 + Sec[e + f*x])^(1/2 - m)*(a + a*Sec[e + f*x])^(-1 + m)*Tan[e + f*x])/(f*(c - c*Sec[e + f*x])))","A",3,3,32,0.09375,1,"{3961, 70, 69}"
155,1,92,0,0.1149296,"\int \frac{\sec (e+f x) (a+a \sec (e+f x))^m}{(c-c \sec (e+f x))^2} \, dx","Int[(Sec[e + f*x]*(a + a*Sec[e + f*x])^m)/(c - c*Sec[e + f*x])^2,x]","-\frac{a 2^{m+\frac{1}{2}} \tan (e+f x) (\sec (e+f x)+1)^{\frac{1}{2}-m} (a \sec (e+f x)+a)^{m-1} \, _2F_1\left(-\frac{3}{2},\frac{1}{2}-m;-\frac{1}{2};\frac{1}{2} (1-\sec (e+f x))\right)}{3 f (c-c \sec (e+f x))^2}","-\frac{a 2^{m+\frac{1}{2}} \tan (e+f x) (\sec (e+f x)+1)^{\frac{1}{2}-m} (a \sec (e+f x)+a)^{m-1} \, _2F_1\left(-\frac{3}{2},\frac{1}{2}-m;-\frac{1}{2};\frac{1}{2} (1-\sec (e+f x))\right)}{3 f (c-c \sec (e+f x))^2}",1,"-(2^(1/2 + m)*a*Hypergeometric2F1[-3/2, 1/2 - m, -1/2, (1 - Sec[e + f*x])/2]*(1 + Sec[e + f*x])^(1/2 - m)*(a + a*Sec[e + f*x])^(-1 + m)*Tan[e + f*x])/(3*f*(c - c*Sec[e + f*x])^2)","A",3,3,32,0.09375,1,"{3961, 70, 69}"
156,1,160,0,0.3802416,"\int \sec (e+f x) (a+a \sec (e+f x))^m (c-c \sec (e+f x))^{5/2} \, dx","Int[Sec[e + f*x]*(a + a*Sec[e + f*x])^m*(c - c*Sec[e + f*x])^(5/2),x]","-\frac{16 c^2 \tan (e+f x) \sqrt{c-c \sec (e+f x)} (a \sec (e+f x)+a)^m}{f \left(4 m^2+16 m+15\right)}-\frac{64 c^3 \tan (e+f x) (a \sec (e+f x)+a)^m}{f (2 m+5) \left(4 m^2+8 m+3\right) \sqrt{c-c \sec (e+f x)}}-\frac{2 c \tan (e+f x) (c-c \sec (e+f x))^{3/2} (a \sec (e+f x)+a)^m}{f (2 m+5)}","-\frac{16 c^2 \tan (e+f x) \sqrt{c-c \sec (e+f x)} (a \sec (e+f x)+a)^m}{f \left(4 m^2+16 m+15\right)}-\frac{64 c^3 \tan (e+f x) (a \sec (e+f x)+a)^m}{f (2 m+5) \left(4 m^2+8 m+3\right) \sqrt{c-c \sec (e+f x)}}-\frac{2 c \tan (e+f x) (c-c \sec (e+f x))^{3/2} (a \sec (e+f x)+a)^m}{f (2 m+5)}",1,"(-64*c^3*(a + a*Sec[e + f*x])^m*Tan[e + f*x])/(f*(5 + 2*m)*(3 + 8*m + 4*m^2)*Sqrt[c - c*Sec[e + f*x]]) - (16*c^2*(a + a*Sec[e + f*x])^m*Sqrt[c - c*Sec[e + f*x]]*Tan[e + f*x])/(f*(15 + 16*m + 4*m^2)) - (2*c*(a + a*Sec[e + f*x])^m*(c - c*Sec[e + f*x])^(3/2)*Tan[e + f*x])/(f*(5 + 2*m))","A",3,2,34,0.05882,1,"{3955, 3953}"
157,1,100,0,0.2217451,"\int \sec (e+f x) (a+a \sec (e+f x))^m (c-c \sec (e+f x))^{3/2} \, dx","Int[Sec[e + f*x]*(a + a*Sec[e + f*x])^m*(c - c*Sec[e + f*x])^(3/2),x]","-\frac{8 c^2 \tan (e+f x) (a \sec (e+f x)+a)^m}{f \left(4 m^2+8 m+3\right) \sqrt{c-c \sec (e+f x)}}-\frac{2 c \tan (e+f x) \sqrt{c-c \sec (e+f x)} (a \sec (e+f x)+a)^m}{f (2 m+3)}","-\frac{8 c^2 \tan (e+f x) (a \sec (e+f x)+a)^m}{f \left(4 m^2+8 m+3\right) \sqrt{c-c \sec (e+f x)}}-\frac{2 c \tan (e+f x) \sqrt{c-c \sec (e+f x)} (a \sec (e+f x)+a)^m}{f (2 m+3)}",1,"(-8*c^2*(a + a*Sec[e + f*x])^m*Tan[e + f*x])/(f*(3 + 8*m + 4*m^2)*Sqrt[c - c*Sec[e + f*x]]) - (2*c*(a + a*Sec[e + f*x])^m*Sqrt[c - c*Sec[e + f*x]]*Tan[e + f*x])/(f*(3 + 2*m))","A",2,2,34,0.05882,1,"{3955, 3953}"
158,1,46,0,0.1018033,"\int \sec (e+f x) (a+a \sec (e+f x))^m \sqrt{c-c \sec (e+f x)} \, dx","Int[Sec[e + f*x]*(a + a*Sec[e + f*x])^m*Sqrt[c - c*Sec[e + f*x]],x]","-\frac{2 c \tan (e+f x) (a \sec (e+f x)+a)^m}{f (2 m+1) \sqrt{c-c \sec (e+f x)}}","-\frac{2 c \tan (e+f x) (a \sec (e+f x)+a)^m}{f (2 m+1) \sqrt{c-c \sec (e+f x)}}",1,"(-2*c*(a + a*Sec[e + f*x])^m*Tan[e + f*x])/(f*(1 + 2*m)*Sqrt[c - c*Sec[e + f*x]])","A",1,1,34,0.02941,1,"{3953}"
159,1,69,0,0.1294819,"\int \frac{\sec (e+f x) (a+a \sec (e+f x))^m}{\sqrt{c-c \sec (e+f x)}} \, dx","Int[(Sec[e + f*x]*(a + a*Sec[e + f*x])^m)/Sqrt[c - c*Sec[e + f*x]],x]","-\frac{\tan (e+f x) (a \sec (e+f x)+a)^m \, _2F_1\left(1,m+\frac{1}{2};m+\frac{3}{2};\frac{1}{2} (\sec (e+f x)+1)\right)}{f (2 m+1) \sqrt{c-c \sec (e+f x)}}","-\frac{\tan (e+f x) (a \sec (e+f x)+a)^m \, _2F_1\left(1,m+\frac{1}{2};m+\frac{3}{2};\frac{1}{2} (\sec (e+f x)+1)\right)}{f (2 m+1) \sqrt{c-c \sec (e+f x)}}",1,"-((Hypergeometric2F1[1, 1/2 + m, 3/2 + m, (1 + Sec[e + f*x])/2]*(a + a*Sec[e + f*x])^m*Tan[e + f*x])/(f*(1 + 2*m)*Sqrt[c - c*Sec[e + f*x]]))","A",2,2,34,0.05882,1,"{3961, 68}"
160,1,74,0,0.1386297,"\int \frac{\sec (e+f x) (a+a \sec (e+f x))^m}{(c-c \sec (e+f x))^{3/2}} \, dx","Int[(Sec[e + f*x]*(a + a*Sec[e + f*x])^m)/(c - c*Sec[e + f*x])^(3/2),x]","-\frac{\tan (e+f x) (a \sec (e+f x)+a)^m \, _2F_1\left(2,m+\frac{1}{2};m+\frac{3}{2};\frac{1}{2} (\sec (e+f x)+1)\right)}{2 c f (2 m+1) \sqrt{c-c \sec (e+f x)}}","-\frac{\tan (e+f x) (a \sec (e+f x)+a)^m \, _2F_1\left(2,m+\frac{1}{2};m+\frac{3}{2};\frac{1}{2} (\sec (e+f x)+1)\right)}{2 c f (2 m+1) \sqrt{c-c \sec (e+f x)}}",1,"-(Hypergeometric2F1[2, 1/2 + m, 3/2 + m, (1 + Sec[e + f*x])/2]*(a + a*Sec[e + f*x])^m*Tan[e + f*x])/(2*c*f*(1 + 2*m)*Sqrt[c - c*Sec[e + f*x]])","A",2,2,34,0.05882,1,"{3961, 68}"
161,1,74,0,0.1370363,"\int \frac{\sec (e+f x) (a+a \sec (e+f x))^m}{(c-c \sec (e+f x))^{5/2}} \, dx","Int[(Sec[e + f*x]*(a + a*Sec[e + f*x])^m)/(c - c*Sec[e + f*x])^(5/2),x]","-\frac{\tan (e+f x) (a \sec (e+f x)+a)^m \, _2F_1\left(3,m+\frac{1}{2};m+\frac{3}{2};\frac{1}{2} (\sec (e+f x)+1)\right)}{4 c^2 f (2 m+1) \sqrt{c-c \sec (e+f x)}}","-\frac{\tan (e+f x) (a \sec (e+f x)+a)^m \, _2F_1\left(3,m+\frac{1}{2};m+\frac{3}{2};\frac{1}{2} (\sec (e+f x)+1)\right)}{4 c^2 f (2 m+1) \sqrt{c-c \sec (e+f x)}}",1,"-(Hypergeometric2F1[3, 1/2 + m, 3/2 + m, (1 + Sec[e + f*x])/2]*(a + a*Sec[e + f*x])^m*Tan[e + f*x])/(4*c^2*f*(1 + 2*m)*Sqrt[c - c*Sec[e + f*x]])","A",2,2,34,0.05882,1,"{3961, 68}"
162,1,169,0,0.3739412,"\int \sec (e+f x) (a+a \sec (e+f x))^m (c-c \sec (e+f x))^{-3-m} \, dx","Int[Sec[e + f*x]*(a + a*Sec[e + f*x])^m*(c - c*Sec[e + f*x])^(-3 - m),x]","-\frac{2 \tan (e+f x) (a \sec (e+f x)+a)^{m+2} (c-c \sec (e+f x))^{-m-3}}{a^2 f (2 m+1) \left(4 m^2+16 m+15\right)}+\frac{2 \tan (e+f x) (a \sec (e+f x)+a)^{m+1} (c-c \sec (e+f x))^{-m-3}}{a f \left(4 m^2+8 m+3\right)}-\frac{\tan (e+f x) (a \sec (e+f x)+a)^m (c-c \sec (e+f x))^{-m-3}}{f (2 m+1)}","-\frac{2 \tan (e+f x) (a \sec (e+f x)+a)^{m+2} (c-c \sec (e+f x))^{-m-3}}{a^2 f (2 m+1) \left(4 m^2+16 m+15\right)}+\frac{2 \tan (e+f x) (a \sec (e+f x)+a)^{m+1} (c-c \sec (e+f x))^{-m-3}}{a f \left(4 m^2+8 m+3\right)}-\frac{\tan (e+f x) (a \sec (e+f x)+a)^m (c-c \sec (e+f x))^{-m-3}}{f (2 m+1)}",1,"-(((a + a*Sec[e + f*x])^m*(c - c*Sec[e + f*x])^(-3 - m)*Tan[e + f*x])/(f*(1 + 2*m))) + (2*(a + a*Sec[e + f*x])^(1 + m)*(c - c*Sec[e + f*x])^(-3 - m)*Tan[e + f*x])/(a*f*(3 + 8*m + 4*m^2)) - (2*(a + a*Sec[e + f*x])^(2 + m)*(c - c*Sec[e + f*x])^(-3 - m)*Tan[e + f*x])/(a^2*f*(1 + 2*m)*(15 + 16*m + 4*m^2))","A",3,2,36,0.05556,1,"{3951, 3950}"
163,1,104,0,0.2247821,"\int \sec (e+f x) (a+a \sec (e+f x))^m (c-c \sec (e+f x))^{-2-m} \, dx","Int[Sec[e + f*x]*(a + a*Sec[e + f*x])^m*(c - c*Sec[e + f*x])^(-2 - m),x]","\frac{\tan (e+f x) (a \sec (e+f x)+a)^{m+1} (c-c \sec (e+f x))^{-m-2}}{a f \left(4 m^2+8 m+3\right)}-\frac{\tan (e+f x) (a \sec (e+f x)+a)^m (c-c \sec (e+f x))^{-m-2}}{f (2 m+1)}","\frac{\tan (e+f x) (a \sec (e+f x)+a)^{m+1} (c-c \sec (e+f x))^{-m-2}}{a f \left(4 m^2+8 m+3\right)}-\frac{\tan (e+f x) (a \sec (e+f x)+a)^m (c-c \sec (e+f x))^{-m-2}}{f (2 m+1)}",1,"-(((a + a*Sec[e + f*x])^m*(c - c*Sec[e + f*x])^(-2 - m)*Tan[e + f*x])/(f*(1 + 2*m))) + ((a + a*Sec[e + f*x])^(1 + m)*(c - c*Sec[e + f*x])^(-2 - m)*Tan[e + f*x])/(a*f*(3 + 8*m + 4*m^2))","A",2,2,36,0.05556,1,"{3951, 3950}"
164,1,47,0,0.1011243,"\int \sec (e+f x) (a+a \sec (e+f x))^m (c-c \sec (e+f x))^{-1-m} \, dx","Int[Sec[e + f*x]*(a + a*Sec[e + f*x])^m*(c - c*Sec[e + f*x])^(-1 - m),x]","-\frac{\tan (e+f x) (a \sec (e+f x)+a)^m (c-c \sec (e+f x))^{-m-1}}{f (2 m+1)}","-\frac{\tan (e+f x) (a \sec (e+f x)+a)^m (c-c \sec (e+f x))^{-m-1}}{f (2 m+1)}",1,"-(((a + a*Sec[e + f*x])^m*(c - c*Sec[e + f*x])^(-1 - m)*Tan[e + f*x])/(f*(1 + 2*m)))","A",1,1,36,0.02778,1,"{3950}"
165,1,101,0,0.1292433,"\int \sec (e+f x) (a+a \sec (e+f x))^m (c-c \sec (e+f x))^{-m} \, dx","Int[(Sec[e + f*x]*(a + a*Sec[e + f*x])^m)/(c - c*Sec[e + f*x])^m,x]","-\frac{c 2^{\frac{1}{2}-m} \tan (e+f x) (1-\sec (e+f x))^{m+\frac{1}{2}} (a \sec (e+f x)+a)^m (c-c \sec (e+f x))^{-m-1} \, _2F_1\left(m+\frac{1}{2},m+\frac{1}{2};m+\frac{3}{2};\frac{1}{2} (\sec (e+f x)+1)\right)}{f (2 m+1)}","-\frac{c 2^{\frac{1}{2}-m} \tan (e+f x) (1-\sec (e+f x))^{m+\frac{1}{2}} (a \sec (e+f x)+a)^m (c-c \sec (e+f x))^{-m-1} \, _2F_1\left(m+\frac{1}{2},m+\frac{1}{2};m+\frac{3}{2};\frac{1}{2} (\sec (e+f x)+1)\right)}{f (2 m+1)}",1,"-((2^(1/2 - m)*c*Hypergeometric2F1[1/2 + m, 1/2 + m, 3/2 + m, (1 + Sec[e + f*x])/2]*(1 - Sec[e + f*x])^(1/2 + m)*(a + a*Sec[e + f*x])^m*(c - c*Sec[e + f*x])^(-1 - m)*Tan[e + f*x])/(f*(1 + 2*m)))","A",3,3,34,0.08824,1,"{3961, 70, 69}"
166,1,99,0,0.143151,"\int \sec (e+f x) (a+a \sec (e+f x))^m (c-c \sec (e+f x))^{1-m} \, dx","Int[Sec[e + f*x]*(a + a*Sec[e + f*x])^m*(c - c*Sec[e + f*x])^(1 - m),x]","-\frac{c 2^{\frac{3}{2}-m} \tan (e+f x) (1-\sec (e+f x))^{m-\frac{1}{2}} (a \sec (e+f x)+a)^m (c-c \sec (e+f x))^{-m} \, _2F_1\left(m-\frac{1}{2},m+\frac{1}{2};m+\frac{3}{2};\frac{1}{2} (\sec (e+f x)+1)\right)}{f (2 m+1)}","-\frac{c 2^{\frac{3}{2}-m} \tan (e+f x) (1-\sec (e+f x))^{m-\frac{1}{2}} (a \sec (e+f x)+a)^m (c-c \sec (e+f x))^{-m} \, _2F_1\left(m-\frac{1}{2},m+\frac{1}{2};m+\frac{3}{2};\frac{1}{2} (\sec (e+f x)+1)\right)}{f (2 m+1)}",1,"-((2^(3/2 - m)*c*Hypergeometric2F1[-1/2 + m, 1/2 + m, 3/2 + m, (1 + Sec[e + f*x])/2]*(1 - Sec[e + f*x])^(-1/2 + m)*(a + a*Sec[e + f*x])^m*Tan[e + f*x])/(f*(1 + 2*m)*(c - c*Sec[e + f*x])^m))","A",3,3,36,0.08333,1,"{3961, 70, 69}"
167,1,101,0,0.154416,"\int \sec (e+f x) (a+a \sec (e+f x))^m (c-c \sec (e+f x))^{2-m} \, dx","Int[Sec[e + f*x]*(a + a*Sec[e + f*x])^m*(c - c*Sec[e + f*x])^(2 - m),x]","-\frac{c^2 2^{\frac{5}{2}-m} \tan (e+f x) (1-\sec (e+f x))^{m-\frac{1}{2}} (a \sec (e+f x)+a)^m (c-c \sec (e+f x))^{-m} \, _2F_1\left(m-\frac{3}{2},m+\frac{1}{2};m+\frac{3}{2};\frac{1}{2} (\sec (e+f x)+1)\right)}{f (2 m+1)}","-\frac{c^2 2^{\frac{5}{2}-m} \tan (e+f x) (1-\sec (e+f x))^{m-\frac{1}{2}} (a \sec (e+f x)+a)^m (c-c \sec (e+f x))^{-m} \, _2F_1\left(m-\frac{3}{2},m+\frac{1}{2};m+\frac{3}{2};\frac{1}{2} (\sec (e+f x)+1)\right)}{f (2 m+1)}",1,"-((2^(5/2 - m)*c^2*Hypergeometric2F1[-3/2 + m, 1/2 + m, 3/2 + m, (1 + Sec[e + f*x])/2]*(1 - Sec[e + f*x])^(-1/2 + m)*(a + a*Sec[e + f*x])^m*Tan[e + f*x])/(f*(1 + 2*m)*(c - c*Sec[e + f*x])^m))","A",3,3,36,0.08333,1,"{3961, 70, 69}"
168,1,105,0,0.1932141,"\int \sec ^2(e+f x) (a+a \sec (e+f x))^3 (c-c \sec (e+f x)) \, dx","Int[Sec[e + f*x]^2*(a + a*Sec[e + f*x])^3*(c - c*Sec[e + f*x]),x]","-\frac{a^3 c \tan ^5(e+f x)}{5 f}-\frac{2 a^3 c \tan ^3(e+f x)}{3 f}+\frac{a^3 c \tanh ^{-1}(\sin (e+f x))}{4 f}-\frac{a^3 c \tan (e+f x) \sec ^3(e+f x)}{2 f}+\frac{a^3 c \tan (e+f x) \sec (e+f x)}{4 f}","-\frac{a^3 c \tan ^5(e+f x)}{5 f}-\frac{2 a^3 c \tan ^3(e+f x)}{3 f}+\frac{a^3 c \tanh ^{-1}(\sin (e+f x))}{4 f}-\frac{a^3 c \tan (e+f x) \sec ^3(e+f x)}{2 f}+\frac{a^3 c \tan (e+f x) \sec (e+f x)}{4 f}",1,"(a^3*c*ArcTanh[Sin[e + f*x]])/(4*f) + (a^3*c*Sec[e + f*x]*Tan[e + f*x])/(4*f) - (a^3*c*Sec[e + f*x]^3*Tan[e + f*x])/(2*f) - (2*a^3*c*Tan[e + f*x]^3)/(3*f) - (a^3*c*Tan[e + f*x]^5)/(5*f)","A",10,7,32,0.2188,1,"{3962, 2607, 30, 2611, 3768, 3770, 14}"
169,1,86,0,0.1560695,"\int \sec ^2(e+f x) (a+a \sec (e+f x))^2 (c-c \sec (e+f x)) \, dx","Int[Sec[e + f*x]^2*(a + a*Sec[e + f*x])^2*(c - c*Sec[e + f*x]),x]","-\frac{a^2 c \tan ^3(e+f x)}{3 f}+\frac{a^2 c \tanh ^{-1}(\sin (e+f x))}{8 f}-\frac{a^2 c \tan (e+f x) \sec ^3(e+f x)}{4 f}+\frac{a^2 c \tan (e+f x) \sec (e+f x)}{8 f}","-\frac{a^2 c \tan ^3(e+f x)}{3 f}+\frac{a^2 c \tanh ^{-1}(\sin (e+f x))}{8 f}-\frac{a^2 c \tan (e+f x) \sec ^3(e+f x)}{4 f}+\frac{a^2 c \tan (e+f x) \sec (e+f x)}{8 f}",1,"(a^2*c*ArcTanh[Sin[e + f*x]])/(8*f) + (a^2*c*Sec[e + f*x]*Tan[e + f*x])/(8*f) - (a^2*c*Sec[e + f*x]^3*Tan[e + f*x])/(4*f) - (a^2*c*Tan[e + f*x]^3)/(3*f)","A",7,6,32,0.1875,1,"{3962, 2607, 30, 2611, 3768, 3770}"
170,1,17,0,0.0710234,"\int \sec ^2(e+f x) (a+a \sec (e+f x)) (c-c \sec (e+f x)) \, dx","Int[Sec[e + f*x]^2*(a + a*Sec[e + f*x])*(c - c*Sec[e + f*x]),x]","-\frac{a c \tan ^3(e+f x)}{3 f}","-\frac{a c \tan ^3(e+f x)}{3 f}",1,"-(a*c*Tan[e + f*x]^3)/(3*f)","A",3,3,30,0.1000,1,"{3962, 2607, 30}"
171,1,56,0,0.108156,"\int \frac{\sec ^2(e+f x) (c-c \sec (e+f x))}{a+a \sec (e+f x)} \, dx","Int[(Sec[e + f*x]^2*(c - c*Sec[e + f*x]))/(a + a*Sec[e + f*x]),x]","-\frac{c \tan (e+f x)}{a f}+\frac{2 c \tanh ^{-1}(\sin (e+f x))}{a f}-\frac{2 c \tan (e+f x)}{f (a \sec (e+f x)+a)}","-\frac{c \tan (e+f x)}{a f}+\frac{2 c \tanh ^{-1}(\sin (e+f x))}{a f}-\frac{2 c \tan (e+f x)}{f (a \sec (e+f x)+a)}",1,"(2*c*ArcTanh[Sin[e + f*x]])/(a*f) - (c*Tan[e + f*x])/(a*f) - (2*c*Tan[e + f*x])/(f*(a + a*Sec[e + f*x]))","A",5,5,32,0.1562,1,"{4008, 3787, 3770, 3767, 8}"
172,1,70,0,0.1614774,"\int \frac{\sec ^2(e+f x) (c-c \sec (e+f x))}{(a+a \sec (e+f x))^2} \, dx","Int[(Sec[e + f*x]^2*(c - c*Sec[e + f*x]))/(a + a*Sec[e + f*x])^2,x]","-\frac{c \tanh ^{-1}(\sin (e+f x))}{a^2 f}+\frac{7 c \tan (e+f x)}{3 a^2 f (\sec (e+f x)+1)}-\frac{2 c \tan (e+f x)}{3 f (a \sec (e+f x)+a)^2}","-\frac{c \tanh ^{-1}(\sin (e+f x))}{a^2 f}+\frac{7 c \tan (e+f x)}{3 a^2 f (\sec (e+f x)+1)}-\frac{2 c \tan (e+f x)}{3 f (a \sec (e+f x)+a)^2}",1,"-((c*ArcTanh[Sin[e + f*x]])/(a^2*f)) + (7*c*Tan[e + f*x])/(3*a^2*f*(1 + Sec[e + f*x])) - (2*c*Tan[e + f*x])/(3*f*(a + a*Sec[e + f*x])^2)","A",4,4,32,0.1250,1,"{4008, 3998, 3770, 3794}"
173,1,86,0,0.1633364,"\int \frac{\sec ^2(e+f x) (c-c \sec (e+f x))}{(a+a \sec (e+f x))^3} \, dx","Int[(Sec[e + f*x]^2*(c - c*Sec[e + f*x]))/(a + a*Sec[e + f*x])^3,x]","-\frac{4 c \tan (e+f x)}{15 f \left(a^3 \sec (e+f x)+a^3\right)}+\frac{11 c \tan (e+f x)}{15 a f (a \sec (e+f x)+a)^2}-\frac{2 c \tan (e+f x)}{5 f (a \sec (e+f x)+a)^3}","-\frac{4 c \tan (e+f x)}{15 f \left(a^3 \sec (e+f x)+a^3\right)}+\frac{11 c \tan (e+f x)}{15 a f (a \sec (e+f x)+a)^2}-\frac{2 c \tan (e+f x)}{5 f (a \sec (e+f x)+a)^3}",1,"(-2*c*Tan[e + f*x])/(5*f*(a + a*Sec[e + f*x])^3) + (11*c*Tan[e + f*x])/(15*a*f*(a + a*Sec[e + f*x])^2) - (4*c*Tan[e + f*x])/(15*f*(a^3 + a^3*Sec[e + f*x]))","A",3,3,32,0.09375,1,"{4008, 4000, 3794}"
174,1,140,0,0.1987323,"\int (g \sec (e+f x))^p (a+a \sec (e+f x))^2 (c-c \sec (e+f x)) \, dx","Int[(g*Sec[e + f*x])^p*(a + a*Sec[e + f*x])^2*(c - c*Sec[e + f*x]),x]","-\frac{a^2 c \tan ^3(e+f x) \cos ^2(e+f x)^{\frac{p+3}{2}} (g \sec (e+f x))^p \, _2F_1\left(\frac{3}{2},\frac{p+3}{2};\frac{5}{2};\sin ^2(e+f x)\right)}{3 f}-\frac{a^2 c \tan ^3(e+f x) \cos ^2(e+f x)^{\frac{p+4}{2}} (g \sec (e+f x))^{p+1} \, _2F_1\left(\frac{3}{2},\frac{p+4}{2};\frac{5}{2};\sin ^2(e+f x)\right)}{3 f g}","-\frac{a^2 c \tan ^3(e+f x) \cos ^2(e+f x)^{\frac{p+3}{2}} (g \sec (e+f x))^p \, _2F_1\left(\frac{3}{2},\frac{p+3}{2};\frac{5}{2};\sin ^2(e+f x)\right)}{3 f}-\frac{a^2 c \tan ^3(e+f x) \cos ^2(e+f x)^{\frac{p+4}{2}} (g \sec (e+f x))^{p+1} \, _2F_1\left(\frac{3}{2},\frac{p+4}{2};\frac{5}{2};\sin ^2(e+f x)\right)}{3 f g}",1,"-(a^2*c*(Cos[e + f*x]^2)^((3 + p)/2)*Hypergeometric2F1[3/2, (3 + p)/2, 5/2, Sin[e + f*x]^2]*(g*Sec[e + f*x])^p*Tan[e + f*x]^3)/(3*f) - (a^2*c*(Cos[e + f*x]^2)^((4 + p)/2)*Hypergeometric2F1[3/2, (4 + p)/2, 5/2, Sin[e + f*x]^2]*(g*Sec[e + f*x])^(1 + p)*Tan[e + f*x]^3)/(3*f*g)","A",5,3,34,0.08824,1,"{3962, 2617, 16}"
175,1,65,0,0.089211,"\int (g \sec (e+f x))^p (a+a \sec (e+f x)) (c-c \sec (e+f x)) \, dx","Int[(g*Sec[e + f*x])^p*(a + a*Sec[e + f*x])*(c - c*Sec[e + f*x]),x]","-\frac{a c \tan ^3(e+f x) \cos ^2(e+f x)^{\frac{p+3}{2}} (g \sec (e+f x))^p \, _2F_1\left(\frac{3}{2},\frac{p+3}{2};\frac{5}{2};\sin ^2(e+f x)\right)}{3 f}","-\frac{a c \tan ^3(e+f x) \cos ^2(e+f x)^{\frac{p+3}{2}} (g \sec (e+f x))^p \, _2F_1\left(\frac{3}{2},\frac{p+3}{2};\frac{5}{2};\sin ^2(e+f x)\right)}{3 f}",1,"-(a*c*(Cos[e + f*x]^2)^((3 + p)/2)*Hypergeometric2F1[3/2, (3 + p)/2, 5/2, Sin[e + f*x]^2]*(g*Sec[e + f*x])^p*Tan[e + f*x]^3)/(3*f)","A",2,2,32,0.06250,1,"{3962, 2617}"
176,1,180,0,0.2316248,"\int \frac{(g \sec (e+f x))^p (c-c \sec (e+f x))}{a+a \sec (e+f x)} \, dx","Int[((g*Sec[e + f*x])^p*(c - c*Sec[e + f*x]))/(a + a*Sec[e + f*x]),x]","-\frac{c g (1-2 p) \sin (e+f x) (g \sec (e+f x))^{p-1} \, _2F_1\left(\frac{1}{2},\frac{1-p}{2};\frac{3-p}{2};\cos ^2(e+f x)\right)}{a f (1-p) \sqrt{\sin ^2(e+f x)}}+\frac{2 c \sin (e+f x) (g \sec (e+f x))^p \, _2F_1\left(\frac{1}{2},-\frac{p}{2};\frac{2-p}{2};\cos ^2(e+f x)\right)}{a f \sqrt{\sin ^2(e+f x)}}-\frac{2 c \tan (e+f x) (g \sec (e+f x))^p}{f (a \sec (e+f x)+a)}","-\frac{c g (1-2 p) \sin (e+f x) (g \sec (e+f x))^{p-1} \, _2F_1\left(\frac{1}{2},\frac{1-p}{2};\frac{3-p}{2};\cos ^2(e+f x)\right)}{a f (1-p) \sqrt{\sin ^2(e+f x)}}+\frac{2 c \sin (e+f x) (g \sec (e+f x))^p \, _2F_1\left(\frac{1}{2},-\frac{p}{2};\frac{2-p}{2};\cos ^2(e+f x)\right)}{a f \sqrt{\sin ^2(e+f x)}}-\frac{2 c \tan (e+f x) (g \sec (e+f x))^p}{f (a \sec (e+f x)+a)}",1,"-((c*g*(1 - 2*p)*Hypergeometric2F1[1/2, (1 - p)/2, (3 - p)/2, Cos[e + f*x]^2]*(g*Sec[e + f*x])^(-1 + p)*Sin[e + f*x])/(a*f*(1 - p)*Sqrt[Sin[e + f*x]^2])) + (2*c*Hypergeometric2F1[1/2, -p/2, (2 - p)/2, Cos[e + f*x]^2]*(g*Sec[e + f*x])^p*Sin[e + f*x])/(a*f*Sqrt[Sin[e + f*x]^2]) - (2*c*(g*Sec[e + f*x])^p*Tan[e + f*x])/(f*(a + a*Sec[e + f*x]))","A",6,4,34,0.1176,1,"{4020, 3787, 3772, 2643}"
177,1,226,0,0.4128846,"\int \frac{(g \sec (e+f x))^p (c-c \sec (e+f x))}{(a+a \sec (e+f x))^2} \, dx","Int[((g*Sec[e + f*x])^p*(c - c*Sec[e + f*x]))/(a + a*Sec[e + f*x])^2,x]","-\frac{c g (3-4 p) \sin (e+f x) (g \sec (e+f x))^{p-1} \, _2F_1\left(\frac{1}{2},\frac{1-p}{2};\frac{3-p}{2};\cos ^2(e+f x)\right)}{3 a^2 f \sqrt{\sin ^2(e+f x)}}+\frac{c (5-4 p) \sin (e+f x) (g \sec (e+f x))^p \, _2F_1\left(\frac{1}{2},-\frac{p}{2};\frac{2-p}{2};\cos ^2(e+f x)\right)}{3 a^2 f \sqrt{\sin ^2(e+f x)}}-\frac{c (5-4 p) \tan (e+f x) (g \sec (e+f x))^p}{3 a^2 f (\sec (e+f x)+1)}-\frac{2 c \tan (e+f x) (g \sec (e+f x))^p}{3 f (a \sec (e+f x)+a)^2}","-\frac{c g (3-4 p) \sin (e+f x) (g \sec (e+f x))^{p-1} \, _2F_1\left(\frac{1}{2},\frac{1-p}{2};\frac{3-p}{2};\cos ^2(e+f x)\right)}{3 a^2 f \sqrt{\sin ^2(e+f x)}}+\frac{c (5-4 p) \sin (e+f x) (g \sec (e+f x))^p \, _2F_1\left(\frac{1}{2},-\frac{p}{2};\frac{2-p}{2};\cos ^2(e+f x)\right)}{3 a^2 f \sqrt{\sin ^2(e+f x)}}-\frac{c (5-4 p) \tan (e+f x) (g \sec (e+f x))^p}{3 a^2 f (\sec (e+f x)+1)}-\frac{2 c \tan (e+f x) (g \sec (e+f x))^p}{3 f (a \sec (e+f x)+a)^2}",1,"-(c*g*(3 - 4*p)*Hypergeometric2F1[1/2, (1 - p)/2, (3 - p)/2, Cos[e + f*x]^2]*(g*Sec[e + f*x])^(-1 + p)*Sin[e + f*x])/(3*a^2*f*Sqrt[Sin[e + f*x]^2]) + (c*(5 - 4*p)*Hypergeometric2F1[1/2, -p/2, (2 - p)/2, Cos[e + f*x]^2]*(g*Sec[e + f*x])^p*Sin[e + f*x])/(3*a^2*f*Sqrt[Sin[e + f*x]^2]) - (c*(5 - 4*p)*(g*Sec[e + f*x])^p*Tan[e + f*x])/(3*a^2*f*(1 + Sec[e + f*x])) - (2*c*(g*Sec[e + f*x])^p*Tan[e + f*x])/(3*f*(a + a*Sec[e + f*x])^2)","A",7,4,34,0.1176,1,"{4020, 3787, 3772, 2643}"
178,1,143,0,0.2781109,"\int \frac{(g \sec (e+f x))^{3/2} \sqrt{a+a \sec (e+f x)}}{c-c \sec (e+f x)} \, dx","Int[((g*Sec[e + f*x])^(3/2)*Sqrt[a + a*Sec[e + f*x]])/(c - c*Sec[e + f*x]),x]","\frac{2 a g^{3/2} \tan (e+f x) \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{g \sec (e+f x)}}{\sqrt{g} \sqrt{c-c \sec (e+f x)}}\right)}{\sqrt{c} f \sqrt{a \sec (e+f x)+a} \sqrt{c-c \sec (e+f x)}}-\frac{2 a g \tan (e+f x) \sqrt{g \sec (e+f x)}}{f \sqrt{a \sec (e+f x)+a} (c-c \sec (e+f x))}","\frac{2 g \cot (e+f x) \sqrt{a \sec (e+f x)+a} \sqrt{g \sec (e+f x)}}{c f}-\frac{2 \sqrt{a} g^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{g} \tan (e+f x)}{\sqrt{a \sec (e+f x)+a} \sqrt{g \sec (e+f x)}}\right)}{c f}",1,"(-2*a*g*Sqrt[g*Sec[e + f*x]]*Tan[e + f*x])/(f*Sqrt[a + a*Sec[e + f*x]]*(c - c*Sec[e + f*x])) + (2*a*g^(3/2)*ArcTan[(Sqrt[c]*Sqrt[g*Sec[e + f*x]])/(Sqrt[g]*Sqrt[c - c*Sec[e + f*x]])]*Tan[e + f*x])/(Sqrt[c]*f*Sqrt[a + a*Sec[e + f*x]]*Sqrt[c - c*Sec[e + f*x]])","A",5,5,40,0.1250,1,"{3964, 47, 63, 217, 203}"
179,1,116,0,0.2317189,"\int \frac{\sec ^2(e+f x)}{\sqrt{a+a \sec (e+f x)} (c-c \sec (e+f x))} \, dx","Int[Sec[e + f*x]^2/(Sqrt[a + a*Sec[e + f*x]]*(c - c*Sec[e + f*x])),x]","-\frac{\tan (e+f x)}{f \sqrt{a \sec (e+f x)+a} (c-c \sec (e+f x))}-\frac{\tan (e+f x) \tanh ^{-1}\left(\frac{\sqrt{c-c \sec (e+f x)}}{\sqrt{2} \sqrt{c}}\right)}{\sqrt{2} \sqrt{c} f \sqrt{a \sec (e+f x)+a} \sqrt{c-c \sec (e+f x)}}","\frac{\cot (e+f x) \sqrt{a \sec (e+f x)+a}}{a c f}-\frac{\tan ^{-1}\left(\frac{\sqrt{a} \tan (e+f x)}{\sqrt{2} \sqrt{a \sec (e+f x)+a}}\right)}{\sqrt{2} \sqrt{a} c f}",1,"-(Tan[e + f*x]/(f*Sqrt[a + a*Sec[e + f*x]]*(c - c*Sec[e + f*x]))) - (ArcTanh[Sqrt[c - c*Sec[e + f*x]]/(Sqrt[2]*Sqrt[c])]*Tan[e + f*x])/(Sqrt[2]*Sqrt[c]*f*Sqrt[a + a*Sec[e + f*x]]*Sqrt[c - c*Sec[e + f*x]])","A",4,4,36,0.1111,1,"{3964, 78, 63, 208}"
180,1,213,0,0.2811888,"\int \frac{\sec ^{\frac{5}{2}}(e+f x)}{\sqrt{a+a \sec (e+f x)} (c-c \sec (e+f x))} \, dx","Int[Sec[e + f*x]^(5/2)/(Sqrt[a + a*Sec[e + f*x]]*(c - c*Sec[e + f*x])),x]","-\frac{\sin (e+f x) \sec ^{\frac{3}{2}}(e+f x)}{f \sqrt{a \sec (e+f x)+a} (c-c \sec (e+f x))}+\frac{2 \tan (e+f x) \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{\sec (e+f x)}}{\sqrt{c-c \sec (e+f x)}}\right)}{\sqrt{c} f \sqrt{a \sec (e+f x)+a} \sqrt{c-c \sec (e+f x)}}-\frac{\tan (e+f x) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{\sec (e+f x)}}{\sqrt{c-c \sec (e+f x)}}\right)}{\sqrt{2} \sqrt{c} f \sqrt{a \sec (e+f x)+a} \sqrt{c-c \sec (e+f x)}}","\frac{\csc (e+f x) \sqrt{a \sec (e+f x)+a}}{a c f \sqrt{\sec (e+f x)}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{a} \sin (e+f x) \sqrt{\sec (e+f x)}}{\sqrt{2} \sqrt{a \sec (e+f x)+a}}\right)}{\sqrt{2} \sqrt{a} c f}-\frac{2 \sinh ^{-1}\left(\frac{\sqrt{a} \tan (e+f x)}{\sqrt{a \sec (e+f x)+a}}\right)}{\sqrt{a} c f}",1,"-((Sec[e + f*x]^(3/2)*Sin[e + f*x])/(f*Sqrt[a + a*Sec[e + f*x]]*(c - c*Sec[e + f*x]))) + (2*ArcTan[(Sqrt[c]*Sqrt[Sec[e + f*x]])/Sqrt[c - c*Sec[e + f*x]]]*Tan[e + f*x])/(Sqrt[c]*f*Sqrt[a + a*Sec[e + f*x]]*Sqrt[c - c*Sec[e + f*x]]) - (ArcTan[(Sqrt[2]*Sqrt[c]*Sqrt[Sec[e + f*x]])/Sqrt[c - c*Sec[e + f*x]]]*Tan[e + f*x])/(Sqrt[2]*Sqrt[c]*f*Sqrt[a + a*Sec[e + f*x]]*Sqrt[c - c*Sec[e + f*x]])","A",8,8,38,0.2105,1,"{3964, 98, 157, 63, 217, 203, 93, 205}"
181,1,150,0,0.3027114,"\int \frac{(g \sec (e+f x))^{3/2}}{\sqrt{a+a \sec (e+f x)} (c-c \sec (e+f x))} \, dx","Int[(g*Sec[e + f*x])^(3/2)/(Sqrt[a + a*Sec[e + f*x]]*(c - c*Sec[e + f*x])),x]","\frac{g^{3/2} \tan (e+f x) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{g \sec (e+f x)}}{\sqrt{g} \sqrt{c-c \sec (e+f x)}}\right)}{\sqrt{2} \sqrt{c} f \sqrt{a \sec (e+f x)+a} \sqrt{c-c \sec (e+f x)}}-\frac{g \tan (e+f x) \sqrt{g \sec (e+f x)}}{f \sqrt{a \sec (e+f x)+a} (c-c \sec (e+f x))}","\frac{g \cot (e+f x) \sqrt{a \sec (e+f x)+a} \sqrt{g \sec (e+f x)}}{a c f}-\frac{g^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{g} \tan (e+f x)}{\sqrt{2} \sqrt{a \sec (e+f x)+a} \sqrt{g \sec (e+f x)}}\right)}{\sqrt{2} \sqrt{a} c f}",1,"-((g*Sqrt[g*Sec[e + f*x]]*Tan[e + f*x])/(f*Sqrt[a + a*Sec[e + f*x]]*(c - c*Sec[e + f*x]))) + (g^(3/2)*ArcTan[(Sqrt[2]*Sqrt[c]*Sqrt[g*Sec[e + f*x]])/(Sqrt[g]*Sqrt[c - c*Sec[e + f*x]])]*Tan[e + f*x])/(Sqrt[2]*Sqrt[c]*f*Sqrt[a + a*Sec[e + f*x]]*Sqrt[c - c*Sec[e + f*x]])","A",4,4,40,0.1000,1,"{3964, 94, 93, 205}"
182,1,242,0,0.3575035,"\int \frac{(g \sec (e+f x))^{5/2}}{\sqrt{a+a \sec (e+f x)} (c-c \sec (e+f x))} \, dx","Int[(g*Sec[e + f*x])^(5/2)/(Sqrt[a + a*Sec[e + f*x]]*(c - c*Sec[e + f*x])),x]","\frac{2 g^{5/2} \tan (e+f x) \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{g \sec (e+f x)}}{\sqrt{g} \sqrt{c-c \sec (e+f x)}}\right)}{\sqrt{c} f \sqrt{a \sec (e+f x)+a} \sqrt{c-c \sec (e+f x)}}-\frac{g^{5/2} \tan (e+f x) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{g \sec (e+f x)}}{\sqrt{g} \sqrt{c-c \sec (e+f x)}}\right)}{\sqrt{2} \sqrt{c} f \sqrt{a \sec (e+f x)+a} \sqrt{c-c \sec (e+f x)}}-\frac{g^2 \tan (e+f x) \sqrt{g \sec (e+f x)}}{f \sqrt{a \sec (e+f x)+a} (c-c \sec (e+f x))}","\frac{g^2 \cot (e+f x) \sqrt{a \sec (e+f x)+a} \sqrt{g \sec (e+f x)}}{a c f}-\frac{2 g^{5/2} \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{g} \tan (e+f x)}{\sqrt{a \sec (e+f x)+a} \sqrt{g \sec (e+f x)}}\right)}{\sqrt{a} c f}+\frac{g^{5/2} \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{g} \tan (e+f x)}{\sqrt{2} \sqrt{a \sec (e+f x)+a} \sqrt{g \sec (e+f x)}}\right)}{\sqrt{2} \sqrt{a} c f}",1,"-((g^2*Sqrt[g*Sec[e + f*x]]*Tan[e + f*x])/(f*Sqrt[a + a*Sec[e + f*x]]*(c - c*Sec[e + f*x]))) + (2*g^(5/2)*ArcTan[(Sqrt[c]*Sqrt[g*Sec[e + f*x]])/(Sqrt[g]*Sqrt[c - c*Sec[e + f*x]])]*Tan[e + f*x])/(Sqrt[c]*f*Sqrt[a + a*Sec[e + f*x]]*Sqrt[c - c*Sec[e + f*x]]) - (g^(5/2)*ArcTan[(Sqrt[2]*Sqrt[c]*Sqrt[g*Sec[e + f*x]])/(Sqrt[g]*Sqrt[c - c*Sec[e + f*x]])]*Tan[e + f*x])/(Sqrt[2]*Sqrt[c]*f*Sqrt[a + a*Sec[e + f*x]]*Sqrt[c - c*Sec[e + f*x]])","A",8,8,40,0.2000,1,"{3964, 98, 157, 63, 217, 203, 93, 205}"
183,1,46,0,0.2554265,"\int \frac{\sec ^2(e+f x)}{\sqrt{a+a \sec (e+f x)} \sqrt{c-c \sec (e+f x)}} \, dx","Int[Sec[e + f*x]^2/(Sqrt[a + a*Sec[e + f*x]]*Sqrt[c - c*Sec[e + f*x]]),x]","\frac{\tan (e+f x) \log (\tan (e+f x))}{f \sqrt{a \sec (e+f x)+a} \sqrt{c-c \sec (e+f x)}}","\frac{\tan (e+f x) \log (\tan (e+f x))}{f \sqrt{a \sec (e+f x)+a} \sqrt{c-c \sec (e+f x)}}",1,"(Log[Tan[e + f*x]]*Tan[e + f*x])/(f*Sqrt[a + a*Sec[e + f*x]]*Sqrt[c - c*Sec[e + f*x]])","A",3,3,38,0.07895,1,"{3963, 2620, 29}"
184,1,65,0,0.1591674,"\int \frac{\sec (e+f x) \sqrt{a+a \sec (e+f x)}}{c-d \sec (e+f x)} \, dx","Int[(Sec[e + f*x]*Sqrt[a + a*Sec[e + f*x]])/(c - d*Sec[e + f*x]),x]","\frac{2 \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{d} \tan (e+f x)}{\sqrt{c-d} \sqrt{a \sec (e+f x)+a}}\right)}{\sqrt{d} f \sqrt{c-d}}","\frac{2 \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{d} \tan (e+f x)}{\sqrt{c-d} \sqrt{a \sec (e+f x)+a}}\right)}{\sqrt{d} f \sqrt{c-d}}",1,"(2*Sqrt[a]*ArcTanh[(Sqrt[a]*Sqrt[d]*Tan[e + f*x])/(Sqrt[c - d]*Sqrt[a + a*Sec[e + f*x]])])/(Sqrt[c - d]*Sqrt[d]*f)","A",2,2,34,0.05882,1,"{3967, 208}"
185,1,236,0,0.4374775,"\int \sec (e+f x) (a+a \sec (e+f x)) (c+d \sec (e+f x))^4 \, dx","Int[Sec[e + f*x]*(a + a*Sec[e + f*x])*(c + d*Sec[e + f*x])^4,x]","\frac{a \left(112 c^2 d^2+95 c^3 d+12 c^4+80 c d^3+16 d^4\right) \tan (e+f x)}{30 f}+\frac{a \left(24 c^2 d^2+16 c^3 d+8 c^4+12 c d^3+3 d^4\right) \tanh ^{-1}(\sin (e+f x))}{8 f}+\frac{a \left(12 c^2+35 c d+16 d^2\right) \tan (e+f x) (c+d \sec (e+f x))^2}{60 f}+\frac{a d \left(130 c^2 d+24 c^3+116 c d^2+45 d^3\right) \tan (e+f x) \sec (e+f x)}{120 f}+\frac{a \tan (e+f x) (c+d \sec (e+f x))^4}{5 f}+\frac{a (4 c+5 d) \tan (e+f x) (c+d \sec (e+f x))^3}{20 f}","\frac{a \left(112 c^2 d^2+95 c^3 d+12 c^4+80 c d^3+16 d^4\right) \tan (e+f x)}{30 f}+\frac{a \left(24 c^2 d^2+16 c^3 d+8 c^4+12 c d^3+3 d^4\right) \tanh ^{-1}(\sin (e+f x))}{8 f}+\frac{a \left(12 c^2+35 c d+16 d^2\right) \tan (e+f x) (c+d \sec (e+f x))^2}{60 f}+\frac{a d \left(130 c^2 d+24 c^3+116 c d^2+45 d^3\right) \tan (e+f x) \sec (e+f x)}{120 f}+\frac{a \tan (e+f x) (c+d \sec (e+f x))^4}{5 f}+\frac{a (4 c+5 d) \tan (e+f x) (c+d \sec (e+f x))^3}{20 f}",1,"(a*(8*c^4 + 16*c^3*d + 24*c^2*d^2 + 12*c*d^3 + 3*d^4)*ArcTanh[Sin[e + f*x]])/(8*f) + (a*(12*c^4 + 95*c^3*d + 112*c^2*d^2 + 80*c*d^3 + 16*d^4)*Tan[e + f*x])/(30*f) + (a*d*(24*c^3 + 130*c^2*d + 116*c*d^2 + 45*d^3)*Sec[e + f*x]*Tan[e + f*x])/(120*f) + (a*(12*c^2 + 35*c*d + 16*d^2)*(c + d*Sec[e + f*x])^2*Tan[e + f*x])/(60*f) + (a*(4*c + 5*d)*(c + d*Sec[e + f*x])^3*Tan[e + f*x])/(20*f) + (a*(c + d*Sec[e + f*x])^4*Tan[e + f*x])/(5*f)","A",8,6,29,0.2069,1,"{4002, 3997, 3787, 3770, 3767, 8}"
186,1,171,0,0.2951377,"\int \sec (e+f x) (a+a \sec (e+f x)) (c+d \sec (e+f x))^3 \, dx","Int[Sec[e + f*x]*(a + a*Sec[e + f*x])*(c + d*Sec[e + f*x])^3,x]","\frac{a \left(16 c^2 d+3 c^3+12 c d^2+4 d^3\right) \tan (e+f x)}{6 f}+\frac{a \left(12 c^2 d+8 c^3+12 c d^2+3 d^3\right) \tanh ^{-1}(\sin (e+f x))}{8 f}+\frac{a d \left(6 c^2+20 c d+9 d^2\right) \tan (e+f x) \sec (e+f x)}{24 f}+\frac{a \tan (e+f x) (c+d \sec (e+f x))^3}{4 f}+\frac{a (3 c+4 d) \tan (e+f x) (c+d \sec (e+f x))^2}{12 f}","\frac{a \left(16 c^2 d+3 c^3+12 c d^2+4 d^3\right) \tan (e+f x)}{6 f}+\frac{a \left(12 c^2 d+8 c^3+12 c d^2+3 d^3\right) \tanh ^{-1}(\sin (e+f x))}{8 f}+\frac{a d \left(6 c^2+20 c d+9 d^2\right) \tan (e+f x) \sec (e+f x)}{24 f}+\frac{a \tan (e+f x) (c+d \sec (e+f x))^3}{4 f}+\frac{a (3 c+4 d) \tan (e+f x) (c+d \sec (e+f x))^2}{12 f}",1,"(a*(8*c^3 + 12*c^2*d + 12*c*d^2 + 3*d^3)*ArcTanh[Sin[e + f*x]])/(8*f) + (a*(3*c^3 + 16*c^2*d + 12*c*d^2 + 4*d^3)*Tan[e + f*x])/(6*f) + (a*d*(6*c^2 + 20*c*d + 9*d^2)*Sec[e + f*x]*Tan[e + f*x])/(24*f) + (a*(3*c + 4*d)*(c + d*Sec[e + f*x])^2*Tan[e + f*x])/(12*f) + (a*(c + d*Sec[e + f*x])^3*Tan[e + f*x])/(4*f)","A",7,6,29,0.2069,1,"{4002, 3997, 3787, 3770, 3767, 8}"
187,1,108,0,0.1650135,"\int \sec (e+f x) (a+a \sec (e+f x)) (c+d \sec (e+f x))^2 \, dx","Int[Sec[e + f*x]*(a + a*Sec[e + f*x])*(c + d*Sec[e + f*x])^2,x]","\frac{2 a \left(c^2+3 c d+d^2\right) \tan (e+f x)}{3 f}+\frac{a \left(2 c^2+2 c d+d^2\right) \tanh ^{-1}(\sin (e+f x))}{2 f}+\frac{a \tan (e+f x) (c+d \sec (e+f x))^2}{3 f}+\frac{a d (2 c+3 d) \tan (e+f x) \sec (e+f x)}{6 f}","\frac{2 a \left(c^2+3 c d+d^2\right) \tan (e+f x)}{3 f}+\frac{a \left(2 c^2+2 c d+d^2\right) \tanh ^{-1}(\sin (e+f x))}{2 f}+\frac{a \tan (e+f x) (c+d \sec (e+f x))^2}{3 f}+\frac{a d (2 c+3 d) \tan (e+f x) \sec (e+f x)}{6 f}",1,"(a*(2*c^2 + 2*c*d + d^2)*ArcTanh[Sin[e + f*x]])/(2*f) + (2*a*(c^2 + 3*c*d + d^2)*Tan[e + f*x])/(3*f) + (a*d*(2*c + 3*d)*Sec[e + f*x]*Tan[e + f*x])/(6*f) + (a*(c + d*Sec[e + f*x])^2*Tan[e + f*x])/(3*f)","A",6,6,29,0.2069,1,"{4002, 3997, 3787, 3770, 3767, 8}"
188,1,56,0,0.0719762,"\int \sec (e+f x) (a+a \sec (e+f x)) (c+d \sec (e+f x)) \, dx","Int[Sec[e + f*x]*(a + a*Sec[e + f*x])*(c + d*Sec[e + f*x]),x]","\frac{a (c+d) \tan (e+f x)}{f}+\frac{a (2 c+d) \tanh ^{-1}(\sin (e+f x))}{2 f}+\frac{a d \tan (e+f x) \sec (e+f x)}{2 f}","\frac{a (c+d) \tan (e+f x)}{f}+\frac{a (2 c+d) \tanh ^{-1}(\sin (e+f x))}{2 f}+\frac{a d \tan (e+f x) \sec (e+f x)}{2 f}",1,"(a*(2*c + d)*ArcTanh[Sin[e + f*x]])/(2*f) + (a*(c + d)*Tan[e + f*x])/f + (a*d*Sec[e + f*x]*Tan[e + f*x])/(2*f)","A",5,5,27,0.1852,1,"{3997, 3787, 3770, 3767, 8}"
189,1,69,0,0.1440888,"\int \frac{\sec (e+f x) (a+a \sec (e+f x))}{c+d \sec (e+f x)} \, dx","Int[(Sec[e + f*x]*(a + a*Sec[e + f*x]))/(c + d*Sec[e + f*x]),x]","\frac{a \tanh ^{-1}(\sin (e+f x))}{d f}-\frac{2 a \sqrt{c-d} \tanh ^{-1}\left(\frac{\sqrt{c-d} \tan \left(\frac{1}{2} (e+f x)\right)}{\sqrt{c+d}}\right)}{d f \sqrt{c+d}}","\frac{a \tanh ^{-1}(\sin (e+f x))}{d f}-\frac{2 a \sqrt{c-d} \tanh ^{-1}\left(\frac{\sqrt{c-d} \tan \left(\frac{1}{2} (e+f x)\right)}{\sqrt{c+d}}\right)}{d f \sqrt{c+d}}",1,"(a*ArcTanh[Sin[e + f*x]])/(d*f) - (2*a*Sqrt[c - d]*ArcTanh[(Sqrt[c - d]*Tan[(e + f*x)/2])/Sqrt[c + d]])/(d*Sqrt[c + d]*f)","A",5,5,29,0.1724,1,"{3998, 3770, 3831, 2659, 208}"
190,1,79,0,0.1390651,"\int \frac{\sec (e+f x) (a+a \sec (e+f x))}{(c+d \sec (e+f x))^2} \, dx","Int[(Sec[e + f*x]*(a + a*Sec[e + f*x]))/(c + d*Sec[e + f*x])^2,x]","\frac{2 a \tanh ^{-1}\left(\frac{\sqrt{c-d} \tan \left(\frac{1}{2} (e+f x)\right)}{\sqrt{c+d}}\right)}{f \sqrt{c-d} (c+d)^{3/2}}+\frac{a \tan (e+f x)}{f (c+d) (c+d \sec (e+f x))}","\frac{2 a \tanh ^{-1}\left(\frac{\sqrt{c-d} \tan \left(\frac{1}{2} (e+f x)\right)}{\sqrt{c+d}}\right)}{f \sqrt{c-d} (c+d)^{3/2}}+\frac{a \tan (e+f x)}{f (c+d) (c+d \sec (e+f x))}",1,"(2*a*ArcTanh[(Sqrt[c - d]*Tan[(e + f*x)/2])/Sqrt[c + d]])/(Sqrt[c - d]*(c + d)^(3/2)*f) + (a*Tan[e + f*x])/((c + d)*f*(c + d*Sec[e + f*x]))","A",5,5,29,0.1724,1,"{4003, 12, 3831, 2659, 208}"
191,1,131,0,0.2704056,"\int \frac{\sec (e+f x) (a+a \sec (e+f x))}{(c+d \sec (e+f x))^3} \, dx","Int[(Sec[e + f*x]*(a + a*Sec[e + f*x]))/(c + d*Sec[e + f*x])^3,x]","\frac{a (2 c-d) \tanh ^{-1}\left(\frac{\sqrt{c-d} \tan \left(\frac{1}{2} (e+f x)\right)}{\sqrt{c+d}}\right)}{f (c-d)^{3/2} (c+d)^{5/2}}+\frac{a (c-2 d) \tan (e+f x)}{2 f (c-d) (c+d)^2 (c+d \sec (e+f x))}+\frac{a \tan (e+f x)}{2 f (c+d) (c+d \sec (e+f x))^2}","\frac{a (2 c-d) \tanh ^{-1}\left(\frac{\sqrt{c-d} \tan \left(\frac{1}{2} (e+f x)\right)}{\sqrt{c+d}}\right)}{f (c-d)^{3/2} (c+d)^{5/2}}+\frac{a (c-2 d) \tan (e+f x)}{2 f (c-d) (c+d)^2 (c+d \sec (e+f x))}+\frac{a \tan (e+f x)}{2 f (c+d) (c+d \sec (e+f x))^2}",1,"(a*(2*c - d)*ArcTanh[(Sqrt[c - d]*Tan[(e + f*x)/2])/Sqrt[c + d]])/((c - d)^(3/2)*(c + d)^(5/2)*f) + (a*Tan[e + f*x])/(2*(c + d)*f*(c + d*Sec[e + f*x])^2) + (a*(c - 2*d)*Tan[e + f*x])/(2*(c - d)*(c + d)^2*f*(c + d*Sec[e + f*x]))","A",6,5,29,0.1724,1,"{4003, 12, 3831, 2659, 208}"
192,1,189,0,0.4542034,"\int \frac{\sec (e+f x) (a+a \sec (e+f x))}{(c+d \sec (e+f x))^4} \, dx","Int[(Sec[e + f*x]*(a + a*Sec[e + f*x]))/(c + d*Sec[e + f*x])^4,x]","\frac{a \left(2 c^2-2 c d+d^2\right) \tanh ^{-1}\left(\frac{\sqrt{c-d} \tan \left(\frac{1}{2} (e+f x)\right)}{\sqrt{c+d}}\right)}{f (c-d)^{5/2} (c+d)^{7/2}}+\frac{a (c-4 d) (2 c-d) \tan (e+f x)}{6 f (c-d)^2 (c+d)^3 (c+d \sec (e+f x))}+\frac{a (2 c-3 d) \tan (e+f x)}{6 f (c-d) (c+d)^2 (c+d \sec (e+f x))^2}+\frac{a \tan (e+f x)}{3 f (c+d) (c+d \sec (e+f x))^3}","\frac{a \left(2 c^2-2 c d+d^2\right) \tanh ^{-1}\left(\frac{\sqrt{c-d} \tan \left(\frac{1}{2} (e+f x)\right)}{\sqrt{c+d}}\right)}{f (c-d)^{5/2} (c+d)^{7/2}}+\frac{a (c-4 d) (2 c-d) \tan (e+f x)}{6 f (c-d)^2 (c+d)^3 (c+d \sec (e+f x))}+\frac{a (2 c-3 d) \tan (e+f x)}{6 f (c-d) (c+d)^2 (c+d \sec (e+f x))^2}+\frac{a \tan (e+f x)}{3 f (c+d) (c+d \sec (e+f x))^3}",1,"(a*(2*c^2 - 2*c*d + d^2)*ArcTanh[(Sqrt[c - d]*Tan[(e + f*x)/2])/Sqrt[c + d]])/((c - d)^(5/2)*(c + d)^(7/2)*f) + (a*Tan[e + f*x])/(3*(c + d)*f*(c + d*Sec[e + f*x])^3) + (a*(2*c - 3*d)*Tan[e + f*x])/(6*(c - d)*(c + d)^2*f*(c + d*Sec[e + f*x])^2) + (a*(c - 4*d)*(2*c - d)*Tan[e + f*x])/(6*(c - d)^2*(c + d)^3*f*(c + d*Sec[e + f*x]))","A",7,5,29,0.1724,1,"{4003, 12, 3831, 2659, 208}"
193,1,371,0,0.4242102,"\int \sec (e+f x) (a+a \sec (e+f x))^2 (c+d \sec (e+f x))^4 \, dx","Int[Sec[e + f*x]*(a + a*Sec[e + f*x])^2*(c + d*Sec[e + f*x])^4,x]","\frac{a^2 \left(84 c^2 d^2+64 c^3 d+24 c^4+48 c d^3+11 d^4\right) \tan (e+f x)}{16 f}+\frac{a^3 \left(84 c^2 d^2+64 c^3 d+24 c^4+48 c d^3+11 d^4\right) \tan (e+f x) \tan ^{-1}\left(\frac{\sqrt{a-a \sec (e+f x)}}{\sqrt{a (\sec (e+f x)+1)}}\right)}{8 f \sqrt{a-a \sec (e+f x)} \sqrt{a \sec (e+f x)+a}}+\frac{\left(84 c^2 d^2+64 c^3 d+24 c^4+48 c d^3+11 d^4\right) \tan (e+f x) \left(a^2 \sec (e+f x)+a^2\right)}{48 f}+\frac{d \tan (e+f x) (a \sec (e+f x)+a)^2 \left(d \left(48 c^2+32 c d+19 d^2\right) \sec (e+f x)+2 \left(56 c^2 d+52 c^3+48 c d^2+9 d^3\right)\right)}{120 f}+\frac{d \tan (e+f x) (a \sec (e+f x)+a)^2 (c+d \sec (e+f x))^3}{6 f}+\frac{d (9 c+2 d) \tan (e+f x) (a \sec (e+f x)+a)^2 (c+d \sec (e+f x))^2}{30 f}","-\frac{a^2 \left(-311 c^3 d^2-448 c^2 d^3-48 c^4 d+4 c^5-288 c d^4-64 d^5\right) \tan (e+f x)}{60 d f}+\frac{a^2 \left(84 c^2 d^2+64 c^3 d+24 c^4+48 c d^3+11 d^4\right) \tanh ^{-1}(\sin (e+f x))}{16 f}-\frac{a^2 \left(4 c^2-48 c d-55 d^2\right) \tan (e+f x) (c+d \sec (e+f x))^3}{120 d f}-\frac{a^2 \left(-48 c^2 d+4 c^3-123 c d^2-64 d^3\right) \tan (e+f x) (c+d \sec (e+f x))^2}{120 d f}-\frac{a^2 \left(-438 c^2 d^2-96 c^3 d+8 c^4-464 c d^3-165 d^4\right) \tan (e+f x) \sec (e+f x)}{240 f}+\frac{a^2 \tan (e+f x) (c+d \sec (e+f x))^5}{6 d f}-\frac{a^2 (c-12 d) \tan (e+f x) (c+d \sec (e+f x))^4}{30 d f}",1,"(a^2*(24*c^4 + 64*c^3*d + 84*c^2*d^2 + 48*c*d^3 + 11*d^4)*Tan[e + f*x])/(16*f) + (a^3*(24*c^4 + 64*c^3*d + 84*c^2*d^2 + 48*c*d^3 + 11*d^4)*ArcTan[Sqrt[a - a*Sec[e + f*x]]/Sqrt[a*(1 + Sec[e + f*x])]]*Tan[e + f*x])/(8*f*Sqrt[a - a*Sec[e + f*x]]*Sqrt[a + a*Sec[e + f*x]]) + ((24*c^4 + 64*c^3*d + 84*c^2*d^2 + 48*c*d^3 + 11*d^4)*(a^2 + a^2*Sec[e + f*x])*Tan[e + f*x])/(48*f) + (d*(9*c + 2*d)*(a + a*Sec[e + f*x])^2*(c + d*Sec[e + f*x])^2*Tan[e + f*x])/(30*f) + (d*(a + a*Sec[e + f*x])^2*(c + d*Sec[e + f*x])^3*Tan[e + f*x])/(6*f) + (d*(a + a*Sec[e + f*x])^2*(2*(52*c^3 + 56*c^2*d + 48*c*d^2 + 9*d^3) + d*(48*c^2 + 32*c*d + 19*d^2)*Sec[e + f*x])*Tan[e + f*x])/(120*f)","A",9,8,31,0.2581,1,"{3987, 100, 153, 147, 50, 63, 217, 203}"
194,1,277,0,0.3427008,"\int \sec (e+f x) (a+a \sec (e+f x))^2 (c+d \sec (e+f x))^3 \, dx","Int[Sec[e + f*x]*(a + a*Sec[e + f*x])^2*(c + d*Sec[e + f*x])^3,x]","\frac{3 a^2 (2 c+d) \left(2 c^2+3 c d+2 d^2\right) \tan (e+f x)}{8 f}+\frac{3 a^3 (2 c+d) \left(2 c^2+3 c d+2 d^2\right) \tan (e+f x) \tan ^{-1}\left(\frac{\sqrt{a-a \sec (e+f x)}}{\sqrt{a (\sec (e+f x)+1)}}\right)}{4 f \sqrt{a-a \sec (e+f x)} \sqrt{a \sec (e+f x)+a}}+\frac{(2 c+d) \left(2 c^2+3 c d+2 d^2\right) \tan (e+f x) \left(a^2 \sec (e+f x)+a^2\right)}{8 f}+\frac{d \tan (e+f x) (a \sec (e+f x)+a)^2 \left(2 \left(8 c^2+5 c d+2 d^2\right)+d (7 c+2 d) \sec (e+f x)\right)}{20 f}+\frac{d \tan (e+f x) (a \sec (e+f x)+a)^2 (c+d \sec (e+f x))^2}{5 f}","-\frac{a^2 \left(-44 c^2 d^2-10 c^3 d+c^4-40 c d^3-12 d^4\right) \tan (e+f x)}{10 d f}+\frac{3 a^2 (2 c+d) \left(2 c^2+3 c d+2 d^2\right) \tanh ^{-1}(\sin (e+f x))}{8 f}-\frac{a^2 \left(c^2-10 c d-12 d^2\right) \tan (e+f x) (c+d \sec (e+f x))^2}{20 d f}-\frac{a^2 \left(-20 c^2 d+2 c^3-57 c d^2-30 d^3\right) \tan (e+f x) \sec (e+f x)}{40 f}+\frac{a^2 \tan (e+f x) (c+d \sec (e+f x))^4}{5 d f}-\frac{a^2 (c-10 d) \tan (e+f x) (c+d \sec (e+f x))^3}{20 d f}",1,"(3*a^2*(2*c + d)*(2*c^2 + 3*c*d + 2*d^2)*Tan[e + f*x])/(8*f) + (3*a^3*(2*c + d)*(2*c^2 + 3*c*d + 2*d^2)*ArcTan[Sqrt[a - a*Sec[e + f*x]]/Sqrt[a*(1 + Sec[e + f*x])]]*Tan[e + f*x])/(4*f*Sqrt[a - a*Sec[e + f*x]]*Sqrt[a + a*Sec[e + f*x]]) + ((2*c + d)*(2*c^2 + 3*c*d + 2*d^2)*(a^2 + a^2*Sec[e + f*x])*Tan[e + f*x])/(8*f) + (d*(a + a*Sec[e + f*x])^2*(c + d*Sec[e + f*x])^2*Tan[e + f*x])/(5*f) + (d*(a + a*Sec[e + f*x])^2*(2*(8*c^2 + 5*c*d + 2*d^2) + d*(7*c + 2*d)*Sec[e + f*x])*Tan[e + f*x])/(20*f)","A",8,7,31,0.2258,1,"{3987, 100, 147, 50, 63, 217, 203}"
195,1,234,0,0.2620411,"\int \sec (e+f x) (a+a \sec (e+f x))^2 (c+d \sec (e+f x))^2 \, dx","Int[Sec[e + f*x]*(a + a*Sec[e + f*x])^2*(c + d*Sec[e + f*x])^2,x]","\frac{a^2 \left(12 c^2+16 c d+7 d^2\right) \tan (e+f x)}{8 f}+\frac{a^3 \left(12 c^2+16 c d+7 d^2\right) \tan (e+f x) \tan ^{-1}\left(\frac{\sqrt{a-a \sec (e+f x)}}{\sqrt{a (\sec (e+f x)+1)}}\right)}{4 f \sqrt{a-a \sec (e+f x)} \sqrt{a \sec (e+f x)+a}}+\frac{\left(12 c^2+16 c d+7 d^2\right) \tan (e+f x) \left(a^2 \sec (e+f x)+a^2\right)}{24 f}+\frac{d (5 c+2 d) \tan (e+f x) (a \sec (e+f x)+a)^2}{12 f}+\frac{d \tan (e+f x) (a \sec (e+f x)+a)^2 (c+d \sec (e+f x))}{4 f}","-\frac{a^2 \left(-8 c^2 d+c^3-20 c d^2-8 d^3\right) \tan (e+f x)}{6 d f}+\frac{a^2 \left(12 c^2+16 c d+7 d^2\right) \tanh ^{-1}(\sin (e+f x))}{8 f}-\frac{a^2 \left(2 c (c-8 d)-21 d^2\right) \tan (e+f x) \sec (e+f x)}{24 f}+\frac{a^2 \tan (e+f x) (c+d \sec (e+f x))^3}{4 d f}-\frac{a^2 (c-8 d) \tan (e+f x) (c+d \sec (e+f x))^2}{12 d f}",1,"(a^2*(12*c^2 + 16*c*d + 7*d^2)*Tan[e + f*x])/(8*f) + (a^3*(12*c^2 + 16*c*d + 7*d^2)*ArcTan[Sqrt[a - a*Sec[e + f*x]]/Sqrt[a*(1 + Sec[e + f*x])]]*Tan[e + f*x])/(4*f*Sqrt[a - a*Sec[e + f*x]]*Sqrt[a + a*Sec[e + f*x]]) + (d*(5*c + 2*d)*(a + a*Sec[e + f*x])^2*Tan[e + f*x])/(12*f) + ((12*c^2 + 16*c*d + 7*d^2)*(a^2 + a^2*Sec[e + f*x])*Tan[e + f*x])/(24*f) + (d*(a + a*Sec[e + f*x])^2*(c + d*Sec[e + f*x])*Tan[e + f*x])/(4*f)","A",8,7,31,0.2258,1,"{3987, 90, 80, 50, 63, 217, 203}"
196,1,103,0,0.1170642,"\int \sec (e+f x) (a+a \sec (e+f x))^2 (c+d \sec (e+f x)) \, dx","Int[Sec[e + f*x]*(a + a*Sec[e + f*x])^2*(c + d*Sec[e + f*x]),x]","\frac{2 a^2 (3 c+2 d) \tan (e+f x)}{3 f}+\frac{a^2 (3 c+2 d) \tanh ^{-1}(\sin (e+f x))}{2 f}+\frac{a^2 (3 c+2 d) \tan (e+f x) \sec (e+f x)}{6 f}+\frac{d \tan (e+f x) (a \sec (e+f x)+a)^2}{3 f}","\frac{2 a^2 (3 c+2 d) \tan (e+f x)}{3 f}+\frac{a^2 (3 c+2 d) \tanh ^{-1}(\sin (e+f x))}{2 f}+\frac{a^2 (3 c+2 d) \tan (e+f x) \sec (e+f x)}{6 f}+\frac{d \tan (e+f x) (a \sec (e+f x)+a)^2}{3 f}",1,"(a^2*(3*c + 2*d)*ArcTanh[Sin[e + f*x]])/(2*f) + (2*a^2*(3*c + 2*d)*Tan[e + f*x])/(3*f) + (a^2*(3*c + 2*d)*Sec[e + f*x]*Tan[e + f*x])/(6*f) + (d*(a + a*Sec[e + f*x])^2*Tan[e + f*x])/(3*f)","A",6,6,29,0.2069,1,"{4001, 3788, 3767, 8, 4046, 3770}"
197,1,208,0,0.2454789,"\int \frac{\sec (e+f x) (a+a \sec (e+f x))^2}{c+d \sec (e+f x)} \, dx","Int[(Sec[e + f*x]*(a + a*Sec[e + f*x])^2)/(c + d*Sec[e + f*x]),x]","-\frac{2 a^3 (c-2 d) \tan (e+f x) \tan ^{-1}\left(\frac{\sqrt{a-a \sec (e+f x)}}{\sqrt{a (\sec (e+f x)+1)}}\right)}{d^2 f \sqrt{a-a \sec (e+f x)} \sqrt{a \sec (e+f x)+a}}-\frac{2 a^3 (c-d)^{3/2} \tan (e+f x) \tan ^{-1}\left(\frac{\sqrt{c+d} \sqrt{a \sec (e+f x)+a}}{\sqrt{c-d} \sqrt{a-a \sec (e+f x)}}\right)}{d^2 f \sqrt{c+d} \sqrt{a-a \sec (e+f x)} \sqrt{a \sec (e+f x)+a}}+\frac{a^2 \tan (e+f x)}{d f}","-\frac{a^2 (c-2 d) \tanh ^{-1}(\sin (e+f x))}{d^2 f}+\frac{2 a^2 (c-d)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c-d} \tan \left(\frac{1}{2} (e+f x)\right)}{\sqrt{c+d}}\right)}{d^2 f \sqrt{c+d}}+\frac{a^2 \tan (e+f x)}{d f}",1,"(a^2*Tan[e + f*x])/(d*f) - (2*a^3*(c - 2*d)*ArcTan[Sqrt[a - a*Sec[e + f*x]]/Sqrt[a*(1 + Sec[e + f*x])]]*Tan[e + f*x])/(d^2*f*Sqrt[a - a*Sec[e + f*x]]*Sqrt[a + a*Sec[e + f*x]]) - (2*a^3*(c - d)^(3/2)*ArcTan[(Sqrt[c + d]*Sqrt[a + a*Sec[e + f*x]])/(Sqrt[c - d]*Sqrt[a - a*Sec[e + f*x]])]*Tan[e + f*x])/(d^2*Sqrt[c + d]*f*Sqrt[a - a*Sec[e + f*x]]*Sqrt[a + a*Sec[e + f*x]])","B",8,8,31,0.2581,1,"{3987, 102, 157, 63, 217, 203, 93, 205}"
198,1,231,0,0.2567903,"\int \frac{\sec (e+f x) (a+a \sec (e+f x))^2}{(c+d \sec (e+f x))^2} \, dx","Int[(Sec[e + f*x]*(a + a*Sec[e + f*x])^2)/(c + d*Sec[e + f*x])^2,x]","\frac{2 a^3 \sqrt{c-d} (c+2 d) \tan (e+f x) \tan ^{-1}\left(\frac{\sqrt{c+d} \sqrt{a \sec (e+f x)+a}}{\sqrt{c-d} \sqrt{a-a \sec (e+f x)}}\right)}{d^2 f (c+d)^{3/2} \sqrt{a-a \sec (e+f x)} \sqrt{a \sec (e+f x)+a}}-\frac{a^2 (c-d) \tan (e+f x)}{d f (c+d) (c+d \sec (e+f x))}+\frac{2 a^3 \tan (e+f x) \tan ^{-1}\left(\frac{\sqrt{a-a \sec (e+f x)}}{\sqrt{a (\sec (e+f x)+1)}}\right)}{d^2 f \sqrt{a-a \sec (e+f x)} \sqrt{a \sec (e+f x)+a}}","-\frac{2 a^2 \sqrt{c-d} (c+2 d) \tanh ^{-1}\left(\frac{\sqrt{c-d} \tan \left(\frac{1}{2} (e+f x)\right)}{\sqrt{c+d}}\right)}{d^2 f (c+d)^{3/2}}-\frac{a^2 (c-d) \tan (e+f x)}{d f (c+d) (c+d \sec (e+f x))}+\frac{a^2 \tanh ^{-1}(\sin (e+f x))}{d^2 f}",1,"(2*a^3*ArcTan[Sqrt[a - a*Sec[e + f*x]]/Sqrt[a*(1 + Sec[e + f*x])]]*Tan[e + f*x])/(d^2*f*Sqrt[a - a*Sec[e + f*x]]*Sqrt[a + a*Sec[e + f*x]]) + (2*a^3*Sqrt[c - d]*(c + 2*d)*ArcTan[(Sqrt[c + d]*Sqrt[a + a*Sec[e + f*x]])/(Sqrt[c - d]*Sqrt[a - a*Sec[e + f*x]])]*Tan[e + f*x])/(d^2*(c + d)^(3/2)*f*Sqrt[a - a*Sec[e + f*x]]*Sqrt[a + a*Sec[e + f*x]]) - (a^2*(c - d)*Tan[e + f*x])/(d*(c + d)*f*(c + d*Sec[e + f*x]))","A",8,8,31,0.2581,1,"{3987, 98, 157, 63, 217, 203, 93, 205}"
199,1,184,0,0.196767,"\int \frac{\sec (e+f x) (a+a \sec (e+f x))^2}{(c+d \sec (e+f x))^3} \, dx","Int[(Sec[e + f*x]*(a + a*Sec[e + f*x])^2)/(c + d*Sec[e + f*x])^3,x]","-\frac{3 a^3 \tan (e+f x) \tan ^{-1}\left(\frac{\sqrt{c+d} \sqrt{a \sec (e+f x)+a}}{\sqrt{c-d} \sqrt{a-a \sec (e+f x)}}\right)}{f \sqrt{c-d} (c+d)^{5/2} \sqrt{a-a \sec (e+f x)} \sqrt{a \sec (e+f x)+a}}+\frac{3 a^2 \tan (e+f x)}{2 f (c+d)^2 (c+d \sec (e+f x))}+\frac{\tan (e+f x) \left(a^2 \sec (e+f x)+a^2\right)}{2 f (c+d) (c+d \sec (e+f x))^2}","\frac{3 a^2 \tanh ^{-1}\left(\frac{\sqrt{c-d} \tan \left(\frac{1}{2} (e+f x)\right)}{\sqrt{c+d}}\right)}{f \sqrt{c-d} (c+d)^{5/2}}+\frac{3 a^2 \tan (e+f x)}{2 f (c+d)^2 (c+d \sec (e+f x))}+\frac{\tan (e+f x) \left(a^2 \sec (e+f x)+a^2\right)}{2 f (c+d) (c+d \sec (e+f x))^2}",1,"(-3*a^3*ArcTan[(Sqrt[c + d]*Sqrt[a + a*Sec[e + f*x]])/(Sqrt[c - d]*Sqrt[a - a*Sec[e + f*x]])]*Tan[e + f*x])/(Sqrt[c - d]*(c + d)^(5/2)*f*Sqrt[a - a*Sec[e + f*x]]*Sqrt[a + a*Sec[e + f*x]]) + ((a^2 + a^2*Sec[e + f*x])*Tan[e + f*x])/(2*(c + d)*f*(c + d*Sec[e + f*x])^2) + (3*a^2*Tan[e + f*x])/(2*(c + d)^2*f*(c + d*Sec[e + f*x]))","A",5,4,31,0.1290,1,"{3987, 94, 93, 205}"
200,1,268,0,0.2826397,"\int \frac{\sec (e+f x) (a+a \sec (e+f x))^2}{(c+d \sec (e+f x))^4} \, dx","Int[(Sec[e + f*x]*(a + a*Sec[e + f*x])^2)/(c + d*Sec[e + f*x])^4,x]","-\frac{a^3 (3 c-2 d) \tan (e+f x) \tan ^{-1}\left(\frac{\sqrt{c+d} \sqrt{a \sec (e+f x)+a}}{\sqrt{c-d} \sqrt{a-a \sec (e+f x)}}\right)}{f (c-d)^{3/2} (c+d)^{7/2} \sqrt{a-a \sec (e+f x)} \sqrt{a \sec (e+f x)+a}}+\frac{a^2 (3 c-2 d) \tan (e+f x)}{2 f (c-d) (c+d)^3 (c+d \sec (e+f x))}+\frac{(3 c-2 d) \tan (e+f x) \left(a^2 \sec (e+f x)+a^2\right)}{6 f (c-d) (c+d)^2 (c+d \sec (e+f x))^2}-\frac{d \tan (e+f x) (a \sec (e+f x)+a)^2}{3 f \left(c^2-d^2\right) (c+d \sec (e+f x))^3}","\frac{a^2 (3 c-2 d) \tanh ^{-1}\left(\frac{\sqrt{c-d} \tan \left(\frac{1}{2} (e+f x)\right)}{\sqrt{c+d}}\right)}{f (c-d)^{3/2} (c+d)^{7/2}}+\frac{a^2 (3 c-2 d) \tan (e+f x)}{2 f (c-d) (c+d)^3 (c+d \sec (e+f x))}+\frac{(3 c-2 d) \tan (e+f x) \left(a^2 \sec (e+f x)+a^2\right)}{6 f (c-d) (c+d)^2 (c+d \sec (e+f x))^2}-\frac{d \tan (e+f x) (a \sec (e+f x)+a)^2}{3 f \left(c^2-d^2\right) (c+d \sec (e+f x))^3}",1,"-((a^3*(3*c - 2*d)*ArcTan[(Sqrt[c + d]*Sqrt[a + a*Sec[e + f*x]])/(Sqrt[c - d]*Sqrt[a - a*Sec[e + f*x]])]*Tan[e + f*x])/((c - d)^(3/2)*(c + d)^(7/2)*f*Sqrt[a - a*Sec[e + f*x]]*Sqrt[a + a*Sec[e + f*x]])) - (d*(a + a*Sec[e + f*x])^2*Tan[e + f*x])/(3*(c^2 - d^2)*f*(c + d*Sec[e + f*x])^3) + ((3*c - 2*d)*(a^2 + a^2*Sec[e + f*x])*Tan[e + f*x])/(6*(c - d)*(c + d)^2*f*(c + d*Sec[e + f*x])^2) + (a^2*(3*c - 2*d)*Tan[e + f*x])/(2*(c - d)*(c + d)^3*f*(c + d*Sec[e + f*x]))","A",6,5,31,0.1613,1,"{3987, 96, 94, 93, 205}"
201,1,330,0,0.5568338,"\int \frac{\sec (e+f x) (a+a \sec (e+f x))^2}{(c+d \sec (e+f x))^5} \, dx","Int[(Sec[e + f*x]*(a + a*Sec[e + f*x])^2)/(c + d*Sec[e + f*x])^5,x]","-\frac{a^3 \left(12 c^2-16 c d+7 d^2\right) \tan (e+f x) \tan ^{-1}\left(\frac{\sqrt{c+d} \sqrt{a \sec (e+f x)+a}}{\sqrt{c-d} \sqrt{a-a \sec (e+f x)}}\right)}{4 f (c-d)^{5/2} (c+d)^{9/2} \sqrt{a-a \sec (e+f x)} \sqrt{a \sec (e+f x)+a}}+\frac{a^2 \left(16 c^2 d+2 c^3-59 c d^2+32 d^3\right) \tan (e+f x)}{24 d f (c-d)^2 (c+d)^4 (c+d \sec (e+f x))}+\frac{a^2 \left(2 c^2+16 c d-21 d^2\right) \tan (e+f x)}{24 d f (c-d) (c+d)^3 (c+d \sec (e+f x))^2}+\frac{a^2 (c+8 d) \tan (e+f x)}{12 d f (c+d)^2 (c+d \sec (e+f x))^3}-\frac{a^2 (c-d) \tan (e+f x)}{4 d f (c+d) (c+d \sec (e+f x))^4}","\frac{a^2 \left(12 c^2-16 c d+7 d^2\right) \tanh ^{-1}\left(\frac{\sqrt{c-d} \tan \left(\frac{1}{2} (e+f x)\right)}{\sqrt{c+d}}\right)}{4 f (c-d)^{5/2} (c+d)^{9/2}}+\frac{a^2 \left(16 c^2 d+2 c^3-59 c d^2+32 d^3\right) \tan (e+f x)}{24 d f (c-d)^2 (c+d)^4 (c+d \sec (e+f x))}+\frac{a^2 \left(2 c^2+16 c d-21 d^2\right) \tan (e+f x)}{24 d f (c-d) (c+d)^3 (c+d \sec (e+f x))^2}+\frac{a^2 (c+8 d) \tan (e+f x)}{12 d f (c+d)^2 (c+d \sec (e+f x))^3}-\frac{a^2 (c-d) \tan (e+f x)}{4 d f (c+d) (c+d \sec (e+f x))^4}",1,"-(a^3*(12*c^2 - 16*c*d + 7*d^2)*ArcTan[(Sqrt[c + d]*Sqrt[a + a*Sec[e + f*x]])/(Sqrt[c - d]*Sqrt[a - a*Sec[e + f*x]])]*Tan[e + f*x])/(4*(c - d)^(5/2)*(c + d)^(9/2)*f*Sqrt[a - a*Sec[e + f*x]]*Sqrt[a + a*Sec[e + f*x]]) - (a^2*(c - d)*Tan[e + f*x])/(4*d*(c + d)*f*(c + d*Sec[e + f*x])^4) + (a^2*(c + 8*d)*Tan[e + f*x])/(12*d*(c + d)^2*f*(c + d*Sec[e + f*x])^3) + (a^2*(2*c^2 + 16*c*d - 21*d^2)*Tan[e + f*x])/(24*(c - d)*d*(c + d)^3*f*(c + d*Sec[e + f*x])^2) + (a^2*(2*c^3 + 16*c^2*d - 59*c*d^2 + 32*d^3)*Tan[e + f*x])/(24*(c - d)^2*d*(c + d)^4*f*(c + d*Sec[e + f*x]))","A",8,6,31,0.1935,1,"{3987, 98, 151, 12, 93, 205}"
202,1,333,0,0.4270777,"\int \sec (e+f x) (a+a \sec (e+f x))^3 (c+d \sec (e+f x))^3 \, dx","Int[Sec[e + f*x]*(a + a*Sec[e + f*x])^3*(c + d*Sec[e + f*x])^3,x]","\frac{a^3 \left(90 c^2 d+40 c^3+78 c d^2+23 d^3\right) \tan (e+f x)}{16 f}+\frac{a^4 \left(90 c^2 d+40 c^3+78 c d^2+23 d^3\right) \tan (e+f x) \tan ^{-1}\left(\frac{\sqrt{a-a \sec (e+f x)}}{\sqrt{a (\sec (e+f x)+1)}}\right)}{8 f \sqrt{a-a \sec (e+f x)} \sqrt{a \sec (e+f x)+a}}+\frac{\left(90 c^2 d+40 c^3+78 c d^2+23 d^3\right) \tan (e+f x) \left(a^3 \sec (e+f x)+a^3\right)}{48 f}+\frac{a \left(90 c^2 d+40 c^3+78 c d^2+23 d^3\right) \tan (e+f x) (a \sec (e+f x)+a)^2}{120 f}+\frac{d \tan (e+f x) (a \sec (e+f x)+a)^3 \left(70 c^2+4 d (8 c+3 d) \sec (e+f x)+54 c d+19 d^2\right)}{120 f}+\frac{d \tan (e+f x) (a \sec (e+f x)+a)^3 (c+d \sec (e+f x))^2}{6 f}","\frac{a^3 \left(90 c^2 d+40 c^3+78 c d^2+23 d^3\right) \tan (e+f x)}{16 f}+\frac{a^3 \left(90 c^2 d+40 c^3+78 c d^2+23 d^3\right) \tanh ^{-1}(\sin (e+f x))}{16 f}+\frac{\left(90 c^2 d+40 c^3+78 c d^2+23 d^3\right) \tan (e+f x) \left(a^3 \sec (e+f x)+a^3\right)}{48 f}+\frac{a \tan (e+f x) (a \sec (e+f x)+a)^2 \left(d \left(6 c^2+62 c d+31 d^2\right) \sec (e+f x)+2 \left(74 c^2 d+4 c^3+66 c d^2+21 d^3\right)\right)}{120 f}+\frac{a \tan (e+f x) (a \sec (e+f x)+a)^2 (c+d \sec (e+f x))^3}{6 f}+\frac{a (3 c+8 d) \tan (e+f x) (a \sec (e+f x)+a)^2 (c+d \sec (e+f x))^2}{30 f}",1,"(a^3*(40*c^3 + 90*c^2*d + 78*c*d^2 + 23*d^3)*Tan[e + f*x])/(16*f) + (a^4*(40*c^3 + 90*c^2*d + 78*c*d^2 + 23*d^3)*ArcTan[Sqrt[a - a*Sec[e + f*x]]/Sqrt[a*(1 + Sec[e + f*x])]]*Tan[e + f*x])/(8*f*Sqrt[a - a*Sec[e + f*x]]*Sqrt[a + a*Sec[e + f*x]]) + (a*(40*c^3 + 90*c^2*d + 78*c*d^2 + 23*d^3)*(a + a*Sec[e + f*x])^2*Tan[e + f*x])/(120*f) + ((40*c^3 + 90*c^2*d + 78*c*d^2 + 23*d^3)*(a^3 + a^3*Sec[e + f*x])*Tan[e + f*x])/(48*f) + (d*(a + a*Sec[e + f*x])^3*(c + d*Sec[e + f*x])^2*Tan[e + f*x])/(6*f) + (d*(a + a*Sec[e + f*x])^3*(70*c^2 + 54*c*d + 19*d^2 + 4*d*(8*c + 3*d)*Sec[e + f*x])*Tan[e + f*x])/(120*f)","A",9,7,31,0.2258,1,"{3987, 100, 147, 50, 63, 217, 203}"
203,1,273,0,0.2996093,"\int \sec (e+f x) (a+a \sec (e+f x))^3 (c+d \sec (e+f x))^2 \, dx","Int[Sec[e + f*x]*(a + a*Sec[e + f*x])^3*(c + d*Sec[e + f*x])^2,x]","\frac{a^3 \left(20 c^2+30 c d+13 d^2\right) \tan (e+f x)}{8 f}+\frac{a^4 \left(20 c^2+30 c d+13 d^2\right) \tan (e+f x) \tan ^{-1}\left(\frac{\sqrt{a-a \sec (e+f x)}}{\sqrt{a (\sec (e+f x)+1)}}\right)}{4 f \sqrt{a-a \sec (e+f x)} \sqrt{a \sec (e+f x)+a}}+\frac{\left(20 c^2+30 c d+13 d^2\right) \tan (e+f x) \left(a^3 \sec (e+f x)+a^3\right)}{24 f}+\frac{a \left(20 c^2+30 c d+13 d^2\right) \tan (e+f x) (a \sec (e+f x)+a)^2}{60 f}+\frac{3 d (2 c+d) \tan (e+f x) (a \sec (e+f x)+a)^3}{20 f}+\frac{d \tan (e+f x) (a \sec (e+f x)+a)^3 (c+d \sec (e+f x))}{5 f}","\frac{a^3 \left(72 c^2 d^2-15 c^3 d+2 c^4+180 c d^3+76 d^4\right) \tan (e+f x)}{30 d^2 f}+\frac{a^3 \left(20 c^2+30 c d+13 d^2\right) \tanh ^{-1}(\sin (e+f x))}{8 f}+\frac{a^3 \left(2 c^2-15 c d+76 d^2\right) \tan (e+f x) (c+d \sec (e+f x))^2}{60 d^2 f}+\frac{a^3 \left(-30 c^2 d+4 c^3+146 c d^2+195 d^3\right) \tan (e+f x) \sec (e+f x)}{120 d f}-\frac{a^3 (2 c-11 d) \tan (e+f x) (c+d \sec (e+f x))^3}{20 d^2 f}+\frac{\tan (e+f x) \left(a^3 \sec (e+f x)+a^3\right) (c+d \sec (e+f x))^3}{5 d f}",1,"(a^3*(20*c^2 + 30*c*d + 13*d^2)*Tan[e + f*x])/(8*f) + (a^4*(20*c^2 + 30*c*d + 13*d^2)*ArcTan[Sqrt[a - a*Sec[e + f*x]]/Sqrt[a*(1 + Sec[e + f*x])]]*Tan[e + f*x])/(4*f*Sqrt[a - a*Sec[e + f*x]]*Sqrt[a + a*Sec[e + f*x]]) + (a*(20*c^2 + 30*c*d + 13*d^2)*(a + a*Sec[e + f*x])^2*Tan[e + f*x])/(60*f) + (3*d*(2*c + d)*(a + a*Sec[e + f*x])^3*Tan[e + f*x])/(20*f) + ((20*c^2 + 30*c*d + 13*d^2)*(a^3 + a^3*Sec[e + f*x])*Tan[e + f*x])/(24*f) + (d*(a + a*Sec[e + f*x])^3*(c + d*Sec[e + f*x])*Tan[e + f*x])/(5*f)","A",9,7,31,0.2258,1,"{3987, 90, 80, 50, 63, 217, 203}"
204,1,125,0,0.1528054,"\int \sec (e+f x) (a+a \sec (e+f x))^3 (c+d \sec (e+f x)) \, dx","Int[Sec[e + f*x]*(a + a*Sec[e + f*x])^3*(c + d*Sec[e + f*x]),x]","\frac{a^3 (4 c+3 d) \tan ^3(e+f x)}{12 f}+\frac{a^3 (4 c+3 d) \tan (e+f x)}{f}+\frac{5 a^3 (4 c+3 d) \tanh ^{-1}(\sin (e+f x))}{8 f}+\frac{3 a^3 (4 c+3 d) \tan (e+f x) \sec (e+f x)}{8 f}+\frac{d \tan (e+f x) (a \sec (e+f x)+a)^3}{4 f}","\frac{a^3 (4 c+3 d) \tan ^3(e+f x)}{12 f}+\frac{a^3 (4 c+3 d) \tan (e+f x)}{f}+\frac{5 a^3 (4 c+3 d) \tanh ^{-1}(\sin (e+f x))}{8 f}+\frac{3 a^3 (4 c+3 d) \tan (e+f x) \sec (e+f x)}{8 f}+\frac{d \tan (e+f x) (a \sec (e+f x)+a)^3}{4 f}",1,"(5*a^3*(4*c + 3*d)*ArcTanh[Sin[e + f*x]])/(8*f) + (a^3*(4*c + 3*d)*Tan[e + f*x])/f + (3*a^3*(4*c + 3*d)*Sec[e + f*x]*Tan[e + f*x])/(8*f) + (d*(a + a*Sec[e + f*x])^3*Tan[e + f*x])/(4*f) + (a^3*(4*c + 3*d)*Tan[e + f*x]^3)/(12*f)","A",10,6,29,0.2069,1,"{4001, 3791, 3770, 3767, 8, 3768}"
205,1,257,0,0.3246123,"\int \frac{\sec (e+f x) (a+a \sec (e+f x))^3}{c+d \sec (e+f x)} \, dx","Int[(Sec[e + f*x]*(a + a*Sec[e + f*x])^3)/(c + d*Sec[e + f*x]),x]","\frac{a^4 \left(2 c^2-6 c d+7 d^2\right) \tan (e+f x) \tan ^{-1}\left(\frac{\sqrt{a-a \sec (e+f x)}}{\sqrt{a (\sec (e+f x)+1)}}\right)}{d^3 f \sqrt{a-a \sec (e+f x)} \sqrt{a \sec (e+f x)+a}}-\frac{a^3 (2 c-5 d) \tan (e+f x)}{2 d^2 f}+\frac{2 a^4 (c-d)^{5/2} \tan (e+f x) \tan ^{-1}\left(\frac{\sqrt{c+d} \sqrt{a \sec (e+f x)+a}}{\sqrt{c-d} \sqrt{a-a \sec (e+f x)}}\right)}{d^3 f \sqrt{c+d} \sqrt{a-a \sec (e+f x)} \sqrt{a \sec (e+f x)+a}}+\frac{\tan (e+f x) \left(a^3 \sec (e+f x)+a^3\right)}{2 d f}","\frac{a^3 \left(c^2-3 c d+3 d^2\right) \tanh ^{-1}(\sin (e+f x))}{d^3 f}-\frac{a^3 (c-3 d) \tan (e+f x)}{d^2 f}-\frac{2 a^3 (c-d)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c-d} \tan \left(\frac{1}{2} (e+f x)\right)}{\sqrt{c+d}}\right)}{d^3 f \sqrt{c+d}}+\frac{a^3 \tanh ^{-1}(\sin (e+f x))}{2 d f}+\frac{a^3 \tan (e+f x) \sec (e+f x)}{2 d f}",1,"-(a^3*(2*c - 5*d)*Tan[e + f*x])/(2*d^2*f) + (a^4*(2*c^2 - 6*c*d + 7*d^2)*ArcTan[Sqrt[a - a*Sec[e + f*x]]/Sqrt[a*(1 + Sec[e + f*x])]]*Tan[e + f*x])/(d^3*f*Sqrt[a - a*Sec[e + f*x]]*Sqrt[a + a*Sec[e + f*x]]) + (2*a^4*(c - d)^(5/2)*ArcTan[(Sqrt[c + d]*Sqrt[a + a*Sec[e + f*x]])/(Sqrt[c - d]*Sqrt[a - a*Sec[e + f*x]])]*Tan[e + f*x])/(d^3*Sqrt[c + d]*f*Sqrt[a - a*Sec[e + f*x]]*Sqrt[a + a*Sec[e + f*x]]) + ((a^3 + a^3*Sec[e + f*x])*Tan[e + f*x])/(2*d*f)","A",9,9,31,0.2903,1,"{3987, 102, 154, 157, 63, 217, 203, 93, 205}"
206,1,274,0,0.3548225,"\int \frac{\sec (e+f x) (a+a \sec (e+f x))^3}{(c+d \sec (e+f x))^2} \, dx","Int[(Sec[e + f*x]*(a + a*Sec[e + f*x])^3)/(c + d*Sec[e + f*x])^2,x]","\frac{2 a^3 c \tan (e+f x)}{d^2 f (c+d)}-\frac{2 a^4 (2 c-3 d) \tan (e+f x) \tan ^{-1}\left(\frac{\sqrt{a-a \sec (e+f x)}}{\sqrt{a (\sec (e+f x)+1)}}\right)}{d^3 f \sqrt{a-a \sec (e+f x)} \sqrt{a \sec (e+f x)+a}}-\frac{2 a^4 (c-d)^{3/2} (2 c+3 d) \tan (e+f x) \tan ^{-1}\left(\frac{\sqrt{c+d} \sqrt{a \sec (e+f x)+a}}{\sqrt{c-d} \sqrt{a-a \sec (e+f x)}}\right)}{d^3 f (c+d)^{3/2} \sqrt{a-a \sec (e+f x)} \sqrt{a \sec (e+f x)+a}}-\frac{(c-d) \tan (e+f x) \left(a^3 \sec (e+f x)+a^3\right)}{d f (c+d) (c+d \sec (e+f x))}","\frac{2 a^3 c \tan (e+f x)}{d^2 f (c+d)}-\frac{a^3 (2 c-3 d) \tanh ^{-1}(\sin (e+f x))}{d^3 f}+\frac{2 a^3 (c-d)^{3/2} (2 c+3 d) \tanh ^{-1}\left(\frac{\sqrt{c-d} \tan \left(\frac{1}{2} (e+f x)\right)}{\sqrt{c+d}}\right)}{d^3 f (c+d)^{3/2}}-\frac{(c-d) \tan (e+f x) \left(a^3 \sec (e+f x)+a^3\right)}{d f (c+d) (c+d \sec (e+f x))}",1,"(2*a^3*c*Tan[e + f*x])/(d^2*(c + d)*f) - (2*a^4*(2*c - 3*d)*ArcTan[Sqrt[a - a*Sec[e + f*x]]/Sqrt[a*(1 + Sec[e + f*x])]]*Tan[e + f*x])/(d^3*f*Sqrt[a - a*Sec[e + f*x]]*Sqrt[a + a*Sec[e + f*x]]) - (2*a^4*(c - d)^(3/2)*(2*c + 3*d)*ArcTan[(Sqrt[c + d]*Sqrt[a + a*Sec[e + f*x]])/(Sqrt[c - d]*Sqrt[a - a*Sec[e + f*x]])]*Tan[e + f*x])/(d^3*(c + d)^(3/2)*f*Sqrt[a - a*Sec[e + f*x]]*Sqrt[a + a*Sec[e + f*x]]) - ((c - d)*(a^3 + a^3*Sec[e + f*x])*Tan[e + f*x])/(d*(c + d)*f*(c + d*Sec[e + f*x]))","A",9,9,31,0.2903,1,"{3987, 98, 154, 157, 63, 217, 203, 93, 205}"
207,1,301,0,0.3944439,"\int \frac{\sec (e+f x) (a+a \sec (e+f x))^3}{(c+d \sec (e+f x))^3} \, dx","Int[(Sec[e + f*x]*(a + a*Sec[e + f*x])^3)/(c + d*Sec[e + f*x])^3,x]","\frac{a^4 \sqrt{c-d} \left(2 c^2+6 c d+7 d^2\right) \tan (e+f x) \tan ^{-1}\left(\frac{\sqrt{c+d} \sqrt{a \sec (e+f x)+a}}{\sqrt{c-d} \sqrt{a-a \sec (e+f x)}}\right)}{d^3 f (c+d)^{5/2} \sqrt{a-a \sec (e+f x)} \sqrt{a \sec (e+f x)+a}}-\frac{a^3 (c-d) (2 c+5 d) \tan (e+f x)}{2 d^2 f (c+d)^2 (c+d \sec (e+f x))}-\frac{(c-d) \tan (e+f x) \left(a^3 \sec (e+f x)+a^3\right)}{2 d f (c+d) (c+d \sec (e+f x))^2}+\frac{2 a^4 \tan (e+f x) \tan ^{-1}\left(\frac{\sqrt{a-a \sec (e+f x)}}{\sqrt{a (\sec (e+f x)+1)}}\right)}{d^3 f \sqrt{a-a \sec (e+f x)} \sqrt{a \sec (e+f x)+a}}","-\frac{a^3 \sqrt{c-d} \left(2 c^2+6 c d+7 d^2\right) \tanh ^{-1}\left(\frac{\sqrt{c-d} \tan \left(\frac{1}{2} (e+f x)\right)}{\sqrt{c+d}}\right)}{d^3 f (c+d)^{5/2}}-\frac{a^3 (c-d) (2 c+5 d) \tan (e+f x)}{2 d^2 f (c+d)^2 (c+d \sec (e+f x))}-\frac{(c-d) \tan (e+f x) \left(a^3 \sec (e+f x)+a^3\right)}{2 d f (c+d) (c+d \sec (e+f x))^2}+\frac{a^3 \tanh ^{-1}(\sin (e+f x))}{d^3 f}",1,"(2*a^4*ArcTan[Sqrt[a - a*Sec[e + f*x]]/Sqrt[a*(1 + Sec[e + f*x])]]*Tan[e + f*x])/(d^3*f*Sqrt[a - a*Sec[e + f*x]]*Sqrt[a + a*Sec[e + f*x]]) + (a^4*Sqrt[c - d]*(2*c^2 + 6*c*d + 7*d^2)*ArcTan[(Sqrt[c + d]*Sqrt[a + a*Sec[e + f*x]])/(Sqrt[c - d]*Sqrt[a - a*Sec[e + f*x]])]*Tan[e + f*x])/(d^3*(c + d)^(5/2)*f*Sqrt[a - a*Sec[e + f*x]]*Sqrt[a + a*Sec[e + f*x]]) - ((c - d)*(a^3 + a^3*Sec[e + f*x])*Tan[e + f*x])/(2*d*(c + d)*f*(c + d*Sec[e + f*x])^2) - (a^3*(c - d)*(2*c + 5*d)*Tan[e + f*x])/(2*d^2*(c + d)^2*f*(c + d*Sec[e + f*x]))","A",9,9,31,0.2903,1,"{3987, 98, 149, 157, 63, 217, 203, 93, 205}"
208,1,227,0,0.2231824,"\int \frac{\sec (e+f x) (a+a \sec (e+f x))^3}{(c+d \sec (e+f x))^4} \, dx","Int[(Sec[e + f*x]*(a + a*Sec[e + f*x])^3)/(c + d*Sec[e + f*x])^4,x]","-\frac{5 a^4 \tan (e+f x) \tan ^{-1}\left(\frac{\sqrt{c+d} \sqrt{a \sec (e+f x)+a}}{\sqrt{c-d} \sqrt{a-a \sec (e+f x)}}\right)}{f \sqrt{c-d} (c+d)^{7/2} \sqrt{a-a \sec (e+f x)} \sqrt{a \sec (e+f x)+a}}+\frac{5 a^3 \tan (e+f x)}{2 f (c+d)^3 (c+d \sec (e+f x))}+\frac{5 \tan (e+f x) \left(a^3 \sec (e+f x)+a^3\right)}{6 f (c+d)^2 (c+d \sec (e+f x))^2}+\frac{a \tan (e+f x) (a \sec (e+f x)+a)^2}{3 f (c+d) (c+d \sec (e+f x))^3}","\frac{5 a^3 \tanh ^{-1}\left(\frac{\sqrt{c-d} \tan \left(\frac{1}{2} (e+f x)\right)}{\sqrt{c+d}}\right)}{f \sqrt{c-d} (c+d)^{7/2}}+\frac{5 a^3 (c+4 d) \tan (e+f x)}{6 d f (c+d)^3 (c+d \sec (e+f x))}-\frac{5 a^3 (c-d) \tan (e+f x)}{6 d f (c+d)^2 (c+d \sec (e+f x))^2}+\frac{a \tan (e+f x) (a \sec (e+f x)+a)^2}{3 f (c+d) (c+d \sec (e+f x))^3}",1,"(-5*a^4*ArcTan[(Sqrt[c + d]*Sqrt[a + a*Sec[e + f*x]])/(Sqrt[c - d]*Sqrt[a - a*Sec[e + f*x]])]*Tan[e + f*x])/(Sqrt[c - d]*(c + d)^(7/2)*f*Sqrt[a - a*Sec[e + f*x]]*Sqrt[a + a*Sec[e + f*x]]) + (a*(a + a*Sec[e + f*x])^2*Tan[e + f*x])/(3*(c + d)*f*(c + d*Sec[e + f*x])^3) + (5*(a^3 + a^3*Sec[e + f*x])*Tan[e + f*x])/(6*(c + d)^2*f*(c + d*Sec[e + f*x])^2) + (5*a^3*Tan[e + f*x])/(2*(c + d)^3*f*(c + d*Sec[e + f*x]))","A",6,4,31,0.1290,1,"{3987, 94, 93, 205}"
209,1,327,0,0.3368296,"\int \frac{\sec (e+f x) (a+a \sec (e+f x))^3}{(c+d \sec (e+f x))^5} \, dx","Int[(Sec[e + f*x]*(a + a*Sec[e + f*x])^3)/(c + d*Sec[e + f*x])^5,x]","-\frac{5 a^4 (4 c-3 d) \tan (e+f x) \tan ^{-1}\left(\frac{\sqrt{c+d} \sqrt{a \sec (e+f x)+a}}{\sqrt{c-d} \sqrt{a-a \sec (e+f x)}}\right)}{4 f (c-d)^{3/2} (c+d)^{9/2} \sqrt{a-a \sec (e+f x)} \sqrt{a \sec (e+f x)+a}}+\frac{5 a^3 (4 c-3 d) \tan (e+f x)}{8 f (c-d) (c+d)^4 (c+d \sec (e+f x))}+\frac{5 (4 c-3 d) \tan (e+f x) \left(a^3 \sec (e+f x)+a^3\right)}{24 f (c-d) (c+d)^3 (c+d \sec (e+f x))^2}-\frac{d \tan (e+f x) (a \sec (e+f x)+a)^3}{4 f \left(c^2-d^2\right) (c+d \sec (e+f x))^4}+\frac{a (4 c-3 d) \tan (e+f x) (a \sec (e+f x)+a)^2}{12 f (c-d) (c+d)^2 (c+d \sec (e+f x))^3}","\frac{5 a^3 (4 c-3 d) \tanh ^{-1}\left(\frac{\sqrt{c-d} \tan \left(\frac{1}{2} (e+f x)\right)}{\sqrt{c+d}}\right)}{4 f (c-d)^{3/2} (c+d)^{9/2}}+\frac{5 a^3 (4 c-3 d) (c+4 d) \tan (e+f x)}{24 d f (c-d) (c+d)^4 (c+d \sec (e+f x))}-\frac{5 a^3 (4 c-3 d) \tan (e+f x)}{24 d f (c+d)^3 (c+d \sec (e+f x))^2}-\frac{d \tan (e+f x) (a \sec (e+f x)+a)^3}{4 f \left(c^2-d^2\right) (c+d \sec (e+f x))^4}+\frac{a (4 c-3 d) \tan (e+f x) (a \sec (e+f x)+a)^2}{12 f (c-d) (c+d)^2 (c+d \sec (e+f x))^3}",1,"(-5*a^4*(4*c - 3*d)*ArcTan[(Sqrt[c + d]*Sqrt[a + a*Sec[e + f*x]])/(Sqrt[c - d]*Sqrt[a - a*Sec[e + f*x]])]*Tan[e + f*x])/(4*(c - d)^(3/2)*(c + d)^(9/2)*f*Sqrt[a - a*Sec[e + f*x]]*Sqrt[a + a*Sec[e + f*x]]) - (d*(a + a*Sec[e + f*x])^3*Tan[e + f*x])/(4*(c^2 - d^2)*f*(c + d*Sec[e + f*x])^4) + (a*(4*c - 3*d)*(a + a*Sec[e + f*x])^2*Tan[e + f*x])/(12*(c - d)*(c + d)^2*f*(c + d*Sec[e + f*x])^3) + (5*(4*c - 3*d)*(a^3 + a^3*Sec[e + f*x])*Tan[e + f*x])/(24*(c - d)*(c + d)^3*f*(c + d*Sec[e + f*x])^2) + (5*a^3*(4*c - 3*d)*Tan[e + f*x])/(8*(c - d)*(c + d)^4*f*(c + d*Sec[e + f*x]))","A",7,5,31,0.1613,1,"{3987, 96, 94, 93, 205}"
210,1,236,0,0.3352728,"\int \frac{\sec (e+f x) (c+d \sec (e+f x))^4}{a+a \sec (e+f x)} \, dx","Int[(Sec[e + f*x]*(c + d*Sec[e + f*x])^4)/(a + a*Sec[e + f*x]),x]","\frac{d \left(-12 c^2 d+8 c^3+12 c d^2-3 d^3\right) \tan (e+f x) \tan ^{-1}\left(\frac{\sqrt{a-a \sec (e+f x)}}{\sqrt{a (\sec (e+f x)+1)}}\right)}{f \sqrt{a-a \sec (e+f x)} \sqrt{a \sec (e+f x)+a}}-\frac{d \tan (e+f x) \left(d \left(6 c^2-20 c d+9 d^2\right) \sec (e+f x)+4 \left(-16 c^2 d+3 c^3+12 c d^2-4 d^3\right)\right)}{6 a f}+\frac{(c-d) \tan (e+f x) (c+d \sec (e+f x))^3}{f (a \sec (e+f x)+a)}-\frac{d (3 c-4 d) \tan (e+f x) (c+d \sec (e+f x))^2}{3 a f}","\frac{d \left(-12 c^2 d+8 c^3+12 c d^2-3 d^3\right) \tanh ^{-1}(\sin (e+f x))}{2 a f}-\frac{d \tan (e+f x) \left(d \left(6 c^2-20 c d+9 d^2\right) \sec (e+f x)+4 \left(-16 c^2 d+3 c^3+12 c d^2-4 d^3\right)\right)}{6 a f}+\frac{(c-d) \tan (e+f x) (c+d \sec (e+f x))^3}{f (a \sec (e+f x)+a)}-\frac{d (3 c-4 d) \tan (e+f x) (c+d \sec (e+f x))^2}{3 a f}",1,"(d*(8*c^3 - 12*c^2*d + 12*c*d^2 - 3*d^3)*ArcTan[Sqrt[a - a*Sec[e + f*x]]/Sqrt[a*(1 + Sec[e + f*x])]]*Tan[e + f*x])/(f*Sqrt[a - a*Sec[e + f*x]]*Sqrt[a + a*Sec[e + f*x]]) - ((3*c - 4*d)*d*(c + d*Sec[e + f*x])^2*Tan[e + f*x])/(3*a*f) + ((c - d)*(c + d*Sec[e + f*x])^3*Tan[e + f*x])/(f*(a + a*Sec[e + f*x])) - (d*(4*(3*c^3 - 16*c^2*d + 12*c*d^2 - 4*d^3) + d*(6*c^2 - 20*c*d + 9*d^2)*Sec[e + f*x])*Tan[e + f*x])/(6*a*f)","A",7,7,31,0.2258,1,"{3987, 98, 153, 147, 63, 217, 203}"
211,1,171,0,0.2537385,"\int \frac{\sec (e+f x) (c+d \sec (e+f x))^3}{a+a \sec (e+f x)} \, dx","Int[(Sec[e + f*x]*(c + d*Sec[e + f*x])^3)/(a + a*Sec[e + f*x]),x]","\frac{3 d \left(2 c^2-2 c d+d^2\right) \tan (e+f x) \tan ^{-1}\left(\frac{\sqrt{a-a \sec (e+f x)}}{\sqrt{a (\sec (e+f x)+1)}}\right)}{f \sqrt{a-a \sec (e+f x)} \sqrt{a \sec (e+f x)+a}}-\frac{d \tan (e+f x) \left(4 \left(c^2-3 c d+d^2\right)+d (2 c-3 d) \sec (e+f x)\right)}{2 a f}+\frac{(c-d) \tan (e+f x) (c+d \sec (e+f x))^2}{f (a \sec (e+f x)+a)}","\frac{3 d \left(2 c^2-2 c d+d^2\right) \tanh ^{-1}(\sin (e+f x))}{2 a f}-\frac{d \tan (e+f x) \left(4 \left(c^2-3 c d+d^2\right)+d (2 c-3 d) \sec (e+f x)\right)}{2 a f}+\frac{(c-d) \tan (e+f x) (c+d \sec (e+f x))^2}{f (a \sec (e+f x)+a)}",1,"(3*d*(2*c^2 - 2*c*d + d^2)*ArcTan[Sqrt[a - a*Sec[e + f*x]]/Sqrt[a*(1 + Sec[e + f*x])]]*Tan[e + f*x])/(f*Sqrt[a - a*Sec[e + f*x]]*Sqrt[a + a*Sec[e + f*x]]) + ((c - d)*(c + d*Sec[e + f*x])^2*Tan[e + f*x])/(f*(a + a*Sec[e + f*x])) - (d*(4*(c^2 - 3*c*d + d^2) + (2*c - 3*d)*d*Sec[e + f*x])*Tan[e + f*x])/(2*a*f)","A",6,6,31,0.1935,1,"{3987, 98, 147, 63, 217, 203}"
212,1,125,0,0.1455299,"\int \frac{\sec (e+f x) (c+d \sec (e+f x))^2}{a+a \sec (e+f x)} \, dx","Int[(Sec[e + f*x]*(c + d*Sec[e + f*x])^2)/(a + a*Sec[e + f*x]),x]","\frac{2 d (2 c-d) \tan (e+f x) \tan ^{-1}\left(\frac{\sqrt{a-a \sec (e+f x)}}{\sqrt{a (\sec (e+f x)+1)}}\right)}{f \sqrt{a-a \sec (e+f x)} \sqrt{a \sec (e+f x)+a}}+\frac{(c-d)^2 \tan (e+f x)}{f (a \sec (e+f x)+a)}+\frac{d^2 \tan (e+f x)}{a f}","\frac{d (2 c-d) \tanh ^{-1}(\sin (e+f x))}{a f}+\frac{(c-d)^2 \tan (e+f x)}{f (a \sec (e+f x)+a)}+\frac{d^2 \tan (e+f x)}{a f}",1,"(d^2*Tan[e + f*x])/(a*f) + ((c - d)^2*Tan[e + f*x])/(f*(a + a*Sec[e + f*x])) + (2*(2*c - d)*d*ArcTan[Sqrt[a - a*Sec[e + f*x]]/Sqrt[a*(1 + Sec[e + f*x])]]*Tan[e + f*x])/(f*Sqrt[a - a*Sec[e + f*x]]*Sqrt[a + a*Sec[e + f*x]])","A",6,6,31,0.1935,1,"{3987, 89, 80, 63, 217, 203}"
213,1,43,0,0.084563,"\int \frac{\sec (e+f x) (c+d \sec (e+f x))}{a+a \sec (e+f x)} \, dx","Int[(Sec[e + f*x]*(c + d*Sec[e + f*x]))/(a + a*Sec[e + f*x]),x]","\frac{(c-d) \tan (e+f x)}{f (a \sec (e+f x)+a)}+\frac{d \tanh ^{-1}(\sin (e+f x))}{a f}","\frac{(c-d) \tan (e+f x)}{f (a \sec (e+f x)+a)}+\frac{d \tanh ^{-1}(\sin (e+f x))}{a f}",1,"(d*ArcTanh[Sin[e + f*x]])/(a*f) + ((c - d)*Tan[e + f*x])/(f*(a + a*Sec[e + f*x]))","A",3,3,29,0.1034,1,"{3998, 3770, 3794}"
214,1,134,0,0.1550814,"\int \frac{\sec (e+f x)}{(a+a \sec (e+f x)) (c+d \sec (e+f x))} \, dx","Int[Sec[e + f*x]/((a + a*Sec[e + f*x])*(c + d*Sec[e + f*x])),x]","\frac{2 d \tan (e+f x) \tan ^{-1}\left(\frac{\sqrt{c+d} \sqrt{a \sec (e+f x)+a}}{\sqrt{c-d} \sqrt{a-a \sec (e+f x)}}\right)}{f (c-d)^{3/2} \sqrt{c+d} \sqrt{a-a \sec (e+f x)} \sqrt{a \sec (e+f x)+a}}+\frac{\tan (e+f x)}{f (c-d) (a \sec (e+f x)+a)}","\frac{\tan (e+f x)}{f (c-d) (a \sec (e+f x)+a)}-\frac{2 d \tanh ^{-1}\left(\frac{\sqrt{c-d} \tan \left(\frac{1}{2} (e+f x)\right)}{\sqrt{c+d}}\right)}{a f (c-d)^{3/2} \sqrt{c+d}}",1,"Tan[e + f*x]/((c - d)*f*(a + a*Sec[e + f*x])) + (2*d*ArcTan[(Sqrt[c + d]*Sqrt[a + a*Sec[e + f*x]])/(Sqrt[c - d]*Sqrt[a - a*Sec[e + f*x]])]*Tan[e + f*x])/((c - d)^(3/2)*Sqrt[c + d]*f*Sqrt[a - a*Sec[e + f*x]]*Sqrt[a + a*Sec[e + f*x]])","A",4,4,31,0.1290,1,"{3987, 96, 93, 205}"
215,1,196,0,0.2529917,"\int \frac{\sec (e+f x)}{(a+a \sec (e+f x)) (c+d \sec (e+f x))^2} \, dx","Int[Sec[e + f*x]/((a + a*Sec[e + f*x])*(c + d*Sec[e + f*x])^2),x]","-\frac{d \tan (e+f x)}{f \left(c^2-d^2\right) (a \sec (e+f x)+a) (c+d \sec (e+f x))}+\frac{2 d (2 c+d) \tan (e+f x) \tan ^{-1}\left(\frac{\sqrt{c+d} \sqrt{a \sec (e+f x)+a}}{\sqrt{c-d} \sqrt{a-a \sec (e+f x)}}\right)}{f (c-d)^{5/2} (c+d)^{3/2} \sqrt{a-a \sec (e+f x)} \sqrt{a \sec (e+f x)+a}}+\frac{(c+2 d) \tan (e+f x)}{f (c-d)^2 (c+d) (a \sec (e+f x)+a)}","-\frac{d \tan (e+f x)}{f \left(c^2-d^2\right) (a \sec (e+f x)+a) (c+d \sec (e+f x))}-\frac{2 d (2 c+d) \tanh ^{-1}\left(\frac{\sqrt{c-d} \tan \left(\frac{1}{2} (e+f x)\right)}{\sqrt{c+d}}\right)}{a f (c-d)^{5/2} (c+d)^{3/2}}+\frac{(c+2 d) \tan (e+f x)}{f (c-d)^2 (c+d) (a \sec (e+f x)+a)}",1,"((c + 2*d)*Tan[e + f*x])/((c - d)^2*(c + d)*f*(a + a*Sec[e + f*x])) + (2*d*(2*c + d)*ArcTan[(Sqrt[c + d]*Sqrt[a + a*Sec[e + f*x]])/(Sqrt[c - d]*Sqrt[a - a*Sec[e + f*x]])]*Tan[e + f*x])/((c - d)^(5/2)*(c + d)^(3/2)*f*Sqrt[a - a*Sec[e + f*x]]*Sqrt[a + a*Sec[e + f*x]]) - (d*Tan[e + f*x])/((c^2 - d^2)*f*(a + a*Sec[e + f*x])*(c + d*Sec[e + f*x]))","A",6,6,31,0.1935,1,"{3987, 103, 152, 12, 93, 205}"
216,1,268,0,0.4000002,"\int \frac{\sec (e+f x)}{(a+a \sec (e+f x)) (c+d \sec (e+f x))^3} \, dx","Int[Sec[e + f*x]/((a + a*Sec[e + f*x])*(c + d*Sec[e + f*x])^3),x]","\frac{3 d \left(2 c^2+2 c d+d^2\right) \tan (e+f x) \tan ^{-1}\left(\frac{\sqrt{c+d} \sqrt{a \sec (e+f x)+a}}{\sqrt{c-d} \sqrt{a-a \sec (e+f x)}}\right)}{f (c-d)^{7/2} (c+d)^{5/2} \sqrt{a-a \sec (e+f x)} \sqrt{a \sec (e+f x)+a}}-\frac{d (4 c+d) \tan (e+f x)}{2 f \left(c^2-d^2\right)^2 (a \sec (e+f x)+a) (c+d \sec (e+f x))}-\frac{d \tan (e+f x)}{2 f \left(c^2-d^2\right) (a \sec (e+f x)+a) (c+d \sec (e+f x))^2}+\frac{(2 c+d) (c+4 d) \tan (e+f x)}{2 f (c-d)^3 (c+d)^2 (a \sec (e+f x)+a)}","-\frac{3 d \left(2 c^2+2 c d+d^2\right) \tanh ^{-1}\left(\frac{\sqrt{c-d} \tan \left(\frac{1}{2} (e+f x)\right)}{\sqrt{c+d}}\right)}{a f (c-d)^{7/2} (c+d)^{5/2}}+\frac{d (2 c+d) (c+4 d) \tan (e+f x)}{2 a f (c-d)^3 (c+d)^2 (c+d \sec (e+f x))}+\frac{d (2 c+3 d) \tan (e+f x)}{2 a f (c-d)^2 (c+d) (c+d \sec (e+f x))^2}+\frac{\tan (e+f x)}{f (c-d) (a \sec (e+f x)+a) (c+d \sec (e+f x))^2}",1,"((2*c + d)*(c + 4*d)*Tan[e + f*x])/(2*(c - d)^3*(c + d)^2*f*(a + a*Sec[e + f*x])) + (3*d*(2*c^2 + 2*c*d + d^2)*ArcTan[(Sqrt[c + d]*Sqrt[a + a*Sec[e + f*x]])/(Sqrt[c - d]*Sqrt[a - a*Sec[e + f*x]])]*Tan[e + f*x])/((c - d)^(7/2)*(c + d)^(5/2)*f*Sqrt[a - a*Sec[e + f*x]]*Sqrt[a + a*Sec[e + f*x]]) - (d*Tan[e + f*x])/(2*(c^2 - d^2)*f*(a + a*Sec[e + f*x])*(c + d*Sec[e + f*x])^2) - (d*(4*c + d)*Tan[e + f*x])/(2*(c^2 - d^2)^2*f*(a + a*Sec[e + f*x])*(c + d*Sec[e + f*x]))","A",7,7,31,0.2258,1,"{3987, 103, 151, 152, 12, 93, 205}"
217,1,315,0,0.4377758,"\int \frac{\sec (e+f x) (c+d \sec (e+f x))^5}{(a+a \sec (e+f x))^2} \, dx","Int[(Sec[e + f*x]*(c + d*Sec[e + f*x])^5)/(a + a*Sec[e + f*x])^2,x]","-\frac{d \left(c^2+10 c d-12 d^2\right) \tan (e+f x) (c+d \sec (e+f x))^2}{3 a^2 f}-\frac{d \tan (e+f x) \left(d \left(20 c^2 d+2 c^3-57 c d^2+30 d^3\right) \sec (e+f x)+4 \left(-44 c^2 d^2+10 c^3 d+c^4+40 c d^3-12 d^4\right)\right)}{6 a^2 f}+\frac{(c-d) (c+10 d) \tan (e+f x) (c+d \sec (e+f x))^3}{3 f \left(a^2 \sec (e+f x)+a^2\right)}+\frac{5 d^2 (2 c-d) \left(2 c^2-3 c d+2 d^2\right) \tan (e+f x) \tan ^{-1}\left(\frac{\sqrt{a-a \sec (e+f x)}}{\sqrt{a (\sec (e+f x)+1)}}\right)}{a f \sqrt{a-a \sec (e+f x)} \sqrt{a \sec (e+f x)+a}}+\frac{(c-d) \tan (e+f x) (c+d \sec (e+f x))^4}{3 f (a \sec (e+f x)+a)^2}","\frac{5 d^2 (2 c-d) \left(2 c^2-3 c d+2 d^2\right) \tanh ^{-1}(\sin (e+f x))}{2 a^2 f}-\frac{d \left(c^2+10 c d-12 d^2\right) \tan (e+f x) (c+d \sec (e+f x))^2}{3 a^2 f}-\frac{d \tan (e+f x) \left(d \left(20 c^2 d+2 c^3-57 c d^2+30 d^3\right) \sec (e+f x)+4 \left(-44 c^2 d^2+10 c^3 d+c^4+40 c d^3-12 d^4\right)\right)}{6 a^2 f}+\frac{(c-d) (c+10 d) \tan (e+f x) (c+d \sec (e+f x))^3}{3 f \left(a^2 \sec (e+f x)+a^2\right)}+\frac{(c-d) \tan (e+f x) (c+d \sec (e+f x))^4}{3 f (a \sec (e+f x)+a)^2}",1,"(5*(2*c - d)*d^2*(2*c^2 - 3*c*d + 2*d^2)*ArcTan[Sqrt[a - a*Sec[e + f*x]]/Sqrt[a*(1 + Sec[e + f*x])]]*Tan[e + f*x])/(a*f*Sqrt[a - a*Sec[e + f*x]]*Sqrt[a + a*Sec[e + f*x]]) - (d*(c^2 + 10*c*d - 12*d^2)*(c + d*Sec[e + f*x])^2*Tan[e + f*x])/(3*a^2*f) + ((c - d)*(c + 10*d)*(c + d*Sec[e + f*x])^3*Tan[e + f*x])/(3*f*(a^2 + a^2*Sec[e + f*x])) + ((c - d)*(c + d*Sec[e + f*x])^4*Tan[e + f*x])/(3*f*(a + a*Sec[e + f*x])^2) - (d*(4*(c^4 + 10*c^3*d - 44*c^2*d^2 + 40*c*d^3 - 12*d^4) + d*(2*c^3 + 20*c^2*d - 57*c*d^2 + 30*d^3)*Sec[e + f*x])*Tan[e + f*x])/(6*a^2*f)","A",8,8,31,0.2581,1,"{3987, 98, 150, 153, 147, 63, 217, 203}"
218,1,249,0,0.3201141,"\int \frac{\sec (e+f x) (c+d \sec (e+f x))^4}{(a+a \sec (e+f x))^2} \, dx","Int[(Sec[e + f*x]*(c + d*Sec[e + f*x])^4)/(a + a*Sec[e + f*x])^2,x]","-\frac{d \tan (e+f x) \left(d \left(2 c^2+16 c d-21 d^2\right) \sec (e+f x)+4 \left(8 c^2 d+c^3-20 c d^2+8 d^3\right)\right)}{6 a^2 f}+\frac{(c-d) (c+8 d) \tan (e+f x) (c+d \sec (e+f x))^2}{3 f \left(a^2 \sec (e+f x)+a^2\right)}+\frac{d^2 \left(12 c^2-16 c d+7 d^2\right) \tan (e+f x) \tan ^{-1}\left(\frac{\sqrt{a-a \sec (e+f x)}}{\sqrt{a (\sec (e+f x)+1)}}\right)}{a f \sqrt{a-a \sec (e+f x)} \sqrt{a \sec (e+f x)+a}}+\frac{(c-d) \tan (e+f x) (c+d \sec (e+f x))^3}{3 f (a \sec (e+f x)+a)^2}","\frac{d^2 \left(12 c^2-16 c d+7 d^2\right) \tanh ^{-1}(\sin (e+f x))}{2 a^2 f}-\frac{d \tan (e+f x) \left(d \left(2 c^2+16 c d-21 d^2\right) \sec (e+f x)+4 \left(8 c^2 d+c^3-20 c d^2+8 d^3\right)\right)}{6 a^2 f}+\frac{(c-d) (c+8 d) \tan (e+f x) (c+d \sec (e+f x))^2}{3 f \left(a^2 \sec (e+f x)+a^2\right)}+\frac{(c-d) \tan (e+f x) (c+d \sec (e+f x))^3}{3 f (a \sec (e+f x)+a)^2}",1,"(d^2*(12*c^2 - 16*c*d + 7*d^2)*ArcTan[Sqrt[a - a*Sec[e + f*x]]/Sqrt[a*(1 + Sec[e + f*x])]]*Tan[e + f*x])/(a*f*Sqrt[a - a*Sec[e + f*x]]*Sqrt[a + a*Sec[e + f*x]]) + ((c - d)*(c + 8*d)*(c + d*Sec[e + f*x])^2*Tan[e + f*x])/(3*f*(a^2 + a^2*Sec[e + f*x])) + ((c - d)*(c + d*Sec[e + f*x])^3*Tan[e + f*x])/(3*f*(a + a*Sec[e + f*x])^2) - (d*(4*(c^3 + 8*c^2*d - 20*c*d^2 + 8*d^3) + d*(2*c^2 + 16*c*d - 21*d^2)*Sec[e + f*x])*Tan[e + f*x])/(6*a^2*f)","A",7,7,31,0.2258,1,"{3987, 98, 150, 147, 63, 217, 203}"
219,1,193,0,0.2330374,"\int \frac{\sec (e+f x) (c+d \sec (e+f x))^3}{(a+a \sec (e+f x))^2} \, dx","Int[(Sec[e + f*x]*(c + d*Sec[e + f*x])^3)/(a + a*Sec[e + f*x])^2,x]","\frac{\tan (e+f x) \left(4 c^2 d+c^3-d^2 (c-4 d) \sec (e+f x)-12 c d^2+10 d^3\right)}{3 f \left(a^2 \sec (e+f x)+a^2\right)}+\frac{2 d^2 (3 c-2 d) \tan (e+f x) \tan ^{-1}\left(\frac{\sqrt{a-a \sec (e+f x)}}{\sqrt{a (\sec (e+f x)+1)}}\right)}{a f \sqrt{a-a \sec (e+f x)} \sqrt{a \sec (e+f x)+a}}+\frac{(c-d) \tan (e+f x) (c+d \sec (e+f x))^2}{3 f (a \sec (e+f x)+a)^2}","\frac{\tan (e+f x) \left(4 c^2 d+c^3-d^2 (c-4 d) \sec (e+f x)-12 c d^2+10 d^3\right)}{3 f \left(a^2 \sec (e+f x)+a^2\right)}+\frac{d^2 (3 c-2 d) \tanh ^{-1}(\sin (e+f x))}{a^2 f}+\frac{(c-d) \tan (e+f x) (c+d \sec (e+f x))^2}{3 f (a \sec (e+f x)+a)^2}",1,"(2*(3*c - 2*d)*d^2*ArcTan[Sqrt[a - a*Sec[e + f*x]]/Sqrt[a*(1 + Sec[e + f*x])]]*Tan[e + f*x])/(a*f*Sqrt[a - a*Sec[e + f*x]]*Sqrt[a + a*Sec[e + f*x]]) + ((c - d)*(c + d*Sec[e + f*x])^2*Tan[e + f*x])/(3*f*(a + a*Sec[e + f*x])^2) + ((c^3 + 4*c^2*d - 12*c*d^2 + 10*d^3 - (c - 4*d)*d^2*Sec[e + f*x])*Tan[e + f*x])/(3*f*(a^2 + a^2*Sec[e + f*x]))","A",6,6,31,0.1935,1,"{3987, 98, 143, 63, 217, 203}"
220,1,149,0,0.1539593,"\int \frac{\sec (e+f x) (c+d \sec (e+f x))^2}{(a+a \sec (e+f x))^2} \, dx","Int[(Sec[e + f*x]*(c + d*Sec[e + f*x])^2)/(a + a*Sec[e + f*x])^2,x]","\frac{(c+5 d) (c-d) \tan (e+f x)}{3 f \left(a^2 \sec (e+f x)+a^2\right)}+\frac{(c-d)^2 \tan (e+f x)}{3 f (a \sec (e+f x)+a)^2}+\frac{2 d^2 \tan (e+f x) \tan ^{-1}\left(\frac{\sqrt{a-a \sec (e+f x)}}{\sqrt{a (\sec (e+f x)+1)}}\right)}{a f \sqrt{a-a \sec (e+f x)} \sqrt{a \sec (e+f x)+a}}","\frac{(c+5 d) (c-d) \tan (e+f x)}{3 f \left(a^2 \sec (e+f x)+a^2\right)}+\frac{d^2 \tanh ^{-1}(\sin (e+f x))}{a^2 f}+\frac{(c-d)^2 \tan (e+f x)}{3 f (a \sec (e+f x)+a)^2}",1,"((c - d)^2*Tan[e + f*x])/(3*f*(a + a*Sec[e + f*x])^2) + (2*d^2*ArcTan[Sqrt[a - a*Sec[e + f*x]]/Sqrt[a*(1 + Sec[e + f*x])]]*Tan[e + f*x])/(a*f*Sqrt[a - a*Sec[e + f*x]]*Sqrt[a + a*Sec[e + f*x]]) + ((c - d)*(c + 5*d)*Tan[e + f*x])/(3*f*(a^2 + a^2*Sec[e + f*x]))","A",6,6,31,0.1935,1,"{3987, 89, 78, 63, 217, 203}"
221,1,65,0,0.0865492,"\int \frac{\sec (e+f x) (c+d \sec (e+f x))}{(a+a \sec (e+f x))^2} \, dx","Int[(Sec[e + f*x]*(c + d*Sec[e + f*x]))/(a + a*Sec[e + f*x])^2,x]","\frac{(c+2 d) \tan (e+f x)}{3 f \left(a^2 \sec (e+f x)+a^2\right)}+\frac{(c-d) \tan (e+f x)}{3 f (a \sec (e+f x)+a)^2}","\frac{(c+2 d) \tan (e+f x)}{3 f \left(a^2 \sec (e+f x)+a^2\right)}+\frac{(c-d) \tan (e+f x)}{3 f (a \sec (e+f x)+a)^2}",1,"((c - d)*Tan[e + f*x])/(3*f*(a + a*Sec[e + f*x])^2) + ((c + 2*d)*Tan[e + f*x])/(3*f*(a^2 + a^2*Sec[e + f*x]))","A",2,2,29,0.06897,1,"{4000, 3794}"
222,1,183,0,0.241377,"\int \frac{\sec (e+f x)}{(a+a \sec (e+f x))^2 (c+d \sec (e+f x))} \, dx","Int[Sec[e + f*x]/((a + a*Sec[e + f*x])^2*(c + d*Sec[e + f*x])),x]","\frac{(c-4 d) \tan (e+f x)}{3 f (c-d)^2 \left(a^2 \sec (e+f x)+a^2\right)}-\frac{2 d^2 \tan (e+f x) \tan ^{-1}\left(\frac{\sqrt{c+d} \sqrt{a \sec (e+f x)+a}}{\sqrt{c-d} \sqrt{a-a \sec (e+f x)}}\right)}{a f (c-d)^{5/2} \sqrt{c+d} \sqrt{a-a \sec (e+f x)} \sqrt{a \sec (e+f x)+a}}+\frac{\tan (e+f x)}{3 f (c-d) (a \sec (e+f x)+a)^2}","\frac{2 d^2 \tanh ^{-1}\left(\frac{\sqrt{c-d} \tan \left(\frac{1}{2} (e+f x)\right)}{\sqrt{c+d}}\right)}{a^2 f (c-d)^{5/2} \sqrt{c+d}}+\frac{(c-4 d) \tan (e+f x)}{3 f (c-d)^2 \left(a^2 \sec (e+f x)+a^2\right)}+\frac{\tan (e+f x)}{3 f (c-d) (a \sec (e+f x)+a)^2}",1,"Tan[e + f*x]/(3*(c - d)*f*(a + a*Sec[e + f*x])^2) - (2*d^2*ArcTan[(Sqrt[c + d]*Sqrt[a + a*Sec[e + f*x]])/(Sqrt[c - d]*Sqrt[a - a*Sec[e + f*x]])]*Tan[e + f*x])/(a*(c - d)^(5/2)*Sqrt[c + d]*f*Sqrt[a - a*Sec[e + f*x]]*Sqrt[a + a*Sec[e + f*x]]) + ((c - 4*d)*Tan[e + f*x])/(3*(c - d)^2*f*(a^2 + a^2*Sec[e + f*x]))","A",6,6,31,0.1935,1,"{3987, 104, 152, 12, 93, 205}"
223,1,260,0,0.3734577,"\int \frac{\sec (e+f x)}{(a+a \sec (e+f x))^2 (c+d \sec (e+f x))^2} \, dx","Int[Sec[e + f*x]/((a + a*Sec[e + f*x])^2*(c + d*Sec[e + f*x])^2),x]","\frac{\left(c^2-6 c d-10 d^2\right) \tan (e+f x)}{3 f (c-d)^3 (c+d) \left(a^2 \sec (e+f x)+a^2\right)}-\frac{d \tan (e+f x)}{f \left(c^2-d^2\right) (a \sec (e+f x)+a)^2 (c+d \sec (e+f x))}-\frac{2 d^2 (3 c+2 d) \tan (e+f x) \tan ^{-1}\left(\frac{\sqrt{c+d} \sqrt{a \sec (e+f x)+a}}{\sqrt{c-d} \sqrt{a-a \sec (e+f x)}}\right)}{a f (c-d)^{7/2} (c+d)^{3/2} \sqrt{a-a \sec (e+f x)} \sqrt{a \sec (e+f x)+a}}+\frac{(c+4 d) \tan (e+f x)}{3 f (c-d)^2 (c+d) (a \sec (e+f x)+a)^2}","\frac{d \left(c^2-6 c d-10 d^2\right) \tan (e+f x)}{3 a^2 f (c-d)^3 (c+d) (c+d \sec (e+f x))}+\frac{2 d^2 (3 c+2 d) \tanh ^{-1}\left(\frac{\sqrt{c-d} \tan \left(\frac{1}{2} (e+f x)\right)}{\sqrt{c+d}}\right)}{a^2 f (c-d)^{7/2} (c+d)^{3/2}}+\frac{(c-6 d) \tan (e+f x)}{3 a^2 f (c-d)^2 (\sec (e+f x)+1) (c+d \sec (e+f x))}+\frac{\tan (e+f x)}{3 f (c-d) (a \sec (e+f x)+a)^2 (c+d \sec (e+f x))}",1,"((c + 4*d)*Tan[e + f*x])/(3*(c - d)^2*(c + d)*f*(a + a*Sec[e + f*x])^2) - (2*d^2*(3*c + 2*d)*ArcTan[(Sqrt[c + d]*Sqrt[a + a*Sec[e + f*x]])/(Sqrt[c - d]*Sqrt[a - a*Sec[e + f*x]])]*Tan[e + f*x])/(a*(c - d)^(7/2)*(c + d)^(3/2)*f*Sqrt[a - a*Sec[e + f*x]]*Sqrt[a + a*Sec[e + f*x]]) + ((c^2 - 6*c*d - 10*d^2)*Tan[e + f*x])/(3*(c - d)^3*(c + d)*f*(a^2 + a^2*Sec[e + f*x])) - (d*Tan[e + f*x])/((c^2 - d^2)*f*(a + a*Sec[e + f*x])^2*(c + d*Sec[e + f*x]))","A",7,6,31,0.1935,1,"{3987, 103, 152, 12, 93, 205}"
224,1,346,0,0.5576502,"\int \frac{\sec (e+f x)}{(a+a \sec (e+f x))^2 (c+d \sec (e+f x))^3} \, dx","Int[Sec[e + f*x]/((a + a*Sec[e + f*x])^2*(c + d*Sec[e + f*x])^3),x]","\frac{\left(-16 c^2 d+2 c^3-59 c d^2-32 d^3\right) \tan (e+f x)}{6 f (c-d)^4 (c+d)^2 \left(a^2 \sec (e+f x)+a^2\right)}-\frac{d^2 \left(12 c^2+16 c d+7 d^2\right) \tan (e+f x) \tan ^{-1}\left(\frac{\sqrt{c+d} \sqrt{a \sec (e+f x)+a}}{\sqrt{c-d} \sqrt{a-a \sec (e+f x)}}\right)}{a f (c-d)^{9/2} (c+d)^{5/2} \sqrt{a-a \sec (e+f x)} \sqrt{a \sec (e+f x)+a}}-\frac{d (5 c+2 d) \tan (e+f x)}{2 f \left(c^2-d^2\right)^2 (a \sec (e+f x)+a)^2 (c+d \sec (e+f x))}-\frac{d \tan (e+f x)}{2 f \left(c^2-d^2\right) (a \sec (e+f x)+a)^2 (c+d \sec (e+f x))^2}+\frac{\left(2 c^2+22 c d+11 d^2\right) \tan (e+f x)}{6 f (c-d)^3 (c+d)^2 (a \sec (e+f x)+a)^2}","\frac{d^2 \left(12 c^2+16 c d+7 d^2\right) \tanh ^{-1}\left(\frac{\sqrt{c-d} \tan \left(\frac{1}{2} (e+f x)\right)}{\sqrt{c+d}}\right)}{a^2 f (c-d)^{9/2} (c+d)^{5/2}}+\frac{d \left(-16 c^2 d+2 c^3-59 c d^2-32 d^3\right) \tan (e+f x)}{6 a^2 f (c-d)^4 (c+d)^2 (c+d \sec (e+f x))}+\frac{d \left(2 c^2-16 c d-21 d^2\right) \tan (e+f x)}{6 a^2 f (c-d)^3 (c+d) (c+d \sec (e+f x))^2}+\frac{(c-8 d) \tan (e+f x)}{3 a^2 f (c-d)^2 (\sec (e+f x)+1) (c+d \sec (e+f x))^2}+\frac{\tan (e+f x)}{3 f (c-d) (a \sec (e+f x)+a)^2 (c+d \sec (e+f x))^2}",1,"((2*c^2 + 22*c*d + 11*d^2)*Tan[e + f*x])/(6*(c - d)^3*(c + d)^2*f*(a + a*Sec[e + f*x])^2) - (d^2*(12*c^2 + 16*c*d + 7*d^2)*ArcTan[(Sqrt[c + d]*Sqrt[a + a*Sec[e + f*x]])/(Sqrt[c - d]*Sqrt[a - a*Sec[e + f*x]])]*Tan[e + f*x])/(a*(c - d)^(9/2)*(c + d)^(5/2)*f*Sqrt[a - a*Sec[e + f*x]]*Sqrt[a + a*Sec[e + f*x]]) + ((2*c^3 - 16*c^2*d - 59*c*d^2 - 32*d^3)*Tan[e + f*x])/(6*(c - d)^4*(c + d)^2*f*(a^2 + a^2*Sec[e + f*x])) - (d*Tan[e + f*x])/(2*(c^2 - d^2)*f*(a + a*Sec[e + f*x])^2*(c + d*Sec[e + f*x])^2) - (d*(5*c + 2*d)*Tan[e + f*x])/(2*(c^2 - d^2)^2*f*(a + a*Sec[e + f*x])^2*(c + d*Sec[e + f*x]))","A",8,7,31,0.2258,1,"{3987, 103, 151, 152, 12, 93, 205}"
225,1,405,0,0.5386176,"\int \frac{\sec (e+f x) (c+d \sec (e+f x))^6}{(a+a \sec (e+f x))^3} \, dx","Int[(Sec[e + f*x]*(c + d*Sec[e + f*x])^6)/(a + a*Sec[e + f*x])^3,x]","\frac{d^3 \left(-90 c^2 d+40 c^3+78 c d^2-23 d^3\right) \tan (e+f x) \tan ^{-1}\left(\frac{\sqrt{a-a \sec (e+f x)}}{\sqrt{a (\sec (e+f x)+1)}}\right)}{a^2 f \sqrt{a-a \sec (e+f x)} \sqrt{a \sec (e+f x)+a}}+\frac{(c-d) \left(2 c^2+18 c d+115 d^2\right) \tan (e+f x) (c+d \sec (e+f x))^3}{15 f \left(a^3 \sec (e+f x)+a^3\right)}-\frac{d \left(18 c^2 d+2 c^3+111 c d^2-136 d^3\right) \tan (e+f x) (c+d \sec (e+f x))^2}{15 a^3 f}-\frac{d \tan (e+f x) \left(d \left(216 c^2 d^2+36 c^3 d+4 c^4-626 c d^3+345 d^4\right) \sec (e+f x)+4 \left(107 c^3 d^2-472 c^2 d^3+18 c^4 d+2 c^5+456 c d^4-136 d^5\right)\right)}{30 a^3 f}+\frac{(c-d) \tan (e+f x) (c+d \sec (e+f x))^5}{5 f (a \sec (e+f x)+a)^3}+\frac{(c-d) (2 c+13 d) \tan (e+f x) (c+d \sec (e+f x))^4}{15 a f (a \sec (e+f x)+a)^2}","-\frac{2 d \left(107 c^3 d^2-472 c^2 d^3+18 c^4 d+2 c^5+456 c d^4-136 d^5\right) \tan (e+f x)}{15 a^3 f}+\frac{d^3 \left(-90 c^2 d+40 c^3+78 c d^2-23 d^3\right) \tanh ^{-1}(\sin (e+f x))}{2 a^3 f}+\frac{(c-d) \left(2 c^2+18 c d+115 d^2\right) \tan (e+f x) (c+d \sec (e+f x))^3}{15 f \left(a^3 \sec (e+f x)+a^3\right)}-\frac{d \left(18 c^2 d+2 c^3+111 c d^2-136 d^3\right) \tan (e+f x) (c+d \sec (e+f x))^2}{15 a^3 f}-\frac{d^2 \left(216 c^2 d^2+36 c^3 d+4 c^4-626 c d^3+345 d^4\right) \tan (e+f x) \sec (e+f x)}{30 a^3 f}+\frac{(c-d) \tan (e+f x) (c+d \sec (e+f x))^5}{5 f (a \sec (e+f x)+a)^3}+\frac{(c-d) (2 c+13 d) \tan (e+f x) (c+d \sec (e+f x))^4}{15 a f (a \sec (e+f x)+a)^2}",1,"(d^3*(40*c^3 - 90*c^2*d + 78*c*d^2 - 23*d^3)*ArcTan[Sqrt[a - a*Sec[e + f*x]]/Sqrt[a*(1 + Sec[e + f*x])]]*Tan[e + f*x])/(a^2*f*Sqrt[a - a*Sec[e + f*x]]*Sqrt[a + a*Sec[e + f*x]]) - (d*(2*c^3 + 18*c^2*d + 111*c*d^2 - 136*d^3)*(c + d*Sec[e + f*x])^2*Tan[e + f*x])/(15*a^3*f) + ((c - d)*(2*c^2 + 18*c*d + 115*d^2)*(c + d*Sec[e + f*x])^3*Tan[e + f*x])/(15*f*(a^3 + a^3*Sec[e + f*x])) + ((c - d)*(2*c + 13*d)*(c + d*Sec[e + f*x])^4*Tan[e + f*x])/(15*a*f*(a + a*Sec[e + f*x])^2) + ((c - d)*(c + d*Sec[e + f*x])^5*Tan[e + f*x])/(5*f*(a + a*Sec[e + f*x])^3) - (d*(4*(2*c^5 + 18*c^4*d + 107*c^3*d^2 - 472*c^2*d^3 + 456*c*d^4 - 136*d^5) + d*(4*c^4 + 36*c^3*d + 216*c^2*d^2 - 626*c*d^3 + 345*d^4)*Sec[e + f*x])*Tan[e + f*x])/(30*a^3*f)","A",9,8,31,0.2581,1,"{3987, 98, 150, 153, 147, 63, 217, 203}"
226,1,329,0,0.4161374,"\int \frac{\sec (e+f x) (c+d \sec (e+f x))^5}{(a+a \sec (e+f x))^3} \, dx","Int[(Sec[e + f*x]*(c + d*Sec[e + f*x])^5)/(a + a*Sec[e + f*x])^3,x]","\frac{d^3 \left(20 c^2-30 c d+13 d^2\right) \tan (e+f x) \tan ^{-1}\left(\frac{\sqrt{a-a \sec (e+f x)}}{\sqrt{a (\sec (e+f x)+1)}}\right)}{a^2 f \sqrt{a-a \sec (e+f x)} \sqrt{a \sec (e+f x)+a}}+\frac{(c-d) \left(2 c^2+15 c d+76 d^2\right) \tan (e+f x) (c+d \sec (e+f x))^2}{15 f \left(a^3 \sec (e+f x)+a^3\right)}-\frac{d \tan (e+f x) \left(d \left(30 c^2 d+4 c^3+146 c d^2-195 d^3\right) \sec (e+f x)+4 \left(72 c^2 d^2+15 c^3 d+2 c^4-180 c d^3+76 d^4\right)\right)}{30 a^3 f}+\frac{(c-d) \tan (e+f x) (c+d \sec (e+f x))^4}{5 f (a \sec (e+f x)+a)^3}+\frac{(c-d) (2 c+11 d) \tan (e+f x) (c+d \sec (e+f x))^3}{15 a f (a \sec (e+f x)+a)^2}","-\frac{2 d \left(72 c^2 d^2+15 c^3 d+2 c^4-180 c d^3+76 d^4\right) \tan (e+f x)}{15 a^3 f}+\frac{d^3 \left(20 c^2-30 c d+13 d^2\right) \tanh ^{-1}(\sin (e+f x))}{2 a^3 f}+\frac{(c-d) \left(2 c^2+15 c d+76 d^2\right) \tan (e+f x) (c+d \sec (e+f x))^2}{15 f \left(a^3 \sec (e+f x)+a^3\right)}-\frac{d^2 \left(30 c^2 d+4 c^3+146 c d^2-195 d^3\right) \tan (e+f x) \sec (e+f x)}{30 a^3 f}+\frac{(c-d) \tan (e+f x) (c+d \sec (e+f x))^4}{5 f (a \sec (e+f x)+a)^3}+\frac{(c-d) (2 c+11 d) \tan (e+f x) (c+d \sec (e+f x))^3}{15 a f (a \sec (e+f x)+a)^2}",1,"(d^3*(20*c^2 - 30*c*d + 13*d^2)*ArcTan[Sqrt[a - a*Sec[e + f*x]]/Sqrt[a*(1 + Sec[e + f*x])]]*Tan[e + f*x])/(a^2*f*Sqrt[a - a*Sec[e + f*x]]*Sqrt[a + a*Sec[e + f*x]]) + ((c - d)*(2*c^2 + 15*c*d + 76*d^2)*(c + d*Sec[e + f*x])^2*Tan[e + f*x])/(15*f*(a^3 + a^3*Sec[e + f*x])) + ((c - d)*(2*c + 11*d)*(c + d*Sec[e + f*x])^3*Tan[e + f*x])/(15*a*f*(a + a*Sec[e + f*x])^2) + ((c - d)*(c + d*Sec[e + f*x])^4*Tan[e + f*x])/(5*f*(a + a*Sec[e + f*x])^3) - (d*(4*(2*c^4 + 15*c^3*d + 72*c^2*d^2 - 180*c*d^3 + 76*d^4) + d*(4*c^3 + 30*c^2*d + 146*c*d^2 - 195*d^3)*Sec[e + f*x])*Tan[e + f*x])/(30*a^3*f)","A",8,7,31,0.2258,1,"{3987, 98, 150, 147, 63, 217, 203}"
227,1,265,0,0.2801869,"\int \frac{\sec (e+f x) (c+d \sec (e+f x))^4}{(a+a \sec (e+f x))^3} \, dx","Int[(Sec[e + f*x]*(c + d*Sec[e + f*x])^4)/(a + a*Sec[e + f*x])^3,x]","\frac{\tan (e+f x) \left(-d^2 \left(2 c^2+10 c d-27 d^2\right) \sec (e+f x)+21 c^2 d^2+8 c^3 d+2 c^4-88 c d^3+72 d^4\right)}{15 f \left(a^3 \sec (e+f x)+a^3\right)}+\frac{2 d^3 (4 c-3 d) \tan (e+f x) \tan ^{-1}\left(\frac{\sqrt{a-a \sec (e+f x)}}{\sqrt{a (\sec (e+f x)+1)}}\right)}{a^2 f \sqrt{a-a \sec (e+f x)} \sqrt{a \sec (e+f x)+a}}+\frac{(c-d) \tan (e+f x) (c+d \sec (e+f x))^3}{5 f (a \sec (e+f x)+a)^3}+\frac{(c-d) (2 c+9 d) \tan (e+f x) (c+d \sec (e+f x))^2}{15 a f (a \sec (e+f x)+a)^2}","\frac{\tan (e+f x) \left(-d^2 \left(2 c^2+10 c d-27 d^2\right) \sec (e+f x)+21 c^2 d^2+8 c^3 d+2 c^4-88 c d^3+72 d^4\right)}{15 f \left(a^3 \sec (e+f x)+a^3\right)}+\frac{d^3 (4 c-3 d) \tanh ^{-1}(\sin (e+f x))}{a^3 f}+\frac{(c-d) \tan (e+f x) (c+d \sec (e+f x))^3}{5 f (a \sec (e+f x)+a)^3}+\frac{(c-d) (2 c+9 d) \tan (e+f x) (c+d \sec (e+f x))^2}{15 a f (a \sec (e+f x)+a)^2}",1,"(2*(4*c - 3*d)*d^3*ArcTan[Sqrt[a - a*Sec[e + f*x]]/Sqrt[a*(1 + Sec[e + f*x])]]*Tan[e + f*x])/(a^2*f*Sqrt[a - a*Sec[e + f*x]]*Sqrt[a + a*Sec[e + f*x]]) + ((c - d)*(2*c + 9*d)*(c + d*Sec[e + f*x])^2*Tan[e + f*x])/(15*a*f*(a + a*Sec[e + f*x])^2) + ((c - d)*(c + d*Sec[e + f*x])^3*Tan[e + f*x])/(5*f*(a + a*Sec[e + f*x])^3) + ((2*c^4 + 8*c^3*d + 21*c^2*d^2 - 88*c*d^3 + 72*d^4 - d^2*(2*c^2 + 10*c*d - 27*d^2)*Sec[e + f*x])*Tan[e + f*x])/(15*f*(a^3 + a^3*Sec[e + f*x]))","A",7,7,31,0.2258,1,"{3987, 98, 150, 143, 63, 217, 203}"
228,1,193,0,0.2008186,"\int \frac{\sec (e+f x) (c+d \sec (e+f x))^3}{(a+a \sec (e+f x))^3} \, dx","Int[(Sec[e + f*x]*(c + d*Sec[e + f*x])^3)/(a + a*Sec[e + f*x])^3,x]","\frac{2 d^3 \tan (e+f x) \tan ^{-1}\left(\frac{\sqrt{a-a \sec (e+f x)}}{\sqrt{a (\sec (e+f x)+1)}}\right)}{a^2 f \sqrt{a-a \sec (e+f x)} \sqrt{a \sec (e+f x)+a}}+\frac{(c-d) \tan (e+f x) \left(\left(2 c^2+11 c d+29 d^2\right) \sec (e+f x)+2 \left(2 c^2+8 c d+11 d^2\right)\right)}{15 a f (a \sec (e+f x)+a)^2}+\frac{(c-d) \tan (e+f x) (c+d \sec (e+f x))^2}{5 f (a \sec (e+f x)+a)^3}","\frac{d^3 \tanh ^{-1}(\sin (e+f x))}{a^3 f}+\frac{(c-d) \tan (e+f x) \left(\left(2 c^2+11 c d+29 d^2\right) \sec (e+f x)+2 \left(2 c^2+8 c d+11 d^2\right)\right)}{15 a f (a \sec (e+f x)+a)^2}+\frac{(c-d) \tan (e+f x) (c+d \sec (e+f x))^2}{5 f (a \sec (e+f x)+a)^3}",1,"(2*d^3*ArcTan[Sqrt[a - a*Sec[e + f*x]]/Sqrt[a*(1 + Sec[e + f*x])]]*Tan[e + f*x])/(a^2*f*Sqrt[a - a*Sec[e + f*x]]*Sqrt[a + a*Sec[e + f*x]]) + ((c - d)*(c + d*Sec[e + f*x])^2*Tan[e + f*x])/(5*f*(a + a*Sec[e + f*x])^3) + ((c - d)*(2*(2*c^2 + 8*c*d + 11*d^2) + (2*c^2 + 11*c*d + 29*d^2)*Sec[e + f*x])*Tan[e + f*x])/(15*a*f*(a + a*Sec[e + f*x])^2)","A",6,6,31,0.1935,1,"{3987, 98, 145, 63, 217, 203}"
229,1,115,0,0.1626028,"\int \frac{\sec (e+f x) (c+d \sec (e+f x))^2}{(a+a \sec (e+f x))^3} \, dx","Int[(Sec[e + f*x]*(c + d*Sec[e + f*x])^2)/(a + a*Sec[e + f*x])^3,x]","\frac{\left(2 c^2+6 c d+7 d^2\right) \tan (e+f x)}{15 f \left(a^3 \sec (e+f x)+a^3\right)}+\frac{(c-d)^2 \tan (e+f x)}{5 f (a \sec (e+f x)+a)^3}+\frac{2 (c+4 d) (c-d) \tan (e+f x)}{15 a f (a \sec (e+f x)+a)^2}","\frac{\left(2 c^2+6 c d+7 d^2\right) \tan (e+f x)}{15 f \left(a^3 \sec (e+f x)+a^3\right)}+\frac{(c-d)^2 \tan (e+f x)}{5 f (a \sec (e+f x)+a)^3}+\frac{2 (c+4 d) (c-d) \tan (e+f x)}{15 a f (a \sec (e+f x)+a)^2}",1,"((c - d)^2*Tan[e + f*x])/(5*f*(a + a*Sec[e + f*x])^3) + (2*(c - d)*(c + 4*d)*Tan[e + f*x])/(15*a*f*(a + a*Sec[e + f*x])^2) + ((2*c^2 + 6*c*d + 7*d^2)*Tan[e + f*x])/(15*f*(a^3 + a^3*Sec[e + f*x]))","A",4,4,31,0.1290,1,"{3987, 89, 78, 37}"
230,1,102,0,0.1152807,"\int \frac{\sec (e+f x) (c+d \sec (e+f x))}{(a+a \sec (e+f x))^3} \, dx","Int[(Sec[e + f*x]*(c + d*Sec[e + f*x]))/(a + a*Sec[e + f*x])^3,x]","\frac{(2 c+3 d) \tan (e+f x)}{15 f \left(a^3 \sec (e+f x)+a^3\right)}+\frac{(2 c+3 d) \tan (e+f x)}{15 a f (a \sec (e+f x)+a)^2}+\frac{(c-d) \tan (e+f x)}{5 f (a \sec (e+f x)+a)^3}","\frac{(2 c+3 d) \tan (e+f x)}{15 f \left(a^3 \sec (e+f x)+a^3\right)}+\frac{(2 c+3 d) \tan (e+f x)}{15 a f (a \sec (e+f x)+a)^2}+\frac{(c-d) \tan (e+f x)}{5 f (a \sec (e+f x)+a)^3}",1,"((c - d)*Tan[e + f*x])/(5*f*(a + a*Sec[e + f*x])^3) + ((2*c + 3*d)*Tan[e + f*x])/(15*a*f*(a + a*Sec[e + f*x])^2) + ((2*c + 3*d)*Tan[e + f*x])/(15*f*(a^3 + a^3*Sec[e + f*x]))","A",3,3,29,0.1034,1,"{4000, 3796, 3794}"
231,1,235,0,0.3229489,"\int \frac{\sec (e+f x)}{(a+a \sec (e+f x))^3 (c+d \sec (e+f x))} \, dx","Int[Sec[e + f*x]/((a + a*Sec[e + f*x])^3*(c + d*Sec[e + f*x])),x]","\frac{\left(2 c^2-9 c d+22 d^2\right) \tan (e+f x)}{15 f (c-d)^3 \left(a^3 \sec (e+f x)+a^3\right)}+\frac{2 d^3 \tan (e+f x) \tan ^{-1}\left(\frac{\sqrt{c+d} \sqrt{a \sec (e+f x)+a}}{\sqrt{c-d} \sqrt{a-a \sec (e+f x)}}\right)}{a^2 f (c-d)^{7/2} \sqrt{c+d} \sqrt{a-a \sec (e+f x)} \sqrt{a \sec (e+f x)+a}}+\frac{(2 c-7 d) \tan (e+f x)}{15 a f (c-d)^2 (a \sec (e+f x)+a)^2}+\frac{\tan (e+f x)}{5 f (c-d) (a \sec (e+f x)+a)^3}","\frac{\left(2 c^2-9 c d+22 d^2\right) \tan (e+f x)}{15 f (c-d)^3 \left(a^3 \sec (e+f x)+a^3\right)}-\frac{2 d^3 \tanh ^{-1}\left(\frac{\sqrt{c-d} \tan \left(\frac{1}{2} (e+f x)\right)}{\sqrt{c+d}}\right)}{a^3 f (c-d)^{7/2} \sqrt{c+d}}+\frac{(2 c-7 d) \tan (e+f x)}{15 a f (c-d)^2 (a \sec (e+f x)+a)^2}+\frac{\tan (e+f x)}{5 f (c-d) (a \sec (e+f x)+a)^3}",1,"Tan[e + f*x]/(5*(c - d)*f*(a + a*Sec[e + f*x])^3) + ((2*c - 7*d)*Tan[e + f*x])/(15*a*(c - d)^2*f*(a + a*Sec[e + f*x])^2) + (2*d^3*ArcTan[(Sqrt[c + d]*Sqrt[a + a*Sec[e + f*x]])/(Sqrt[c - d]*Sqrt[a - a*Sec[e + f*x]])]*Tan[e + f*x])/(a^2*(c - d)^(7/2)*Sqrt[c + d]*f*Sqrt[a - a*Sec[e + f*x]]*Sqrt[a + a*Sec[e + f*x]]) + ((2*c^2 - 9*c*d + 22*d^2)*Tan[e + f*x])/(15*(c - d)^3*f*(a^3 + a^3*Sec[e + f*x]))","A",7,6,31,0.1935,1,"{3987, 104, 152, 12, 93, 205}"
232,1,325,0,0.4860906,"\int \frac{\sec (e+f x)}{(a+a \sec (e+f x))^3 (c+d \sec (e+f x))^2} \, dx","Int[Sec[e + f*x]/((a + a*Sec[e + f*x])^3*(c + d*Sec[e + f*x])^2),x]","\frac{\left(-12 c^2 d+2 c^3+43 c d^2+72 d^3\right) \tan (e+f x)}{15 f (c-d)^4 (c+d) \left(a^3 \sec (e+f x)+a^3\right)}+\frac{2 d^3 (4 c+3 d) \tan (e+f x) \tan ^{-1}\left(\frac{\sqrt{c+d} \sqrt{a \sec (e+f x)+a}}{\sqrt{c-d} \sqrt{a-a \sec (e+f x)}}\right)}{a^2 f (c-d)^{9/2} (c+d)^{3/2} \sqrt{a-a \sec (e+f x)} \sqrt{a \sec (e+f x)+a}}-\frac{d \tan (e+f x)}{f \left(c^2-d^2\right) (a \sec (e+f x)+a)^3 (c+d \sec (e+f x))}+\frac{\left(2 c^2-10 c d-27 d^2\right) \tan (e+f x)}{15 a f (c-d)^3 (c+d) (a \sec (e+f x)+a)^2}+\frac{(c+6 d) \tan (e+f x)}{5 f (c-d)^2 (c+d) (a \sec (e+f x)+a)^3}","\frac{d \left(-12 c^2 d+2 c^3+43 c d^2+72 d^3\right) \tan (e+f x)}{15 a^3 f (c-d)^4 (c+d) (c+d \sec (e+f x))}+\frac{\left(2 c^2-12 c d+45 d^2\right) \tan (e+f x)}{15 f (c-d)^3 \left(a^3 \sec (e+f x)+a^3\right) (c+d \sec (e+f x))}-\frac{2 d^3 (4 c+3 d) \tanh ^{-1}\left(\frac{\sqrt{c-d} \tan \left(\frac{1}{2} (e+f x)\right)}{\sqrt{c+d}}\right)}{a^3 f (c-d)^{9/2} (c+d)^{3/2}}+\frac{(2 c-9 d) \tan (e+f x)}{15 a f (c-d)^2 (a \sec (e+f x)+a)^2 (c+d \sec (e+f x))}+\frac{\tan (e+f x)}{5 f (c-d) (a \sec (e+f x)+a)^3 (c+d \sec (e+f x))}",1,"((c + 6*d)*Tan[e + f*x])/(5*(c - d)^2*(c + d)*f*(a + a*Sec[e + f*x])^3) + ((2*c^2 - 10*c*d - 27*d^2)*Tan[e + f*x])/(15*a*(c - d)^3*(c + d)*f*(a + a*Sec[e + f*x])^2) + (2*d^3*(4*c + 3*d)*ArcTan[(Sqrt[c + d]*Sqrt[a + a*Sec[e + f*x]])/(Sqrt[c - d]*Sqrt[a - a*Sec[e + f*x]])]*Tan[e + f*x])/(a^2*(c - d)^(9/2)*(c + d)^(3/2)*f*Sqrt[a - a*Sec[e + f*x]]*Sqrt[a + a*Sec[e + f*x]]) + ((2*c^3 - 12*c^2*d + 43*c*d^2 + 72*d^3)*Tan[e + f*x])/(15*(c - d)^4*(c + d)*f*(a^3 + a^3*Sec[e + f*x])) - (d*Tan[e + f*x])/((c^2 - d^2)*f*(a + a*Sec[e + f*x])^3*(c + d*Sec[e + f*x]))","A",8,6,31,0.1935,1,"{3987, 103, 152, 12, 93, 205}"
233,1,414,0,0.7064367,"\int \frac{\sec (e+f x)}{(a+a \sec (e+f x))^3 (c+d \sec (e+f x))^3} \, dx","Int[Sec[e + f*x]/((a + a*Sec[e + f*x])^3*(c + d*Sec[e + f*x])^3),x]","\frac{d^3 \left(20 c^2+30 c d+13 d^2\right) \tan (e+f x) \tan ^{-1}\left(\frac{\sqrt{c+d} \sqrt{a \sec (e+f x)+a}}{\sqrt{c-d} \sqrt{a-a \sec (e+f x)}}\right)}{a^2 f (c-d)^{11/2} (c+d)^{5/2} \sqrt{a-a \sec (e+f x)} \sqrt{a \sec (e+f x)+a}}+\frac{\left(142 c^2 d^2-30 c^3 d+4 c^4+525 c d^3+304 d^4\right) \tan (e+f x)}{30 f (c-d)^5 (c+d)^2 \left(a^3 \sec (e+f x)+a^3\right)}-\frac{3 d (2 c+d) \tan (e+f x)}{2 f \left(c^2-d^2\right)^2 (a \sec (e+f x)+a)^3 (c+d \sec (e+f x))}-\frac{d \tan (e+f x)}{2 f \left(c^2-d^2\right) (a \sec (e+f x)+a)^3 (c+d \sec (e+f x))^2}+\frac{\left(-26 c^2 d+4 c^3-184 c d^2-109 d^3\right) \tan (e+f x)}{30 a f (c-d)^4 (c+d)^2 (a \sec (e+f x)+a)^2}+\frac{\left(2 c^2+39 c d+22 d^2\right) \tan (e+f x)}{10 f (c-d)^3 (c+d)^2 (a \sec (e+f x)+a)^3}","-\frac{d^3 \left(20 c^2+30 c d+13 d^2\right) \tanh ^{-1}\left(\frac{\sqrt{c-d} \tan \left(\frac{1}{2} (e+f x)\right)}{\sqrt{c+d}}\right)}{a^3 f (c-d)^{11/2} (c+d)^{5/2}}+\frac{d \left(142 c^2 d^2-30 c^3 d+4 c^4+525 c d^3+304 d^4\right) \tan (e+f x)}{30 a^3 f (c-d)^5 (c+d)^2 (c+d \sec (e+f x))}+\frac{d \left(-30 c^2 d+4 c^3+146 c d^2+195 d^3\right) \tan (e+f x)}{30 a^3 f (c-d)^4 (c+d) (c+d \sec (e+f x))^2}+\frac{\left(2 c^2-15 c d+76 d^2\right) \tan (e+f x)}{15 f (c-d)^3 \left(a^3 \sec (e+f x)+a^3\right) (c+d \sec (e+f x))^2}+\frac{(2 c-11 d) \tan (e+f x)}{15 a f (c-d)^2 (a \sec (e+f x)+a)^2 (c+d \sec (e+f x))^2}+\frac{\tan (e+f x)}{5 f (c-d) (a \sec (e+f x)+a)^3 (c+d \sec (e+f x))^2}",1,"((2*c^2 + 39*c*d + 22*d^2)*Tan[e + f*x])/(10*(c - d)^3*(c + d)^2*f*(a + a*Sec[e + f*x])^3) + ((4*c^3 - 26*c^2*d - 184*c*d^2 - 109*d^3)*Tan[e + f*x])/(30*a*(c - d)^4*(c + d)^2*f*(a + a*Sec[e + f*x])^2) + (d^3*(20*c^2 + 30*c*d + 13*d^2)*ArcTan[(Sqrt[c + d]*Sqrt[a + a*Sec[e + f*x]])/(Sqrt[c - d]*Sqrt[a - a*Sec[e + f*x]])]*Tan[e + f*x])/(a^2*(c - d)^(11/2)*(c + d)^(5/2)*f*Sqrt[a - a*Sec[e + f*x]]*Sqrt[a + a*Sec[e + f*x]]) + ((4*c^4 - 30*c^3*d + 142*c^2*d^2 + 525*c*d^3 + 304*d^4)*Tan[e + f*x])/(30*(c - d)^5*(c + d)^2*f*(a^3 + a^3*Sec[e + f*x])) - (d*Tan[e + f*x])/(2*(c^2 - d^2)*f*(a + a*Sec[e + f*x])^3*(c + d*Sec[e + f*x])^2) - (3*d*(2*c + d)*Tan[e + f*x])/(2*(c^2 - d^2)^2*f*(a + a*Sec[e + f*x])^3*(c + d*Sec[e + f*x]))","A",9,7,31,0.2258,1,"{3987, 103, 151, 152, 12, 93, 205}"
234,1,61,0,0.1546081,"\int \frac{\sec (e+f x) \sqrt{a+a \sec (e+f x)}}{\sqrt{c+d \sec (e+f x)}} \, dx","Int[(Sec[e + f*x]*Sqrt[a + a*Sec[e + f*x]])/Sqrt[c + d*Sec[e + f*x]],x]","\frac{2 \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{d} \tan (e+f x)}{\sqrt{a \sec (e+f x)+a} \sqrt{c+d \sec (e+f x)}}\right)}{\sqrt{d} f}","\frac{2 \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{d} \tan (e+f x)}{\sqrt{a \sec (e+f x)+a} \sqrt{c+d \sec (e+f x)}}\right)}{\sqrt{d} f}",1,"(2*Sqrt[a]*ArcTanh[(Sqrt[a]*Sqrt[d]*Tan[e + f*x])/(Sqrt[a + a*Sec[e + f*x]]*Sqrt[c + d*Sec[e + f*x]])])/(Sqrt[d]*f)","A",2,2,35,0.05714,1,"{3980, 206}"
235,1,140,0,0.4622874,"\int \frac{\sec (e+f x) \sqrt{c+d \sec (e+f x)}}{\sqrt{a+a \sec (e+f x)}} \, dx","Int[(Sec[e + f*x]*Sqrt[c + d*Sec[e + f*x]])/Sqrt[a + a*Sec[e + f*x]],x]","\frac{\sqrt{2} \sqrt{c-d} \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{c-d} \tan (e+f x)}{\sqrt{2} \sqrt{a \sec (e+f x)+a} \sqrt{c+d \sec (e+f x)}}\right)}{\sqrt{a} f}+\frac{2 \sqrt{d} \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{d} \tan (e+f x)}{\sqrt{a \sec (e+f x)+a} \sqrt{c+d \sec (e+f x)}}\right)}{\sqrt{a} f}","\frac{\sqrt{2} \sqrt{c-d} \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{c-d} \tan (e+f x)}{\sqrt{2} \sqrt{a \sec (e+f x)+a} \sqrt{c+d \sec (e+f x)}}\right)}{\sqrt{a} f}+\frac{2 \sqrt{d} \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{d} \tan (e+f x)}{\sqrt{a \sec (e+f x)+a} \sqrt{c+d \sec (e+f x)}}\right)}{\sqrt{a} f}",1,"(Sqrt[2]*Sqrt[c - d]*ArcTan[(Sqrt[a]*Sqrt[c - d]*Tan[e + f*x])/(Sqrt[2]*Sqrt[a + a*Sec[e + f*x]]*Sqrt[c + d*Sec[e + f*x]])])/(Sqrt[a]*f) + (2*Sqrt[d]*ArcTanh[(Sqrt[a]*Sqrt[d]*Tan[e + f*x])/(Sqrt[a + a*Sec[e + f*x]]*Sqrt[c + d*Sec[e + f*x]])])/(Sqrt[a]*f)","A",5,5,35,0.1429,1,"{3981, 3983, 203, 3980, 206}"
236,1,78,0,0.1572622,"\int \frac{\sec (e+f x)}{\sqrt{a+a \sec (e+f x)} \sqrt{c+d \sec (e+f x)}} \, dx","Int[Sec[e + f*x]/(Sqrt[a + a*Sec[e + f*x]]*Sqrt[c + d*Sec[e + f*x]]),x]","\frac{\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{c-d} \tan (e+f x)}{\sqrt{2} \sqrt{a \sec (e+f x)+a} \sqrt{c+d \sec (e+f x)}}\right)}{\sqrt{a} f \sqrt{c-d}}","\frac{\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{c-d} \tan (e+f x)}{\sqrt{2} \sqrt{a \sec (e+f x)+a} \sqrt{c+d \sec (e+f x)}}\right)}{\sqrt{a} f \sqrt{c-d}}",1,"(Sqrt[2]*ArcTan[(Sqrt[a]*Sqrt[c - d]*Tan[e + f*x])/(Sqrt[2]*Sqrt[a + a*Sec[e + f*x]]*Sqrt[c + d*Sec[e + f*x]])])/(Sqrt[a]*Sqrt[c - d]*f)","A",2,2,35,0.05714,1,"{3983, 203}"
237,1,141,0,0.5289376,"\int \frac{\sec ^2(e+f x)}{\sqrt{a+a \sec (e+f x)} \sqrt{c+d \sec (e+f x)}} \, dx","Int[Sec[e + f*x]^2/(Sqrt[a + a*Sec[e + f*x]]*Sqrt[c + d*Sec[e + f*x]]),x]","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{d} \tan (e+f x)}{\sqrt{a \sec (e+f x)+a} \sqrt{c+d \sec (e+f x)}}\right)}{\sqrt{a} \sqrt{d} f}-\frac{\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{c-d} \tan (e+f x)}{\sqrt{2} \sqrt{a \sec (e+f x)+a} \sqrt{c+d \sec (e+f x)}}\right)}{\sqrt{a} f \sqrt{c-d}}","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{d} \tan (e+f x)}{\sqrt{a \sec (e+f x)+a} \sqrt{c+d \sec (e+f x)}}\right)}{\sqrt{a} \sqrt{d} f}-\frac{\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{c-d} \tan (e+f x)}{\sqrt{2} \sqrt{a \sec (e+f x)+a} \sqrt{c+d \sec (e+f x)}}\right)}{\sqrt{a} f \sqrt{c-d}}",1,"-((Sqrt[2]*ArcTan[(Sqrt[a]*Sqrt[c - d]*Tan[e + f*x])/(Sqrt[2]*Sqrt[a + a*Sec[e + f*x]]*Sqrt[c + d*Sec[e + f*x]])])/(Sqrt[a]*Sqrt[c - d]*f)) + (2*ArcTanh[(Sqrt[a]*Sqrt[d]*Tan[e + f*x])/(Sqrt[a + a*Sec[e + f*x]]*Sqrt[c + d*Sec[e + f*x]])])/(Sqrt[a]*Sqrt[d]*f)","A",5,5,37,0.1351,1,"{3985, 3983, 203, 3980, 206}"
238,1,61,0,0.1364758,"\int \frac{\sec (e+f x) \sqrt{a+a \sec (e+f x)}}{c+d \sec (e+f x)} \, dx","Int[(Sec[e + f*x]*Sqrt[a + a*Sec[e + f*x]])/(c + d*Sec[e + f*x]),x]","\frac{2 \sqrt{a} \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{d} \tan (e+f x)}{\sqrt{c+d} \sqrt{a \sec (e+f x)+a}}\right)}{\sqrt{d} f \sqrt{c+d}}","\frac{2 \sqrt{a} \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{d} \tan (e+f x)}{\sqrt{c+d} \sqrt{a \sec (e+f x)+a}}\right)}{\sqrt{d} f \sqrt{c+d}}",1,"(2*Sqrt[a]*ArcTan[(Sqrt[a]*Sqrt[d]*Tan[e + f*x])/(Sqrt[c + d]*Sqrt[a + a*Sec[e + f*x]])])/(Sqrt[d]*Sqrt[c + d]*f)","A",2,2,33,0.06061,1,"{3967, 205}"
239,1,149,0,0.5699804,"\int \frac{(g \sec (e+f x))^{3/2} \sqrt{a+a \sec (e+f x)}}{c+d \sec (e+f x)} \, dx","Int[((g*Sec[e + f*x])^(3/2)*Sqrt[a + a*Sec[e + f*x]])/(c + d*Sec[e + f*x]),x]","\frac{2 \sqrt{a} g^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{g} \tan (e+f x)}{\sqrt{a \sec (e+f x)+a} \sqrt{g \sec (e+f x)}}\right)}{d f}-\frac{2 \sqrt{a} \sqrt{c} g^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{c} \sqrt{g} \tan (e+f x)}{\sqrt{c+d} \sqrt{a \sec (e+f x)+a} \sqrt{g \sec (e+f x)}}\right)}{d f \sqrt{c+d}}","\frac{2 \sqrt{a} g^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{g} \tan (e+f x)}{\sqrt{a \sec (e+f x)+a} \sqrt{g \sec (e+f x)}}\right)}{d f}-\frac{2 \sqrt{a} \sqrt{c} g^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{c} \sqrt{g} \tan (e+f x)}{\sqrt{c+d} \sqrt{a \sec (e+f x)+a} \sqrt{g \sec (e+f x)}}\right)}{d f \sqrt{c+d}}",1,"(2*Sqrt[a]*g^(3/2)*ArcTanh[(Sqrt[a]*Sqrt[g]*Tan[e + f*x])/(Sqrt[g*Sec[e + f*x]]*Sqrt[a + a*Sec[e + f*x]])])/(d*f) - (2*Sqrt[a]*Sqrt[c]*g^(3/2)*ArcTanh[(Sqrt[a]*Sqrt[c]*Sqrt[g]*Tan[e + f*x])/(Sqrt[c + d]*Sqrt[g*Sec[e + f*x]]*Sqrt[a + a*Sec[e + f*x]])])/(d*Sqrt[c + d]*f)","A",5,4,39,0.1026,1,"{3970, 3802, 208, 3965}"
240,1,122,0,0.3011941,"\int \frac{\sec (e+f x)}{\sqrt{a+a \sec (e+f x)} (c+d \sec (e+f x))} \, dx","Int[Sec[e + f*x]/(Sqrt[a + a*Sec[e + f*x]]*(c + d*Sec[e + f*x])),x]","\frac{\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{a} \tan (e+f x)}{\sqrt{2} \sqrt{a \sec (e+f x)+a}}\right)}{\sqrt{a} f (c-d)}-\frac{2 \sqrt{d} \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{d} \tan (e+f x)}{\sqrt{c+d} \sqrt{a \sec (e+f x)+a}}\right)}{\sqrt{a} f (c-d) \sqrt{c+d}}","\frac{\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{a} \tan (e+f x)}{\sqrt{2} \sqrt{a \sec (e+f x)+a}}\right)}{\sqrt{a} f (c-d)}-\frac{2 \sqrt{d} \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{d} \tan (e+f x)}{\sqrt{c+d} \sqrt{a \sec (e+f x)+a}}\right)}{\sqrt{a} f (c-d) \sqrt{c+d}}",1,"(Sqrt[2]*ArcTan[(Sqrt[a]*Tan[e + f*x])/(Sqrt[2]*Sqrt[a + a*Sec[e + f*x]])])/(Sqrt[a]*(c - d)*f) - (2*Sqrt[d]*ArcTan[(Sqrt[a]*Sqrt[d]*Tan[e + f*x])/(Sqrt[c + d]*Sqrt[a + a*Sec[e + f*x]])])/(Sqrt[a]*(c - d)*Sqrt[c + d]*f)","A",5,5,33,0.1515,1,"{3972, 3795, 203, 3967, 205}"
241,1,124,0,0.3679643,"\int \frac{\sec ^2(e+f x)}{\sqrt{a+a \sec (e+f x)} (c+d \sec (e+f x))} \, dx","Int[Sec[e + f*x]^2/(Sqrt[a + a*Sec[e + f*x]]*(c + d*Sec[e + f*x])),x]","\frac{2 c \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{d} \tan (e+f x)}{\sqrt{c+d} \sqrt{a \sec (e+f x)+a}}\right)}{\sqrt{a} \sqrt{d} f (c-d) \sqrt{c+d}}-\frac{\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{a} \tan (e+f x)}{\sqrt{2} \sqrt{a \sec (e+f x)+a}}\right)}{\sqrt{a} f (c-d)}","\frac{2 c \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{d} \tan (e+f x)}{\sqrt{c+d} \sqrt{a \sec (e+f x)+a}}\right)}{\sqrt{a} \sqrt{d} f (c-d) \sqrt{c+d}}-\frac{\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{a} \tan (e+f x)}{\sqrt{2} \sqrt{a \sec (e+f x)+a}}\right)}{\sqrt{a} f (c-d)}",1,"-((Sqrt[2]*ArcTan[(Sqrt[a]*Tan[e + f*x])/(Sqrt[2]*Sqrt[a + a*Sec[e + f*x]])])/(Sqrt[a]*(c - d)*f)) + (2*c*ArcTan[(Sqrt[a]*Sqrt[d]*Tan[e + f*x])/(Sqrt[c + d]*Sqrt[a + a*Sec[e + f*x]])])/(Sqrt[a]*(c - d)*Sqrt[d]*Sqrt[c + d]*f)","A",5,5,35,0.1429,1,"{3976, 3795, 203, 3967, 205}"
242,1,167,0,0.5828279,"\int \frac{(g \sec (e+f x))^{3/2}}{\sqrt{a+a \sec (e+f x)} (c+d \sec (e+f x))} \, dx","Int[(g*Sec[e + f*x])^(3/2)/(Sqrt[a + a*Sec[e + f*x]]*(c + d*Sec[e + f*x])),x]","\frac{2 \sqrt{c} g^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{c} \sqrt{g} \tan (e+f x)}{\sqrt{c+d} \sqrt{a \sec (e+f x)+a} \sqrt{g \sec (e+f x)}}\right)}{\sqrt{a} f (c-d) \sqrt{c+d}}-\frac{\sqrt{2} g^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{g} \tan (e+f x)}{\sqrt{2} \sqrt{a \sec (e+f x)+a} \sqrt{g \sec (e+f x)}}\right)}{\sqrt{a} f (c-d)}","\frac{2 \sqrt{c} g^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{c} \sqrt{g} \tan (e+f x)}{\sqrt{c+d} \sqrt{a \sec (e+f x)+a} \sqrt{g \sec (e+f x)}}\right)}{\sqrt{a} f (c-d) \sqrt{c+d}}-\frac{\sqrt{2} g^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{g} \tan (e+f x)}{\sqrt{2} \sqrt{a \sec (e+f x)+a} \sqrt{g \sec (e+f x)}}\right)}{\sqrt{a} f (c-d)}",1,"-((Sqrt[2]*g^(3/2)*ArcTanh[(Sqrt[a]*Sqrt[g]*Tan[e + f*x])/(Sqrt[2]*Sqrt[g*Sec[e + f*x]]*Sqrt[a + a*Sec[e + f*x]])])/(Sqrt[a]*(c - d)*f)) + (2*Sqrt[c]*g^(3/2)*ArcTanh[(Sqrt[a]*Sqrt[c]*Sqrt[g]*Tan[e + f*x])/(Sqrt[c + d]*Sqrt[g*Sec[e + f*x]]*Sqrt[a + a*Sec[e + f*x]])])/(Sqrt[a]*(c - d)*Sqrt[c + d]*f)","A",5,4,39,0.1026,1,"{3974, 3808, 208, 3965}"
243,1,231,0,0.8158618,"\int \frac{(g \sec (e+f x))^{5/2}}{\sqrt{a+a \sec (e+f x)} (c+d \sec (e+f x))} \, dx","Int[(g*Sec[e + f*x])^(5/2)/(Sqrt[a + a*Sec[e + f*x]]*(c + d*Sec[e + f*x])),x]","-\frac{2 c^{3/2} g^{5/2} \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{c} \sqrt{g} \tan (e+f x)}{\sqrt{c+d} \sqrt{a \sec (e+f x)+a} \sqrt{g \sec (e+f x)}}\right)}{\sqrt{a} d f (c-d) \sqrt{c+d}}+\frac{\sqrt{2} g^{5/2} \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{g} \tan (e+f x)}{\sqrt{2} \sqrt{a \sec (e+f x)+a} \sqrt{g \sec (e+f x)}}\right)}{\sqrt{a} f (c-d)}+\frac{2 g^{5/2} \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{g} \tan (e+f x)}{\sqrt{a \sec (e+f x)+a} \sqrt{g \sec (e+f x)}}\right)}{\sqrt{a} d f}","-\frac{2 c^{3/2} g^{5/2} \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{c} \sqrt{g} \tan (e+f x)}{\sqrt{c+d} \sqrt{a \sec (e+f x)+a} \sqrt{g \sec (e+f x)}}\right)}{\sqrt{a} d f (c-d) \sqrt{c+d}}+\frac{\sqrt{2} g^{5/2} \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{g} \tan (e+f x)}{\sqrt{2} \sqrt{a \sec (e+f x)+a} \sqrt{g \sec (e+f x)}}\right)}{\sqrt{a} f (c-d)}+\frac{2 g^{5/2} \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{g} \tan (e+f x)}{\sqrt{a \sec (e+f x)+a} \sqrt{g \sec (e+f x)}}\right)}{\sqrt{a} d f}",1,"(2*g^(5/2)*ArcTanh[(Sqrt[a]*Sqrt[g]*Tan[e + f*x])/(Sqrt[g*Sec[e + f*x]]*Sqrt[a + a*Sec[e + f*x]])])/(Sqrt[a]*d*f) + (Sqrt[2]*g^(5/2)*ArcTanh[(Sqrt[a]*Sqrt[g]*Tan[e + f*x])/(Sqrt[2]*Sqrt[g*Sec[e + f*x]]*Sqrt[a + a*Sec[e + f*x]])])/(Sqrt[a]*(c - d)*f) - (2*c^(3/2)*g^(5/2)*ArcTanh[(Sqrt[a]*Sqrt[c]*Sqrt[g]*Tan[e + f*x])/(Sqrt[c + d]*Sqrt[g*Sec[e + f*x]]*Sqrt[a + a*Sec[e + f*x]])])/(Sqrt[a]*(c - d)*d*Sqrt[c + d]*f)","A",8,6,39,0.1538,1,"{3978, 3965, 208, 4023, 3808, 3802}"
244,1,250,0,0.5009906,"\int \sec (e+f x) (a+b \sec (e+f x)) (c+d \sec (e+f x))^4 \, dx","Int[Sec[e + f*x]*(a + b*Sec[e + f*x])*(c + d*Sec[e + f*x])^4,x]","\frac{\left(95 a c^3 d+80 a c d^3+112 b c^2 d^2+12 b c^4+16 b d^4\right) \tan (e+f x)}{30 f}+\frac{\left(24 a c^2 d^2+8 a c^4+3 a d^4+16 b c^3 d+12 b c d^3\right) \tanh ^{-1}(\sin (e+f x))}{8 f}+\frac{\left(35 a c d+12 b c^2+16 b d^2\right) \tan (e+f x) (c+d \sec (e+f x))^2}{60 f}+\frac{d \left(130 a c^2 d+45 a d^3+24 b c^3+116 b c d^2\right) \tan (e+f x) \sec (e+f x)}{120 f}+\frac{(5 a d+4 b c) \tan (e+f x) (c+d \sec (e+f x))^3}{20 f}+\frac{b \tan (e+f x) (c+d \sec (e+f x))^4}{5 f}","\frac{\left(95 a c^3 d+80 a c d^3+112 b c^2 d^2+12 b c^4+16 b d^4\right) \tan (e+f x)}{30 f}+\frac{\left(24 a c^2 d^2+8 a c^4+3 a d^4+16 b c^3 d+12 b c d^3\right) \tanh ^{-1}(\sin (e+f x))}{8 f}+\frac{\left(35 a c d+12 b c^2+16 b d^2\right) \tan (e+f x) (c+d \sec (e+f x))^2}{60 f}+\frac{d \left(130 a c^2 d+45 a d^3+24 b c^3+116 b c d^2\right) \tan (e+f x) \sec (e+f x)}{120 f}+\frac{(5 a d+4 b c) \tan (e+f x) (c+d \sec (e+f x))^3}{20 f}+\frac{b \tan (e+f x) (c+d \sec (e+f x))^4}{5 f}",1,"((8*a*c^4 + 16*b*c^3*d + 24*a*c^2*d^2 + 12*b*c*d^3 + 3*a*d^4)*ArcTanh[Sin[e + f*x]])/(8*f) + ((12*b*c^4 + 95*a*c^3*d + 112*b*c^2*d^2 + 80*a*c*d^3 + 16*b*d^4)*Tan[e + f*x])/(30*f) + (d*(24*b*c^3 + 130*a*c^2*d + 116*b*c*d^2 + 45*a*d^3)*Sec[e + f*x]*Tan[e + f*x])/(120*f) + ((12*b*c^2 + 35*a*c*d + 16*b*d^2)*(c + d*Sec[e + f*x])^2*Tan[e + f*x])/(60*f) + ((4*b*c + 5*a*d)*(c + d*Sec[e + f*x])^3*Tan[e + f*x])/(20*f) + (b*(c + d*Sec[e + f*x])^4*Tan[e + f*x])/(5*f)","A",8,6,29,0.2069,1,"{4002, 3997, 3787, 3770, 3767, 8}"
245,1,180,0,0.3562962,"\int \sec (e+f x) (a+b \sec (e+f x)) (c+d \sec (e+f x))^3 \, dx","Int[Sec[e + f*x]*(a + b*Sec[e + f*x])*(c + d*Sec[e + f*x])^3,x]","\frac{\left(4 a d \left(4 c^2+d^2\right)+3 b \left(c^3+4 c d^2\right)\right) \tan (e+f x)}{6 f}+\frac{\left(8 a c^3+12 a c d^2+12 b c^2 d+3 b d^3\right) \tanh ^{-1}(\sin (e+f x))}{8 f}+\frac{d \left(20 a c d+6 b c^2+9 b d^2\right) \tan (e+f x) \sec (e+f x)}{24 f}+\frac{(4 a d+3 b c) \tan (e+f x) (c+d \sec (e+f x))^2}{12 f}+\frac{b \tan (e+f x) (c+d \sec (e+f x))^3}{4 f}","\frac{\left(4 a d \left(4 c^2+d^2\right)+3 b \left(c^3+4 c d^2\right)\right) \tan (e+f x)}{6 f}+\frac{\left(8 a c^3+12 a c d^2+12 b c^2 d+3 b d^3\right) \tanh ^{-1}(\sin (e+f x))}{8 f}+\frac{d \left(20 a c d+6 b c^2+9 b d^2\right) \tan (e+f x) \sec (e+f x)}{24 f}+\frac{(4 a d+3 b c) \tan (e+f x) (c+d \sec (e+f x))^2}{12 f}+\frac{b \tan (e+f x) (c+d \sec (e+f x))^3}{4 f}",1,"((8*a*c^3 + 12*b*c^2*d + 12*a*c*d^2 + 3*b*d^3)*ArcTanh[Sin[e + f*x]])/(8*f) + ((4*a*d*(4*c^2 + d^2) + 3*b*(c^3 + 4*c*d^2))*Tan[e + f*x])/(6*f) + (d*(6*b*c^2 + 20*a*c*d + 9*b*d^2)*Sec[e + f*x]*Tan[e + f*x])/(24*f) + ((3*b*c + 4*a*d)*(c + d*Sec[e + f*x])^2*Tan[e + f*x])/(12*f) + (b*(c + d*Sec[e + f*x])^3*Tan[e + f*x])/(4*f)","A",7,6,29,0.2069,1,"{4002, 3997, 3787, 3770, 3767, 8}"
246,1,115,0,0.1850808,"\int \sec (e+f x) (a+b \sec (e+f x)) (c+d \sec (e+f x))^2 \, dx","Int[Sec[e + f*x]*(a + b*Sec[e + f*x])*(c + d*Sec[e + f*x])^2,x]","\frac{2 \left(3 a c d+b \left(c^2+d^2\right)\right) \tan (e+f x)}{3 f}+\frac{\left(a \left(2 c^2+d^2\right)+2 b c d\right) \tanh ^{-1}(\sin (e+f x))}{2 f}+\frac{d (3 a d+2 b c) \tan (e+f x) \sec (e+f x)}{6 f}+\frac{b \tan (e+f x) (c+d \sec (e+f x))^2}{3 f}","\frac{2 \left(3 a c d+b \left(c^2+d^2\right)\right) \tan (e+f x)}{3 f}+\frac{\left(a \left(2 c^2+d^2\right)+2 b c d\right) \tanh ^{-1}(\sin (e+f x))}{2 f}+\frac{d (3 a d+2 b c) \tan (e+f x) \sec (e+f x)}{6 f}+\frac{b \tan (e+f x) (c+d \sec (e+f x))^2}{3 f}",1,"((2*b*c*d + a*(2*c^2 + d^2))*ArcTanh[Sin[e + f*x]])/(2*f) + (2*(3*a*c*d + b*(c^2 + d^2))*Tan[e + f*x])/(3*f) + (d*(2*b*c + 3*a*d)*Sec[e + f*x]*Tan[e + f*x])/(6*f) + (b*(c + d*Sec[e + f*x])^2*Tan[e + f*x])/(3*f)","A",6,6,29,0.2069,1,"{4002, 3997, 3787, 3770, 3767, 8}"
247,1,61,0,0.0750499,"\int \sec (e+f x) (a+b \sec (e+f x)) (c+d \sec (e+f x)) \, dx","Int[Sec[e + f*x]*(a + b*Sec[e + f*x])*(c + d*Sec[e + f*x]),x]","\frac{(a d+b c) \tan (e+f x)}{f}+\frac{(2 a c+b d) \tanh ^{-1}(\sin (e+f x))}{2 f}+\frac{b d \tan (e+f x) \sec (e+f x)}{2 f}","\frac{(a d+b c) \tan (e+f x)}{f}+\frac{(2 a c+b d) \tanh ^{-1}(\sin (e+f x))}{2 f}+\frac{b d \tan (e+f x) \sec (e+f x)}{2 f}",1,"((2*a*c + b*d)*ArcTanh[Sin[e + f*x]])/(2*f) + ((b*c + a*d)*Tan[e + f*x])/f + (b*d*Sec[e + f*x]*Tan[e + f*x])/(2*f)","A",5,5,27,0.1852,1,"{3997, 3787, 3770, 3767, 8}"
248,1,76,0,0.1287895,"\int \frac{\sec (e+f x) (a+b \sec (e+f x))}{c+d \sec (e+f x)} \, dx","Int[(Sec[e + f*x]*(a + b*Sec[e + f*x]))/(c + d*Sec[e + f*x]),x]","\frac{b \tanh ^{-1}(\sin (e+f x))}{d f}-\frac{2 (b c-a d) \tanh ^{-1}\left(\frac{\sqrt{c-d} \tan \left(\frac{1}{2} (e+f x)\right)}{\sqrt{c+d}}\right)}{d f \sqrt{c-d} \sqrt{c+d}}","\frac{b \tanh ^{-1}(\sin (e+f x))}{d f}-\frac{2 (b c-a d) \tanh ^{-1}\left(\frac{\sqrt{c-d} \tan \left(\frac{1}{2} (e+f x)\right)}{\sqrt{c+d}}\right)}{d f \sqrt{c-d} \sqrt{c+d}}",1,"(b*ArcTanh[Sin[e + f*x]])/(d*f) - (2*(b*c - a*d)*ArcTanh[(Sqrt[c - d]*Tan[(e + f*x)/2])/Sqrt[c + d]])/(Sqrt[c - d]*d*Sqrt[c + d]*f)","A",5,5,29,0.1724,1,"{3998, 3770, 3831, 2659, 208}"
249,1,99,0,0.1438866,"\int \frac{\sec (e+f x) (a+b \sec (e+f x))}{(c+d \sec (e+f x))^2} \, dx","Int[(Sec[e + f*x]*(a + b*Sec[e + f*x]))/(c + d*Sec[e + f*x])^2,x]","\frac{(b c-a d) \tan (e+f x)}{f \left(c^2-d^2\right) (c+d \sec (e+f x))}+\frac{2 (a c-b d) \tanh ^{-1}\left(\frac{\sqrt{c-d} \tan \left(\frac{1}{2} (e+f x)\right)}{\sqrt{c+d}}\right)}{f (c-d)^{3/2} (c+d)^{3/2}}","\frac{(b c-a d) \tan (e+f x)}{f \left(c^2-d^2\right) (c+d \sec (e+f x))}+\frac{2 (a c-b d) \tanh ^{-1}\left(\frac{\sqrt{c-d} \tan \left(\frac{1}{2} (e+f x)\right)}{\sqrt{c+d}}\right)}{f (c-d)^{3/2} (c+d)^{3/2}}",1,"(2*(a*c - b*d)*ArcTanh[(Sqrt[c - d]*Tan[(e + f*x)/2])/Sqrt[c + d]])/((c - d)^(3/2)*(c + d)^(3/2)*f) + ((b*c - a*d)*Tan[e + f*x])/((c^2 - d^2)*f*(c + d*Sec[e + f*x]))","A",5,5,29,0.1724,1,"{4003, 12, 3831, 2659, 208}"
250,1,166,0,0.3006563,"\int \frac{\sec (e+f x) (a+b \sec (e+f x))}{(c+d \sec (e+f x))^3} \, dx","Int[(Sec[e + f*x]*(a + b*Sec[e + f*x]))/(c + d*Sec[e + f*x])^3,x]","-\frac{\left(3 b c d-a \left(2 c^2+d^2\right)\right) \tanh ^{-1}\left(\frac{\sqrt{c-d} \tan \left(\frac{1}{2} (e+f x)\right)}{\sqrt{c+d}}\right)}{f (c-d)^{5/2} (c+d)^{5/2}}-\frac{\left(3 a c d-b \left(c^2+2 d^2\right)\right) \tan (e+f x)}{2 f \left(c^2-d^2\right)^2 (c+d \sec (e+f x))}+\frac{(b c-a d) \tan (e+f x)}{2 f \left(c^2-d^2\right) (c+d \sec (e+f x))^2}","-\frac{\left(3 b c d-a \left(2 c^2+d^2\right)\right) \tanh ^{-1}\left(\frac{\sqrt{c-d} \tan \left(\frac{1}{2} (e+f x)\right)}{\sqrt{c+d}}\right)}{f (c-d)^{5/2} (c+d)^{5/2}}-\frac{\left(3 a c d-b \left(c^2+2 d^2\right)\right) \tan (e+f x)}{2 f \left(c^2-d^2\right)^2 (c+d \sec (e+f x))}+\frac{(b c-a d) \tan (e+f x)}{2 f \left(c^2-d^2\right) (c+d \sec (e+f x))^2}",1,"-(((3*b*c*d - a*(2*c^2 + d^2))*ArcTanh[(Sqrt[c - d]*Tan[(e + f*x)/2])/Sqrt[c + d]])/((c - d)^(5/2)*(c + d)^(5/2)*f)) + ((b*c - a*d)*Tan[e + f*x])/(2*(c^2 - d^2)*f*(c + d*Sec[e + f*x])^2) - ((3*a*c*d - b*(c^2 + 2*d^2))*Tan[e + f*x])/(2*(c^2 - d^2)^2*f*(c + d*Sec[e + f*x]))","A",6,5,29,0.1724,1,"{4003, 12, 3831, 2659, 208}"
251,1,237,0,0.5118875,"\int \frac{\sec (e+f x) (a+b \sec (e+f x))}{(c+d \sec (e+f x))^4} \, dx","Int[(Sec[e + f*x]*(a + b*Sec[e + f*x]))/(c + d*Sec[e + f*x])^4,x]","\frac{\left(2 a c^3+3 a c d^2-4 b c^2 d-b d^3\right) \tanh ^{-1}\left(\frac{\sqrt{c-d} \tan \left(\frac{1}{2} (e+f x)\right)}{\sqrt{c+d}}\right)}{f (c-d)^{7/2} (c+d)^{7/2}}+\frac{\left(-11 a c^2 d-4 a d^3+2 b c^3+13 b c d^2\right) \tan (e+f x)}{6 f \left(c^2-d^2\right)^3 (c+d \sec (e+f x))}+\frac{\left(-5 a c d+2 b c^2+3 b d^2\right) \tan (e+f x)}{6 f \left(c^2-d^2\right)^2 (c+d \sec (e+f x))^2}+\frac{(b c-a d) \tan (e+f x)}{3 f \left(c^2-d^2\right) (c+d \sec (e+f x))^3}","\frac{\left(2 a c^3+3 a c d^2-4 b c^2 d-b d^3\right) \tanh ^{-1}\left(\frac{\sqrt{c-d} \tan \left(\frac{1}{2} (e+f x)\right)}{\sqrt{c+d}}\right)}{f (c-d)^{7/2} (c+d)^{7/2}}+\frac{\left(-11 a c^2 d-4 a d^3+2 b c^3+13 b c d^2\right) \tan (e+f x)}{6 f \left(c^2-d^2\right)^3 (c+d \sec (e+f x))}+\frac{\left(-5 a c d+2 b c^2+3 b d^2\right) \tan (e+f x)}{6 f \left(c^2-d^2\right)^2 (c+d \sec (e+f x))^2}+\frac{(b c-a d) \tan (e+f x)}{3 f \left(c^2-d^2\right) (c+d \sec (e+f x))^3}",1,"((2*a*c^3 - 4*b*c^2*d + 3*a*c*d^2 - b*d^3)*ArcTanh[(Sqrt[c - d]*Tan[(e + f*x)/2])/Sqrt[c + d]])/((c - d)^(7/2)*(c + d)^(7/2)*f) + ((b*c - a*d)*Tan[e + f*x])/(3*(c^2 - d^2)*f*(c + d*Sec[e + f*x])^3) + ((2*b*c^2 - 5*a*c*d + 3*b*d^2)*Tan[e + f*x])/(6*(c^2 - d^2)^2*f*(c + d*Sec[e + f*x])^2) + ((2*b*c^3 - 11*a*c^2*d + 13*b*c*d^2 - 4*a*d^3)*Tan[e + f*x])/(6*(c^2 - d^2)^3*f*(c + d*Sec[e + f*x]))","A",7,5,29,0.1724,1,"{4003, 12, 3831, 2659, 208}"
252,1,247,0,0.4445539,"\int \frac{\sec (e+f x) (c+d \sec (e+f x))^4}{a+b \sec (e+f x)} \, dx","Int[(Sec[e + f*x]*(c + d*Sec[e + f*x])^4)/(a + b*Sec[e + f*x]),x]","\frac{d^2 \left(a^2 d^2-4 a b c d+6 b^2 c^2\right) \tan (e+f x)}{b^3 f}+\frac{d (2 b c-a d) \left(a^2 d^2-2 a b c d+2 b^2 c^2\right) \tanh ^{-1}(\sin (e+f x))}{b^4 f}+\frac{d^3 (4 b c-a d) \tanh ^{-1}(\sin (e+f x))}{2 b^2 f}+\frac{d^3 (4 b c-a d) \tan (e+f x) \sec (e+f x)}{2 b^2 f}+\frac{2 (b c-a d)^4 \tanh ^{-1}\left(\frac{\sqrt{a-b} \tan \left(\frac{1}{2} (e+f x)\right)}{\sqrt{a+b}}\right)}{b^4 f \sqrt{a-b} \sqrt{a+b}}+\frac{d^4 \tan ^3(e+f x)}{3 b f}+\frac{d^4 \tan (e+f x)}{b f}","\frac{d^2 \left(a^2 d^2-4 a b c d+6 b^2 c^2\right) \tan (e+f x)}{b^3 f}+\frac{d (2 b c-a d) \left(a^2 d^2-2 a b c d+2 b^2 c^2\right) \tanh ^{-1}(\sin (e+f x))}{b^4 f}+\frac{d^3 (4 b c-a d) \tanh ^{-1}(\sin (e+f x))}{2 b^2 f}+\frac{d^3 (4 b c-a d) \tan (e+f x) \sec (e+f x)}{2 b^2 f}+\frac{2 (b c-a d)^4 \tanh ^{-1}\left(\frac{\sqrt{a-b} \tan \left(\frac{1}{2} (e+f x)\right)}{\sqrt{a+b}}\right)}{b^4 f \sqrt{a-b} \sqrt{a+b}}+\frac{d^4 \tan ^3(e+f x)}{3 b f}+\frac{d^4 \tan (e+f x)}{b f}",1,"(d^3*(4*b*c - a*d)*ArcTanh[Sin[e + f*x]])/(2*b^2*f) + (d*(2*b*c - a*d)*(2*b^2*c^2 - 2*a*b*c*d + a^2*d^2)*ArcTanh[Sin[e + f*x]])/(b^4*f) + (2*(b*c - a*d)^4*ArcTanh[(Sqrt[a - b]*Tan[(e + f*x)/2])/Sqrt[a + b]])/(Sqrt[a - b]*b^4*Sqrt[a + b]*f) + (d^4*Tan[e + f*x])/(b*f) + (d^2*(6*b^2*c^2 - 4*a*b*c*d + a^2*d^2)*Tan[e + f*x])/(b^3*f) + (d^3*(4*b*c - a*d)*Sec[e + f*x]*Tan[e + f*x])/(2*b^2*f) + (d^4*Tan[e + f*x]^3)/(3*b*f)","A",12,8,31,0.2581,1,"{3988, 2952, 2659, 208, 3770, 3767, 8, 3768}"
253,1,170,0,0.3504735,"\int \frac{\sec (e+f x) (c+d \sec (e+f x))^3}{a+b \sec (e+f x)} \, dx","Int[(Sec[e + f*x]*(c + d*Sec[e + f*x])^3)/(a + b*Sec[e + f*x]),x]","\frac{d \left(a^2 d^2-3 a b c d+3 b^2 c^2\right) \tanh ^{-1}(\sin (e+f x))}{b^3 f}+\frac{d^2 (3 b c-a d) \tan (e+f x)}{b^2 f}+\frac{2 (b c-a d)^3 \tanh ^{-1}\left(\frac{\sqrt{a-b} \tan \left(\frac{1}{2} (e+f x)\right)}{\sqrt{a+b}}\right)}{b^3 f \sqrt{a-b} \sqrt{a+b}}+\frac{d^3 \tanh ^{-1}(\sin (e+f x))}{2 b f}+\frac{d^3 \tan (e+f x) \sec (e+f x)}{2 b f}","\frac{d \left(a^2 d^2-3 a b c d+3 b^2 c^2\right) \tanh ^{-1}(\sin (e+f x))}{b^3 f}+\frac{d^2 (3 b c-a d) \tan (e+f x)}{b^2 f}+\frac{2 (b c-a d)^3 \tanh ^{-1}\left(\frac{\sqrt{a-b} \tan \left(\frac{1}{2} (e+f x)\right)}{\sqrt{a+b}}\right)}{b^3 f \sqrt{a-b} \sqrt{a+b}}+\frac{d^3 \tanh ^{-1}(\sin (e+f x))}{2 b f}+\frac{d^3 \tan (e+f x) \sec (e+f x)}{2 b f}",1,"(d^3*ArcTanh[Sin[e + f*x]])/(2*b*f) + (d*(3*b^2*c^2 - 3*a*b*c*d + a^2*d^2)*ArcTanh[Sin[e + f*x]])/(b^3*f) + (2*(b*c - a*d)^3*ArcTanh[(Sqrt[a - b]*Tan[(e + f*x)/2])/Sqrt[a + b]])/(Sqrt[a - b]*b^3*Sqrt[a + b]*f) + (d^2*(3*b*c - a*d)*Tan[e + f*x])/(b^2*f) + (d^3*Sec[e + f*x]*Tan[e + f*x])/(2*b*f)","A",10,8,31,0.2581,1,"{3988, 2952, 2659, 208, 3770, 3767, 8, 3768}"
254,1,103,0,0.2974478,"\int \frac{\sec (e+f x) (c+d \sec (e+f x))^2}{a+b \sec (e+f x)} \, dx","Int[(Sec[e + f*x]*(c + d*Sec[e + f*x])^2)/(a + b*Sec[e + f*x]),x]","\frac{d (2 b c-a d) \tanh ^{-1}(\sin (e+f x))}{b^2 f}+\frac{2 (b c-a d)^2 \tanh ^{-1}\left(\frac{\sqrt{a-b} \tan \left(\frac{1}{2} (e+f x)\right)}{\sqrt{a+b}}\right)}{b^2 f \sqrt{a-b} \sqrt{a+b}}+\frac{d^2 \tan (e+f x)}{b f}","\frac{d (2 b c-a d) \tanh ^{-1}(\sin (e+f x))}{b^2 f}+\frac{2 (b c-a d)^2 \tanh ^{-1}\left(\frac{\sqrt{a-b} \tan \left(\frac{1}{2} (e+f x)\right)}{\sqrt{a+b}}\right)}{b^2 f \sqrt{a-b} \sqrt{a+b}}+\frac{d^2 \tan (e+f x)}{b f}",1,"(d*(2*b*c - a*d)*ArcTanh[Sin[e + f*x]])/(b^2*f) + (2*(b*c - a*d)^2*ArcTanh[(Sqrt[a - b]*Tan[(e + f*x)/2])/Sqrt[a + b]])/(Sqrt[a - b]*b^2*Sqrt[a + b]*f) + (d^2*Tan[e + f*x])/(b*f)","A",8,7,31,0.2258,1,"{3988, 2952, 2659, 208, 3770, 3767, 8}"
255,1,76,0,0.1269875,"\int \frac{\sec (e+f x) (c+d \sec (e+f x))}{a+b \sec (e+f x)} \, dx","Int[(Sec[e + f*x]*(c + d*Sec[e + f*x]))/(a + b*Sec[e + f*x]),x]","\frac{2 (b c-a d) \tanh ^{-1}\left(\frac{\sqrt{a-b} \tan \left(\frac{1}{2} (e+f x)\right)}{\sqrt{a+b}}\right)}{b f \sqrt{a-b} \sqrt{a+b}}+\frac{d \tanh ^{-1}(\sin (e+f x))}{b f}","\frac{2 (b c-a d) \tanh ^{-1}\left(\frac{\sqrt{a-b} \tan \left(\frac{1}{2} (e+f x)\right)}{\sqrt{a+b}}\right)}{b f \sqrt{a-b} \sqrt{a+b}}+\frac{d \tanh ^{-1}(\sin (e+f x))}{b f}",1,"(d*ArcTanh[Sin[e + f*x]])/(b*f) + (2*(b*c - a*d)*ArcTanh[(Sqrt[a - b]*Tan[(e + f*x)/2])/Sqrt[a + b]])/(Sqrt[a - b]*b*Sqrt[a + b]*f)","A",5,5,29,0.1724,1,"{3998, 3770, 3831, 2659, 208}"
256,1,121,0,0.2745758,"\int \frac{\sec (e+f x)}{(a+b \sec (e+f x)) (c+d \sec (e+f x))} \, dx","Int[Sec[e + f*x]/((a + b*Sec[e + f*x])*(c + d*Sec[e + f*x])),x]","\frac{2 b \tanh ^{-1}\left(\frac{\sqrt{a-b} \tan \left(\frac{1}{2} (e+f x)\right)}{\sqrt{a+b}}\right)}{f \sqrt{a-b} \sqrt{a+b} (b c-a d)}-\frac{2 d \tanh ^{-1}\left(\frac{\sqrt{c-d} \tan \left(\frac{1}{2} (e+f x)\right)}{\sqrt{c+d}}\right)}{f \sqrt{c-d} \sqrt{c+d} (b c-a d)}","\frac{2 b \tanh ^{-1}\left(\frac{\sqrt{a-b} \tan \left(\frac{1}{2} (e+f x)\right)}{\sqrt{a+b}}\right)}{f \sqrt{a-b} \sqrt{a+b} (b c-a d)}-\frac{2 d \tanh ^{-1}\left(\frac{\sqrt{c-d} \tan \left(\frac{1}{2} (e+f x)\right)}{\sqrt{c+d}}\right)}{f \sqrt{c-d} \sqrt{c+d} (b c-a d)}",1,"(2*b*ArcTanh[(Sqrt[a - b]*Tan[(e + f*x)/2])/Sqrt[a + b]])/(Sqrt[a - b]*Sqrt[a + b]*(b*c - a*d)*f) - (2*d*ArcTanh[(Sqrt[c - d]*Tan[(e + f*x)/2])/Sqrt[c + d]])/(Sqrt[c - d]*Sqrt[c + d]*(b*c - a*d)*f)","A",6,4,31,0.1290,1,"{3988, 3001, 2659, 208}"
257,1,187,0,0.6124315,"\int \frac{\sec (e+f x)}{(a+b \sec (e+f x)) (c+d \sec (e+f x))^2} \, dx","Int[Sec[e + f*x]/((a + b*Sec[e + f*x])*(c + d*Sec[e + f*x])^2),x]","\frac{2 b^2 \tanh ^{-1}\left(\frac{\sqrt{a-b} \tan \left(\frac{1}{2} (e+f x)\right)}{\sqrt{a+b}}\right)}{f \sqrt{a-b} \sqrt{a+b} (b c-a d)^2}+\frac{d^2 \sin (e+f x)}{f \left(c^2-d^2\right) (b c-a d) (c \cos (e+f x)+d)}-\frac{2 d \left(-a c d+2 b c^2-b d^2\right) \tanh ^{-1}\left(\frac{\sqrt{c-d} \tan \left(\frac{1}{2} (e+f x)\right)}{\sqrt{c+d}}\right)}{f (c-d)^{3/2} (c+d)^{3/2} (b c-a d)^2}","\frac{2 b^2 \tanh ^{-1}\left(\frac{\sqrt{a-b} \tan \left(\frac{1}{2} (e+f x)\right)}{\sqrt{a+b}}\right)}{f \sqrt{a-b} \sqrt{a+b} (b c-a d)^2}+\frac{d^2 \sin (e+f x)}{f \left(c^2-d^2\right) (b c-a d) (c \cos (e+f x)+d)}-\frac{2 d \left(-a c d+2 b c^2-b d^2\right) \tanh ^{-1}\left(\frac{\sqrt{c-d} \tan \left(\frac{1}{2} (e+f x)\right)}{\sqrt{c+d}}\right)}{f (c-d)^{3/2} (c+d)^{3/2} (b c-a d)^2}",1,"(2*b^2*ArcTanh[(Sqrt[a - b]*Tan[(e + f*x)/2])/Sqrt[a + b]])/(Sqrt[a - b]*Sqrt[a + b]*(b*c - a*d)^2*f) - (2*d*(2*b*c^2 - a*c*d - b*d^2)*ArcTanh[(Sqrt[c - d]*Tan[(e + f*x)/2])/Sqrt[c + d]])/((c - d)^(3/2)*(c + d)^(3/2)*(b*c - a*d)^2*f) + (d^2*Sin[e + f*x])/((b*c - a*d)*(c^2 - d^2)*f*(d + c*Cos[e + f*x]))","A",7,5,31,0.1613,1,"{3988, 3056, 3001, 2659, 208}"
258,1,379,0,0.6679929,"\int \frac{\sec (e+f x) (c+d \sec (e+f x))^5}{(a+b \sec (e+f x))^2} \, dx","Int[(Sec[e + f*x]*(c + d*Sec[e + f*x])^5)/(a + b*Sec[e + f*x])^2,x]","\frac{d^3 \left(3 a^2 d^2-10 a b c d+10 b^2 c^2\right) \tan (e+f x)}{b^4 f}+\frac{d^2 \left(15 a^2 b c d^2-4 a^3 d^3-20 a b^2 c^2 d+10 b^3 c^3\right) \tanh ^{-1}(\sin (e+f x))}{b^5 f}-\frac{(b c-a d)^5 \sin (e+f x)}{b^4 f \left(a^2-b^2\right) (a \cos (e+f x)+b)}+\frac{d^4 (5 b c-2 a d) \tanh ^{-1}(\sin (e+f x))}{2 b^3 f}+\frac{d^4 (5 b c-2 a d) \tan (e+f x) \sec (e+f x)}{2 b^3 f}+\frac{2 (b c-a d)^5 \tanh ^{-1}\left(\frac{\sqrt{a-b} \tan \left(\frac{1}{2} (e+f x)\right)}{\sqrt{a+b}}\right)}{a b^3 f (a-b)^{3/2} (a+b)^{3/2}}+\frac{2 (b c-a d)^4 (4 a d+b c) \tanh ^{-1}\left(\frac{\sqrt{a-b} \tan \left(\frac{1}{2} (e+f x)\right)}{\sqrt{a+b}}\right)}{a b^5 f \sqrt{a-b} \sqrt{a+b}}+\frac{d^5 \tan ^3(e+f x)}{3 b^2 f}+\frac{d^5 \tan (e+f x)}{b^2 f}","\frac{d^3 \left(3 a^2 d^2-10 a b c d+10 b^2 c^2\right) \tan (e+f x)}{b^4 f}+\frac{d^2 \left(15 a^2 b c d^2-4 a^3 d^3-20 a b^2 c^2 d+10 b^3 c^3\right) \tanh ^{-1}(\sin (e+f x))}{b^5 f}-\frac{(b c-a d)^5 \sin (e+f x)}{b^4 f \left(a^2-b^2\right) (a \cos (e+f x)+b)}+\frac{d^4 (5 b c-2 a d) \tanh ^{-1}(\sin (e+f x))}{2 b^3 f}+\frac{d^4 (5 b c-2 a d) \tan (e+f x) \sec (e+f x)}{2 b^3 f}+\frac{2 (b c-a d)^5 \tanh ^{-1}\left(\frac{\sqrt{a-b} \tan \left(\frac{1}{2} (e+f x)\right)}{\sqrt{a+b}}\right)}{a b^3 f (a-b)^{3/2} (a+b)^{3/2}}+\frac{2 (b c-a d)^4 (4 a d+b c) \tanh ^{-1}\left(\frac{\sqrt{a-b} \tan \left(\frac{1}{2} (e+f x)\right)}{\sqrt{a+b}}\right)}{a b^5 f \sqrt{a-b} \sqrt{a+b}}+\frac{d^5 \tan ^3(e+f x)}{3 b^2 f}+\frac{d^5 \tan (e+f x)}{b^2 f}",1,"(d^4*(5*b*c - 2*a*d)*ArcTanh[Sin[e + f*x]])/(2*b^3*f) + (d^2*(10*b^3*c^3 - 20*a*b^2*c^2*d + 15*a^2*b*c*d^2 - 4*a^3*d^3)*ArcTanh[Sin[e + f*x]])/(b^5*f) + (2*(b*c - a*d)^5*ArcTanh[(Sqrt[a - b]*Tan[(e + f*x)/2])/Sqrt[a + b]])/(a*(a - b)^(3/2)*b^3*(a + b)^(3/2)*f) + (2*(b*c - a*d)^4*(b*c + 4*a*d)*ArcTanh[(Sqrt[a - b]*Tan[(e + f*x)/2])/Sqrt[a + b]])/(a*Sqrt[a - b]*b^5*Sqrt[a + b]*f) - ((b*c - a*d)^5*Sin[e + f*x])/(b^4*(a^2 - b^2)*f*(b + a*Cos[e + f*x])) + (d^5*Tan[e + f*x])/(b^2*f) + (d^3*(10*b^2*c^2 - 10*a*b*c*d + 3*a^2*d^2)*Tan[e + f*x])/(b^4*f) + (d^4*(5*b*c - 2*a*d)*Sec[e + f*x]*Tan[e + f*x])/(2*b^3*f) + (d^5*Tan[e + f*x]^3)/(3*b^2*f)","A",16,10,31,0.3226,1,"{3988, 2952, 2664, 12, 2659, 208, 3770, 3767, 8, 3768}"
259,1,297,0,0.5268493,"\int \frac{\sec (e+f x) (c+d \sec (e+f x))^4}{(a+b \sec (e+f x))^2} \, dx","Int[(Sec[e + f*x]*(c + d*Sec[e + f*x])^4)/(a + b*Sec[e + f*x])^2,x]","\frac{d^2 \left(3 a^2 d^2-8 a b c d+6 b^2 c^2\right) \tanh ^{-1}(\sin (e+f x))}{b^4 f}-\frac{(b c-a d)^4 \sin (e+f x)}{b^3 f \left(a^2-b^2\right) (a \cos (e+f x)+b)}+\frac{2 d^3 (2 b c-a d) \tan (e+f x)}{b^3 f}+\frac{2 (b c-a d)^4 \tanh ^{-1}\left(\frac{\sqrt{a-b} \tan \left(\frac{1}{2} (e+f x)\right)}{\sqrt{a+b}}\right)}{a b^2 f (a-b)^{3/2} (a+b)^{3/2}}+\frac{2 (b c-a d)^3 (3 a d+b c) \tanh ^{-1}\left(\frac{\sqrt{a-b} \tan \left(\frac{1}{2} (e+f x)\right)}{\sqrt{a+b}}\right)}{a b^4 f \sqrt{a-b} \sqrt{a+b}}+\frac{d^4 \tanh ^{-1}(\sin (e+f x))}{2 b^2 f}+\frac{d^4 \tan (e+f x) \sec (e+f x)}{2 b^2 f}","\frac{d^2 \left(3 a^2 d^2-8 a b c d+6 b^2 c^2\right) \tanh ^{-1}(\sin (e+f x))}{b^4 f}-\frac{(b c-a d)^4 \sin (e+f x)}{b^3 f \left(a^2-b^2\right) (a \cos (e+f x)+b)}+\frac{2 d^3 (2 b c-a d) \tan (e+f x)}{b^3 f}+\frac{2 (b c-a d)^4 \tanh ^{-1}\left(\frac{\sqrt{a-b} \tan \left(\frac{1}{2} (e+f x)\right)}{\sqrt{a+b}}\right)}{a b^2 f (a-b)^{3/2} (a+b)^{3/2}}+\frac{2 (b c-a d)^3 (3 a d+b c) \tanh ^{-1}\left(\frac{\sqrt{a-b} \tan \left(\frac{1}{2} (e+f x)\right)}{\sqrt{a+b}}\right)}{a b^4 f \sqrt{a-b} \sqrt{a+b}}+\frac{d^4 \tanh ^{-1}(\sin (e+f x))}{2 b^2 f}+\frac{d^4 \tan (e+f x) \sec (e+f x)}{2 b^2 f}",1,"(d^4*ArcTanh[Sin[e + f*x]])/(2*b^2*f) + (d^2*(6*b^2*c^2 - 8*a*b*c*d + 3*a^2*d^2)*ArcTanh[Sin[e + f*x]])/(b^4*f) + (2*(b*c - a*d)^4*ArcTanh[(Sqrt[a - b]*Tan[(e + f*x)/2])/Sqrt[a + b]])/(a*(a - b)^(3/2)*b^2*(a + b)^(3/2)*f) + (2*(b*c - a*d)^3*(b*c + 3*a*d)*ArcTanh[(Sqrt[a - b]*Tan[(e + f*x)/2])/Sqrt[a + b]])/(a*Sqrt[a - b]*b^4*Sqrt[a + b]*f) - ((b*c - a*d)^4*Sin[e + f*x])/(b^3*(a^2 - b^2)*f*(b + a*Cos[e + f*x])) + (2*d^3*(2*b*c - a*d)*Tan[e + f*x])/(b^3*f) + (d^4*Sec[e + f*x]*Tan[e + f*x])/(2*b^2*f)","A",14,10,31,0.3226,1,"{3988, 2952, 2664, 12, 2659, 208, 3770, 3767, 8, 3768}"
260,1,228,0,0.4672639,"\int \frac{\sec (e+f x) (c+d \sec (e+f x))^3}{(a+b \sec (e+f x))^2} \, dx","Int[(Sec[e + f*x]*(c + d*Sec[e + f*x])^3)/(a + b*Sec[e + f*x])^2,x]","-\frac{(b c-a d)^3 \sin (e+f x)}{b^2 f \left(a^2-b^2\right) (a \cos (e+f x)+b)}+\frac{d^2 (3 b c-2 a d) \tanh ^{-1}(\sin (e+f x))}{b^3 f}+\frac{2 (b c-a d)^2 (2 a d+b c) \tanh ^{-1}\left(\frac{\sqrt{a-b} \tan \left(\frac{1}{2} (e+f x)\right)}{\sqrt{a+b}}\right)}{a b^3 f \sqrt{a-b} \sqrt{a+b}}+\frac{2 (b c-a d)^3 \tanh ^{-1}\left(\frac{\sqrt{a-b} \tan \left(\frac{1}{2} (e+f x)\right)}{\sqrt{a+b}}\right)}{a b f (a-b)^{3/2} (a+b)^{3/2}}+\frac{d^3 \tan (e+f x)}{b^2 f}","-\frac{(b c-a d)^3 \sin (e+f x)}{b^2 f \left(a^2-b^2\right) (a \cos (e+f x)+b)}+\frac{d^2 (3 b c-2 a d) \tanh ^{-1}(\sin (e+f x))}{b^3 f}+\frac{2 (b c-a d)^2 (2 a d+b c) \tanh ^{-1}\left(\frac{\sqrt{a-b} \tan \left(\frac{1}{2} (e+f x)\right)}{\sqrt{a+b}}\right)}{a b^3 f \sqrt{a-b} \sqrt{a+b}}+\frac{2 (b c-a d)^3 \tanh ^{-1}\left(\frac{\sqrt{a-b} \tan \left(\frac{1}{2} (e+f x)\right)}{\sqrt{a+b}}\right)}{a b f (a-b)^{3/2} (a+b)^{3/2}}+\frac{d^3 \tan (e+f x)}{b^2 f}",1,"(d^2*(3*b*c - 2*a*d)*ArcTanh[Sin[e + f*x]])/(b^3*f) + (2*(b*c - a*d)^3*ArcTanh[(Sqrt[a - b]*Tan[(e + f*x)/2])/Sqrt[a + b]])/(a*(a - b)^(3/2)*b*(a + b)^(3/2)*f) + (2*(b*c - a*d)^2*(b*c + 2*a*d)*ArcTanh[(Sqrt[a - b]*Tan[(e + f*x)/2])/Sqrt[a + b]])/(a*Sqrt[a - b]*b^3*Sqrt[a + b]*f) - ((b*c - a*d)^3*Sin[e + f*x])/(b^2*(a^2 - b^2)*f*(b + a*Cos[e + f*x])) + (d^3*Tan[e + f*x])/(b^2*f)","A",12,9,31,0.2903,1,"{3988, 2952, 2664, 12, 2659, 208, 3770, 3767, 8}"
261,1,198,0,0.3669552,"\int \frac{\sec (e+f x) (c+d \sec (e+f x))^2}{(a+b \sec (e+f x))^2} \, dx","Int[(Sec[e + f*x]*(c + d*Sec[e + f*x])^2)/(a + b*Sec[e + f*x])^2,x]","\frac{2 \left(b^2 c^2-a^2 d^2\right) \tanh ^{-1}\left(\frac{\sqrt{a-b} \tan \left(\frac{1}{2} (e+f x)\right)}{\sqrt{a+b}}\right)}{a b^2 f \sqrt{a-b} \sqrt{a+b}}-\frac{(b c-a d)^2 \sin (e+f x)}{b f \left(a^2-b^2\right) (a \cos (e+f x)+b)}+\frac{2 (b c-a d)^2 \tanh ^{-1}\left(\frac{\sqrt{a-b} \tan \left(\frac{1}{2} (e+f x)\right)}{\sqrt{a+b}}\right)}{a f (a-b)^{3/2} (a+b)^{3/2}}+\frac{d^2 \tanh ^{-1}(\sin (e+f x))}{b^2 f}","\frac{2 \left(b^2 c^2-a^2 d^2\right) \tanh ^{-1}\left(\frac{\sqrt{a-b} \tan \left(\frac{1}{2} (e+f x)\right)}{\sqrt{a+b}}\right)}{a b^2 f \sqrt{a-b} \sqrt{a+b}}-\frac{(b c-a d)^2 \sin (e+f x)}{b f \left(a^2-b^2\right) (a \cos (e+f x)+b)}+\frac{2 (b c-a d)^2 \tanh ^{-1}\left(\frac{\sqrt{a-b} \tan \left(\frac{1}{2} (e+f x)\right)}{\sqrt{a+b}}\right)}{a f (a-b)^{3/2} (a+b)^{3/2}}+\frac{d^2 \tanh ^{-1}(\sin (e+f x))}{b^2 f}",1,"(d^2*ArcTanh[Sin[e + f*x]])/(b^2*f) + (2*(b*c - a*d)^2*ArcTanh[(Sqrt[a - b]*Tan[(e + f*x)/2])/Sqrt[a + b]])/(a*(a - b)^(3/2)*(a + b)^(3/2)*f) + (2*(b^2*c^2 - a^2*d^2)*ArcTanh[(Sqrt[a - b]*Tan[(e + f*x)/2])/Sqrt[a + b]])/(a*Sqrt[a - b]*b^2*Sqrt[a + b]*f) - ((b*c - a*d)^2*Sin[e + f*x])/(b*(a^2 - b^2)*f*(b + a*Cos[e + f*x]))","A",10,7,31,0.2258,1,"{3988, 2952, 2664, 12, 2659, 208, 3770}"
262,1,100,0,0.1363876,"\int \frac{\sec (e+f x) (c+d \sec (e+f x))}{(a+b \sec (e+f x))^2} \, dx","Int[(Sec[e + f*x]*(c + d*Sec[e + f*x]))/(a + b*Sec[e + f*x])^2,x]","\frac{2 (a c-b d) \tanh ^{-1}\left(\frac{\sqrt{a-b} \tan \left(\frac{1}{2} (e+f x)\right)}{\sqrt{a+b}}\right)}{f (a-b)^{3/2} (a+b)^{3/2}}-\frac{(b c-a d) \tan (e+f x)}{f \left(a^2-b^2\right) (a+b \sec (e+f x))}","\frac{2 (a c-b d) \tanh ^{-1}\left(\frac{\sqrt{a-b} \tan \left(\frac{1}{2} (e+f x)\right)}{\sqrt{a+b}}\right)}{f (a-b)^{3/2} (a+b)^{3/2}}-\frac{(b c-a d) \tan (e+f x)}{f \left(a^2-b^2\right) (a+b \sec (e+f x))}",1,"(2*(a*c - b*d)*ArcTanh[(Sqrt[a - b]*Tan[(e + f*x)/2])/Sqrt[a + b]])/((a - b)^(3/2)*(a + b)^(3/2)*f) - ((b*c - a*d)*Tan[e + f*x])/((a^2 - b^2)*f*(a + b*Sec[e + f*x]))","A",5,5,29,0.1724,1,"{4003, 12, 3831, 2659, 208}"
263,1,186,0,0.6045093,"\int \frac{\sec (e+f x)}{(a+b \sec (e+f x))^2 (c+d \sec (e+f x))} \, dx","Int[Sec[e + f*x]/((a + b*Sec[e + f*x])^2*(c + d*Sec[e + f*x])),x]","-\frac{b^2 \sin (e+f x)}{f \left(a^2-b^2\right) (b c-a d) (a \cos (e+f x)+b)}+\frac{2 b \left(-2 a^2 d+a b c+b^2 d\right) \tanh ^{-1}\left(\frac{\sqrt{a-b} \tan \left(\frac{1}{2} (e+f x)\right)}{\sqrt{a+b}}\right)}{f (a-b)^{3/2} (a+b)^{3/2} (b c-a d)^2}+\frac{2 d^2 \tanh ^{-1}\left(\frac{\sqrt{c-d} \tan \left(\frac{1}{2} (e+f x)\right)}{\sqrt{c+d}}\right)}{f \sqrt{c-d} \sqrt{c+d} (b c-a d)^2}","-\frac{b^2 \sin (e+f x)}{f \left(a^2-b^2\right) (b c-a d) (a \cos (e+f x)+b)}+\frac{2 b \left(-2 a^2 d+a b c+b^2 d\right) \tanh ^{-1}\left(\frac{\sqrt{a-b} \tan \left(\frac{1}{2} (e+f x)\right)}{\sqrt{a+b}}\right)}{f (a-b)^{3/2} (a+b)^{3/2} (b c-a d)^2}+\frac{2 d^2 \tanh ^{-1}\left(\frac{\sqrt{c-d} \tan \left(\frac{1}{2} (e+f x)\right)}{\sqrt{c+d}}\right)}{f \sqrt{c-d} \sqrt{c+d} (b c-a d)^2}",1,"(2*b*(a*b*c - 2*a^2*d + b^2*d)*ArcTanh[(Sqrt[a - b]*Tan[(e + f*x)/2])/Sqrt[a + b]])/((a - b)^(3/2)*(a + b)^(3/2)*(b*c - a*d)^2*f) + (2*d^2*ArcTanh[(Sqrt[c - d]*Tan[(e + f*x)/2])/Sqrt[c + d]])/(Sqrt[c - d]*Sqrt[c + d]*(b*c - a*d)^2*f) - (b^2*Sin[e + f*x])/((a^2 - b^2)*(b*c - a*d)*f*(b + a*Cos[e + f*x]))","A",7,5,31,0.1613,1,"{3988, 3056, 3001, 2659, 208}"
264,1,213,0,0.293255,"\int \frac{\sec (e+f x) \sqrt{a+b \sec (e+f x)}}{c+d \sec (e+f x)} \, dx","Int[(Sec[e + f*x]*Sqrt[a + b*Sec[e + f*x]])/(c + d*Sec[e + f*x]),x]","\frac{2 \sqrt{a+b} \cot (e+f x) \sqrt{\frac{b (1-\sec (e+f x))}{a+b}} \sqrt{-\frac{b (\sec (e+f x)+1)}{a-b}} F\left(\sin ^{-1}\left(\frac{\sqrt{a+b \sec (e+f x)}}{\sqrt{a+b}}\right)|\frac{a+b}{a-b}\right)}{d f}-\frac{2 (b c-a d) \tan (e+f x) \sqrt{\frac{a+b \sec (e+f x)}{a+b}} \Pi \left(\frac{2 d}{c+d};\sin ^{-1}\left(\frac{\sqrt{1-\sec (e+f x)}}{\sqrt{2}}\right)|\frac{2 b}{a+b}\right)}{d f (c+d) \sqrt{-\tan ^2(e+f x)} \sqrt{a+b \sec (e+f x)}}","\frac{2 \sqrt{a+b} \cot (e+f x) \sqrt{\frac{b (1-\sec (e+f x))}{a+b}} \sqrt{-\frac{b (\sec (e+f x)+1)}{a-b}} F\left(\sin ^{-1}\left(\frac{\sqrt{a+b \sec (e+f x)}}{\sqrt{a+b}}\right)|\frac{a+b}{a-b}\right)}{d f}-\frac{2 (b c-a d) \tan (e+f x) \sqrt{\frac{a+b \sec (e+f x)}{a+b}} \Pi \left(\frac{2 d}{c+d};\sin ^{-1}\left(\frac{\sqrt{1-\sec (e+f x)}}{\sqrt{2}}\right)|\frac{2 b}{a+b}\right)}{d f (c+d) \sqrt{-\tan ^2(e+f x)} \sqrt{a+b \sec (e+f x)}}",1,"(2*Sqrt[a + b]*Cot[e + f*x]*EllipticF[ArcSin[Sqrt[a + b*Sec[e + f*x]]/Sqrt[a + b]], (a + b)/(a - b)]*Sqrt[(b*(1 - Sec[e + f*x]))/(a + b)]*Sqrt[-((b*(1 + Sec[e + f*x]))/(a - b))])/(d*f) - (2*(b*c - a*d)*EllipticPi[(2*d)/(c + d), ArcSin[Sqrt[1 - Sec[e + f*x]]/Sqrt[2]], (2*b)/(a + b)]*Sqrt[(a + b*Sec[e + f*x])/(a + b)]*Tan[e + f*x])/(d*(c + d)*f*Sqrt[a + b*Sec[e + f*x]]*Sqrt[-Tan[e + f*x]^2])","A",3,3,33,0.09091,1,"{3969, 3832, 3973}"
265,1,196,0,0.1929916,"\int \frac{\sec (e+f x) \sqrt{a+b \sec (e+f x)}}{\sqrt{c+d \sec (e+f x)}} \, dx","Int[(Sec[e + f*x]*Sqrt[a + b*Sec[e + f*x]])/Sqrt[c + d*Sec[e + f*x]],x]","\frac{2 \cot (e+f x) (a+b \sec (e+f x)) \sqrt{-\frac{(b c-a d) (1-\sec (e+f x))}{(c+d) (a+b \sec (e+f x))}} \sqrt{\frac{(b c-a d) (\sec (e+f x)+1)}{(c-d) (a+b \sec (e+f x))}} \Pi \left(\frac{b (c+d)}{(a+b) d};\sin ^{-1}\left(\frac{\sqrt{\frac{a+b}{c+d}} \sqrt{c+d \sec (e+f x)}}{\sqrt{a+b \sec (e+f x)}}\right)|\frac{(a-b) (c+d)}{(a+b) (c-d)}\right)}{d f \sqrt{\frac{a+b}{c+d}}}","\frac{2 \cot (e+f x) (a+b \sec (e+f x)) \sqrt{-\frac{(b c-a d) (1-\sec (e+f x))}{(c+d) (a+b \sec (e+f x))}} \sqrt{\frac{(b c-a d) (\sec (e+f x)+1)}{(c-d) (a+b \sec (e+f x))}} \Pi \left(\frac{b (c+d)}{(a+b) d};\sin ^{-1}\left(\frac{\sqrt{\frac{a+b}{c+d}} \sqrt{c+d \sec (e+f x)}}{\sqrt{a+b \sec (e+f x)}}\right)|\frac{(a-b) (c+d)}{(a+b) (c-d)}\right)}{d f \sqrt{\frac{a+b}{c+d}}}",1,"(2*Cot[e + f*x]*EllipticPi[(b*(c + d))/((a + b)*d), ArcSin[(Sqrt[(a + b)/(c + d)]*Sqrt[c + d*Sec[e + f*x]])/Sqrt[a + b*Sec[e + f*x]]], ((a - b)*(c + d))/((a + b)*(c - d))]*Sqrt[-(((b*c - a*d)*(1 - Sec[e + f*x]))/((c + d)*(a + b*Sec[e + f*x])))]*Sqrt[((b*c - a*d)*(1 + Sec[e + f*x]))/((c - d)*(a + b*Sec[e + f*x]))]*(a + b*Sec[e + f*x]))/(d*Sqrt[(a + b)/(c + d)]*f)","A",1,1,35,0.02857,1,"{3982}"
266,1,192,0,0.1681256,"\int \frac{\sec (e+f x)}{\sqrt{a+b \sec (e+f x)} \sqrt{c+d \sec (e+f x)}} \, dx","Int[Sec[e + f*x]/(Sqrt[a + b*Sec[e + f*x]]*Sqrt[c + d*Sec[e + f*x]]),x]","\frac{2 \sqrt{a+b} \cot (e+f x) (c+d \sec (e+f x)) \sqrt{\frac{(b c-a d) (1-\sec (e+f x))}{(a+b) (c+d \sec (e+f x))}} \sqrt{-\frac{(b c-a d) (\sec (e+f x)+1)}{(a-b) (c+d \sec (e+f x))}} F\left(\sin ^{-1}\left(\frac{\sqrt{c+d} \sqrt{a+b \sec (e+f x)}}{\sqrt{a+b} \sqrt{c+d \sec (e+f x)}}\right)|\frac{(a+b) (c-d)}{(a-b) (c+d)}\right)}{f \sqrt{c+d} (b c-a d)}","\frac{2 \sqrt{a+b} \cot (e+f x) (c+d \sec (e+f x)) \sqrt{\frac{(b c-a d) (1-\sec (e+f x))}{(a+b) (c+d \sec (e+f x))}} \sqrt{-\frac{(b c-a d) (\sec (e+f x)+1)}{(a-b) (c+d \sec (e+f x))}} F\left(\sin ^{-1}\left(\frac{\sqrt{c+d} \sqrt{a+b \sec (e+f x)}}{\sqrt{a+b} \sqrt{c+d \sec (e+f x)}}\right)|\frac{(a+b) (c-d)}{(a-b) (c+d)}\right)}{f \sqrt{c+d} (b c-a d)}",1,"(2*Sqrt[a + b]*Cot[e + f*x]*EllipticF[ArcSin[(Sqrt[c + d]*Sqrt[a + b*Sec[e + f*x]])/(Sqrt[a + b]*Sqrt[c + d*Sec[e + f*x]])], ((a + b)*(c - d))/((a - b)*(c + d))]*Sqrt[((b*c - a*d)*(1 - Sec[e + f*x]))/((a + b)*(c + d*Sec[e + f*x]))]*Sqrt[-(((b*c - a*d)*(1 + Sec[e + f*x]))/((a - b)*(c + d*Sec[e + f*x])))]*(c + d*Sec[e + f*x]))/(Sqrt[c + d]*(b*c - a*d)*f)","A",1,1,35,0.02857,1,"{3984}"
267,1,110,0,0.12409,"\int \frac{\sec (e+f x)}{\sqrt{2+3 \sec (e+f x)} \sqrt{-4+5 \sec (e+f x)}} \, dx","Int[Sec[e + f*x]/(Sqrt[2 + 3*Sec[e + f*x]]*Sqrt[-4 + 5*Sec[e + f*x]]),x]","\frac{2 \cot (e+f x) (4-5 \sec (e+f x)) \sqrt{\frac{1-\sec (e+f x)}{4-5 \sec (e+f x)}} \sqrt{\frac{\sec (e+f x)+1}{4-5 \sec (e+f x)}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{3 \sec (e+f x)+2}}{\sqrt{5} \sqrt{5 \sec (e+f x)-4}}\right)\right|45\right)}{f}","\frac{2 \cot (e+f x) (4-5 \sec (e+f x)) \sqrt{\frac{1-\sec (e+f x)}{4-5 \sec (e+f x)}} \sqrt{\frac{\sec (e+f x)+1}{4-5 \sec (e+f x)}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{3 \sec (e+f x)+2}}{\sqrt{5} \sqrt{5 \sec (e+f x)-4}}\right)\right|45\right)}{f}",1,"(2*Cot[e + f*x]*EllipticF[ArcSin[Sqrt[2 + 3*Sec[e + f*x]]/(Sqrt[5]*Sqrt[-4 + 5*Sec[e + f*x]])], 45]*(4 - 5*Sec[e + f*x])*Sqrt[(1 - Sec[e + f*x])/(4 - 5*Sec[e + f*x])]*Sqrt[(1 + Sec[e + f*x])/(4 - 5*Sec[e + f*x])])/f","A",1,1,35,0.02857,1,"{3984}"
268,1,125,0,0.1195244,"\int \frac{\sec (e+f x)}{\sqrt{4-5 \sec (e+f x)} \sqrt{2+3 \sec (e+f x)}} \, dx","Int[Sec[e + f*x]/(Sqrt[4 - 5*Sec[e + f*x]]*Sqrt[2 + 3*Sec[e + f*x]]),x]","\frac{2 i \cot (e+f x) \sqrt{\frac{1-\sec (e+f x)}{3 \sec (e+f x)+2}} \sqrt{\frac{\sec (e+f x)+1}{3 \sec (e+f x)+2}} (3 \sec (e+f x)+2) F\left(i \sinh ^{-1}\left(\frac{\sqrt{5} \sqrt{4-5 \sec (e+f x)}}{\sqrt{3 \sec (e+f x)+2}}\right)|\frac{1}{45}\right)}{3 \sqrt{5} f}","\frac{2 i \cot (e+f x) \sqrt{\frac{1-\sec (e+f x)}{3 \sec (e+f x)+2}} \sqrt{\frac{\sec (e+f x)+1}{3 \sec (e+f x)+2}} (3 \sec (e+f x)+2) F\left(i \sinh ^{-1}\left(\frac{\sqrt{5} \sqrt{4-5 \sec (e+f x)}}{\sqrt{3 \sec (e+f x)+2}}\right)|\frac{1}{45}\right)}{3 \sqrt{5} f}",1,"(((2*I)/3)*Cot[e + f*x]*EllipticF[I*ArcSinh[(Sqrt[5]*Sqrt[4 - 5*Sec[e + f*x]])/Sqrt[2 + 3*Sec[e + f*x]]], 1/45]*Sqrt[(1 - Sec[e + f*x])/(2 + 3*Sec[e + f*x])]*Sqrt[(1 + Sec[e + f*x])/(2 + 3*Sec[e + f*x])]*(2 + 3*Sec[e + f*x]))/(Sqrt[5]*f)","A",1,1,35,0.02857,1,"{3984}"
269,1,396,0,0.6105295,"\int \frac{\sec ^2(e+f x)}{\sqrt{a+b \sec (e+f x)} \sqrt{c+d \sec (e+f x)}} \, dx","Int[Sec[e + f*x]^2/(Sqrt[a + b*Sec[e + f*x]]*Sqrt[c + d*Sec[e + f*x]]),x]","\frac{2 \cot (e+f x) (a+b \sec (e+f x)) \sqrt{-\frac{(b c-a d) (1-\sec (e+f x))}{(c+d) (a+b \sec (e+f x))}} \sqrt{\frac{(b c-a d) (\sec (e+f x)+1)}{(c-d) (a+b \sec (e+f x))}} \Pi \left(\frac{b (c+d)}{(a+b) d};\sin ^{-1}\left(\frac{\sqrt{\frac{a+b}{c+d}} \sqrt{c+d \sec (e+f x)}}{\sqrt{a+b \sec (e+f x)}}\right)|\frac{(a-b) (c+d)}{(a+b) (c-d)}\right)}{b d f \sqrt{\frac{a+b}{c+d}}}-\frac{2 a \sqrt{a+b} \cot (e+f x) (c+d \sec (e+f x)) \sqrt{\frac{(b c-a d) (1-\sec (e+f x))}{(a+b) (c+d \sec (e+f x))}} \sqrt{-\frac{(b c-a d) (\sec (e+f x)+1)}{(a-b) (c+d \sec (e+f x))}} F\left(\sin ^{-1}\left(\frac{\sqrt{c+d} \sqrt{a+b \sec (e+f x)}}{\sqrt{a+b} \sqrt{c+d \sec (e+f x)}}\right)|\frac{(a+b) (c-d)}{(a-b) (c+d)}\right)}{b f \sqrt{c+d} (b c-a d)}","\frac{2 \cot (e+f x) (a+b \sec (e+f x)) \sqrt{-\frac{(b c-a d) (1-\sec (e+f x))}{(c+d) (a+b \sec (e+f x))}} \sqrt{\frac{(b c-a d) (\sec (e+f x)+1)}{(c-d) (a+b \sec (e+f x))}} \Pi \left(\frac{b (c+d)}{(a+b) d};\sin ^{-1}\left(\frac{\sqrt{\frac{a+b}{c+d}} \sqrt{c+d \sec (e+f x)}}{\sqrt{a+b \sec (e+f x)}}\right)|\frac{(a-b) (c+d)}{(a+b) (c-d)}\right)}{b d f \sqrt{\frac{a+b}{c+d}}}-\frac{2 a \sqrt{a+b} \cot (e+f x) (c+d \sec (e+f x)) \sqrt{\frac{(b c-a d) (1-\sec (e+f x))}{(a+b) (c+d \sec (e+f x))}} \sqrt{-\frac{(b c-a d) (\sec (e+f x)+1)}{(a-b) (c+d \sec (e+f x))}} F\left(\sin ^{-1}\left(\frac{\sqrt{c+d} \sqrt{a+b \sec (e+f x)}}{\sqrt{a+b} \sqrt{c+d \sec (e+f x)}}\right)|\frac{(a+b) (c-d)}{(a-b) (c+d)}\right)}{b f \sqrt{c+d} (b c-a d)}",1,"(2*Cot[e + f*x]*EllipticPi[(b*(c + d))/((a + b)*d), ArcSin[(Sqrt[(a + b)/(c + d)]*Sqrt[c + d*Sec[e + f*x]])/Sqrt[a + b*Sec[e + f*x]]], ((a - b)*(c + d))/((a + b)*(c - d))]*Sqrt[-(((b*c - a*d)*(1 - Sec[e + f*x]))/((c + d)*(a + b*Sec[e + f*x])))]*Sqrt[((b*c - a*d)*(1 + Sec[e + f*x]))/((c - d)*(a + b*Sec[e + f*x]))]*(a + b*Sec[e + f*x]))/(b*d*Sqrt[(a + b)/(c + d)]*f) - (2*a*Sqrt[a + b]*Cot[e + f*x]*EllipticF[ArcSin[(Sqrt[c + d]*Sqrt[a + b*Sec[e + f*x]])/(Sqrt[a + b]*Sqrt[c + d*Sec[e + f*x]])], ((a + b)*(c - d))/((a - b)*(c + d))]*Sqrt[((b*c - a*d)*(1 - Sec[e + f*x]))/((a + b)*(c + d*Sec[e + f*x]))]*Sqrt[-(((b*c - a*d)*(1 + Sec[e + f*x]))/((a - b)*(c + d*Sec[e + f*x])))]*(c + d*Sec[e + f*x]))/(b*Sqrt[c + d]*(b*c - a*d)*f)","A",3,3,37,0.08108,1,"{3985, 3984, 3982}"
270,1,170,0,0.8487208,"\int \frac{(g \sec (e+f x))^{3/2} \sqrt{c+d \sec (e+f x)}}{a+b \sec (e+f x)} \, dx","Int[((g*Sec[e + f*x])^(3/2)*Sqrt[c + d*Sec[e + f*x]])/(a + b*Sec[e + f*x]),x]","\frac{2 g (b c-a d) \sqrt{g \sec (e+f x)} \sqrt{\frac{c \cos (e+f x)+d}{c+d}} \Pi \left(\frac{2 a}{a+b};\frac{1}{2} (e+f x)|\frac{2 c}{c+d}\right)}{b f (a+b) \sqrt{c+d \sec (e+f x)}}+\frac{2 d g \sqrt{g \sec (e+f x)} \sqrt{\frac{c \cos (e+f x)+d}{c+d}} \Pi \left(2;\frac{1}{2} (e+f x)|\frac{2 c}{c+d}\right)}{b f \sqrt{c+d \sec (e+f x)}}","\frac{2 g (b c-a d) \sqrt{g \sec (e+f x)} \sqrt{\frac{c \cos (e+f x)+d}{c+d}} \Pi \left(\frac{2 a}{a+b};\frac{1}{2} (e+f x)|\frac{2 c}{c+d}\right)}{b f (a+b) \sqrt{c+d \sec (e+f x)}}+\frac{2 d g \sqrt{g \sec (e+f x)} \sqrt{\frac{c \cos (e+f x)+d}{c+d}} \Pi \left(2;\frac{1}{2} (e+f x)|\frac{2 c}{c+d}\right)}{b f \sqrt{c+d \sec (e+f x)}}",1,"(2*d*g*Sqrt[(d + c*Cos[e + f*x])/(c + d)]*EllipticPi[2, (e + f*x)/2, (2*c)/(c + d)]*Sqrt[g*Sec[e + f*x]])/(b*f*Sqrt[c + d*Sec[e + f*x]]) + (2*(b*c - a*d)*g*Sqrt[(d + c*Cos[e + f*x])/(c + d)]*EllipticPi[(2*a)/(a + b), (e + f*x)/2, (2*c)/(c + d)]*Sqrt[g*Sec[e + f*x]])/(b*(a + b)*f*Sqrt[c + d*Sec[e + f*x]])","A",7,5,39,0.1282,1,"{3971, 3859, 2807, 2805, 3975}"
271,1,83,0,0.4334136,"\int \frac{(g \sec (e+f x))^{3/2}}{(a+b \sec (e+f x)) \sqrt{c+d \sec (e+f x)}} \, dx","Int[(g*Sec[e + f*x])^(3/2)/((a + b*Sec[e + f*x])*Sqrt[c + d*Sec[e + f*x]]),x]","\frac{2 g \sqrt{g \sec (e+f x)} \sqrt{\frac{c \cos (e+f x)+d}{c+d}} \Pi \left(\frac{2 a}{a+b};\frac{1}{2} (e+f x)|\frac{2 c}{c+d}\right)}{f (a+b) \sqrt{c+d \sec (e+f x)}}","\frac{2 g \sqrt{g \sec (e+f x)} \sqrt{\frac{c \cos (e+f x)+d}{c+d}} \Pi \left(\frac{2 a}{a+b};\frac{1}{2} (e+f x)|\frac{2 c}{c+d}\right)}{f (a+b) \sqrt{c+d \sec (e+f x)}}",1,"(2*g*Sqrt[(d + c*Cos[e + f*x])/(c + d)]*EllipticPi[(2*a)/(a + b), (e + f*x)/2, (2*c)/(c + d)]*Sqrt[g*Sec[e + f*x]])/((a + b)*f*Sqrt[c + d*Sec[e + f*x]])","A",3,3,39,0.07692,1,"{3975, 2807, 2805}"
272,1,168,0,1.0696077,"\int \frac{\sqrt{g \sec (e+f x)} \sqrt{c+d \sec (e+f x)}}{a+b \cos (e+f x)} \, dx","Int[(Sqrt[g*Sec[e + f*x]]*Sqrt[c + d*Sec[e + f*x]])/(a + b*Cos[e + f*x]),x]","\frac{2 (a c-b d) \sqrt{g \sec (e+f x)} \sqrt{\frac{c \cos (e+f x)+d}{c+d}} \Pi \left(\frac{2 b}{a+b};\frac{1}{2} (e+f x)|\frac{2 c}{c+d}\right)}{a f (a+b) \sqrt{c+d \sec (e+f x)}}+\frac{2 d \sqrt{g \sec (e+f x)} \sqrt{\frac{c \cos (e+f x)+d}{c+d}} \Pi \left(2;\frac{1}{2} (e+f x)|\frac{2 c}{c+d}\right)}{a f \sqrt{c+d \sec (e+f x)}}","\frac{2 (a c-b d) \sqrt{g \sec (e+f x)} \sqrt{\frac{c \cos (e+f x)+d}{c+d}} \Pi \left(\frac{2 b}{a+b};\frac{1}{2} (e+f x)|\frac{2 c}{c+d}\right)}{a f (a+b) \sqrt{c+d \sec (e+f x)}}+\frac{2 d \sqrt{g \sec (e+f x)} \sqrt{\frac{c \cos (e+f x)+d}{c+d}} \Pi \left(2;\frac{1}{2} (e+f x)|\frac{2 c}{c+d}\right)}{a f \sqrt{c+d \sec (e+f x)}}",1,"(2*d*Sqrt[(d + c*Cos[e + f*x])/(c + d)]*EllipticPi[2, (e + f*x)/2, (2*c)/(c + d)]*Sqrt[g*Sec[e + f*x]])/(a*f*Sqrt[c + d*Sec[e + f*x]]) + (2*(a*c - b*d)*Sqrt[(d + c*Cos[e + f*x])/(c + d)]*EllipticPi[(2*b)/(a + b), (e + f*x)/2, (2*c)/(c + d)]*Sqrt[g*Sec[e + f*x]])/(a*(a + b)*f*Sqrt[c + d*Sec[e + f*x]])","A",8,6,39,0.1538,1,"{2962, 3971, 3859, 2807, 2805, 3975}"
273,1,95,0,0.1193709,"\int \frac{\sec (e+f x) \sqrt{a+b \sec (e+f x)}}{c+c \sec (e+f x)} \, dx","Int[(Sec[e + f*x]*Sqrt[a + b*Sec[e + f*x]])/(c + c*Sec[e + f*x]),x]","\frac{\sqrt{\frac{1}{\sec (e+f x)+1}} \sqrt{a+b \sec (e+f x)} E\left(\sin ^{-1}\left(\frac{\tan (e+f x)}{\sec (e+f x)+1}\right)|\frac{a-b}{a+b}\right)}{c f \sqrt{\frac{a+b \sec (e+f x)}{(a+b) (\sec (e+f x)+1)}}}","\frac{\sqrt{\frac{1}{\sec (e+f x)+1}} \sqrt{a+b \sec (e+f x)} E\left(\sin ^{-1}\left(\frac{\tan (e+f x)}{\sec (e+f x)+1}\right)|\frac{a-b}{a+b}\right)}{c f \sqrt{\frac{a+b \sec (e+f x)}{(a+b) (\sec (e+f x)+1)}}}",1,"(EllipticE[ArcSin[Tan[e + f*x]/(1 + Sec[e + f*x])], (a - b)/(a + b)]*Sqrt[(1 + Sec[e + f*x])^(-1)]*Sqrt[a + b*Sec[e + f*x]])/(c*f*Sqrt[(a + b*Sec[e + f*x])/((a + b)*(1 + Sec[e + f*x]))])","A",1,1,33,0.03030,1,"{3968}"
274,1,295,0,0.9223003,"\int \frac{(g \sec (e+f x))^{3/2} \sqrt{a+b \sec (e+f x)}}{c+c \sec (e+f x)} \, dx","Int[((g*Sec[e + f*x])^(3/2)*Sqrt[a + b*Sec[e + f*x]])/(c + c*Sec[e + f*x]),x]","-\frac{g \sin (e+f x) \sqrt{g \sec (e+f x)} (a \cos (e+f x)+b)}{f (c \cos (e+f x)+c) \sqrt{a+b \sec (e+f x)}}+\frac{g (a-b) \sqrt{g \sec (e+f x)} \sqrt{\frac{a \cos (e+f x)+b}{a+b}} F\left(\frac{1}{2} (e+f x)|\frac{2 a}{a+b}\right)}{c f \sqrt{a+b \sec (e+f x)}}+\frac{g \sqrt{g \sec (e+f x)} (a \cos (e+f x)+b) E\left(\frac{1}{2} (e+f x)|\frac{2 a}{a+b}\right)}{c f \sqrt{\frac{a \cos (e+f x)+b}{a+b}} \sqrt{a+b \sec (e+f x)}}+\frac{2 b g \sqrt{g \sec (e+f x)} \sqrt{\frac{a \cos (e+f x)+b}{a+b}} \Pi \left(2;\frac{1}{2} (e+f x)|\frac{2 a}{a+b}\right)}{c f \sqrt{a+b \sec (e+f x)}}","-\frac{g \sin (e+f x) \sqrt{g \sec (e+f x)} (a \cos (e+f x)+b)}{f (c \cos (e+f x)+c) \sqrt{a+b \sec (e+f x)}}+\frac{g (a-b) \sqrt{g \sec (e+f x)} \sqrt{\frac{a \cos (e+f x)+b}{a+b}} F\left(\frac{1}{2} (e+f x)|\frac{2 a}{a+b}\right)}{c f \sqrt{a+b \sec (e+f x)}}+\frac{g \sqrt{g \sec (e+f x)} (a \cos (e+f x)+b) E\left(\frac{1}{2} (e+f x)|\frac{2 a}{a+b}\right)}{c f \sqrt{\frac{a \cos (e+f x)+b}{a+b}} \sqrt{a+b \sec (e+f x)}}+\frac{2 b g \sqrt{g \sec (e+f x)} \sqrt{\frac{a \cos (e+f x)+b}{a+b}} \Pi \left(2;\frac{1}{2} (e+f x)|\frac{2 a}{a+b}\right)}{c f \sqrt{a+b \sec (e+f x)}}",1,"(g*(b + a*Cos[e + f*x])*EllipticE[(e + f*x)/2, (2*a)/(a + b)]*Sqrt[g*Sec[e + f*x]])/(c*f*Sqrt[(b + a*Cos[e + f*x])/(a + b)]*Sqrt[a + b*Sec[e + f*x]]) + ((a - b)*g*Sqrt[(b + a*Cos[e + f*x])/(a + b)]*EllipticF[(e + f*x)/2, (2*a)/(a + b)]*Sqrt[g*Sec[e + f*x]])/(c*f*Sqrt[a + b*Sec[e + f*x]]) + (2*b*g*Sqrt[(b + a*Cos[e + f*x])/(a + b)]*EllipticPi[2, (e + f*x)/2, (2*a)/(a + b)]*Sqrt[g*Sec[e + f*x]])/(c*f*Sqrt[a + b*Sec[e + f*x]]) - (g*(b + a*Cos[e + f*x])*Sqrt[g*Sec[e + f*x]]*Sin[e + f*x])/(f*(c + c*Cos[e + f*x])*Sqrt[a + b*Sec[e + f*x]])","A",11,11,39,0.2821,1,"{3971, 3859, 2807, 2805, 3975, 2768, 2752, 2663, 2661, 2655, 2653}"
275,1,209,0,0.2878197,"\int \frac{\sec (e+f x)}{\sqrt{a+b \sec (e+f x)} (c+c \sec (e+f x))} \, dx","Int[Sec[e + f*x]/(Sqrt[a + b*Sec[e + f*x]]*(c + c*Sec[e + f*x])),x]","\frac{\sqrt{\frac{1}{\sec (e+f x)+1}} \sqrt{a+b \sec (e+f x)} E\left(\sin ^{-1}\left(\frac{\tan (e+f x)}{\sec (e+f x)+1}\right)|\frac{a-b}{a+b}\right)}{c f (a-b) \sqrt{\frac{a+b \sec (e+f x)}{(a+b) (\sec (e+f x)+1)}}}-\frac{2 \sqrt{a+b} \cot (e+f x) \sqrt{\frac{b (1-\sec (e+f x))}{a+b}} \sqrt{-\frac{b (\sec (e+f x)+1)}{a-b}} F\left(\sin ^{-1}\left(\frac{\sqrt{a+b \sec (e+f x)}}{\sqrt{a+b}}\right)|\frac{a+b}{a-b}\right)}{c f (a-b)}","\frac{\sqrt{\frac{1}{\sec (e+f x)+1}} \sqrt{a+b \sec (e+f x)} E\left(\sin ^{-1}\left(\frac{\tan (e+f x)}{\sec (e+f x)+1}\right)|\frac{a-b}{a+b}\right)}{c f (a-b) \sqrt{\frac{a+b \sec (e+f x)}{(a+b) (\sec (e+f x)+1)}}}-\frac{2 \sqrt{a+b} \cot (e+f x) \sqrt{\frac{b (1-\sec (e+f x))}{a+b}} \sqrt{-\frac{b (\sec (e+f x)+1)}{a-b}} F\left(\sin ^{-1}\left(\frac{\sqrt{a+b \sec (e+f x)}}{\sqrt{a+b}}\right)|\frac{a+b}{a-b}\right)}{c f (a-b)}",1,"(-2*Sqrt[a + b]*Cot[e + f*x]*EllipticF[ArcSin[Sqrt[a + b*Sec[e + f*x]]/Sqrt[a + b]], (a + b)/(a - b)]*Sqrt[(b*(1 - Sec[e + f*x]))/(a + b)]*Sqrt[-((b*(1 + Sec[e + f*x]))/(a - b))])/((a - b)*c*f) + (EllipticE[ArcSin[Tan[e + f*x]/(1 + Sec[e + f*x])], (a - b)/(a + b)]*Sqrt[(1 + Sec[e + f*x])^(-1)]*Sqrt[a + b*Sec[e + f*x]])/((a - b)*c*f*Sqrt[(a + b*Sec[e + f*x])/((a + b)*(1 + Sec[e + f*x]))])","A",3,3,33,0.09091,1,"{3972, 3832, 3968}"
276,1,214,0,0.3600718,"\int \frac{\sec ^2(e+f x)}{\sqrt{a+b \sec (e+f x)} (c+c \sec (e+f x))} \, dx","Int[Sec[e + f*x]^2/(Sqrt[a + b*Sec[e + f*x]]*(c + c*Sec[e + f*x])),x]","\frac{2 a \sqrt{a+b} \cot (e+f x) \sqrt{\frac{b (1-\sec (e+f x))}{a+b}} \sqrt{-\frac{b (\sec (e+f x)+1)}{a-b}} F\left(\sin ^{-1}\left(\frac{\sqrt{a+b \sec (e+f x)}}{\sqrt{a+b}}\right)|\frac{a+b}{a-b}\right)}{b c f (a-b)}-\frac{\sqrt{\frac{1}{\sec (e+f x)+1}} \sqrt{a+b \sec (e+f x)} E\left(\sin ^{-1}\left(\frac{\tan (e+f x)}{\sec (e+f x)+1}\right)|\frac{a-b}{a+b}\right)}{c f (a-b) \sqrt{\frac{a+b \sec (e+f x)}{(a+b) (\sec (e+f x)+1)}}}","\frac{2 a \sqrt{a+b} \cot (e+f x) \sqrt{\frac{b (1-\sec (e+f x))}{a+b}} \sqrt{-\frac{b (\sec (e+f x)+1)}{a-b}} F\left(\sin ^{-1}\left(\frac{\sqrt{a+b \sec (e+f x)}}{\sqrt{a+b}}\right)|\frac{a+b}{a-b}\right)}{b c f (a-b)}-\frac{\sqrt{\frac{1}{\sec (e+f x)+1}} \sqrt{a+b \sec (e+f x)} E\left(\sin ^{-1}\left(\frac{\tan (e+f x)}{\sec (e+f x)+1}\right)|\frac{a-b}{a+b}\right)}{c f (a-b) \sqrt{\frac{a+b \sec (e+f x)}{(a+b) (\sec (e+f x)+1)}}}",1,"(2*a*Sqrt[a + b]*Cot[e + f*x]*EllipticF[ArcSin[Sqrt[a + b*Sec[e + f*x]]/Sqrt[a + b]], (a + b)/(a - b)]*Sqrt[(b*(1 - Sec[e + f*x]))/(a + b)]*Sqrt[-((b*(1 + Sec[e + f*x]))/(a - b))])/((a - b)*b*c*f) - (EllipticE[ArcSin[Tan[e + f*x]/(1 + Sec[e + f*x])], (a - b)/(a + b)]*Sqrt[(1 + Sec[e + f*x])^(-1)]*Sqrt[a + b*Sec[e + f*x]])/((a - b)*c*f*Sqrt[(a + b*Sec[e + f*x])/((a + b)*(1 + Sec[e + f*x]))])","A",3,3,35,0.08571,1,"{3976, 3832, 3968}"
277,1,229,0,0.4395183,"\int \frac{(g \sec (e+f x))^{3/2}}{\sqrt{a+b \sec (e+f x)} (c+c \sec (e+f x))} \, dx","Int[(g*Sec[e + f*x])^(3/2)/(Sqrt[a + b*Sec[e + f*x]]*(c + c*Sec[e + f*x])),x]","-\frac{g \sin (e+f x) \sqrt{g \sec (e+f x)} (a \cos (e+f x)+b)}{f (a-b) (c \cos (e+f x)+c) \sqrt{a+b \sec (e+f x)}}+\frac{g \sqrt{g \sec (e+f x)} \sqrt{\frac{a \cos (e+f x)+b}{a+b}} F\left(\frac{1}{2} (e+f x)|\frac{2 a}{a+b}\right)}{c f \sqrt{a+b \sec (e+f x)}}+\frac{g \sqrt{g \sec (e+f x)} (a \cos (e+f x)+b) E\left(\frac{1}{2} (e+f x)|\frac{2 a}{a+b}\right)}{c f (a-b) \sqrt{\frac{a \cos (e+f x)+b}{a+b}} \sqrt{a+b \sec (e+f x)}}","-\frac{g \sin (e+f x) \sqrt{g \sec (e+f x)} (a \cos (e+f x)+b)}{f (a-b) (c \cos (e+f x)+c) \sqrt{a+b \sec (e+f x)}}+\frac{g \sqrt{g \sec (e+f x)} \sqrt{\frac{a \cos (e+f x)+b}{a+b}} F\left(\frac{1}{2} (e+f x)|\frac{2 a}{a+b}\right)}{c f \sqrt{a+b \sec (e+f x)}}+\frac{g \sqrt{g \sec (e+f x)} (a \cos (e+f x)+b) E\left(\frac{1}{2} (e+f x)|\frac{2 a}{a+b}\right)}{c f (a-b) \sqrt{\frac{a \cos (e+f x)+b}{a+b}} \sqrt{a+b \sec (e+f x)}}",1,"(g*(b + a*Cos[e + f*x])*EllipticE[(e + f*x)/2, (2*a)/(a + b)]*Sqrt[g*Sec[e + f*x]])/((a - b)*c*f*Sqrt[(b + a*Cos[e + f*x])/(a + b)]*Sqrt[a + b*Sec[e + f*x]]) + (g*Sqrt[(b + a*Cos[e + f*x])/(a + b)]*EllipticF[(e + f*x)/2, (2*a)/(a + b)]*Sqrt[g*Sec[e + f*x]])/(c*f*Sqrt[a + b*Sec[e + f*x]]) - (g*(b + a*Cos[e + f*x])*Sqrt[g*Sec[e + f*x]]*Sin[e + f*x])/((a - b)*f*(c + c*Cos[e + f*x])*Sqrt[a + b*Sec[e + f*x]])","A",7,7,39,0.1795,1,"{3975, 2768, 2752, 2663, 2661, 2655, 2653}"
278,1,312,0,0.8893498,"\int \frac{(g \sec (e+f x))^{5/2}}{\sqrt{a+b \sec (e+f x)} (c+c \sec (e+f x))} \, dx","Int[(g*Sec[e + f*x])^(5/2)/(Sqrt[a + b*Sec[e + f*x]]*(c + c*Sec[e + f*x])),x]","\frac{g^2 \sin (e+f x) \sqrt{g \sec (e+f x)} (a \cos (e+f x)+b)}{f (a-b) (c \cos (e+f x)+c) \sqrt{a+b \sec (e+f x)}}-\frac{g^2 \sqrt{g \sec (e+f x)} \sqrt{\frac{a \cos (e+f x)+b}{a+b}} F\left(\frac{1}{2} (e+f x)|\frac{2 a}{a+b}\right)}{c f \sqrt{a+b \sec (e+f x)}}-\frac{g^2 \sqrt{g \sec (e+f x)} (a \cos (e+f x)+b) E\left(\frac{1}{2} (e+f x)|\frac{2 a}{a+b}\right)}{c f (a-b) \sqrt{\frac{a \cos (e+f x)+b}{a+b}} \sqrt{a+b \sec (e+f x)}}+\frac{2 g^2 \sqrt{g \sec (e+f x)} \sqrt{\frac{a \cos (e+f x)+b}{a+b}} \Pi \left(2;\frac{1}{2} (e+f x)|\frac{2 a}{a+b}\right)}{c f \sqrt{a+b \sec (e+f x)}}","\frac{g^2 \sin (e+f x) \sqrt{g \sec (e+f x)} (a \cos (e+f x)+b)}{f (a-b) (c \cos (e+f x)+c) \sqrt{a+b \sec (e+f x)}}-\frac{g^2 \sqrt{g \sec (e+f x)} \sqrt{\frac{a \cos (e+f x)+b}{a+b}} F\left(\frac{1}{2} (e+f x)|\frac{2 a}{a+b}\right)}{c f \sqrt{a+b \sec (e+f x)}}-\frac{g^2 \sqrt{g \sec (e+f x)} (a \cos (e+f x)+b) E\left(\frac{1}{2} (e+f x)|\frac{2 a}{a+b}\right)}{c f (a-b) \sqrt{\frac{a \cos (e+f x)+b}{a+b}} \sqrt{a+b \sec (e+f x)}}+\frac{2 g^2 \sqrt{g \sec (e+f x)} \sqrt{\frac{a \cos (e+f x)+b}{a+b}} \Pi \left(2;\frac{1}{2} (e+f x)|\frac{2 a}{a+b}\right)}{c f \sqrt{a+b \sec (e+f x)}}",1,"-((g^2*(b + a*Cos[e + f*x])*EllipticE[(e + f*x)/2, (2*a)/(a + b)]*Sqrt[g*Sec[e + f*x]])/((a - b)*c*f*Sqrt[(b + a*Cos[e + f*x])/(a + b)]*Sqrt[a + b*Sec[e + f*x]])) - (g^2*Sqrt[(b + a*Cos[e + f*x])/(a + b)]*EllipticF[(e + f*x)/2, (2*a)/(a + b)]*Sqrt[g*Sec[e + f*x]])/(c*f*Sqrt[a + b*Sec[e + f*x]]) + (2*g^2*Sqrt[(b + a*Cos[e + f*x])/(a + b)]*EllipticPi[2, (e + f*x)/2, (2*a)/(a + b)]*Sqrt[g*Sec[e + f*x]])/(c*f*Sqrt[a + b*Sec[e + f*x]]) + (g^2*(b + a*Cos[e + f*x])*Sqrt[g*Sec[e + f*x]]*Sin[e + f*x])/((a - b)*f*(c + c*Cos[e + f*x])*Sqrt[a + b*Sec[e + f*x]])","A",11,11,39,0.2821,1,"{3979, 3859, 2807, 2805, 3975, 2768, 2752, 2663, 2661, 2655, 2653}"
279,1,213,0,0.2770107,"\int \frac{\sec (e+f x) \sqrt{a+b \sec (e+f x)}}{c+d \sec (e+f x)} \, dx","Int[(Sec[e + f*x]*Sqrt[a + b*Sec[e + f*x]])/(c + d*Sec[e + f*x]),x]","\frac{2 \sqrt{a+b} \cot (e+f x) \sqrt{\frac{b (1-\sec (e+f x))}{a+b}} \sqrt{-\frac{b (\sec (e+f x)+1)}{a-b}} F\left(\sin ^{-1}\left(\frac{\sqrt{a+b \sec (e+f x)}}{\sqrt{a+b}}\right)|\frac{a+b}{a-b}\right)}{d f}-\frac{2 (b c-a d) \tan (e+f x) \sqrt{\frac{a+b \sec (e+f x)}{a+b}} \Pi \left(\frac{2 d}{c+d};\sin ^{-1}\left(\frac{\sqrt{1-\sec (e+f x)}}{\sqrt{2}}\right)|\frac{2 b}{a+b}\right)}{d f (c+d) \sqrt{-\tan ^2(e+f x)} \sqrt{a+b \sec (e+f x)}}","\frac{2 \sqrt{a+b} \cot (e+f x) \sqrt{\frac{b (1-\sec (e+f x))}{a+b}} \sqrt{-\frac{b (\sec (e+f x)+1)}{a-b}} F\left(\sin ^{-1}\left(\frac{\sqrt{a+b \sec (e+f x)}}{\sqrt{a+b}}\right)|\frac{a+b}{a-b}\right)}{d f}-\frac{2 (b c-a d) \tan (e+f x) \sqrt{\frac{a+b \sec (e+f x)}{a+b}} \Pi \left(\frac{2 d}{c+d};\sin ^{-1}\left(\frac{\sqrt{1-\sec (e+f x)}}{\sqrt{2}}\right)|\frac{2 b}{a+b}\right)}{d f (c+d) \sqrt{-\tan ^2(e+f x)} \sqrt{a+b \sec (e+f x)}}",1,"(2*Sqrt[a + b]*Cot[e + f*x]*EllipticF[ArcSin[Sqrt[a + b*Sec[e + f*x]]/Sqrt[a + b]], (a + b)/(a - b)]*Sqrt[(b*(1 - Sec[e + f*x]))/(a + b)]*Sqrt[-((b*(1 + Sec[e + f*x]))/(a - b))])/(d*f) - (2*(b*c - a*d)*EllipticPi[(2*d)/(c + d), ArcSin[Sqrt[1 - Sec[e + f*x]]/Sqrt[2]], (2*b)/(a + b)]*Sqrt[(a + b*Sec[e + f*x])/(a + b)]*Tan[e + f*x])/(d*(c + d)*f*Sqrt[a + b*Sec[e + f*x]]*Sqrt[-Tan[e + f*x]^2])","A",3,3,33,0.09091,1,"{3969, 3832, 3973}"
280,1,170,0,0.8428112,"\int \frac{(g \sec (e+f x))^{3/2} \sqrt{a+b \sec (e+f x)}}{c+d \sec (e+f x)} \, dx","Int[((g*Sec[e + f*x])^(3/2)*Sqrt[a + b*Sec[e + f*x]])/(c + d*Sec[e + f*x]),x]","\frac{2 b g \sqrt{g \sec (e+f x)} \sqrt{\frac{a \cos (e+f x)+b}{a+b}} \Pi \left(2;\frac{1}{2} (e+f x)|\frac{2 a}{a+b}\right)}{d f \sqrt{a+b \sec (e+f x)}}-\frac{2 g (b c-a d) \sqrt{g \sec (e+f x)} \sqrt{\frac{a \cos (e+f x)+b}{a+b}} \Pi \left(\frac{2 c}{c+d};\frac{1}{2} (e+f x)|\frac{2 a}{a+b}\right)}{d f (c+d) \sqrt{a+b \sec (e+f x)}}","\frac{2 b g \sqrt{g \sec (e+f x)} \sqrt{\frac{a \cos (e+f x)+b}{a+b}} \Pi \left(2;\frac{1}{2} (e+f x)|\frac{2 a}{a+b}\right)}{d f \sqrt{a+b \sec (e+f x)}}-\frac{2 g (b c-a d) \sqrt{g \sec (e+f x)} \sqrt{\frac{a \cos (e+f x)+b}{a+b}} \Pi \left(\frac{2 c}{c+d};\frac{1}{2} (e+f x)|\frac{2 a}{a+b}\right)}{d f (c+d) \sqrt{a+b \sec (e+f x)}}",1,"(2*b*g*Sqrt[(b + a*Cos[e + f*x])/(a + b)]*EllipticPi[2, (e + f*x)/2, (2*a)/(a + b)]*Sqrt[g*Sec[e + f*x]])/(d*f*Sqrt[a + b*Sec[e + f*x]]) - (2*(b*c - a*d)*g*Sqrt[(b + a*Cos[e + f*x])/(a + b)]*EllipticPi[(2*c)/(c + d), (e + f*x)/2, (2*a)/(a + b)]*Sqrt[g*Sec[e + f*x]])/(d*(c + d)*f*Sqrt[a + b*Sec[e + f*x]])","A",7,5,39,0.1282,1,"{3971, 3859, 2807, 2805, 3975}"
281,1,102,0,0.121654,"\int \frac{\sec (e+f x)}{\sqrt{a+b \sec (e+f x)} (c+d \sec (e+f x))} \, dx","Int[Sec[e + f*x]/(Sqrt[a + b*Sec[e + f*x]]*(c + d*Sec[e + f*x])),x]","\frac{2 \tan (e+f x) \sqrt{\frac{a+b \sec (e+f x)}{a+b}} \Pi \left(\frac{2 d}{c+d};\sin ^{-1}\left(\frac{\sqrt{1-\sec (e+f x)}}{\sqrt{2}}\right)|\frac{2 b}{a+b}\right)}{f (c+d) \sqrt{-\tan ^2(e+f x)} \sqrt{a+b \sec (e+f x)}}","\frac{2 \tan (e+f x) \sqrt{\frac{a+b \sec (e+f x)}{a+b}} \Pi \left(\frac{2 d}{c+d};\sin ^{-1}\left(\frac{\sqrt{1-\sec (e+f x)}}{\sqrt{2}}\right)|\frac{2 b}{a+b}\right)}{f (c+d) \sqrt{-\tan ^2(e+f x)} \sqrt{a+b \sec (e+f x)}}",1,"(2*EllipticPi[(2*d)/(c + d), ArcSin[Sqrt[1 - Sec[e + f*x]]/Sqrt[2]], (2*b)/(a + b)]*Sqrt[(a + b*Sec[e + f*x])/(a + b)]*Tan[e + f*x])/((c + d)*f*Sqrt[a + b*Sec[e + f*x]]*Sqrt[-Tan[e + f*x]^2])","A",1,1,33,0.03030,1,"{3973}"
282,1,209,0,0.3612433,"\int \frac{\sec ^2(e+f x)}{\sqrt{a+b \sec (e+f x)} (c+d \sec (e+f x))} \, dx","Int[Sec[e + f*x]^2/(Sqrt[a + b*Sec[e + f*x]]*(c + d*Sec[e + f*x])),x]","\frac{2 \sqrt{a+b} \cot (e+f x) \sqrt{\frac{b (1-\sec (e+f x))}{a+b}} \sqrt{-\frac{b (\sec (e+f x)+1)}{a-b}} F\left(\sin ^{-1}\left(\frac{\sqrt{a+b \sec (e+f x)}}{\sqrt{a+b}}\right)|\frac{a+b}{a-b}\right)}{b d f}-\frac{2 c \tan (e+f x) \sqrt{\frac{a+b \sec (e+f x)}{a+b}} \Pi \left(\frac{2 d}{c+d};\sin ^{-1}\left(\frac{\sqrt{1-\sec (e+f x)}}{\sqrt{2}}\right)|\frac{2 b}{a+b}\right)}{d f (c+d) \sqrt{-\tan ^2(e+f x)} \sqrt{a+b \sec (e+f x)}}","\frac{2 \sqrt{a+b} \cot (e+f x) \sqrt{\frac{b (1-\sec (e+f x))}{a+b}} \sqrt{-\frac{b (\sec (e+f x)+1)}{a-b}} F\left(\sin ^{-1}\left(\frac{\sqrt{a+b \sec (e+f x)}}{\sqrt{a+b}}\right)|\frac{a+b}{a-b}\right)}{b d f}-\frac{2 c \tan (e+f x) \sqrt{\frac{a+b \sec (e+f x)}{a+b}} \Pi \left(\frac{2 d}{c+d};\sin ^{-1}\left(\frac{\sqrt{1-\sec (e+f x)}}{\sqrt{2}}\right)|\frac{2 b}{a+b}\right)}{d f (c+d) \sqrt{-\tan ^2(e+f x)} \sqrt{a+b \sec (e+f x)}}",1,"(2*Sqrt[a + b]*Cot[e + f*x]*EllipticF[ArcSin[Sqrt[a + b*Sec[e + f*x]]/Sqrt[a + b]], (a + b)/(a - b)]*Sqrt[(b*(1 - Sec[e + f*x]))/(a + b)]*Sqrt[-((b*(1 + Sec[e + f*x]))/(a - b))])/(b*d*f) - (2*c*EllipticPi[(2*d)/(c + d), ArcSin[Sqrt[1 - Sec[e + f*x]]/Sqrt[2]], (2*b)/(a + b)]*Sqrt[(a + b*Sec[e + f*x])/(a + b)]*Tan[e + f*x])/(d*(c + d)*f*Sqrt[a + b*Sec[e + f*x]]*Sqrt[-Tan[e + f*x]^2])","A",3,3,35,0.08571,1,"{3977, 3832, 3973}"
283,1,83,0,0.424288,"\int \frac{(g \sec (e+f x))^{3/2}}{\sqrt{a+b \sec (e+f x)} (c+d \sec (e+f x))} \, dx","Int[(g*Sec[e + f*x])^(3/2)/(Sqrt[a + b*Sec[e + f*x]]*(c + d*Sec[e + f*x])),x]","\frac{2 g \sqrt{g \sec (e+f x)} \sqrt{\frac{a \cos (e+f x)+b}{a+b}} \Pi \left(\frac{2 c}{c+d};\frac{1}{2} (e+f x)|\frac{2 a}{a+b}\right)}{f (c+d) \sqrt{a+b \sec (e+f x)}}","\frac{2 g \sqrt{g \sec (e+f x)} \sqrt{\frac{a \cos (e+f x)+b}{a+b}} \Pi \left(\frac{2 c}{c+d};\frac{1}{2} (e+f x)|\frac{2 a}{a+b}\right)}{f (c+d) \sqrt{a+b \sec (e+f x)}}",1,"(2*g*Sqrt[(b + a*Cos[e + f*x])/(a + b)]*EllipticPi[(2*c)/(c + d), (e + f*x)/2, (2*a)/(a + b)]*Sqrt[g*Sec[e + f*x]])/((c + d)*f*Sqrt[a + b*Sec[e + f*x]])","A",3,3,39,0.07692,1,"{3975, 2807, 2805}"
284,1,166,0,0.8556324,"\int \frac{(g \sec (e+f x))^{5/2}}{\sqrt{a+b \sec (e+f x)} (c+d \sec (e+f x))} \, dx","Int[(g*Sec[e + f*x])^(5/2)/(Sqrt[a + b*Sec[e + f*x]]*(c + d*Sec[e + f*x])),x]","\frac{2 g^2 \sqrt{g \sec (e+f x)} \sqrt{\frac{a \cos (e+f x)+b}{a+b}} \Pi \left(2;\frac{1}{2} (e+f x)|\frac{2 a}{a+b}\right)}{d f \sqrt{a+b \sec (e+f x)}}-\frac{2 c g^2 \sqrt{g \sec (e+f x)} \sqrt{\frac{a \cos (e+f x)+b}{a+b}} \Pi \left(\frac{2 c}{c+d};\frac{1}{2} (e+f x)|\frac{2 a}{a+b}\right)}{d f (c+d) \sqrt{a+b \sec (e+f x)}}","\frac{2 g^2 \sqrt{g \sec (e+f x)} \sqrt{\frac{a \cos (e+f x)+b}{a+b}} \Pi \left(2;\frac{1}{2} (e+f x)|\frac{2 a}{a+b}\right)}{d f \sqrt{a+b \sec (e+f x)}}-\frac{2 c g^2 \sqrt{g \sec (e+f x)} \sqrt{\frac{a \cos (e+f x)+b}{a+b}} \Pi \left(\frac{2 c}{c+d};\frac{1}{2} (e+f x)|\frac{2 a}{a+b}\right)}{d f (c+d) \sqrt{a+b \sec (e+f x)}}",1,"(2*g^2*Sqrt[(b + a*Cos[e + f*x])/(a + b)]*EllipticPi[2, (e + f*x)/2, (2*a)/(a + b)]*Sqrt[g*Sec[e + f*x]])/(d*f*Sqrt[a + b*Sec[e + f*x]]) - (2*c*g^2*Sqrt[(b + a*Cos[e + f*x])/(a + b)]*EllipticPi[(2*c)/(c + d), (e + f*x)/2, (2*a)/(a + b)]*Sqrt[g*Sec[e + f*x]])/(d*(c + d)*f*Sqrt[a + b*Sec[e + f*x]])","A",7,5,39,0.1282,1,"{3979, 3859, 2807, 2805, 3975}"
285,1,67,0,0.2980532,"\int \frac{\sec (e+f x) \tan ^4(e+f x)}{(c-c \sec (e+f x))^7} \, dx","Int[(Sec[e + f*x]*Tan[e + f*x]^4)/(c - c*Sec[e + f*x])^7,x]","\frac{\cot ^9\left(\frac{1}{2} (e+f x)\right)}{36 c^7 f}-\frac{\cot ^7\left(\frac{1}{2} (e+f x)\right)}{14 c^7 f}+\frac{\cot ^5\left(\frac{1}{2} (e+f x)\right)}{20 c^7 f}","\frac{\cot ^9\left(\frac{1}{2} (e+f x)\right)}{36 c^7 f}-\frac{\cot ^7\left(\frac{1}{2} (e+f x)\right)}{14 c^7 f}+\frac{\cot ^5\left(\frac{1}{2} (e+f x)\right)}{20 c^7 f}",1,"Cot[(e + f*x)/2]^5/(20*c^7*f) - Cot[(e + f*x)/2]^7/(14*c^7*f) + Cot[(e + f*x)/2]^9/(36*c^7*f)","A",4,2,28,0.07143,1,"{12, 270}"
286,1,89,0,0.3356914,"\int \frac{\sec (e+f x) \tan ^4(e+f x)}{(c-c \sec (e+f x))^8} \, dx","Int[(Sec[e + f*x]*Tan[e + f*x]^4)/(c - c*Sec[e + f*x])^8,x]","-\frac{\cot ^{11}\left(\frac{1}{2} (e+f x)\right)}{88 c^8 f}+\frac{\cot ^9\left(\frac{1}{2} (e+f x)\right)}{24 c^8 f}-\frac{3 \cot ^7\left(\frac{1}{2} (e+f x)\right)}{56 c^8 f}+\frac{\cot ^5\left(\frac{1}{2} (e+f x)\right)}{40 c^8 f}","-\frac{\cot ^{11}\left(\frac{1}{2} (e+f x)\right)}{88 c^8 f}+\frac{\cot ^9\left(\frac{1}{2} (e+f x)\right)}{24 c^8 f}-\frac{3 \cot ^7\left(\frac{1}{2} (e+f x)\right)}{56 c^8 f}+\frac{\cot ^5\left(\frac{1}{2} (e+f x)\right)}{40 c^8 f}",1,"Cot[(e + f*x)/2]^5/(40*c^8*f) - (3*Cot[(e + f*x)/2]^7)/(56*c^8*f) + Cot[(e + f*x)/2]^9/(24*c^8*f) - Cot[(e + f*x)/2]^11/(88*c^8*f)","A",4,2,28,0.07143,1,"{12, 270}"