1,1,94,0,0.188289,"\int \sec ^{10}(c+d x) (a+i a \tan (c+d x)) \, dx","Int[Sec[c + d*x]^10*(a + I*a*Tan[c + d*x]),x]","\frac{a \tan ^9(c+d x)}{9 d}+\frac{4 a \tan ^7(c+d x)}{7 d}+\frac{6 a \tan ^5(c+d x)}{5 d}+\frac{4 a \tan ^3(c+d x)}{3 d}+\frac{a \tan (c+d x)}{d}+\frac{i a \sec ^{10}(c+d x)}{10 d}","\frac{a \tan ^9(c+d x)}{9 d}+\frac{4 a \tan ^7(c+d x)}{7 d}+\frac{6 a \tan ^5(c+d x)}{5 d}+\frac{4 a \tan ^3(c+d x)}{3 d}+\frac{a \tan (c+d x)}{d}+\frac{i a \sec ^{10}(c+d x)}{10 d}",1,"((I/10)*a*Sec[c + d*x]^10)/d + (a*Tan[c + d*x])/d + (4*a*Tan[c + d*x]^3)/(3*d) + (6*a*Tan[c + d*x]^5)/(5*d) + (4*a*Tan[c + d*x]^7)/(7*d) + (a*Tan[c + d*x]^9)/(9*d)","A",3,2,22,0.09091,1,"{3486, 3767}"
2,1,75,0,0.0407898,"\int \sec ^8(c+d x) (a+i a \tan (c+d x)) \, dx","Int[Sec[c + d*x]^8*(a + I*a*Tan[c + d*x]),x]","\frac{a \tan ^7(c+d x)}{7 d}+\frac{3 a \tan ^5(c+d x)}{5 d}+\frac{a \tan ^3(c+d x)}{d}+\frac{a \tan (c+d x)}{d}+\frac{i a \sec ^8(c+d x)}{8 d}","\frac{a \tan ^7(c+d x)}{7 d}+\frac{3 a \tan ^5(c+d x)}{5 d}+\frac{a \tan ^3(c+d x)}{d}+\frac{a \tan (c+d x)}{d}+\frac{i a \sec ^8(c+d x)}{8 d}",1,"((I/8)*a*Sec[c + d*x]^8)/d + (a*Tan[c + d*x])/d + (a*Tan[c + d*x]^3)/d + (3*a*Tan[c + d*x]^5)/(5*d) + (a*Tan[c + d*x]^7)/(7*d)","A",3,2,22,0.09091,1,"{3486, 3767}"
3,1,62,0,0.0373904,"\int \sec ^6(c+d x) (a+i a \tan (c+d x)) \, dx","Int[Sec[c + d*x]^6*(a + I*a*Tan[c + d*x]),x]","\frac{a \tan ^5(c+d x)}{5 d}+\frac{2 a \tan ^3(c+d x)}{3 d}+\frac{a \tan (c+d x)}{d}+\frac{i a \sec ^6(c+d x)}{6 d}","\frac{a \tan ^5(c+d x)}{5 d}+\frac{2 a \tan ^3(c+d x)}{3 d}+\frac{a \tan (c+d x)}{d}+\frac{i a \sec ^6(c+d x)}{6 d}",1,"((I/6)*a*Sec[c + d*x]^6)/d + (a*Tan[c + d*x])/d + (2*a*Tan[c + d*x]^3)/(3*d) + (a*Tan[c + d*x]^5)/(5*d)","A",3,2,22,0.09091,1,"{3486, 3767}"
4,1,46,0,0.0342313,"\int \sec ^4(c+d x) (a+i a \tan (c+d x)) \, dx","Int[Sec[c + d*x]^4*(a + I*a*Tan[c + d*x]),x]","\frac{a \tan ^3(c+d x)}{3 d}+\frac{a \tan (c+d x)}{d}+\frac{i a \sec ^4(c+d x)}{4 d}","\frac{a \tan ^3(c+d x)}{3 d}+\frac{a \tan (c+d x)}{d}+\frac{i a \sec ^4(c+d x)}{4 d}",1,"((I/4)*a*Sec[c + d*x]^4)/d + (a*Tan[c + d*x])/d + (a*Tan[c + d*x]^3)/(3*d)","A",3,2,22,0.09091,1,"{3486, 3767}"
5,1,30,0,0.0306043,"\int \sec ^2(c+d x) (a+i a \tan (c+d x)) \, dx","Int[Sec[c + d*x]^2*(a + I*a*Tan[c + d*x]),x]","\frac{a \tan (c+d x)}{d}+\frac{i a \sec ^2(c+d x)}{2 d}","-\frac{i (a+i a \tan (c+d x))^2}{2 a d}",1,"((I/2)*a*Sec[c + d*x]^2)/d + (a*Tan[c + d*x])/d","A",3,3,22,0.1364,1,"{3486, 3767, 8}"
6,1,19,0,0.0074034,"\int (a+i a \tan (c+d x)) \, dx","Int[a + I*a*Tan[c + d*x],x]","a x-\frac{i a \log (\cos (c+d x))}{d}","a x-\frac{i a \log (\cos (c+d x))}{d}",1,"a*x - (I*a*Log[Cos[c + d*x]])/d","A",2,1,13,0.07692,1,"{3475}"
7,1,45,0,0.0310949,"\int \cos ^2(c+d x) (a+i a \tan (c+d x)) \, dx","Int[Cos[c + d*x]^2*(a + I*a*Tan[c + d*x]),x]","-\frac{i a \cos ^2(c+d x)}{2 d}+\frac{a \sin (c+d x) \cos (c+d x)}{2 d}+\frac{a x}{2}","-\frac{i a \cos ^2(c+d x)}{2 d}+\frac{a \sin (c+d x) \cos (c+d x)}{2 d}+\frac{a x}{2}",1,"(a*x)/2 - ((I/2)*a*Cos[c + d*x]^2)/d + (a*Cos[c + d*x]*Sin[c + d*x])/(2*d)","A",3,3,22,0.1364,1,"{3486, 2635, 8}"
8,1,67,0,0.03995,"\int \cos ^4(c+d x) (a+i a \tan (c+d x)) \, dx","Int[Cos[c + d*x]^4*(a + I*a*Tan[c + d*x]),x]","-\frac{i a \cos ^4(c+d x)}{4 d}+\frac{a \sin (c+d x) \cos ^3(c+d x)}{4 d}+\frac{3 a \sin (c+d x) \cos (c+d x)}{8 d}+\frac{3 a x}{8}","-\frac{i a \cos ^4(c+d x)}{4 d}+\frac{a \sin (c+d x) \cos ^3(c+d x)}{4 d}+\frac{3 a \sin (c+d x) \cos (c+d x)}{8 d}+\frac{3 a x}{8}",1,"(3*a*x)/8 - ((I/4)*a*Cos[c + d*x]^4)/d + (3*a*Cos[c + d*x]*Sin[c + d*x])/(8*d) + (a*Cos[c + d*x]^3*Sin[c + d*x])/(4*d)","A",4,3,22,0.1364,1,"{3486, 2635, 8}"
9,1,89,0,0.0522472,"\int \cos ^6(c+d x) (a+i a \tan (c+d x)) \, dx","Int[Cos[c + d*x]^6*(a + I*a*Tan[c + d*x]),x]","-\frac{i a \cos ^6(c+d x)}{6 d}+\frac{a \sin (c+d x) \cos ^5(c+d x)}{6 d}+\frac{5 a \sin (c+d x) \cos ^3(c+d x)}{24 d}+\frac{5 a \sin (c+d x) \cos (c+d x)}{16 d}+\frac{5 a x}{16}","-\frac{i a \cos ^6(c+d x)}{6 d}+\frac{a \sin (c+d x) \cos ^5(c+d x)}{6 d}+\frac{5 a \sin (c+d x) \cos ^3(c+d x)}{24 d}+\frac{5 a \sin (c+d x) \cos (c+d x)}{16 d}+\frac{5 a x}{16}",1,"(5*a*x)/16 - ((I/6)*a*Cos[c + d*x]^6)/d + (5*a*Cos[c + d*x]*Sin[c + d*x])/(16*d) + (5*a*Cos[c + d*x]^3*Sin[c + d*x])/(24*d) + (a*Cos[c + d*x]^5*Sin[c + d*x])/(6*d)","A",5,3,22,0.1364,1,"{3486, 2635, 8}"
10,1,111,0,0.067046,"\int \cos ^8(c+d x) (a+i a \tan (c+d x)) \, dx","Int[Cos[c + d*x]^8*(a + I*a*Tan[c + d*x]),x]","-\frac{i a \cos ^8(c+d x)}{8 d}+\frac{a \sin (c+d x) \cos ^7(c+d x)}{8 d}+\frac{7 a \sin (c+d x) \cos ^5(c+d x)}{48 d}+\frac{35 a \sin (c+d x) \cos ^3(c+d x)}{192 d}+\frac{35 a \sin (c+d x) \cos (c+d x)}{128 d}+\frac{35 a x}{128}","-\frac{i a \cos ^8(c+d x)}{8 d}+\frac{a \sin (c+d x) \cos ^7(c+d x)}{8 d}+\frac{7 a \sin (c+d x) \cos ^5(c+d x)}{48 d}+\frac{35 a \sin (c+d x) \cos ^3(c+d x)}{192 d}+\frac{35 a \sin (c+d x) \cos (c+d x)}{128 d}+\frac{35 a x}{128}",1,"(35*a*x)/128 - ((I/8)*a*Cos[c + d*x]^8)/d + (35*a*Cos[c + d*x]*Sin[c + d*x])/(128*d) + (35*a*Cos[c + d*x]^3*Sin[c + d*x])/(192*d) + (7*a*Cos[c + d*x]^5*Sin[c + d*x])/(48*d) + (a*Cos[c + d*x]^7*Sin[c + d*x])/(8*d)","A",6,3,22,0.1364,1,"{3486, 2635, 8}"
11,1,98,0,0.0606778,"\int \sec ^7(c+d x) (a+i a \tan (c+d x)) \, dx","Int[Sec[c + d*x]^7*(a + I*a*Tan[c + d*x]),x]","\frac{i a \sec ^7(c+d x)}{7 d}+\frac{5 a \tanh ^{-1}(\sin (c+d x))}{16 d}+\frac{a \tan (c+d x) \sec ^5(c+d x)}{6 d}+\frac{5 a \tan (c+d x) \sec ^3(c+d x)}{24 d}+\frac{5 a \tan (c+d x) \sec (c+d x)}{16 d}","\frac{i a \sec ^7(c+d x)}{7 d}+\frac{5 a \tanh ^{-1}(\sin (c+d x))}{16 d}+\frac{a \tan (c+d x) \sec ^5(c+d x)}{6 d}+\frac{5 a \tan (c+d x) \sec ^3(c+d x)}{24 d}+\frac{5 a \tan (c+d x) \sec (c+d x)}{16 d}",1,"(5*a*ArcTanh[Sin[c + d*x]])/(16*d) + ((I/7)*a*Sec[c + d*x]^7)/d + (5*a*Sec[c + d*x]*Tan[c + d*x])/(16*d) + (5*a*Sec[c + d*x]^3*Tan[c + d*x])/(24*d) + (a*Sec[c + d*x]^5*Tan[c + d*x])/(6*d)","A",5,3,22,0.1364,1,"{3486, 3768, 3770}"
12,1,76,0,0.0483808,"\int \sec ^5(c+d x) (a+i a \tan (c+d x)) \, dx","Int[Sec[c + d*x]^5*(a + I*a*Tan[c + d*x]),x]","\frac{i a \sec ^5(c+d x)}{5 d}+\frac{3 a \tanh ^{-1}(\sin (c+d x))}{8 d}+\frac{a \tan (c+d x) \sec ^3(c+d x)}{4 d}+\frac{3 a \tan (c+d x) \sec (c+d x)}{8 d}","\frac{i a \sec ^5(c+d x)}{5 d}+\frac{3 a \tanh ^{-1}(\sin (c+d x))}{8 d}+\frac{a \tan (c+d x) \sec ^3(c+d x)}{4 d}+\frac{3 a \tan (c+d x) \sec (c+d x)}{8 d}",1,"(3*a*ArcTanh[Sin[c + d*x]])/(8*d) + ((I/5)*a*Sec[c + d*x]^5)/d + (3*a*Sec[c + d*x]*Tan[c + d*x])/(8*d) + (a*Sec[c + d*x]^3*Tan[c + d*x])/(4*d)","A",4,3,22,0.1364,1,"{3486, 3768, 3770}"
13,1,54,0,0.0352547,"\int \sec ^3(c+d x) (a+i a \tan (c+d x)) \, dx","Int[Sec[c + d*x]^3*(a + I*a*Tan[c + d*x]),x]","\frac{i a \sec ^3(c+d x)}{3 d}+\frac{a \tanh ^{-1}(\sin (c+d x))}{2 d}+\frac{a \tan (c+d x) \sec (c+d x)}{2 d}","\frac{i a \sec ^3(c+d x)}{3 d}+\frac{a \tanh ^{-1}(\sin (c+d x))}{2 d}+\frac{a \tan (c+d x) \sec (c+d x)}{2 d}",1,"(a*ArcTanh[Sin[c + d*x]])/(2*d) + ((I/3)*a*Sec[c + d*x]^3)/d + (a*Sec[c + d*x]*Tan[c + d*x])/(2*d)","A",3,3,22,0.1364,1,"{3486, 3768, 3770}"
14,1,27,0,0.0158266,"\int \sec (c+d x) (a+i a \tan (c+d x)) \, dx","Int[Sec[c + d*x]*(a + I*a*Tan[c + d*x]),x]","\frac{a \tanh ^{-1}(\sin (c+d x))}{d}+\frac{i a \sec (c+d x)}{d}","\frac{a \tanh ^{-1}(\sin (c+d x))}{d}+\frac{i a \sec (c+d x)}{d}",1,"(a*ArcTanh[Sin[c + d*x]])/d + (I*a*Sec[c + d*x])/d","A",2,2,20,0.1000,1,"{3486, 3770}"
15,1,26,0,0.020528,"\int \cos (c+d x) (a+i a \tan (c+d x)) \, dx","Int[Cos[c + d*x]*(a + I*a*Tan[c + d*x]),x]","\frac{a \sin (c+d x)}{d}-\frac{i a \cos (c+d x)}{d}","\frac{a \sin (c+d x)}{d}-\frac{i a \cos (c+d x)}{d}",1,"((-I)*a*Cos[c + d*x])/d + (a*Sin[c + d*x])/d","A",2,2,20,0.1000,1,"{3486, 2637}"
16,1,46,0,0.0323892,"\int \cos ^3(c+d x) (a+i a \tan (c+d x)) \, dx","Int[Cos[c + d*x]^3*(a + I*a*Tan[c + d*x]),x]","-\frac{a \sin ^3(c+d x)}{3 d}+\frac{a \sin (c+d x)}{d}-\frac{i a \cos ^3(c+d x)}{3 d}","-\frac{a \sin ^3(c+d x)}{3 d}+\frac{a \sin (c+d x)}{d}-\frac{i a \cos ^3(c+d x)}{3 d}",1,"((-I/3)*a*Cos[c + d*x]^3)/d + (a*Sin[c + d*x])/d - (a*Sin[c + d*x]^3)/(3*d)","A",3,2,22,0.09091,1,"{3486, 2633}"
17,1,62,0,0.0347422,"\int \cos ^5(c+d x) (a+i a \tan (c+d x)) \, dx","Int[Cos[c + d*x]^5*(a + I*a*Tan[c + d*x]),x]","\frac{a \sin ^5(c+d x)}{5 d}-\frac{2 a \sin ^3(c+d x)}{3 d}+\frac{a \sin (c+d x)}{d}-\frac{i a \cos ^5(c+d x)}{5 d}","\frac{a \sin ^5(c+d x)}{5 d}-\frac{2 a \sin ^3(c+d x)}{3 d}+\frac{a \sin (c+d x)}{d}-\frac{i a \cos ^5(c+d x)}{5 d}",1,"((-I/5)*a*Cos[c + d*x]^5)/d + (a*Sin[c + d*x])/d - (2*a*Sin[c + d*x]^3)/(3*d) + (a*Sin[c + d*x]^5)/(5*d)","A",3,2,22,0.09091,1,"{3486, 2633}"
18,1,76,0,0.0381817,"\int \cos ^7(c+d x) (a+i a \tan (c+d x)) \, dx","Int[Cos[c + d*x]^7*(a + I*a*Tan[c + d*x]),x]","-\frac{a \sin ^7(c+d x)}{7 d}+\frac{3 a \sin ^5(c+d x)}{5 d}-\frac{a \sin ^3(c+d x)}{d}+\frac{a \sin (c+d x)}{d}-\frac{i a \cos ^7(c+d x)}{7 d}","-\frac{a \sin ^7(c+d x)}{7 d}+\frac{3 a \sin ^5(c+d x)}{5 d}-\frac{a \sin ^3(c+d x)}{d}+\frac{a \sin (c+d x)}{d}-\frac{i a \cos ^7(c+d x)}{7 d}",1,"((-I/7)*a*Cos[c + d*x]^7)/d + (a*Sin[c + d*x])/d - (a*Sin[c + d*x]^3)/d + (3*a*Sin[c + d*x]^5)/(5*d) - (a*Sin[c + d*x]^7)/(7*d)","A",3,2,22,0.09091,1,"{3486, 2633}"
19,1,109,0,0.0662851,"\int \sec ^8(c+d x) (a+i a \tan (c+d x))^2 \, dx","Int[Sec[c + d*x]^8*(a + I*a*Tan[c + d*x])^2,x]","\frac{i (a+i a \tan (c+d x))^9}{9 a^7 d}-\frac{3 i (a+i a \tan (c+d x))^8}{4 a^6 d}+\frac{12 i (a+i a \tan (c+d x))^7}{7 a^5 d}-\frac{4 i (a+i a \tan (c+d x))^6}{3 a^4 d}","\frac{i (a+i a \tan (c+d x))^9}{9 a^7 d}-\frac{3 i (a+i a \tan (c+d x))^8}{4 a^6 d}+\frac{12 i (a+i a \tan (c+d x))^7}{7 a^5 d}-\frac{4 i (a+i a \tan (c+d x))^6}{3 a^4 d}",1,"(((-4*I)/3)*(a + I*a*Tan[c + d*x])^6)/(a^4*d) + (((12*I)/7)*(a + I*a*Tan[c + d*x])^7)/(a^5*d) - (((3*I)/4)*(a + I*a*Tan[c + d*x])^8)/(a^6*d) + ((I/9)*(a + I*a*Tan[c + d*x])^9)/(a^7*d)","A",3,2,24,0.08333,1,"{3487, 43}"
20,1,82,0,0.056461,"\int \sec ^6(c+d x) (a+i a \tan (c+d x))^2 \, dx","Int[Sec[c + d*x]^6*(a + I*a*Tan[c + d*x])^2,x]","-\frac{i (a+i a \tan (c+d x))^7}{7 a^5 d}+\frac{2 i (a+i a \tan (c+d x))^6}{3 a^4 d}-\frac{4 i (a+i a \tan (c+d x))^5}{5 a^3 d}","-\frac{i (a+i a \tan (c+d x))^7}{7 a^5 d}+\frac{2 i (a+i a \tan (c+d x))^6}{3 a^4 d}-\frac{4 i (a+i a \tan (c+d x))^5}{5 a^3 d}",1,"(((-4*I)/5)*(a + I*a*Tan[c + d*x])^5)/(a^3*d) + (((2*I)/3)*(a + I*a*Tan[c + d*x])^6)/(a^4*d) - ((I/7)*(a + I*a*Tan[c + d*x])^7)/(a^5*d)","A",3,2,24,0.08333,1,"{3487, 43}"
21,1,55,0,0.0431053,"\int \sec ^4(c+d x) (a+i a \tan (c+d x))^2 \, dx","Int[Sec[c + d*x]^4*(a + I*a*Tan[c + d*x])^2,x]","\frac{i (a+i a \tan (c+d x))^5}{5 a^3 d}-\frac{i (a+i a \tan (c+d x))^4}{2 a^2 d}","\frac{i (a+i a \tan (c+d x))^5}{5 a^3 d}-\frac{i (a+i a \tan (c+d x))^4}{2 a^2 d}",1,"((-I/2)*(a + I*a*Tan[c + d*x])^4)/(a^2*d) + ((I/5)*(a + I*a*Tan[c + d*x])^5)/(a^3*d)","A",3,2,24,0.08333,1,"{3487, 43}"
22,1,27,0,0.0375375,"\int \sec ^2(c+d x) (a+i a \tan (c+d x))^2 \, dx","Int[Sec[c + d*x]^2*(a + I*a*Tan[c + d*x])^2,x]","-\frac{i (a+i a \tan (c+d x))^3}{3 a d}","-\frac{i (a+i a \tan (c+d x))^3}{3 a d}",1,"((-I/3)*(a + I*a*Tan[c + d*x])^3)/(a*d)","A",2,2,24,0.08333,1,"{3487, 32}"
23,1,38,0,0.0169765,"\int (a+i a \tan (c+d x))^2 \, dx","Int[(a + I*a*Tan[c + d*x])^2,x]","-\frac{a^2 \tan (c+d x)}{d}-\frac{2 i a^2 \log (\cos (c+d x))}{d}+2 a^2 x","-\frac{a^2 \tan (c+d x)}{d}-\frac{2 i a^2 \log (\cos (c+d x))}{d}+2 a^2 x",1,"2*a^2*x - ((2*I)*a^2*Log[Cos[c + d*x]])/d - (a^2*Tan[c + d*x])/d","A",2,2,15,0.1333,1,"{3477, 3475}"
24,1,25,0,0.0372104,"\int \cos ^2(c+d x) (a+i a \tan (c+d x))^2 \, dx","Int[Cos[c + d*x]^2*(a + I*a*Tan[c + d*x])^2,x]","-\frac{i a^3}{d (a-i a \tan (c+d x))}","-\frac{i a^3}{d (a-i a \tan (c+d x))}",1,"((-I)*a^3)/(d*(a - I*a*Tan[c + d*x]))","A",2,2,24,0.08333,1,"{3487, 32}"
25,1,63,0,0.0607932,"\int \cos ^4(c+d x) (a+i a \tan (c+d x))^2 \, dx","Int[Cos[c + d*x]^4*(a + I*a*Tan[c + d*x])^2,x]","-\frac{i a^4}{4 d (a-i a \tan (c+d x))^2}-\frac{i a^3}{4 d (a-i a \tan (c+d x))}+\frac{a^2 x}{4}","-\frac{i a^4}{4 d (a-i a \tan (c+d x))^2}-\frac{i a^3}{4 d (a-i a \tan (c+d x))}+\frac{a^2 x}{4}",1,"(a^2*x)/4 - ((I/4)*a^4)/(d*(a - I*a*Tan[c + d*x])^2) - ((I/4)*a^3)/(d*(a - I*a*Tan[c + d*x]))","A",4,3,24,0.1250,1,"{3487, 44, 206}"
26,1,117,0,0.0815212,"\int \cos ^6(c+d x) (a+i a \tan (c+d x))^2 \, dx","Int[Cos[c + d*x]^6*(a + I*a*Tan[c + d*x])^2,x]","-\frac{i a^5}{12 d (a-i a \tan (c+d x))^3}-\frac{i a^4}{8 d (a-i a \tan (c+d x))^2}-\frac{3 i a^3}{16 d (a-i a \tan (c+d x))}+\frac{i a^3}{16 d (a+i a \tan (c+d x))}+\frac{a^2 x}{4}","-\frac{i a^5}{12 d (a-i a \tan (c+d x))^3}-\frac{i a^4}{8 d (a-i a \tan (c+d x))^2}-\frac{3 i a^3}{16 d (a-i a \tan (c+d x))}+\frac{i a^3}{16 d (a+i a \tan (c+d x))}+\frac{a^2 x}{4}",1,"(a^2*x)/4 - ((I/12)*a^5)/(d*(a - I*a*Tan[c + d*x])^3) - ((I/8)*a^4)/(d*(a - I*a*Tan[c + d*x])^2) - (((3*I)/16)*a^3)/(d*(a - I*a*Tan[c + d*x])) + ((I/16)*a^3)/(d*(a + I*a*Tan[c + d*x]))","A",4,3,24,0.1250,1,"{3487, 44, 206}"
27,1,171,0,0.1069483,"\int \cos ^8(c+d x) (a+i a \tan (c+d x))^2 \, dx","Int[Cos[c + d*x]^8*(a + I*a*Tan[c + d*x])^2,x]","-\frac{i a^6}{32 d (a-i a \tan (c+d x))^4}-\frac{i a^5}{16 d (a-i a \tan (c+d x))^3}-\frac{3 i a^4}{32 d (a-i a \tan (c+d x))^2}+\frac{i a^4}{64 d (a+i a \tan (c+d x))^2}-\frac{5 i a^3}{32 d (a-i a \tan (c+d x))}+\frac{5 i a^3}{64 d (a+i a \tan (c+d x))}+\frac{15 a^2 x}{64}","-\frac{i a^6}{32 d (a-i a \tan (c+d x))^4}-\frac{i a^5}{16 d (a-i a \tan (c+d x))^3}-\frac{3 i a^4}{32 d (a-i a \tan (c+d x))^2}+\frac{i a^4}{64 d (a+i a \tan (c+d x))^2}-\frac{5 i a^3}{32 d (a-i a \tan (c+d x))}+\frac{5 i a^3}{64 d (a+i a \tan (c+d x))}+\frac{15 a^2 x}{64}",1,"(15*a^2*x)/64 - ((I/32)*a^6)/(d*(a - I*a*Tan[c + d*x])^4) - ((I/16)*a^5)/(d*(a - I*a*Tan[c + d*x])^3) - (((3*I)/32)*a^4)/(d*(a - I*a*Tan[c + d*x])^2) - (((5*I)/32)*a^3)/(d*(a - I*a*Tan[c + d*x])) + ((I/64)*a^4)/(d*(a + I*a*Tan[c + d*x])^2) + (((5*I)/64)*a^3)/(d*(a + I*a*Tan[c + d*x]))","A",4,3,24,0.1250,1,"{3487, 44, 206}"
28,1,118,0,0.0871915,"\int \sec ^5(c+d x) (a+i a \tan (c+d x))^2 \, dx","Int[Sec[c + d*x]^5*(a + I*a*Tan[c + d*x])^2,x]","\frac{7 i a^2 \sec ^5(c+d x)}{30 d}+\frac{7 a^2 \tanh ^{-1}(\sin (c+d x))}{16 d}+\frac{i \sec ^5(c+d x) \left(a^2+i a^2 \tan (c+d x)\right)}{6 d}+\frac{7 a^2 \tan (c+d x) \sec ^3(c+d x)}{24 d}+\frac{7 a^2 \tan (c+d x) \sec (c+d x)}{16 d}","\frac{7 i a^2 \sec ^5(c+d x)}{30 d}+\frac{7 a^2 \tanh ^{-1}(\sin (c+d x))}{16 d}+\frac{i \sec ^5(c+d x) \left(a^2+i a^2 \tan (c+d x)\right)}{6 d}+\frac{7 a^2 \tan (c+d x) \sec ^3(c+d x)}{24 d}+\frac{7 a^2 \tan (c+d x) \sec (c+d x)}{16 d}",1,"(7*a^2*ArcTanh[Sin[c + d*x]])/(16*d) + (((7*I)/30)*a^2*Sec[c + d*x]^5)/d + (7*a^2*Sec[c + d*x]*Tan[c + d*x])/(16*d) + (7*a^2*Sec[c + d*x]^3*Tan[c + d*x])/(24*d) + ((I/6)*Sec[c + d*x]^5*(a^2 + I*a^2*Tan[c + d*x]))/d","A",5,4,24,0.1667,1,"{3498, 3486, 3768, 3770}"
29,1,94,0,0.0766581,"\int \sec ^3(c+d x) (a+i a \tan (c+d x))^2 \, dx","Int[Sec[c + d*x]^3*(a + I*a*Tan[c + d*x])^2,x]","\frac{5 i a^2 \sec ^3(c+d x)}{12 d}+\frac{5 a^2 \tanh ^{-1}(\sin (c+d x))}{8 d}+\frac{i \sec ^3(c+d x) \left(a^2+i a^2 \tan (c+d x)\right)}{4 d}+\frac{5 a^2 \tan (c+d x) \sec (c+d x)}{8 d}","\frac{5 i a^2 \sec ^3(c+d x)}{12 d}+\frac{5 a^2 \tanh ^{-1}(\sin (c+d x))}{8 d}+\frac{i \sec ^3(c+d x) \left(a^2+i a^2 \tan (c+d x)\right)}{4 d}+\frac{5 a^2 \tan (c+d x) \sec (c+d x)}{8 d}",1,"(5*a^2*ArcTanh[Sin[c + d*x]])/(8*d) + (((5*I)/12)*a^2*Sec[c + d*x]^3)/d + (5*a^2*Sec[c + d*x]*Tan[c + d*x])/(8*d) + ((I/4)*Sec[c + d*x]^3*(a^2 + I*a^2*Tan[c + d*x]))/d","A",4,4,24,0.1667,1,"{3498, 3486, 3768, 3770}"
30,1,68,0,0.0399934,"\int \sec (c+d x) (a+i a \tan (c+d x))^2 \, dx","Int[Sec[c + d*x]*(a + I*a*Tan[c + d*x])^2,x]","\frac{3 i a^2 \sec (c+d x)}{2 d}+\frac{3 a^2 \tanh ^{-1}(\sin (c+d x))}{2 d}+\frac{i \sec (c+d x) \left(a^2+i a^2 \tan (c+d x)\right)}{2 d}","\frac{3 i a^2 \sec (c+d x)}{2 d}+\frac{3 a^2 \tanh ^{-1}(\sin (c+d x))}{2 d}+\frac{i \sec (c+d x) \left(a^2+i a^2 \tan (c+d x)\right)}{2 d}",1,"(3*a^2*ArcTanh[Sin[c + d*x]])/(2*d) + (((3*I)/2)*a^2*Sec[c + d*x])/d + ((I/2)*Sec[c + d*x]*(a^2 + I*a^2*Tan[c + d*x]))/d","A",3,3,22,0.1364,1,"{3498, 3486, 3770}"
31,1,46,0,0.0344902,"\int \cos (c+d x) (a+i a \tan (c+d x))^2 \, dx","Int[Cos[c + d*x]*(a + I*a*Tan[c + d*x])^2,x]","-\frac{a^2 \tanh ^{-1}(\sin (c+d x))}{d}-\frac{2 i \cos (c+d x) \left(a^2+i a^2 \tan (c+d x)\right)}{d}","-\frac{a^2 \tanh ^{-1}(\sin (c+d x))}{d}-\frac{2 i \cos (c+d x) \left(a^2+i a^2 \tan (c+d x)\right)}{d}",1,"-((a^2*ArcTanh[Sin[c + d*x]])/d) - ((2*I)*Cos[c + d*x]*(a^2 + I*a^2*Tan[c + d*x]))/d","A",2,2,22,0.09091,1,"{3496, 3770}"
32,1,51,0,0.0419488,"\int \cos ^3(c+d x) (a+i a \tan (c+d x))^2 \, dx","Int[Cos[c + d*x]^3*(a + I*a*Tan[c + d*x])^2,x]","\frac{a^2 \sin (c+d x)}{3 d}-\frac{2 i \cos ^3(c+d x) \left(a^2+i a^2 \tan (c+d x)\right)}{3 d}","\frac{a^2 \sin (c+d x)}{3 d}-\frac{2 i \cos ^3(c+d x) \left(a^2+i a^2 \tan (c+d x)\right)}{3 d}",1,"(a^2*Sin[c + d*x])/(3*d) - (((2*I)/3)*Cos[c + d*x]^3*(a^2 + I*a^2*Tan[c + d*x]))/d","A",2,2,24,0.08333,1,"{3496, 2637}"
33,1,69,0,0.0491498,"\int \cos ^5(c+d x) (a+i a \tan (c+d x))^2 \, dx","Int[Cos[c + d*x]^5*(a + I*a*Tan[c + d*x])^2,x]","-\frac{a^2 \sin ^3(c+d x)}{5 d}+\frac{3 a^2 \sin (c+d x)}{5 d}-\frac{2 i \cos ^5(c+d x) \left(a^2+i a^2 \tan (c+d x)\right)}{5 d}","-\frac{a^2 \sin ^3(c+d x)}{5 d}+\frac{3 a^2 \sin (c+d x)}{5 d}-\frac{2 i \cos ^5(c+d x) \left(a^2+i a^2 \tan (c+d x)\right)}{5 d}",1,"(3*a^2*Sin[c + d*x])/(5*d) - (a^2*Sin[c + d*x]^3)/(5*d) - (((2*I)/5)*Cos[c + d*x]^5*(a^2 + I*a^2*Tan[c + d*x]))/d","A",3,2,24,0.08333,1,"{3496, 2633}"
34,1,87,0,0.0523546,"\int \cos ^7(c+d x) (a+i a \tan (c+d x))^2 \, dx","Int[Cos[c + d*x]^7*(a + I*a*Tan[c + d*x])^2,x]","\frac{a^2 \sin ^5(c+d x)}{7 d}-\frac{10 a^2 \sin ^3(c+d x)}{21 d}+\frac{5 a^2 \sin (c+d x)}{7 d}-\frac{2 i \cos ^7(c+d x) \left(a^2+i a^2 \tan (c+d x)\right)}{7 d}","\frac{a^2 \sin ^5(c+d x)}{7 d}-\frac{10 a^2 \sin ^3(c+d x)}{21 d}+\frac{5 a^2 \sin (c+d x)}{7 d}-\frac{2 i \cos ^7(c+d x) \left(a^2+i a^2 \tan (c+d x)\right)}{7 d}",1,"(5*a^2*Sin[c + d*x])/(7*d) - (10*a^2*Sin[c + d*x]^3)/(21*d) + (a^2*Sin[c + d*x]^5)/(7*d) - (((2*I)/7)*Cos[c + d*x]^7*(a^2 + I*a^2*Tan[c + d*x]))/d","A",3,2,24,0.08333,1,"{3496, 2633}"
35,1,105,0,0.0559433,"\int \cos ^9(c+d x) (a+i a \tan (c+d x))^2 \, dx","Int[Cos[c + d*x]^9*(a + I*a*Tan[c + d*x])^2,x]","-\frac{a^2 \sin ^7(c+d x)}{9 d}+\frac{7 a^2 \sin ^5(c+d x)}{15 d}-\frac{7 a^2 \sin ^3(c+d x)}{9 d}+\frac{7 a^2 \sin (c+d x)}{9 d}-\frac{2 i \cos ^9(c+d x) \left(a^2+i a^2 \tan (c+d x)\right)}{9 d}","-\frac{a^2 \sin ^7(c+d x)}{9 d}+\frac{7 a^2 \sin ^5(c+d x)}{15 d}-\frac{7 a^2 \sin ^3(c+d x)}{9 d}+\frac{7 a^2 \sin (c+d x)}{9 d}-\frac{2 i \cos ^9(c+d x) \left(a^2+i a^2 \tan (c+d x)\right)}{9 d}",1,"(7*a^2*Sin[c + d*x])/(9*d) - (7*a^2*Sin[c + d*x]^3)/(9*d) + (7*a^2*Sin[c + d*x]^5)/(15*d) - (a^2*Sin[c + d*x]^7)/(9*d) - (((2*I)/9)*Cos[c + d*x]^9*(a^2 + I*a^2*Tan[c + d*x]))/d","A",3,2,24,0.08333,1,"{3496, 2633}"
36,1,109,0,0.0637078,"\int \sec ^8(c+d x) (a+i a \tan (c+d x))^3 \, dx","Int[Sec[c + d*x]^8*(a + I*a*Tan[c + d*x])^3,x]","\frac{i (a+i a \tan (c+d x))^{10}}{10 a^7 d}-\frac{2 i (a+i a \tan (c+d x))^9}{3 a^6 d}+\frac{3 i (a+i a \tan (c+d x))^8}{2 a^5 d}-\frac{8 i (a+i a \tan (c+d x))^7}{7 a^4 d}","\frac{i (a+i a \tan (c+d x))^{10}}{10 a^7 d}-\frac{2 i (a+i a \tan (c+d x))^9}{3 a^6 d}+\frac{3 i (a+i a \tan (c+d x))^8}{2 a^5 d}-\frac{8 i (a+i a \tan (c+d x))^7}{7 a^4 d}",1,"(((-8*I)/7)*(a + I*a*Tan[c + d*x])^7)/(a^4*d) + (((3*I)/2)*(a + I*a*Tan[c + d*x])^8)/(a^5*d) - (((2*I)/3)*(a + I*a*Tan[c + d*x])^9)/(a^6*d) + ((I/10)*(a + I*a*Tan[c + d*x])^10)/(a^7*d)","A",3,2,24,0.08333,1,"{3487, 43}"
37,1,82,0,0.0563161,"\int \sec ^6(c+d x) (a+i a \tan (c+d x))^3 \, dx","Int[Sec[c + d*x]^6*(a + I*a*Tan[c + d*x])^3,x]","-\frac{i (a+i a \tan (c+d x))^8}{8 a^5 d}+\frac{4 i (a+i a \tan (c+d x))^7}{7 a^4 d}-\frac{2 i (a+i a \tan (c+d x))^6}{3 a^3 d}","-\frac{i (a+i a \tan (c+d x))^8}{8 a^5 d}+\frac{4 i (a+i a \tan (c+d x))^7}{7 a^4 d}-\frac{2 i (a+i a \tan (c+d x))^6}{3 a^3 d}",1,"(((-2*I)/3)*(a + I*a*Tan[c + d*x])^6)/(a^3*d) + (((4*I)/7)*(a + I*a*Tan[c + d*x])^7)/(a^4*d) - ((I/8)*(a + I*a*Tan[c + d*x])^8)/(a^5*d)","A",3,2,24,0.08333,1,"{3487, 43}"
38,1,55,0,0.0426855,"\int \sec ^4(c+d x) (a+i a \tan (c+d x))^3 \, dx","Int[Sec[c + d*x]^4*(a + I*a*Tan[c + d*x])^3,x]","\frac{i (a+i a \tan (c+d x))^6}{6 a^3 d}-\frac{2 i (a+i a \tan (c+d x))^5}{5 a^2 d}","\frac{i (a+i a \tan (c+d x))^6}{6 a^3 d}-\frac{2 i (a+i a \tan (c+d x))^5}{5 a^2 d}",1,"(((-2*I)/5)*(a + I*a*Tan[c + d*x])^5)/(a^2*d) + ((I/6)*(a + I*a*Tan[c + d*x])^6)/(a^3*d)","A",3,2,24,0.08333,1,"{3487, 43}"
39,1,27,0,0.0365777,"\int \sec ^2(c+d x) (a+i a \tan (c+d x))^3 \, dx","Int[Sec[c + d*x]^2*(a + I*a*Tan[c + d*x])^3,x]","-\frac{i (a+i a \tan (c+d x))^4}{4 a d}","-\frac{i (a+i a \tan (c+d x))^4}{4 a d}",1,"((-I/4)*(a + I*a*Tan[c + d*x])^4)/(a*d)","A",2,2,24,0.08333,1,"{3487, 32}"
40,1,63,0,0.0317299,"\int (a+i a \tan (c+d x))^3 \, dx","Int[(a + I*a*Tan[c + d*x])^3,x]","-\frac{2 a^3 \tan (c+d x)}{d}-\frac{4 i a^3 \log (\cos (c+d x))}{d}+4 a^3 x+\frac{i a (a+i a \tan (c+d x))^2}{2 d}","-\frac{2 a^3 \tan (c+d x)}{d}-\frac{4 i a^3 \log (\cos (c+d x))}{d}+4 a^3 x+\frac{i a (a+i a \tan (c+d x))^2}{2 d}",1,"4*a^3*x - ((4*I)*a^3*Log[Cos[c + d*x]])/d - (2*a^3*Tan[c + d*x])/d + ((I/2)*a*(a + I*a*Tan[c + d*x])^2)/d","A",3,3,15,0.2000,1,"{3478, 3477, 3475}"
41,1,49,0,0.0486997,"\int \cos ^2(c+d x) (a+i a \tan (c+d x))^3 \, dx","Int[Cos[c + d*x]^2*(a + I*a*Tan[c + d*x])^3,x]","-\frac{2 i a^4}{d (a-i a \tan (c+d x))}+\frac{i a^3 \log (\cos (c+d x))}{d}-a^3 x","-\frac{2 i a^4}{d (a-i a \tan (c+d x))}+\frac{i a^3 \log (\cos (c+d x))}{d}-a^3 x",1,"-(a^3*x) + (I*a^3*Log[Cos[c + d*x]])/d - ((2*I)*a^4)/(d*(a - I*a*Tan[c + d*x]))","A",3,2,24,0.08333,1,"{3487, 43}"
42,1,27,0,0.0378988,"\int \cos ^4(c+d x) (a+i a \tan (c+d x))^3 \, dx","Int[Cos[c + d*x]^4*(a + I*a*Tan[c + d*x])^3,x]","-\frac{i a^5}{2 d (a-i a \tan (c+d x))^2}","-\frac{i a^5}{2 d (a-i a \tan (c+d x))^2}",1,"((-I/2)*a^5)/(d*(a - I*a*Tan[c + d*x])^2)","A",2,2,24,0.08333,1,"{3487, 32}"
43,1,90,0,0.0667252,"\int \cos ^6(c+d x) (a+i a \tan (c+d x))^3 \, dx","Int[Cos[c + d*x]^6*(a + I*a*Tan[c + d*x])^3,x]","-\frac{i a^6}{6 d (a-i a \tan (c+d x))^3}-\frac{i a^5}{8 d (a-i a \tan (c+d x))^2}-\frac{i a^4}{8 d (a-i a \tan (c+d x))}+\frac{a^3 x}{8}","-\frac{i a^6}{6 d (a-i a \tan (c+d x))^3}-\frac{i a^5}{8 d (a-i a \tan (c+d x))^2}-\frac{i a^4}{8 d (a-i a \tan (c+d x))}+\frac{a^3 x}{8}",1,"(a^3*x)/8 - ((I/6)*a^6)/(d*(a - I*a*Tan[c + d*x])^3) - ((I/8)*a^5)/(d*(a - I*a*Tan[c + d*x])^2) - ((I/8)*a^4)/(d*(a - I*a*Tan[c + d*x]))","A",4,3,24,0.1250,1,"{3487, 44, 206}"
44,1,144,0,0.091226,"\int \cos ^8(c+d x) (a+i a \tan (c+d x))^3 \, dx","Int[Cos[c + d*x]^8*(a + I*a*Tan[c + d*x])^3,x]","-\frac{i a^7}{16 d (a-i a \tan (c+d x))^4}-\frac{i a^6}{12 d (a-i a \tan (c+d x))^3}-\frac{3 i a^5}{32 d (a-i a \tan (c+d x))^2}-\frac{i a^4}{8 d (a-i a \tan (c+d x))}+\frac{i a^4}{32 d (a+i a \tan (c+d x))}+\frac{5 a^3 x}{32}","-\frac{i a^7}{16 d (a-i a \tan (c+d x))^4}-\frac{i a^6}{12 d (a-i a \tan (c+d x))^3}-\frac{3 i a^5}{32 d (a-i a \tan (c+d x))^2}-\frac{i a^4}{8 d (a-i a \tan (c+d x))}+\frac{i a^4}{32 d (a+i a \tan (c+d x))}+\frac{5 a^3 x}{32}",1,"(5*a^3*x)/32 - ((I/16)*a^7)/(d*(a - I*a*Tan[c + d*x])^4) - ((I/12)*a^6)/(d*(a - I*a*Tan[c + d*x])^3) - (((3*I)/32)*a^5)/(d*(a - I*a*Tan[c + d*x])^2) - ((I/8)*a^4)/(d*(a - I*a*Tan[c + d*x])) + ((I/32)*a^4)/(d*(a + I*a*Tan[c + d*x]))","A",4,3,24,0.1250,1,"{3487, 44, 206}"
45,1,127,0,0.1199557,"\int \sec ^3(c+d x) (a+i a \tan (c+d x))^3 \, dx","Int[Sec[c + d*x]^3*(a + I*a*Tan[c + d*x])^3,x]","\frac{7 i a^3 \sec ^3(c+d x)}{12 d}+\frac{7 a^3 \tanh ^{-1}(\sin (c+d x))}{8 d}+\frac{7 i \sec ^3(c+d x) \left(a^3+i a^3 \tan (c+d x)\right)}{20 d}+\frac{7 a^3 \tan (c+d x) \sec (c+d x)}{8 d}+\frac{i a \sec ^3(c+d x) (a+i a \tan (c+d x))^2}{5 d}","\frac{7 i a^3 \sec ^3(c+d x)}{12 d}+\frac{7 a^3 \tanh ^{-1}(\sin (c+d x))}{8 d}+\frac{7 i \sec ^3(c+d x) \left(a^3+i a^3 \tan (c+d x)\right)}{20 d}+\frac{7 a^3 \tan (c+d x) \sec (c+d x)}{8 d}+\frac{i a \sec ^3(c+d x) (a+i a \tan (c+d x))^2}{5 d}",1,"(7*a^3*ArcTanh[Sin[c + d*x]])/(8*d) + (((7*I)/12)*a^3*Sec[c + d*x]^3)/d + (7*a^3*Sec[c + d*x]*Tan[c + d*x])/(8*d) + ((I/5)*a*Sec[c + d*x]^3*(a + I*a*Tan[c + d*x])^2)/d + (((7*I)/20)*Sec[c + d*x]^3*(a^3 + I*a^3*Tan[c + d*x]))/d","A",5,4,24,0.1667,1,"{3498, 3486, 3768, 3770}"
46,1,99,0,0.0660193,"\int \sec (c+d x) (a+i a \tan (c+d x))^3 \, dx","Int[Sec[c + d*x]*(a + I*a*Tan[c + d*x])^3,x]","\frac{5 i a^3 \sec (c+d x)}{2 d}+\frac{5 a^3 \tanh ^{-1}(\sin (c+d x))}{2 d}+\frac{5 i \sec (c+d x) \left(a^3+i a^3 \tan (c+d x)\right)}{6 d}+\frac{i a \sec (c+d x) (a+i a \tan (c+d x))^2}{3 d}","\frac{5 i a^3 \sec (c+d x)}{2 d}+\frac{5 a^3 \tanh ^{-1}(\sin (c+d x))}{2 d}+\frac{5 i \sec (c+d x) \left(a^3+i a^3 \tan (c+d x)\right)}{6 d}+\frac{i a \sec (c+d x) (a+i a \tan (c+d x))^2}{3 d}",1,"(5*a^3*ArcTanh[Sin[c + d*x]])/(2*d) + (((5*I)/2)*a^3*Sec[c + d*x])/d + ((I/3)*a*Sec[c + d*x]*(a + I*a*Tan[c + d*x])^2)/d + (((5*I)/6)*Sec[c + d*x]*(a^3 + I*a^3*Tan[c + d*x]))/d","A",4,3,22,0.1364,1,"{3498, 3486, 3770}"
47,1,61,0,0.0501246,"\int \cos (c+d x) (a+i a \tan (c+d x))^3 \, dx","Int[Cos[c + d*x]*(a + I*a*Tan[c + d*x])^3,x]","-\frac{3 i a^3 \sec (c+d x)}{d}-\frac{3 a^3 \tanh ^{-1}(\sin (c+d x))}{d}-\frac{2 i a \cos (c+d x) (a+i a \tan (c+d x))^2}{d}","-\frac{3 i a^3 \sec (c+d x)}{d}-\frac{3 a^3 \tanh ^{-1}(\sin (c+d x))}{d}-\frac{2 i a \cos (c+d x) (a+i a \tan (c+d x))^2}{d}",1,"(-3*a^3*ArcTanh[Sin[c + d*x]])/d - ((3*I)*a^3*Sec[c + d*x])/d - ((2*I)*a*Cos[c + d*x]*(a + I*a*Tan[c + d*x])^2)/d","A",3,3,22,0.1364,1,"{3496, 3486, 3770}"
48,1,32,0,0.0366968,"\int \cos ^3(c+d x) (a+i a \tan (c+d x))^3 \, dx","Int[Cos[c + d*x]^3*(a + I*a*Tan[c + d*x])^3,x]","-\frac{i \cos ^3(c+d x) (a+i a \tan (c+d x))^3}{3 d}","-\frac{i \cos ^3(c+d x) (a+i a \tan (c+d x))^3}{3 d}",1,"((-I/3)*Cos[c + d*x]^3*(a + I*a*Tan[c + d*x])^3)/d","A",1,1,24,0.04167,1,"{3488}"
49,1,88,0,0.0710485,"\int \cos ^5(c+d x) (a+i a \tan (c+d x))^3 \, dx","Int[Cos[c + d*x]^5*(a + I*a*Tan[c + d*x])^3,x]","-\frac{a^3 \sin ^3(c+d x)}{15 d}+\frac{a^3 \sin (c+d x)}{5 d}-\frac{i a^3 \cos ^3(c+d x)}{15 d}-\frac{2 i a \cos ^5(c+d x) (a+i a \tan (c+d x))^2}{5 d}","-\frac{a^3 \sin ^3(c+d x)}{15 d}+\frac{a^3 \sin (c+d x)}{5 d}-\frac{i a^3 \cos ^3(c+d x)}{15 d}-\frac{2 i a \cos ^5(c+d x) (a+i a \tan (c+d x))^2}{5 d}",1,"((-I/15)*a^3*Cos[c + d*x]^3)/d + (a^3*Sin[c + d*x])/(5*d) - (a^3*Sin[c + d*x]^3)/(15*d) - (((2*I)/5)*a*Cos[c + d*x]^5*(a + I*a*Tan[c + d*x])^2)/d","A",4,3,24,0.1250,1,"{3496, 3486, 2633}"
50,1,106,0,0.0757118,"\int \cos ^7(c+d x) (a+i a \tan (c+d x))^3 \, dx","Int[Cos[c + d*x]^7*(a + I*a*Tan[c + d*x])^3,x]","\frac{3 a^3 \sin ^5(c+d x)}{35 d}-\frac{2 a^3 \sin ^3(c+d x)}{7 d}+\frac{3 a^3 \sin (c+d x)}{7 d}-\frac{3 i a^3 \cos ^5(c+d x)}{35 d}-\frac{2 i a \cos ^7(c+d x) (a+i a \tan (c+d x))^2}{7 d}","\frac{3 a^3 \sin ^5(c+d x)}{35 d}-\frac{2 a^3 \sin ^3(c+d x)}{7 d}+\frac{3 a^3 \sin (c+d x)}{7 d}-\frac{3 i a^3 \cos ^5(c+d x)}{35 d}-\frac{2 i a \cos ^7(c+d x) (a+i a \tan (c+d x))^2}{7 d}",1,"(((-3*I)/35)*a^3*Cos[c + d*x]^5)/d + (3*a^3*Sin[c + d*x])/(7*d) - (2*a^3*Sin[c + d*x]^3)/(7*d) + (3*a^3*Sin[c + d*x]^5)/(35*d) - (((2*I)/7)*a*Cos[c + d*x]^7*(a + I*a*Tan[c + d*x])^2)/d","A",4,3,24,0.1250,1,"{3496, 3486, 2633}"
51,1,124,0,0.083663,"\int \cos ^9(c+d x) (a+i a \tan (c+d x))^3 \, dx","Int[Cos[c + d*x]^9*(a + I*a*Tan[c + d*x])^3,x]","-\frac{5 a^3 \sin ^7(c+d x)}{63 d}+\frac{a^3 \sin ^5(c+d x)}{3 d}-\frac{5 a^3 \sin ^3(c+d x)}{9 d}+\frac{5 a^3 \sin (c+d x)}{9 d}-\frac{5 i a^3 \cos ^7(c+d x)}{63 d}-\frac{2 i a \cos ^9(c+d x) (a+i a \tan (c+d x))^2}{9 d}","-\frac{5 a^3 \sin ^7(c+d x)}{63 d}+\frac{a^3 \sin ^5(c+d x)}{3 d}-\frac{5 a^3 \sin ^3(c+d x)}{9 d}+\frac{5 a^3 \sin (c+d x)}{9 d}-\frac{5 i a^3 \cos ^7(c+d x)}{63 d}-\frac{2 i a \cos ^9(c+d x) (a+i a \tan (c+d x))^2}{9 d}",1,"(((-5*I)/63)*a^3*Cos[c + d*x]^7)/d + (5*a^3*Sin[c + d*x])/(9*d) - (5*a^3*Sin[c + d*x]^3)/(9*d) + (a^3*Sin[c + d*x]^5)/(3*d) - (5*a^3*Sin[c + d*x]^7)/(63*d) - (((2*I)/9)*a*Cos[c + d*x]^9*(a + I*a*Tan[c + d*x])^2)/d","A",4,3,24,0.1250,1,"{3496, 3486, 2633}"
52,1,163,0,0.161987,"\int \sec ^3(c+d x) (a+i a \tan (c+d x))^4 \, dx","Int[Sec[c + d*x]^3*(a + I*a*Tan[c + d*x])^4,x]","\frac{7 i a^4 \sec ^3(c+d x)}{8 d}+\frac{21 a^4 \tanh ^{-1}(\sin (c+d x))}{16 d}+\frac{3 i \sec ^3(c+d x) \left(a^2+i a^2 \tan (c+d x)\right)^2}{10 d}+\frac{21 i \sec ^3(c+d x) \left(a^4+i a^4 \tan (c+d x)\right)}{40 d}+\frac{21 a^4 \tan (c+d x) \sec (c+d x)}{16 d}+\frac{i a \sec ^3(c+d x) (a+i a \tan (c+d x))^3}{6 d}","\frac{7 i a^4 \sec ^3(c+d x)}{8 d}+\frac{21 a^4 \tanh ^{-1}(\sin (c+d x))}{16 d}+\frac{3 i \sec ^3(c+d x) \left(a^2+i a^2 \tan (c+d x)\right)^2}{10 d}+\frac{21 i \sec ^3(c+d x) \left(a^4+i a^4 \tan (c+d x)\right)}{40 d}+\frac{21 a^4 \tan (c+d x) \sec (c+d x)}{16 d}+\frac{i a \sec ^3(c+d x) (a+i a \tan (c+d x))^3}{6 d}",1,"(21*a^4*ArcTanh[Sin[c + d*x]])/(16*d) + (((7*I)/8)*a^4*Sec[c + d*x]^3)/d + (21*a^4*Sec[c + d*x]*Tan[c + d*x])/(16*d) + ((I/6)*a*Sec[c + d*x]^3*(a + I*a*Tan[c + d*x])^3)/d + (((3*I)/10)*Sec[c + d*x]^3*(a^2 + I*a^2*Tan[c + d*x])^2)/d + (((21*I)/40)*Sec[c + d*x]^3*(a^4 + I*a^4*Tan[c + d*x]))/d","A",6,4,24,0.1667,1,"{3498, 3486, 3768, 3770}"
53,1,133,0,0.0956145,"\int \sec (c+d x) (a+i a \tan (c+d x))^4 \, dx","Int[Sec[c + d*x]*(a + I*a*Tan[c + d*x])^4,x]","\frac{35 i a^4 \sec (c+d x)}{8 d}+\frac{35 a^4 \tanh ^{-1}(\sin (c+d x))}{8 d}+\frac{7 i \sec (c+d x) \left(a^2+i a^2 \tan (c+d x)\right)^2}{12 d}+\frac{35 i \sec (c+d x) \left(a^4+i a^4 \tan (c+d x)\right)}{24 d}+\frac{i a \sec (c+d x) (a+i a \tan (c+d x))^3}{4 d}","\frac{35 i a^4 \sec (c+d x)}{8 d}+\frac{35 a^4 \tanh ^{-1}(\sin (c+d x))}{8 d}+\frac{7 i \sec (c+d x) \left(a^2+i a^2 \tan (c+d x)\right)^2}{12 d}+\frac{35 i \sec (c+d x) \left(a^4+i a^4 \tan (c+d x)\right)}{24 d}+\frac{i a \sec (c+d x) (a+i a \tan (c+d x))^3}{4 d}",1,"(35*a^4*ArcTanh[Sin[c + d*x]])/(8*d) + (((35*I)/8)*a^4*Sec[c + d*x])/d + ((I/4)*a*Sec[c + d*x]*(a + I*a*Tan[c + d*x])^3)/d + (((7*I)/12)*Sec[c + d*x]*(a^2 + I*a^2*Tan[c + d*x])^2)/d + (((35*I)/24)*Sec[c + d*x]*(a^4 + I*a^4*Tan[c + d*x]))/d","A",5,3,22,0.1364,1,"{3498, 3486, 3770}"
54,1,97,0,0.0744401,"\int \cos (c+d x) (a+i a \tan (c+d x))^4 \, dx","Int[Cos[c + d*x]*(a + I*a*Tan[c + d*x])^4,x]","-\frac{15 i a^4 \sec (c+d x)}{2 d}-\frac{15 a^4 \tanh ^{-1}(\sin (c+d x))}{2 d}-\frac{5 i \sec (c+d x) \left(a^4+i a^4 \tan (c+d x)\right)}{2 d}-\frac{2 i a \cos (c+d x) (a+i a \tan (c+d x))^3}{d}","-\frac{15 i a^4 \sec (c+d x)}{2 d}-\frac{15 a^4 \tanh ^{-1}(\sin (c+d x))}{2 d}-\frac{5 i \sec (c+d x) \left(a^4+i a^4 \tan (c+d x)\right)}{2 d}-\frac{2 i a \cos (c+d x) (a+i a \tan (c+d x))^3}{d}",1,"(-15*a^4*ArcTanh[Sin[c + d*x]])/(2*d) - (((15*I)/2)*a^4*Sec[c + d*x])/d - ((2*I)*a*Cos[c + d*x]*(a + I*a*Tan[c + d*x])^3)/d - (((5*I)/2)*Sec[c + d*x]*(a^4 + I*a^4*Tan[c + d*x]))/d","A",4,4,22,0.1818,1,"{3496, 3498, 3486, 3770}"
55,1,78,0,0.075611,"\int \cos ^3(c+d x) (a+i a \tan (c+d x))^4 \, dx","Int[Cos[c + d*x]^3*(a + I*a*Tan[c + d*x])^4,x]","\frac{a^4 \tanh ^{-1}(\sin (c+d x))}{d}+\frac{2 i \cos (c+d x) \left(a^4+i a^4 \tan (c+d x)\right)}{d}-\frac{2 i a \cos ^3(c+d x) (a+i a \tan (c+d x))^3}{3 d}","\frac{a^4 \tanh ^{-1}(\sin (c+d x))}{d}+\frac{2 i \cos (c+d x) \left(a^4+i a^4 \tan (c+d x)\right)}{d}-\frac{2 i a \cos ^3(c+d x) (a+i a \tan (c+d x))^3}{3 d}",1,"(a^4*ArcTanh[Sin[c + d*x]])/d - (((2*I)/3)*a*Cos[c + d*x]^3*(a + I*a*Tan[c + d*x])^3)/d + ((2*I)*Cos[c + d*x]*(a^4 + I*a^4*Tan[c + d*x]))/d","A",3,2,24,0.08333,1,"{3496, 3770}"
56,1,66,0,0.0736642,"\int \cos ^5(c+d x) (a+i a \tan (c+d x))^4 \, dx","Int[Cos[c + d*x]^5*(a + I*a*Tan[c + d*x])^4,x]","-\frac{i \cos ^5(c+d x) (a+i a \tan (c+d x))^4}{5 d}-\frac{i a \cos ^3(c+d x) (a+i a \tan (c+d x))^3}{15 d}","-\frac{i \cos ^5(c+d x) (a+i a \tan (c+d x))^4}{5 d}-\frac{i a \cos ^3(c+d x) (a+i a \tan (c+d x))^3}{15 d}",1,"((-I/15)*a*Cos[c + d*x]^3*(a + I*a*Tan[c + d*x])^3)/d - ((I/5)*Cos[c + d*x]^5*(a + I*a*Tan[c + d*x])^4)/d","A",2,2,24,0.08333,1,"{3497, 3488}"
57,1,102,0,0.0889054,"\int \cos ^7(c+d x) (a+i a \tan (c+d x))^4 \, dx","Int[Cos[c + d*x]^7*(a + I*a*Tan[c + d*x])^4,x]","-\frac{a^4 \sin ^3(c+d x)}{35 d}+\frac{3 a^4 \sin (c+d x)}{35 d}-\frac{2 i \cos ^5(c+d x) \left(a^4+i a^4 \tan (c+d x)\right)}{35 d}-\frac{2 i a \cos ^7(c+d x) (a+i a \tan (c+d x))^3}{7 d}","-\frac{a^4 \sin ^3(c+d x)}{35 d}+\frac{3 a^4 \sin (c+d x)}{35 d}-\frac{2 i \cos ^5(c+d x) \left(a^4+i a^4 \tan (c+d x)\right)}{35 d}-\frac{2 i a \cos ^7(c+d x) (a+i a \tan (c+d x))^3}{7 d}",1,"(3*a^4*Sin[c + d*x])/(35*d) - (a^4*Sin[c + d*x]^3)/(35*d) - (((2*I)/7)*a*Cos[c + d*x]^7*(a + I*a*Tan[c + d*x])^3)/d - (((2*I)/35)*Cos[c + d*x]^5*(a^4 + I*a^4*Tan[c + d*x]))/d","A",4,2,24,0.08333,1,"{3496, 2633}"
58,1,120,0,0.1007766,"\int \cos ^9(c+d x) (a+i a \tan (c+d x))^4 \, dx","Int[Cos[c + d*x]^9*(a + I*a*Tan[c + d*x])^4,x]","\frac{a^4 \sin ^5(c+d x)}{21 d}-\frac{10 a^4 \sin ^3(c+d x)}{63 d}+\frac{5 a^4 \sin (c+d x)}{21 d}-\frac{2 i \cos ^7(c+d x) \left(a^4+i a^4 \tan (c+d x)\right)}{21 d}-\frac{2 i a \cos ^9(c+d x) (a+i a \tan (c+d x))^3}{9 d}","\frac{a^4 \sin ^5(c+d x)}{21 d}-\frac{10 a^4 \sin ^3(c+d x)}{63 d}+\frac{5 a^4 \sin (c+d x)}{21 d}-\frac{2 i \cos ^7(c+d x) \left(a^4+i a^4 \tan (c+d x)\right)}{21 d}-\frac{2 i a \cos ^9(c+d x) (a+i a \tan (c+d x))^3}{9 d}",1,"(5*a^4*Sin[c + d*x])/(21*d) - (10*a^4*Sin[c + d*x]^3)/(63*d) + (a^4*Sin[c + d*x]^5)/(21*d) - (((2*I)/9)*a*Cos[c + d*x]^9*(a + I*a*Tan[c + d*x])^3)/d - (((2*I)/21)*Cos[c + d*x]^7*(a^4 + I*a^4*Tan[c + d*x]))/d","A",4,2,24,0.08333,1,"{3496, 2633}"
59,1,109,0,0.073068,"\int \sec ^8(c+d x) (a+i a \tan (c+d x))^5 \, dx","Int[Sec[c + d*x]^8*(a + I*a*Tan[c + d*x])^5,x]","\frac{i (a+i a \tan (c+d x))^{12}}{12 a^7 d}-\frac{6 i (a+i a \tan (c+d x))^{11}}{11 a^6 d}+\frac{6 i (a+i a \tan (c+d x))^{10}}{5 a^5 d}-\frac{8 i (a+i a \tan (c+d x))^9}{9 a^4 d}","\frac{i (a+i a \tan (c+d x))^{12}}{12 a^7 d}-\frac{6 i (a+i a \tan (c+d x))^{11}}{11 a^6 d}+\frac{6 i (a+i a \tan (c+d x))^{10}}{5 a^5 d}-\frac{8 i (a+i a \tan (c+d x))^9}{9 a^4 d}",1,"(((-8*I)/9)*(a + I*a*Tan[c + d*x])^9)/(a^4*d) + (((6*I)/5)*(a + I*a*Tan[c + d*x])^10)/(a^5*d) - (((6*I)/11)*(a + I*a*Tan[c + d*x])^11)/(a^6*d) + ((I/12)*(a + I*a*Tan[c + d*x])^12)/(a^7*d)","A",3,2,24,0.08333,1,"{3487, 43}"
60,1,82,0,0.0566016,"\int \sec ^6(c+d x) (a+i a \tan (c+d x))^5 \, dx","Int[Sec[c + d*x]^6*(a + I*a*Tan[c + d*x])^5,x]","-\frac{i (a+i a \tan (c+d x))^{10}}{10 a^5 d}+\frac{4 i (a+i a \tan (c+d x))^9}{9 a^4 d}-\frac{i (a+i a \tan (c+d x))^8}{2 a^3 d}","-\frac{i (a+i a \tan (c+d x))^{10}}{10 a^5 d}+\frac{4 i (a+i a \tan (c+d x))^9}{9 a^4 d}-\frac{i (a+i a \tan (c+d x))^8}{2 a^3 d}",1,"((-I/2)*(a + I*a*Tan[c + d*x])^8)/(a^3*d) + (((4*I)/9)*(a + I*a*Tan[c + d*x])^9)/(a^4*d) - ((I/10)*(a + I*a*Tan[c + d*x])^10)/(a^5*d)","A",3,2,24,0.08333,1,"{3487, 43}"
61,1,55,0,0.0429323,"\int \sec ^4(c+d x) (a+i a \tan (c+d x))^5 \, dx","Int[Sec[c + d*x]^4*(a + I*a*Tan[c + d*x])^5,x]","\frac{i (a+i a \tan (c+d x))^8}{8 a^3 d}-\frac{2 i (a+i a \tan (c+d x))^7}{7 a^2 d}","\frac{i (a+i a \tan (c+d x))^8}{8 a^3 d}-\frac{2 i (a+i a \tan (c+d x))^7}{7 a^2 d}",1,"(((-2*I)/7)*(a + I*a*Tan[c + d*x])^7)/(a^2*d) + ((I/8)*(a + I*a*Tan[c + d*x])^8)/(a^3*d)","A",3,2,24,0.08333,1,"{3487, 43}"
62,1,27,0,0.0361545,"\int \sec ^2(c+d x) (a+i a \tan (c+d x))^5 \, dx","Int[Sec[c + d*x]^2*(a + I*a*Tan[c + d*x])^5,x]","-\frac{i (a+i a \tan (c+d x))^6}{6 a d}","-\frac{i (a+i a \tan (c+d x))^6}{6 a d}",1,"((-I/6)*(a + I*a*Tan[c + d*x])^6)/(a*d)","A",2,2,24,0.08333,1,"{3487, 32}"
63,1,117,0,0.0658658,"\int (a+i a \tan (c+d x))^5 \, dx","Int[(a + I*a*Tan[c + d*x])^5,x]","-\frac{8 a^5 \tan (c+d x)}{d}+\frac{2 i a^2 (a+i a \tan (c+d x))^3}{3 d}+\frac{2 i a \left(a^2+i a^2 \tan (c+d x)\right)^2}{d}-\frac{16 i a^5 \log (\cos (c+d x))}{d}+16 a^5 x+\frac{i a (a+i a \tan (c+d x))^4}{4 d}","-\frac{8 a^5 \tan (c+d x)}{d}+\frac{2 i a^2 (a+i a \tan (c+d x))^3}{3 d}+\frac{2 i a \left(a^2+i a^2 \tan (c+d x)\right)^2}{d}-\frac{16 i a^5 \log (\cos (c+d x))}{d}+16 a^5 x+\frac{i a (a+i a \tan (c+d x))^4}{4 d}",1,"16*a^5*x - ((16*I)*a^5*Log[Cos[c + d*x]])/d - (8*a^5*Tan[c + d*x])/d + (((2*I)/3)*a^2*(a + I*a*Tan[c + d*x])^3)/d + ((I/4)*a*(a + I*a*Tan[c + d*x])^4)/d + ((2*I)*a*(a^2 + I*a^2*Tan[c + d*x])^2)/d","A",5,3,15,0.2000,1,"{3478, 3477, 3475}"
64,1,83,0,0.0585825,"\int \cos ^2(c+d x) (a+i a \tan (c+d x))^5 \, dx","Int[Cos[c + d*x]^2*(a + I*a*Tan[c + d*x])^5,x]","\frac{i a^5 \tan ^2(c+d x)}{2 d}-\frac{8 i a^6}{d (a-i a \tan (c+d x))}+\frac{5 a^5 \tan (c+d x)}{d}+\frac{12 i a^5 \log (\cos (c+d x))}{d}-12 a^5 x","\frac{i a^5 \tan ^2(c+d x)}{2 d}-\frac{8 i a^6}{d (a-i a \tan (c+d x))}+\frac{5 a^5 \tan (c+d x)}{d}+\frac{12 i a^5 \log (\cos (c+d x))}{d}-12 a^5 x",1,"-12*a^5*x + ((12*I)*a^5*Log[Cos[c + d*x]])/d + (5*a^5*Tan[c + d*x])/d + ((I/2)*a^5*Tan[c + d*x]^2)/d - ((8*I)*a^6)/(d*(a - I*a*Tan[c + d*x]))","A",3,2,24,0.08333,1,"{3487, 43}"
65,1,73,0,0.0550322,"\int \cos ^4(c+d x) (a+i a \tan (c+d x))^5 \, dx","Int[Cos[c + d*x]^4*(a + I*a*Tan[c + d*x])^5,x]","-\frac{2 i a^7}{d (a-i a \tan (c+d x))^2}+\frac{4 i a^6}{d (a-i a \tan (c+d x))}-\frac{i a^5 \log (\cos (c+d x))}{d}+a^5 x","-\frac{2 i a^7}{d (a-i a \tan (c+d x))^2}+\frac{4 i a^6}{d (a-i a \tan (c+d x))}-\frac{i a^5 \log (\cos (c+d x))}{d}+a^5 x",1,"a^5*x - (I*a^5*Log[Cos[c + d*x]])/d - ((2*I)*a^7)/(d*(a - I*a*Tan[c + d*x])^2) + ((4*I)*a^6)/(d*(a - I*a*Tan[c + d*x]))","A",3,2,24,0.08333,1,"{3487, 43}"
66,1,55,0,0.0485425,"\int \cos ^6(c+d x) (a+i a \tan (c+d x))^5 \, dx","Int[Cos[c + d*x]^6*(a + I*a*Tan[c + d*x])^5,x]","\frac{i a^7}{2 d (a-i a \tan (c+d x))^2}-\frac{2 i a^8}{3 d (a-i a \tan (c+d x))^3}","\frac{i a^7}{2 d (a-i a \tan (c+d x))^2}-\frac{2 i a^8}{3 d (a-i a \tan (c+d x))^3}",1,"(((-2*I)/3)*a^8)/(d*(a - I*a*Tan[c + d*x])^3) + ((I/2)*a^7)/(d*(a - I*a*Tan[c + d*x])^2)","A",3,2,24,0.08333,1,"{3487, 43}"
67,1,27,0,0.0378692,"\int \cos ^8(c+d x) (a+i a \tan (c+d x))^5 \, dx","Int[Cos[c + d*x]^8*(a + I*a*Tan[c + d*x])^5,x]","-\frac{i a^9}{4 d (a-i a \tan (c+d x))^4}","-\frac{i a^9}{4 d (a-i a \tan (c+d x))^4}",1,"((-I/4)*a^9)/(d*(a - I*a*Tan[c + d*x])^4)","A",2,2,24,0.08333,1,"{3487, 32}"
68,1,144,0,0.0859356,"\int \cos ^{10}(c+d x) (a+i a \tan (c+d x))^5 \, dx","Int[Cos[c + d*x]^10*(a + I*a*Tan[c + d*x])^5,x]","-\frac{i a^{10}}{10 d (a-i a \tan (c+d x))^5}-\frac{i a^9}{16 d (a-i a \tan (c+d x))^4}-\frac{i a^8}{24 d (a-i a \tan (c+d x))^3}-\frac{i a^7}{32 d (a-i a \tan (c+d x))^2}-\frac{i a^6}{32 d (a-i a \tan (c+d x))}+\frac{a^5 x}{32}","-\frac{i a^{10}}{10 d (a-i a \tan (c+d x))^5}-\frac{i a^9}{16 d (a-i a \tan (c+d x))^4}-\frac{i a^8}{24 d (a-i a \tan (c+d x))^3}-\frac{i a^7}{32 d (a-i a \tan (c+d x))^2}-\frac{i a^6}{32 d (a-i a \tan (c+d x))}+\frac{a^5 x}{32}",1,"(a^5*x)/32 - ((I/10)*a^10)/(d*(a - I*a*Tan[c + d*x])^5) - ((I/16)*a^9)/(d*(a - I*a*Tan[c + d*x])^4) - ((I/24)*a^8)/(d*(a - I*a*Tan[c + d*x])^3) - ((I/32)*a^7)/(d*(a - I*a*Tan[c + d*x])^2) - ((I/32)*a^6)/(d*(a - I*a*Tan[c + d*x]))","A",4,3,24,0.1250,1,"{3487, 44, 206}"
69,1,198,0,0.11411,"\int \cos ^{12}(c+d x) (a+i a \tan (c+d x))^5 \, dx","Int[Cos[c + d*x]^12*(a + I*a*Tan[c + d*x])^5,x]","-\frac{i a^{11}}{24 d (a-i a \tan (c+d x))^6}-\frac{i a^{10}}{20 d (a-i a \tan (c+d x))^5}-\frac{3 i a^9}{64 d (a-i a \tan (c+d x))^4}-\frac{i a^8}{24 d (a-i a \tan (c+d x))^3}-\frac{5 i a^7}{128 d (a-i a \tan (c+d x))^2}-\frac{3 i a^6}{64 d (a-i a \tan (c+d x))}+\frac{i a^6}{128 d (a+i a \tan (c+d x))}+\frac{7 a^5 x}{128}","-\frac{i a^{11}}{24 d (a-i a \tan (c+d x))^6}-\frac{i a^{10}}{20 d (a-i a \tan (c+d x))^5}-\frac{3 i a^9}{64 d (a-i a \tan (c+d x))^4}-\frac{i a^8}{24 d (a-i a \tan (c+d x))^3}-\frac{5 i a^7}{128 d (a-i a \tan (c+d x))^2}-\frac{3 i a^6}{64 d (a-i a \tan (c+d x))}+\frac{i a^6}{128 d (a+i a \tan (c+d x))}+\frac{7 a^5 x}{128}",1,"(7*a^5*x)/128 - ((I/24)*a^11)/(d*(a - I*a*Tan[c + d*x])^6) - ((I/20)*a^10)/(d*(a - I*a*Tan[c + d*x])^5) - (((3*I)/64)*a^9)/(d*(a - I*a*Tan[c + d*x])^4) - ((I/24)*a^8)/(d*(a - I*a*Tan[c + d*x])^3) - (((5*I)/128)*a^7)/(d*(a - I*a*Tan[c + d*x])^2) - (((3*I)/64)*a^6)/(d*(a - I*a*Tan[c + d*x])) + ((I/128)*a^6)/(d*(a + I*a*Tan[c + d*x]))","A",4,3,24,0.1250,1,"{3487, 44, 206}"
70,1,167,0,0.1263434,"\int \sec (c+d x) (a+i a \tan (c+d x))^5 \, dx","Int[Sec[c + d*x]*(a + I*a*Tan[c + d*x])^5,x]","\frac{63 i a^5 \sec (c+d x)}{8 d}+\frac{63 a^5 \tanh ^{-1}(\sin (c+d x))}{8 d}+\frac{9 i a^2 \sec (c+d x) (a+i a \tan (c+d x))^3}{20 d}+\frac{21 i a \sec (c+d x) \left(a^2+i a^2 \tan (c+d x)\right)^2}{20 d}+\frac{21 i \sec (c+d x) \left(a^5+i a^5 \tan (c+d x)\right)}{8 d}+\frac{i a \sec (c+d x) (a+i a \tan (c+d x))^4}{5 d}","\frac{63 i a^5 \sec (c+d x)}{8 d}+\frac{63 a^5 \tanh ^{-1}(\sin (c+d x))}{8 d}+\frac{9 i a^2 \sec (c+d x) (a+i a \tan (c+d x))^3}{20 d}+\frac{21 i a \sec (c+d x) \left(a^2+i a^2 \tan (c+d x)\right)^2}{20 d}+\frac{21 i \sec (c+d x) \left(a^5+i a^5 \tan (c+d x)\right)}{8 d}+\frac{i a \sec (c+d x) (a+i a \tan (c+d x))^4}{5 d}",1,"(63*a^5*ArcTanh[Sin[c + d*x]])/(8*d) + (((63*I)/8)*a^5*Sec[c + d*x])/d + (((9*I)/20)*a^2*Sec[c + d*x]*(a + I*a*Tan[c + d*x])^3)/d + ((I/5)*a*Sec[c + d*x]*(a + I*a*Tan[c + d*x])^4)/d + (((21*I)/20)*a*Sec[c + d*x]*(a^2 + I*a^2*Tan[c + d*x])^2)/d + (((21*I)/8)*Sec[c + d*x]*(a^5 + I*a^5*Tan[c + d*x]))/d","A",6,3,22,0.1364,1,"{3498, 3486, 3770}"
71,1,130,0,0.1042302,"\int \cos (c+d x) (a+i a \tan (c+d x))^5 \, dx","Int[Cos[c + d*x]*(a + I*a*Tan[c + d*x])^5,x]","-\frac{35 i a^5 \sec (c+d x)}{2 d}-\frac{35 a^5 \tanh ^{-1}(\sin (c+d x))}{2 d}-\frac{7 i a^3 \sec (c+d x) (a+i a \tan (c+d x))^2}{3 d}-\frac{35 i \sec (c+d x) \left(a^5+i a^5 \tan (c+d x)\right)}{6 d}-\frac{2 i a \cos (c+d x) (a+i a \tan (c+d x))^4}{d}","-\frac{35 i a^5 \sec (c+d x)}{2 d}-\frac{35 a^5 \tanh ^{-1}(\sin (c+d x))}{2 d}-\frac{7 i a^3 \sec (c+d x) (a+i a \tan (c+d x))^2}{3 d}-\frac{35 i \sec (c+d x) \left(a^5+i a^5 \tan (c+d x)\right)}{6 d}-\frac{2 i a \cos (c+d x) (a+i a \tan (c+d x))^4}{d}",1,"(-35*a^5*ArcTanh[Sin[c + d*x]])/(2*d) - (((35*I)/2)*a^5*Sec[c + d*x])/d - (((7*I)/3)*a^3*Sec[c + d*x]*(a + I*a*Tan[c + d*x])^2)/d - ((2*I)*a*Cos[c + d*x]*(a + I*a*Tan[c + d*x])^4)/d - (((35*I)/6)*Sec[c + d*x]*(a^5 + I*a^5*Tan[c + d*x]))/d","A",5,4,22,0.1818,1,"{3496, 3498, 3486, 3770}"
72,1,98,0,0.0892792,"\int \cos ^3(c+d x) (a+i a \tan (c+d x))^5 \, dx","Int[Cos[c + d*x]^3*(a + I*a*Tan[c + d*x])^5,x]","\frac{5 i a^5 \sec (c+d x)}{d}+\frac{5 a^5 \tanh ^{-1}(\sin (c+d x))}{d}+\frac{10 i a^3 \cos (c+d x) (a+i a \tan (c+d x))^2}{3 d}-\frac{2 i a \cos ^3(c+d x) (a+i a \tan (c+d x))^4}{3 d}","\frac{5 i a^5 \sec (c+d x)}{d}+\frac{5 a^5 \tanh ^{-1}(\sin (c+d x))}{d}+\frac{10 i a^3 \cos (c+d x) (a+i a \tan (c+d x))^2}{3 d}-\frac{2 i a \cos ^3(c+d x) (a+i a \tan (c+d x))^4}{3 d}",1,"(5*a^5*ArcTanh[Sin[c + d*x]])/d + ((5*I)*a^5*Sec[c + d*x])/d + (((10*I)/3)*a^3*Cos[c + d*x]*(a + I*a*Tan[c + d*x])^2)/d - (((2*I)/3)*a*Cos[c + d*x]^3*(a + I*a*Tan[c + d*x])^4)/d","A",4,3,24,0.1250,1,"{3496, 3486, 3770}"
73,1,32,0,0.0356342,"\int \cos ^5(c+d x) (a+i a \tan (c+d x))^5 \, dx","Int[Cos[c + d*x]^5*(a + I*a*Tan[c + d*x])^5,x]","-\frac{i \cos ^5(c+d x) (a+i a \tan (c+d x))^5}{5 d}","-\frac{i \cos ^5(c+d x) (a+i a \tan (c+d x))^5}{5 d}",1,"((-I/5)*Cos[c + d*x]^5*(a + I*a*Tan[c + d*x])^5)/d","A",1,1,24,0.04167,1,"{3488}"
74,1,101,0,0.1136553,"\int \cos ^7(c+d x) (a+i a \tan (c+d x))^5 \, dx","Int[Cos[c + d*x]^7*(a + I*a*Tan[c + d*x])^5,x]","-\frac{2 i a^2 \cos ^3(c+d x) (a+i a \tan (c+d x))^3}{105 d}-\frac{i \cos ^7(c+d x) (a+i a \tan (c+d x))^5}{7 d}-\frac{2 i a \cos ^5(c+d x) (a+i a \tan (c+d x))^4}{35 d}","-\frac{2 i a^2 \cos ^3(c+d x) (a+i a \tan (c+d x))^3}{105 d}-\frac{i \cos ^7(c+d x) (a+i a \tan (c+d x))^5}{7 d}-\frac{2 i a \cos ^5(c+d x) (a+i a \tan (c+d x))^4}{35 d}",1,"(((-2*I)/105)*a^2*Cos[c + d*x]^3*(a + I*a*Tan[c + d*x])^3)/d - (((2*I)/35)*a*Cos[c + d*x]^5*(a + I*a*Tan[c + d*x])^4)/d - ((I/7)*Cos[c + d*x]^7*(a + I*a*Tan[c + d*x])^5)/d","A",3,2,24,0.08333,1,"{3497, 3488}"
75,1,141,0,0.1215765,"\int \cos ^9(c+d x) (a+i a \tan (c+d x))^5 \, dx","Int[Cos[c + d*x]^9*(a + I*a*Tan[c + d*x])^5,x]","\frac{a^5 \sin ^5(c+d x)}{105 d}-\frac{2 a^5 \sin ^3(c+d x)}{63 d}+\frac{a^5 \sin (c+d x)}{21 d}-\frac{i a^5 \cos ^5(c+d x)}{105 d}-\frac{2 i a^3 \cos ^7(c+d x) (a+i a \tan (c+d x))^2}{63 d}-\frac{2 i a \cos ^9(c+d x) (a+i a \tan (c+d x))^4}{9 d}","\frac{a^5 \sin ^5(c+d x)}{105 d}-\frac{2 a^5 \sin ^3(c+d x)}{63 d}+\frac{a^5 \sin (c+d x)}{21 d}-\frac{i a^5 \cos ^5(c+d x)}{105 d}-\frac{2 i a^3 \cos ^7(c+d x) (a+i a \tan (c+d x))^2}{63 d}-\frac{2 i a \cos ^9(c+d x) (a+i a \tan (c+d x))^4}{9 d}",1,"((-I/105)*a^5*Cos[c + d*x]^5)/d + (a^5*Sin[c + d*x])/(21*d) - (2*a^5*Sin[c + d*x]^3)/(63*d) + (a^5*Sin[c + d*x]^5)/(105*d) - (((2*I)/63)*a^3*Cos[c + d*x]^7*(a + I*a*Tan[c + d*x])^2)/d - (((2*I)/9)*a*Cos[c + d*x]^9*(a + I*a*Tan[c + d*x])^4)/d","A",5,3,24,0.1250,1,"{3496, 3486, 2633}"
76,1,159,0,0.1259851,"\int \cos ^{11}(c+d x) (a+i a \tan (c+d x))^5 \, dx","Int[Cos[c + d*x]^11*(a + I*a*Tan[c + d*x])^5,x]","-\frac{5 a^5 \sin ^7(c+d x)}{231 d}+\frac{a^5 \sin ^5(c+d x)}{11 d}-\frac{5 a^5 \sin ^3(c+d x)}{33 d}+\frac{5 a^5 \sin (c+d x)}{33 d}-\frac{5 i a^5 \cos ^7(c+d x)}{231 d}-\frac{2 i a^3 \cos ^9(c+d x) (a+i a \tan (c+d x))^2}{33 d}-\frac{2 i a \cos ^{11}(c+d x) (a+i a \tan (c+d x))^4}{11 d}","-\frac{5 a^5 \sin ^7(c+d x)}{231 d}+\frac{a^5 \sin ^5(c+d x)}{11 d}-\frac{5 a^5 \sin ^3(c+d x)}{33 d}+\frac{5 a^5 \sin (c+d x)}{33 d}-\frac{5 i a^5 \cos ^7(c+d x)}{231 d}-\frac{2 i a^3 \cos ^9(c+d x) (a+i a \tan (c+d x))^2}{33 d}-\frac{2 i a \cos ^{11}(c+d x) (a+i a \tan (c+d x))^4}{11 d}",1,"(((-5*I)/231)*a^5*Cos[c + d*x]^7)/d + (5*a^5*Sin[c + d*x])/(33*d) - (5*a^5*Sin[c + d*x]^3)/(33*d) + (a^5*Sin[c + d*x]^5)/(11*d) - (5*a^5*Sin[c + d*x]^7)/(231*d) - (((2*I)/33)*a^3*Cos[c + d*x]^9*(a + I*a*Tan[c + d*x])^2)/d - (((2*I)/11)*a*Cos[c + d*x]^11*(a + I*a*Tan[c + d*x])^4)/d","A",5,3,24,0.1250,1,"{3496, 3486, 2633}"
77,1,109,0,0.0808121,"\int \sec ^8(c+d x) (a+i a \tan (c+d x))^8 \, dx","Int[Sec[c + d*x]^8*(a + I*a*Tan[c + d*x])^8,x]","\frac{i (a+i a \tan (c+d x))^{15}}{15 a^7 d}-\frac{3 i (a+i a \tan (c+d x))^{14}}{7 a^6 d}+\frac{12 i (a+i a \tan (c+d x))^{13}}{13 a^5 d}-\frac{2 i (a+i a \tan (c+d x))^{12}}{3 a^4 d}","\frac{i (a+i a \tan (c+d x))^{15}}{15 a^7 d}-\frac{3 i (a+i a \tan (c+d x))^{14}}{7 a^6 d}+\frac{12 i (a+i a \tan (c+d x))^{13}}{13 a^5 d}-\frac{2 i (a+i a \tan (c+d x))^{12}}{3 a^4 d}",1,"(((-2*I)/3)*(a + I*a*Tan[c + d*x])^12)/(a^4*d) + (((12*I)/13)*(a + I*a*Tan[c + d*x])^13)/(a^5*d) - (((3*I)/7)*(a + I*a*Tan[c + d*x])^14)/(a^6*d) + ((I/15)*(a + I*a*Tan[c + d*x])^15)/(a^7*d)","A",3,2,24,0.08333,1,"{3487, 43}"
78,1,82,0,0.0705574,"\int \sec ^6(c+d x) (a+i a \tan (c+d x))^8 \, dx","Int[Sec[c + d*x]^6*(a + I*a*Tan[c + d*x])^8,x]","-\frac{i (a+i a \tan (c+d x))^{13}}{13 a^5 d}+\frac{i (a+i a \tan (c+d x))^{12}}{3 a^4 d}-\frac{4 i (a+i a \tan (c+d x))^{11}}{11 a^3 d}","-\frac{i (a+i a \tan (c+d x))^{13}}{13 a^5 d}+\frac{i (a+i a \tan (c+d x))^{12}}{3 a^4 d}-\frac{4 i (a+i a \tan (c+d x))^{11}}{11 a^3 d}",1,"(((-4*I)/11)*(a + I*a*Tan[c + d*x])^11)/(a^3*d) + ((I/3)*(a + I*a*Tan[c + d*x])^12)/(a^4*d) - ((I/13)*(a + I*a*Tan[c + d*x])^13)/(a^5*d)","A",3,2,24,0.08333,1,"{3487, 43}"
79,1,55,0,0.0454868,"\int \sec ^4(c+d x) (a+i a \tan (c+d x))^8 \, dx","Int[Sec[c + d*x]^4*(a + I*a*Tan[c + d*x])^8,x]","\frac{i (a+i a \tan (c+d x))^{11}}{11 a^3 d}-\frac{i (a+i a \tan (c+d x))^{10}}{5 a^2 d}","\frac{i (a+i a \tan (c+d x))^{11}}{11 a^3 d}-\frac{i (a+i a \tan (c+d x))^{10}}{5 a^2 d}",1,"((-I/5)*(a + I*a*Tan[c + d*x])^10)/(a^2*d) + ((I/11)*(a + I*a*Tan[c + d*x])^11)/(a^3*d)","A",3,2,24,0.08333,1,"{3487, 43}"
80,1,27,0,0.0377482,"\int \sec ^2(c+d x) (a+i a \tan (c+d x))^8 \, dx","Int[Sec[c + d*x]^2*(a + I*a*Tan[c + d*x])^8,x]","-\frac{i (a+i a \tan (c+d x))^9}{9 a d}","-\frac{i (a+i a \tan (c+d x))^9}{9 a d}",1,"((-I/9)*(a + I*a*Tan[c + d*x])^9)/(a*d)","A",2,2,24,0.08333,1,"{3487, 32}"
81,1,200,0,0.1388168,"\int (a+i a \tan (c+d x))^8 \, dx","Int[(a + I*a*Tan[c + d*x])^8,x]","-\frac{64 a^8 \tan (c+d x)}{d}+\frac{4 i a^3 (a+i a \tan (c+d x))^5}{5 d}+\frac{i a^2 (a+i a \tan (c+d x))^6}{3 d}+\frac{16 i a^2 \left(a^2+i a^2 \tan (c+d x)\right)^3}{3 d}+\frac{2 i \left(a^2+i a^2 \tan (c+d x)\right)^4}{d}+\frac{16 i \left(a^4+i a^4 \tan (c+d x)\right)^2}{d}-\frac{128 i a^8 \log (\cos (c+d x))}{d}+128 a^8 x+\frac{i a (a+i a \tan (c+d x))^7}{7 d}","-\frac{64 a^8 \tan (c+d x)}{d}+\frac{4 i a^3 (a+i a \tan (c+d x))^5}{5 d}+\frac{i a^2 (a+i a \tan (c+d x))^6}{3 d}+\frac{16 i a^2 \left(a^2+i a^2 \tan (c+d x)\right)^3}{3 d}+\frac{2 i \left(a^2+i a^2 \tan (c+d x)\right)^4}{d}+\frac{16 i \left(a^4+i a^4 \tan (c+d x)\right)^2}{d}-\frac{128 i a^8 \log (\cos (c+d x))}{d}+128 a^8 x+\frac{i a (a+i a \tan (c+d x))^7}{7 d}",1,"128*a^8*x - ((128*I)*a^8*Log[Cos[c + d*x]])/d - (64*a^8*Tan[c + d*x])/d + (((4*I)/5)*a^3*(a + I*a*Tan[c + d*x])^5)/d + ((I/3)*a^2*(a + I*a*Tan[c + d*x])^6)/d + ((I/7)*a*(a + I*a*Tan[c + d*x])^7)/d + (((16*I)/3)*a^2*(a^2 + I*a^2*Tan[c + d*x])^3)/d + ((2*I)*(a^2 + I*a^2*Tan[c + d*x])^4)/d + ((16*I)*(a^4 + I*a^4*Tan[c + d*x])^2)/d","A",8,3,15,0.2000,1,"{3478, 3477, 3475}"
82,1,133,0,0.0816082,"\int \cos ^2(c+d x) (a+i a \tan (c+d x))^8 \, dx","Int[Cos[c + d*x]^2*(a + I*a*Tan[c + d*x])^8,x]","\frac{a^8 \tan ^5(c+d x)}{5 d}-\frac{2 i a^8 \tan ^4(c+d x)}{d}-\frac{10 a^8 \tan ^3(c+d x)}{d}+\frac{36 i a^8 \tan ^2(c+d x)}{d}-\frac{64 i a^9}{d (a-i a \tan (c+d x))}+\frac{129 a^8 \tan (c+d x)}{d}+\frac{192 i a^8 \log (\cos (c+d x))}{d}-192 a^8 x","\frac{a^8 \tan ^5(c+d x)}{5 d}-\frac{2 i a^8 \tan ^4(c+d x)}{d}-\frac{10 a^8 \tan ^3(c+d x)}{d}+\frac{36 i a^8 \tan ^2(c+d x)}{d}-\frac{64 i a^9}{d (a-i a \tan (c+d x))}+\frac{129 a^8 \tan (c+d x)}{d}+\frac{192 i a^8 \log (\cos (c+d x))}{d}-192 a^8 x",1,"-192*a^8*x + ((192*I)*a^8*Log[Cos[c + d*x]])/d + (129*a^8*Tan[c + d*x])/d + ((36*I)*a^8*Tan[c + d*x]^2)/d - (10*a^8*Tan[c + d*x]^3)/d - ((2*I)*a^8*Tan[c + d*x]^4)/d + (a^8*Tan[c + d*x]^5)/(5*d) - ((64*I)*a^9)/(d*(a - I*a*Tan[c + d*x]))","A",3,2,24,0.08333,1,"{3487, 43}"
83,1,124,0,0.077228,"\int \cos ^4(c+d x) (a+i a \tan (c+d x))^8 \, dx","Int[Cos[c + d*x]^4*(a + I*a*Tan[c + d*x])^8,x]","\frac{a^8 \tan ^3(c+d x)}{3 d}-\frac{4 i a^8 \tan ^2(c+d x)}{d}-\frac{16 i a^{10}}{d (a-i a \tan (c+d x))^2}+\frac{80 i a^9}{d (a-i a \tan (c+d x))}-\frac{31 a^8 \tan (c+d x)}{d}-\frac{80 i a^8 \log (\cos (c+d x))}{d}+80 a^8 x","\frac{a^8 \tan ^3(c+d x)}{3 d}-\frac{4 i a^8 \tan ^2(c+d x)}{d}-\frac{16 i a^{10}}{d (a-i a \tan (c+d x))^2}+\frac{80 i a^9}{d (a-i a \tan (c+d x))}-\frac{31 a^8 \tan (c+d x)}{d}-\frac{80 i a^8 \log (\cos (c+d x))}{d}+80 a^8 x",1,"80*a^8*x - ((80*I)*a^8*Log[Cos[c + d*x]])/d - (31*a^8*Tan[c + d*x])/d - ((4*I)*a^8*Tan[c + d*x]^2)/d + (a^8*Tan[c + d*x]^3)/(3*d) - ((16*I)*a^10)/(d*(a - I*a*Tan[c + d*x])^2) + ((80*I)*a^9)/(d*(a - I*a*Tan[c + d*x]))","A",3,2,24,0.08333,1,"{3487, 43}"
84,1,114,0,0.0709375,"\int \cos ^6(c+d x) (a+i a \tan (c+d x))^8 \, dx","Int[Cos[c + d*x]^6*(a + I*a*Tan[c + d*x])^8,x]","-\frac{16 i a^{11}}{3 d (a-i a \tan (c+d x))^3}+\frac{16 i a^{10}}{d (a-i a \tan (c+d x))^2}-\frac{24 i a^9}{d (a-i a \tan (c+d x))}+\frac{a^8 \tan (c+d x)}{d}+\frac{8 i a^8 \log (\cos (c+d x))}{d}-8 a^8 x","-\frac{16 i a^{11}}{3 d (a-i a \tan (c+d x))^3}+\frac{16 i a^{10}}{d (a-i a \tan (c+d x))^2}-\frac{24 i a^9}{d (a-i a \tan (c+d x))}+\frac{a^8 \tan (c+d x)}{d}+\frac{8 i a^8 \log (\cos (c+d x))}{d}-8 a^8 x",1,"-8*a^8*x + ((8*I)*a^8*Log[Cos[c + d*x]])/d + (a^8*Tan[c + d*x])/d - (((16*I)/3)*a^11)/(d*(a - I*a*Tan[c + d*x])^3) + ((16*I)*a^10)/(d*(a - I*a*Tan[c + d*x])^2) - ((24*I)*a^9)/(d*(a - I*a*Tan[c + d*x]))","A",3,2,24,0.08333,1,"{3487, 43}"
85,1,43,0,0.0422143,"\int \cos ^8(c+d x) (a+i a \tan (c+d x))^8 \, dx","Int[Cos[c + d*x]^8*(a + I*a*Tan[c + d*x])^8,x]","-\frac{i \left(a^3+i a^3 \tan (c+d x)\right)^4}{8 d (a-i a \tan (c+d x))^4}","-\frac{i \left(a^3+i a^3 \tan (c+d x)\right)^4}{8 d (a-i a \tan (c+d x))^4}",1,"((-I/8)*(a^3 + I*a^3*Tan[c + d*x])^4)/(d*(a - I*a*Tan[c + d*x])^4)","A",2,2,24,0.08333,1,"{3487, 37}"
86,1,80,0,0.0562357,"\int \cos ^{10}(c+d x) (a+i a \tan (c+d x))^8 \, dx","Int[Cos[c + d*x]^10*(a + I*a*Tan[c + d*x])^8,x]","-\frac{4 i a^{13}}{5 d (a-i a \tan (c+d x))^5}+\frac{i a^{12}}{d (a-i a \tan (c+d x))^4}-\frac{i a^{11}}{3 d (a-i a \tan (c+d x))^3}","-\frac{4 i a^{13}}{5 d (a-i a \tan (c+d x))^5}+\frac{i a^{12}}{d (a-i a \tan (c+d x))^4}-\frac{i a^{11}}{3 d (a-i a \tan (c+d x))^3}",1,"(((-4*I)/5)*a^13)/(d*(a - I*a*Tan[c + d*x])^5) + (I*a^12)/(d*(a - I*a*Tan[c + d*x])^4) - ((I/3)*a^11)/(d*(a - I*a*Tan[c + d*x])^3)","A",3,2,24,0.08333,1,"{3487, 43}"
87,1,55,0,0.0476216,"\int \cos ^{12}(c+d x) (a+i a \tan (c+d x))^8 \, dx","Int[Cos[c + d*x]^12*(a + I*a*Tan[c + d*x])^8,x]","\frac{i a^{13}}{5 d (a-i a \tan (c+d x))^5}-\frac{i a^{14}}{3 d (a-i a \tan (c+d x))^6}","\frac{i a^{13}}{5 d (a-i a \tan (c+d x))^5}-\frac{i a^{14}}{3 d (a-i a \tan (c+d x))^6}",1,"((-I/3)*a^14)/(d*(a - I*a*Tan[c + d*x])^6) + ((I/5)*a^13)/(d*(a - I*a*Tan[c + d*x])^5)","A",3,2,24,0.08333,1,"{3487, 43}"
88,1,27,0,0.0378439,"\int \cos ^{14}(c+d x) (a+i a \tan (c+d x))^8 \, dx","Int[Cos[c + d*x]^14*(a + I*a*Tan[c + d*x])^8,x]","-\frac{i a^{15}}{7 d (a-i a \tan (c+d x))^7}","-\frac{i a^{15}}{7 d (a-i a \tan (c+d x))^7}",1,"((-I/7)*a^15)/(d*(a - I*a*Tan[c + d*x])^7)","A",2,2,24,0.08333,1,"{3487, 32}"
89,1,225,0,0.1150786,"\int \cos ^{16}(c+d x) (a+i a \tan (c+d x))^8 \, dx","Int[Cos[c + d*x]^16*(a + I*a*Tan[c + d*x])^8,x]","-\frac{i a^{16}}{16 d (a-i a \tan (c+d x))^8}-\frac{i a^{15}}{28 d (a-i a \tan (c+d x))^7}-\frac{i a^{14}}{48 d (a-i a \tan (c+d x))^6}-\frac{i a^{13}}{80 d (a-i a \tan (c+d x))^5}-\frac{i a^{12}}{128 d (a-i a \tan (c+d x))^4}-\frac{i a^{11}}{192 d (a-i a \tan (c+d x))^3}-\frac{i a^{10}}{256 d (a-i a \tan (c+d x))^2}-\frac{i a^9}{256 d (a-i a \tan (c+d x))}+\frac{a^8 x}{256}","-\frac{i a^{16}}{16 d (a-i a \tan (c+d x))^8}-\frac{i a^{15}}{28 d (a-i a \tan (c+d x))^7}-\frac{i a^{14}}{48 d (a-i a \tan (c+d x))^6}-\frac{i a^{13}}{80 d (a-i a \tan (c+d x))^5}-\frac{i a^{12}}{128 d (a-i a \tan (c+d x))^4}-\frac{i a^{11}}{192 d (a-i a \tan (c+d x))^3}-\frac{i a^{10}}{256 d (a-i a \tan (c+d x))^2}-\frac{i a^9}{256 d (a-i a \tan (c+d x))}+\frac{a^8 x}{256}",1,"(a^8*x)/256 - ((I/16)*a^16)/(d*(a - I*a*Tan[c + d*x])^8) - ((I/28)*a^15)/(d*(a - I*a*Tan[c + d*x])^7) - ((I/48)*a^14)/(d*(a - I*a*Tan[c + d*x])^6) - ((I/80)*a^13)/(d*(a - I*a*Tan[c + d*x])^5) - ((I/128)*a^12)/(d*(a - I*a*Tan[c + d*x])^4) - ((I/192)*a^11)/(d*(a - I*a*Tan[c + d*x])^3) - ((I/256)*a^10)/(d*(a - I*a*Tan[c + d*x])^2) - ((I/256)*a^9)/(d*(a - I*a*Tan[c + d*x]))","A",4,3,24,0.1250,1,"{3487, 44, 206}"
90,1,279,0,0.1559922,"\int \cos ^{18}(c+d x) (a+i a \tan (c+d x))^8 \, dx","Int[Cos[c + d*x]^18*(a + I*a*Tan[c + d*x])^8,x]","-\frac{i a^{17}}{36 d (a-i a \tan (c+d x))^9}-\frac{i a^{16}}{32 d (a-i a \tan (c+d x))^8}-\frac{3 i a^{15}}{112 d (a-i a \tan (c+d x))^7}-\frac{i a^{14}}{48 d (a-i a \tan (c+d x))^6}-\frac{i a^{13}}{64 d (a-i a \tan (c+d x))^5}-\frac{3 i a^{12}}{256 d (a-i a \tan (c+d x))^4}-\frac{7 i a^{11}}{768 d (a-i a \tan (c+d x))^3}-\frac{i a^{10}}{128 d (a-i a \tan (c+d x))^2}-\frac{9 i a^9}{1024 d (a-i a \tan (c+d x))}+\frac{i a^9}{1024 d (a+i a \tan (c+d x))}+\frac{5 a^8 x}{512}","-\frac{i a^{17}}{36 d (a-i a \tan (c+d x))^9}-\frac{i a^{16}}{32 d (a-i a \tan (c+d x))^8}-\frac{3 i a^{15}}{112 d (a-i a \tan (c+d x))^7}-\frac{i a^{14}}{48 d (a-i a \tan (c+d x))^6}-\frac{i a^{13}}{64 d (a-i a \tan (c+d x))^5}-\frac{3 i a^{12}}{256 d (a-i a \tan (c+d x))^4}-\frac{7 i a^{11}}{768 d (a-i a \tan (c+d x))^3}-\frac{i a^{10}}{128 d (a-i a \tan (c+d x))^2}-\frac{9 i a^9}{1024 d (a-i a \tan (c+d x))}+\frac{i a^9}{1024 d (a+i a \tan (c+d x))}+\frac{5 a^8 x}{512}",1,"(5*a^8*x)/512 - ((I/36)*a^17)/(d*(a - I*a*Tan[c + d*x])^9) - ((I/32)*a^16)/(d*(a - I*a*Tan[c + d*x])^8) - (((3*I)/112)*a^15)/(d*(a - I*a*Tan[c + d*x])^7) - ((I/48)*a^14)/(d*(a - I*a*Tan[c + d*x])^6) - ((I/64)*a^13)/(d*(a - I*a*Tan[c + d*x])^5) - (((3*I)/256)*a^12)/(d*(a - I*a*Tan[c + d*x])^4) - (((7*I)/768)*a^11)/(d*(a - I*a*Tan[c + d*x])^3) - ((I/128)*a^10)/(d*(a - I*a*Tan[c + d*x])^2) - (((9*I)/1024)*a^9)/(d*(a - I*a*Tan[c + d*x])) + ((I/1024)*a^9)/(d*(a + I*a*Tan[c + d*x]))","A",4,3,24,0.1250,1,"{3487, 44, 206}"
91,1,235,0,0.2037103,"\int \cos (c+d x) (a+i a \tan (c+d x))^8 \, dx","Int[Cos[c + d*x]*(a + I*a*Tan[c + d*x])^8,x]","-\frac{3003 i a^8 \sec (c+d x)}{16 d}-\frac{3003 a^8 \tanh ^{-1}(\sin (c+d x))}{16 d}-\frac{13 i a^3 \sec (c+d x) (a+i a \tan (c+d x))^5}{6 d}-\frac{429 i a^2 \sec (c+d x) \left(a^2+i a^2 \tan (c+d x)\right)^3}{40 d}-\frac{143 i \sec (c+d x) \left(a^2+i a^2 \tan (c+d x)\right)^4}{30 d}-\frac{1001 i \sec (c+d x) \left(a^4+i a^4 \tan (c+d x)\right)^2}{40 d}-\frac{1001 i \sec (c+d x) \left(a^8+i a^8 \tan (c+d x)\right)}{16 d}-\frac{2 i a \cos (c+d x) (a+i a \tan (c+d x))^7}{d}","-\frac{3003 i a^8 \sec (c+d x)}{16 d}-\frac{3003 a^8 \tanh ^{-1}(\sin (c+d x))}{16 d}-\frac{13 i a^3 \sec (c+d x) (a+i a \tan (c+d x))^5}{6 d}-\frac{429 i a^2 \sec (c+d x) \left(a^2+i a^2 \tan (c+d x)\right)^3}{40 d}-\frac{143 i \sec (c+d x) \left(a^2+i a^2 \tan (c+d x)\right)^4}{30 d}-\frac{1001 i \sec (c+d x) \left(a^4+i a^4 \tan (c+d x)\right)^2}{40 d}-\frac{1001 i \sec (c+d x) \left(a^8+i a^8 \tan (c+d x)\right)}{16 d}-\frac{2 i a \cos (c+d x) (a+i a \tan (c+d x))^7}{d}",1,"(-3003*a^8*ArcTanh[Sin[c + d*x]])/(16*d) - (((3003*I)/16)*a^8*Sec[c + d*x])/d - (((13*I)/6)*a^3*Sec[c + d*x]*(a + I*a*Tan[c + d*x])^5)/d - ((2*I)*a*Cos[c + d*x]*(a + I*a*Tan[c + d*x])^7)/d - (((429*I)/40)*a^2*Sec[c + d*x]*(a^2 + I*a^2*Tan[c + d*x])^3)/d - (((143*I)/30)*Sec[c + d*x]*(a^2 + I*a^2*Tan[c + d*x])^4)/d - (((1001*I)/40)*Sec[c + d*x]*(a^4 + I*a^4*Tan[c + d*x])^2)/d - (((1001*I)/16)*Sec[c + d*x]*(a^8 + I*a^8*Tan[c + d*x]))/d","A",8,4,22,0.1818,1,"{3496, 3498, 3486, 3770}"
92,1,205,0,0.1933074,"\int \cos ^3(c+d x) (a+i a \tan (c+d x))^8 \, dx","Int[Cos[c + d*x]^3*(a + I*a*Tan[c + d*x])^8,x]","\frac{1155 i a^8 \sec (c+d x)}{8 d}+\frac{1155 a^8 \tanh ^{-1}(\sin (c+d x))}{8 d}+\frac{22 i a^3 \cos (c+d x) (a+i a \tan (c+d x))^5}{3 d}+\frac{33 i a^2 \sec (c+d x) \left(a^2+i a^2 \tan (c+d x)\right)^3}{4 d}+\frac{77 i \sec (c+d x) \left(a^4+i a^4 \tan (c+d x)\right)^2}{4 d}+\frac{385 i \sec (c+d x) \left(a^8+i a^8 \tan (c+d x)\right)}{8 d}-\frac{2 i a \cos ^3(c+d x) (a+i a \tan (c+d x))^7}{3 d}","\frac{1155 i a^8 \sec (c+d x)}{8 d}+\frac{1155 a^8 \tanh ^{-1}(\sin (c+d x))}{8 d}+\frac{22 i a^3 \cos (c+d x) (a+i a \tan (c+d x))^5}{3 d}+\frac{33 i a^2 \sec (c+d x) \left(a^2+i a^2 \tan (c+d x)\right)^3}{4 d}+\frac{77 i \sec (c+d x) \left(a^4+i a^4 \tan (c+d x)\right)^2}{4 d}+\frac{385 i \sec (c+d x) \left(a^8+i a^8 \tan (c+d x)\right)}{8 d}-\frac{2 i a \cos ^3(c+d x) (a+i a \tan (c+d x))^7}{3 d}",1,"(1155*a^8*ArcTanh[Sin[c + d*x]])/(8*d) + (((1155*I)/8)*a^8*Sec[c + d*x])/d + (((22*I)/3)*a^3*Cos[c + d*x]*(a + I*a*Tan[c + d*x])^5)/d - (((2*I)/3)*a*Cos[c + d*x]^3*(a + I*a*Tan[c + d*x])^7)/d + (((33*I)/4)*a^2*Sec[c + d*x]*(a^2 + I*a^2*Tan[c + d*x])^3)/d + (((77*I)/4)*Sec[c + d*x]*(a^4 + I*a^4*Tan[c + d*x])^2)/d + (((385*I)/8)*Sec[c + d*x]*(a^8 + I*a^8*Tan[c + d*x]))/d","A",7,4,24,0.1667,1,"{3496, 3498, 3486, 3770}"
93,1,173,0,0.1674139,"\int \cos ^5(c+d x) (a+i a \tan (c+d x))^8 \, dx","Int[Cos[c + d*x]^5*(a + I*a*Tan[c + d*x])^8,x]","-\frac{63 i a^8 \sec (c+d x)}{2 d}-\frac{63 a^8 \tanh ^{-1}(\sin (c+d x))}{2 d}+\frac{6 i a^3 \cos ^3(c+d x) (a+i a \tan (c+d x))^5}{5 d}-\frac{42 i a^2 \cos (c+d x) \left(a^2+i a^2 \tan (c+d x)\right)^3}{5 d}-\frac{21 i \sec (c+d x) \left(a^8+i a^8 \tan (c+d x)\right)}{2 d}-\frac{2 i a \cos ^5(c+d x) (a+i a \tan (c+d x))^7}{5 d}","-\frac{63 i a^8 \sec (c+d x)}{2 d}-\frac{63 a^8 \tanh ^{-1}(\sin (c+d x))}{2 d}+\frac{6 i a^3 \cos ^3(c+d x) (a+i a \tan (c+d x))^5}{5 d}-\frac{42 i a^2 \cos (c+d x) \left(a^2+i a^2 \tan (c+d x)\right)^3}{5 d}-\frac{21 i \sec (c+d x) \left(a^8+i a^8 \tan (c+d x)\right)}{2 d}-\frac{2 i a \cos ^5(c+d x) (a+i a \tan (c+d x))^7}{5 d}",1,"(-63*a^8*ArcTanh[Sin[c + d*x]])/(2*d) - (((63*I)/2)*a^8*Sec[c + d*x])/d + (((6*I)/5)*a^3*Cos[c + d*x]^3*(a + I*a*Tan[c + d*x])^5)/d - (((2*I)/5)*a*Cos[c + d*x]^5*(a + I*a*Tan[c + d*x])^7)/d - (((42*I)/5)*a^2*Cos[c + d*x]*(a^2 + I*a^2*Tan[c + d*x])^3)/d - (((21*I)/2)*Sec[c + d*x]*(a^8 + I*a^8*Tan[c + d*x]))/d","A",6,4,24,0.1667,1,"{3496, 3498, 3486, 3770}"
94,1,152,0,0.1599178,"\int \cos ^7(c+d x) (a+i a \tan (c+d x))^8 \, dx","Int[Cos[c + d*x]^7*(a + I*a*Tan[c + d*x])^8,x]","\frac{a^8 \tanh ^{-1}(\sin (c+d x))}{d}+\frac{2 i a^3 \cos ^5(c+d x) (a+i a \tan (c+d x))^5}{5 d}-\frac{2 i a^2 \cos ^3(c+d x) \left(a^2+i a^2 \tan (c+d x)\right)^3}{3 d}+\frac{2 i \cos (c+d x) \left(a^8+i a^8 \tan (c+d x)\right)}{d}-\frac{2 i a \cos ^7(c+d x) (a+i a \tan (c+d x))^7}{7 d}","\frac{a^8 \tanh ^{-1}(\sin (c+d x))}{d}+\frac{2 i a^3 \cos ^5(c+d x) (a+i a \tan (c+d x))^5}{5 d}-\frac{2 i a^2 \cos ^3(c+d x) \left(a^2+i a^2 \tan (c+d x)\right)^3}{3 d}+\frac{2 i \cos (c+d x) \left(a^8+i a^8 \tan (c+d x)\right)}{d}-\frac{2 i a \cos ^7(c+d x) (a+i a \tan (c+d x))^7}{7 d}",1,"(a^8*ArcTanh[Sin[c + d*x]])/d + (((2*I)/5)*a^3*Cos[c + d*x]^5*(a + I*a*Tan[c + d*x])^5)/d - (((2*I)/7)*a*Cos[c + d*x]^7*(a + I*a*Tan[c + d*x])^7)/d - (((2*I)/3)*a^2*Cos[c + d*x]^3*(a^2 + I*a^2*Tan[c + d*x])^3)/d + ((2*I)*Cos[c + d*x]*(a^8 + I*a^8*Tan[c + d*x]))/d","A",5,2,24,0.08333,1,"{3496, 3770}"
95,1,66,0,0.073501,"\int \cos ^9(c+d x) (a+i a \tan (c+d x))^8 \, dx","Int[Cos[c + d*x]^9*(a + I*a*Tan[c + d*x])^8,x]","-\frac{i \cos ^9(c+d x) (a+i a \tan (c+d x))^8}{9 d}-\frac{i a \cos ^7(c+d x) (a+i a \tan (c+d x))^7}{63 d}","-\frac{i \cos ^9(c+d x) (a+i a \tan (c+d x))^8}{9 d}-\frac{i a \cos ^7(c+d x) (a+i a \tan (c+d x))^7}{63 d}",1,"((-I/63)*a*Cos[c + d*x]^7*(a + I*a*Tan[c + d*x])^7)/d - ((I/9)*Cos[c + d*x]^9*(a + I*a*Tan[c + d*x])^8)/d","A",2,2,24,0.08333,1,"{3497, 3488}"
96,1,136,0,0.1559855,"\int \cos ^{11}(c+d x) (a+i a \tan (c+d x))^8 \, dx","Int[Cos[c + d*x]^11*(a + I*a*Tan[c + d*x])^8,x]","-\frac{2 i a^2 \cos ^7(c+d x) (a+i a \tan (c+d x))^6}{231 d}-\frac{2 i a^3 \cos ^5(c+d x) (a+i a \tan (c+d x))^5}{1155 d}-\frac{i \cos ^{11}(c+d x) (a+i a \tan (c+d x))^8}{11 d}-\frac{i a \cos ^9(c+d x) (a+i a \tan (c+d x))^7}{33 d}","-\frac{2 i a^2 \cos ^7(c+d x) (a+i a \tan (c+d x))^6}{231 d}-\frac{2 i a^3 \cos ^5(c+d x) (a+i a \tan (c+d x))^5}{1155 d}-\frac{i \cos ^{11}(c+d x) (a+i a \tan (c+d x))^8}{11 d}-\frac{i a \cos ^9(c+d x) (a+i a \tan (c+d x))^7}{33 d}",1,"(((-2*I)/1155)*a^3*Cos[c + d*x]^5*(a + I*a*Tan[c + d*x])^5)/d - (((2*I)/231)*a^2*Cos[c + d*x]^7*(a + I*a*Tan[c + d*x])^6)/d - ((I/33)*a*Cos[c + d*x]^9*(a + I*a*Tan[c + d*x])^7)/d - ((I/11)*Cos[c + d*x]^11*(a + I*a*Tan[c + d*x])^8)/d","A",4,2,24,0.08333,1,"{3497, 3488}"
97,1,211,0,0.2537666,"\int \cos ^{13}(c+d x) (a+i a \tan (c+d x))^8 \, dx","Int[Cos[c + d*x]^13*(a + I*a*Tan[c + d*x])^8,x]","-\frac{20 i a^2 \cos ^9(c+d x) (a+i a \tan (c+d x))^6}{1287 d}-\frac{20 i a^3 \cos ^7(c+d x) (a+i a \tan (c+d x))^5}{3003 d}-\frac{8 i \cos ^5(c+d x) \left(a^2+i a^2 \tan (c+d x)\right)^4}{3003 d}-\frac{8 i a^2 \cos ^3(c+d x) \left(a^2+i a^2 \tan (c+d x)\right)^3}{9009 d}-\frac{i \cos ^{13}(c+d x) (a+i a \tan (c+d x))^8}{13 d}-\frac{5 i a \cos ^{11}(c+d x) (a+i a \tan (c+d x))^7}{143 d}","-\frac{20 i a^2 \cos ^9(c+d x) (a+i a \tan (c+d x))^6}{1287 d}-\frac{20 i a^3 \cos ^7(c+d x) (a+i a \tan (c+d x))^5}{3003 d}-\frac{8 i \cos ^5(c+d x) \left(a^2+i a^2 \tan (c+d x)\right)^4}{3003 d}-\frac{8 i a^2 \cos ^3(c+d x) \left(a^2+i a^2 \tan (c+d x)\right)^3}{9009 d}-\frac{i \cos ^{13}(c+d x) (a+i a \tan (c+d x))^8}{13 d}-\frac{5 i a \cos ^{11}(c+d x) (a+i a \tan (c+d x))^7}{143 d}",1,"(((-20*I)/3003)*a^3*Cos[c + d*x]^7*(a + I*a*Tan[c + d*x])^5)/d - (((20*I)/1287)*a^2*Cos[c + d*x]^9*(a + I*a*Tan[c + d*x])^6)/d - (((5*I)/143)*a*Cos[c + d*x]^11*(a + I*a*Tan[c + d*x])^7)/d - ((I/13)*Cos[c + d*x]^13*(a + I*a*Tan[c + d*x])^8)/d - (((8*I)/9009)*a^2*Cos[c + d*x]^3*(a^2 + I*a^2*Tan[c + d*x])^3)/d - (((8*I)/3003)*Cos[c + d*x]^5*(a^2 + I*a^2*Tan[c + d*x])^4)/d","A",6,2,24,0.08333,1,"{3497, 3488}"
98,1,212,0,0.1974204,"\int \cos ^{15}(c+d x) (a+i a \tan (c+d x))^8 \, dx","Int[Cos[c + d*x]^15*(a + I*a*Tan[c + d*x])^8,x]","-\frac{a^8 \sin ^7(c+d x)}{1287 d}+\frac{7 a^8 \sin ^5(c+d x)}{2145 d}-\frac{7 a^8 \sin ^3(c+d x)}{1287 d}+\frac{7 a^8 \sin (c+d x)}{1287 d}-\frac{2 i a^3 \cos ^{13}(c+d x) (a+i a \tan (c+d x))^5}{195 d}-\frac{2 i a^2 \cos ^{11}(c+d x) \left(a^2+i a^2 \tan (c+d x)\right)^3}{715 d}-\frac{2 i \cos ^9(c+d x) \left(a^8+i a^8 \tan (c+d x)\right)}{1287 d}-\frac{2 i a \cos ^{15}(c+d x) (a+i a \tan (c+d x))^7}{15 d}","-\frac{a^8 \sin ^7(c+d x)}{1287 d}+\frac{7 a^8 \sin ^5(c+d x)}{2145 d}-\frac{7 a^8 \sin ^3(c+d x)}{1287 d}+\frac{7 a^8 \sin (c+d x)}{1287 d}-\frac{2 i a^3 \cos ^{13}(c+d x) (a+i a \tan (c+d x))^5}{195 d}-\frac{2 i a^2 \cos ^{11}(c+d x) \left(a^2+i a^2 \tan (c+d x)\right)^3}{715 d}-\frac{2 i \cos ^9(c+d x) \left(a^8+i a^8 \tan (c+d x)\right)}{1287 d}-\frac{2 i a \cos ^{15}(c+d x) (a+i a \tan (c+d x))^7}{15 d}",1,"(7*a^8*Sin[c + d*x])/(1287*d) - (7*a^8*Sin[c + d*x]^3)/(1287*d) + (7*a^8*Sin[c + d*x]^5)/(2145*d) - (a^8*Sin[c + d*x]^7)/(1287*d) - (((2*I)/195)*a^3*Cos[c + d*x]^13*(a + I*a*Tan[c + d*x])^5)/d - (((2*I)/15)*a*Cos[c + d*x]^15*(a + I*a*Tan[c + d*x])^7)/d - (((2*I)/715)*a^2*Cos[c + d*x]^11*(a^2 + I*a^2*Tan[c + d*x])^3)/d - (((2*I)/1287)*Cos[c + d*x]^9*(a^8 + I*a^8*Tan[c + d*x]))/d","A",6,2,24,0.08333,1,"{3496, 2633}"
99,1,107,0,0.0695333,"\int \frac{\sec ^{10}(c+d x)}{a+i a \tan (c+d x)} \, dx","Int[Sec[c + d*x]^10/(a + I*a*Tan[c + d*x]),x]","-\frac{i (a-i a \tan (c+d x))^8}{8 a^9 d}+\frac{6 i (a-i a \tan (c+d x))^7}{7 a^8 d}-\frac{2 i (a-i a \tan (c+d x))^6}{a^7 d}+\frac{8 i (a-i a \tan (c+d x))^5}{5 a^6 d}","-\frac{i (a-i a \tan (c+d x))^8}{8 a^9 d}+\frac{6 i (a-i a \tan (c+d x))^7}{7 a^8 d}-\frac{2 i (a-i a \tan (c+d x))^6}{a^7 d}+\frac{8 i (a-i a \tan (c+d x))^5}{5 a^6 d}",1,"(((8*I)/5)*(a - I*a*Tan[c + d*x])^5)/(a^6*d) - ((2*I)*(a - I*a*Tan[c + d*x])^6)/(a^7*d) + (((6*I)/7)*(a - I*a*Tan[c + d*x])^7)/(a^8*d) - ((I/8)*(a - I*a*Tan[c + d*x])^8)/(a^9*d)","A",3,2,24,0.08333,1,"{3487, 43}"
100,1,80,0,0.0620516,"\int \frac{\sec ^8(c+d x)}{a+i a \tan (c+d x)} \, dx","Int[Sec[c + d*x]^8/(a + I*a*Tan[c + d*x]),x]","\frac{i (a-i a \tan (c+d x))^6}{6 a^7 d}-\frac{4 i (a-i a \tan (c+d x))^5}{5 a^6 d}+\frac{i (a-i a \tan (c+d x))^4}{a^5 d}","\frac{i (a-i a \tan (c+d x))^6}{6 a^7 d}-\frac{4 i (a-i a \tan (c+d x))^5}{5 a^6 d}+\frac{i (a-i a \tan (c+d x))^4}{a^5 d}",1,"(I*(a - I*a*Tan[c + d*x])^4)/(a^5*d) - (((4*I)/5)*(a - I*a*Tan[c + d*x])^5)/(a^6*d) + ((I/6)*(a - I*a*Tan[c + d*x])^6)/(a^7*d)","A",3,2,24,0.08333,1,"{3487, 43}"
101,1,55,0,0.0511579,"\int \frac{\sec ^6(c+d x)}{a+i a \tan (c+d x)} \, dx","Int[Sec[c + d*x]^6/(a + I*a*Tan[c + d*x]),x]","\frac{2 i (a-i a \tan (c+d x))^3}{3 a^4 d}-\frac{i (a-i a \tan (c+d x))^4}{4 a^5 d}","\frac{2 i (a-i a \tan (c+d x))^3}{3 a^4 d}-\frac{i (a-i a \tan (c+d x))^4}{4 a^5 d}",1,"(((2*I)/3)*(a - I*a*Tan[c + d*x])^3)/(a^4*d) - ((I/4)*(a - I*a*Tan[c + d*x])^4)/(a^5*d)","A",3,2,24,0.08333,1,"{3487, 43}"
102,1,34,0,0.0431182,"\int \frac{\sec ^4(c+d x)}{a+i a \tan (c+d x)} \, dx","Int[Sec[c + d*x]^4/(a + I*a*Tan[c + d*x]),x]","\frac{\tan (c+d x)}{a d}-\frac{i \tan ^2(c+d x)}{2 a d}","\frac{\tan (c+d x)}{a d}-\frac{i \tan ^2(c+d x)}{2 a d}",1,"Tan[c + d*x]/(a*d) - ((I/2)*Tan[c + d*x]^2)/(a*d)","A",2,1,24,0.04167,1,"{3487}"
103,1,23,0,0.0408845,"\int \frac{\sec ^2(c+d x)}{a+i a \tan (c+d x)} \, dx","Int[Sec[c + d*x]^2/(a + I*a*Tan[c + d*x]),x]","\frac{x}{a}+\frac{i \log (\cos (c+d x))}{a d}","\frac{x}{a}+\frac{i \log (\cos (c+d x))}{a d}",1,"x/a + (I*Log[Cos[c + d*x]])/(a*d)","A",2,2,24,0.08333,1,"{3487, 31}"
104,1,33,0,0.0120401,"\int \frac{1}{a+i a \tan (c+d x)} \, dx","Int[(a + I*a*Tan[c + d*x])^(-1),x]","\frac{x}{2 a}+\frac{i}{2 d (a+i a \tan (c+d x))}","\frac{x}{2 a}+\frac{i}{2 d (a+i a \tan (c+d x))}",1,"x/(2*a) + (I/2)/(d*(a + I*a*Tan[c + d*x]))","A",2,2,15,0.1333,1,"{3479, 8}"
105,1,82,0,0.0682929,"\int \frac{\cos ^2(c+d x)}{a+i a \tan (c+d x)} \, dx","Int[Cos[c + d*x]^2/(a + I*a*Tan[c + d*x]),x]","\frac{i a}{8 d (a+i a \tan (c+d x))^2}-\frac{i}{8 d (a-i a \tan (c+d x))}+\frac{i}{4 d (a+i a \tan (c+d x))}+\frac{3 x}{8 a}","\frac{i a}{8 d (a+i a \tan (c+d x))^2}-\frac{i}{8 d (a-i a \tan (c+d x))}+\frac{i}{4 d (a+i a \tan (c+d x))}+\frac{3 x}{8 a}",1,"(3*x)/(8*a) - (I/8)/(d*(a - I*a*Tan[c + d*x])) + ((I/8)*a)/(d*(a + I*a*Tan[c + d*x])^2) + (I/4)/(d*(a + I*a*Tan[c + d*x]))","A",4,3,24,0.1250,1,"{3487, 44, 206}"
106,1,134,0,0.0872302,"\int \frac{\cos ^4(c+d x)}{a+i a \tan (c+d x)} \, dx","Int[Cos[c + d*x]^4/(a + I*a*Tan[c + d*x]),x]","\frac{i a^2}{24 d (a+i a \tan (c+d x))^3}-\frac{i a}{32 d (a-i a \tan (c+d x))^2}+\frac{3 i a}{32 d (a+i a \tan (c+d x))^2}-\frac{i}{8 d (a-i a \tan (c+d x))}+\frac{3 i}{16 d (a+i a \tan (c+d x))}+\frac{5 x}{16 a}","\frac{i a^2}{24 d (a+i a \tan (c+d x))^3}-\frac{i a}{32 d (a-i a \tan (c+d x))^2}+\frac{3 i a}{32 d (a+i a \tan (c+d x))^2}-\frac{i}{8 d (a-i a \tan (c+d x))}+\frac{3 i}{16 d (a+i a \tan (c+d x))}+\frac{5 x}{16 a}",1,"(5*x)/(16*a) - ((I/32)*a)/(d*(a - I*a*Tan[c + d*x])^2) - (I/8)/(d*(a - I*a*Tan[c + d*x])) + ((I/24)*a^2)/(d*(a + I*a*Tan[c + d*x])^3) + (((3*I)/32)*a)/(d*(a + I*a*Tan[c + d*x])^2) + ((3*I)/16)/(d*(a + I*a*Tan[c + d*x]))","A",4,3,24,0.1250,1,"{3487, 44, 206}"
107,1,84,0,0.0767625,"\int \frac{\sec ^7(c+d x)}{a+i a \tan (c+d x)} \, dx","Int[Sec[c + d*x]^7/(a + I*a*Tan[c + d*x]),x]","-\frac{i \sec ^5(c+d x)}{5 a d}+\frac{3 \tanh ^{-1}(\sin (c+d x))}{8 a d}+\frac{\tan (c+d x) \sec ^3(c+d x)}{4 a d}+\frac{3 \tan (c+d x) \sec (c+d x)}{8 a d}","-\frac{i \sec ^5(c+d x)}{5 a d}+\frac{3 \tanh ^{-1}(\sin (c+d x))}{8 a d}+\frac{\tan (c+d x) \sec ^3(c+d x)}{4 a d}+\frac{3 \tan (c+d x) \sec (c+d x)}{8 a d}",1,"(3*ArcTanh[Sin[c + d*x]])/(8*a*d) - ((I/5)*Sec[c + d*x]^5)/(a*d) + (3*Sec[c + d*x]*Tan[c + d*x])/(8*a*d) + (Sec[c + d*x]^3*Tan[c + d*x])/(4*a*d)","A",4,3,24,0.1250,1,"{3501, 3768, 3770}"
108,1,60,0,0.0535457,"\int \frac{\sec ^5(c+d x)}{a+i a \tan (c+d x)} \, dx","Int[Sec[c + d*x]^5/(a + I*a*Tan[c + d*x]),x]","-\frac{i \sec ^3(c+d x)}{3 a d}+\frac{\tanh ^{-1}(\sin (c+d x))}{2 a d}+\frac{\tan (c+d x) \sec (c+d x)}{2 a d}","-\frac{i \sec ^3(c+d x)}{3 a d}+\frac{\tanh ^{-1}(\sin (c+d x))}{2 a d}+\frac{\tan (c+d x) \sec (c+d x)}{2 a d}",1,"ArcTanh[Sin[c + d*x]]/(2*a*d) - ((I/3)*Sec[c + d*x]^3)/(a*d) + (Sec[c + d*x]*Tan[c + d*x])/(2*a*d)","A",3,3,24,0.1250,1,"{3501, 3768, 3770}"
109,1,31,0,0.0435518,"\int \frac{\sec ^3(c+d x)}{a+i a \tan (c+d x)} \, dx","Int[Sec[c + d*x]^3/(a + I*a*Tan[c + d*x]),x]","\frac{\tanh ^{-1}(\sin (c+d x))}{a d}-\frac{i \sec (c+d x)}{a d}","\frac{\tanh ^{-1}(\sin (c+d x))}{a d}-\frac{i \sec (c+d x)}{a d}",1,"ArcTanh[Sin[c + d*x]]/(a*d) - (I*Sec[c + d*x])/(a*d)","A",2,2,24,0.08333,1,"{3501, 3770}"
110,1,28,0,0.0228633,"\int \frac{\sec (c+d x)}{a+i a \tan (c+d x)} \, dx","Int[Sec[c + d*x]/(a + I*a*Tan[c + d*x]),x]","\frac{i \sec (c+d x)}{d (a+i a \tan (c+d x))}","\frac{i \sec (c+d x)}{d (a+i a \tan (c+d x))}",1,"(I*Sec[c + d*x])/(d*(a + I*a*Tan[c + d*x]))","A",1,1,22,0.04545,1,"{3488}"
111,1,47,0,0.0370954,"\int \frac{\cos (c+d x)}{a+i a \tan (c+d x)} \, dx","Int[Cos[c + d*x]/(a + I*a*Tan[c + d*x]),x]","\frac{2 \sin (c+d x)}{3 a d}+\frac{i \cos (c+d x)}{3 d (a+i a \tan (c+d x))}","\frac{2 \sin (c+d x)}{3 a d}+\frac{i \cos (c+d x)}{3 d (a+i a \tan (c+d x))}",1,"(2*Sin[c + d*x])/(3*a*d) + ((I/3)*Cos[c + d*x])/(d*(a + I*a*Tan[c + d*x]))","A",2,2,22,0.09091,1,"{3502, 2637}"
112,1,67,0,0.0519919,"\int \frac{\cos ^3(c+d x)}{a+i a \tan (c+d x)} \, dx","Int[Cos[c + d*x]^3/(a + I*a*Tan[c + d*x]),x]","-\frac{4 \sin ^3(c+d x)}{15 a d}+\frac{4 \sin (c+d x)}{5 a d}+\frac{i \cos ^3(c+d x)}{5 d (a+i a \tan (c+d x))}","-\frac{4 \sin ^3(c+d x)}{15 a d}+\frac{4 \sin (c+d x)}{5 a d}+\frac{i \cos ^3(c+d x)}{5 d (a+i a \tan (c+d x))}",1,"(4*Sin[c + d*x])/(5*a*d) - (4*Sin[c + d*x]^3)/(15*a*d) + ((I/5)*Cos[c + d*x]^3)/(d*(a + I*a*Tan[c + d*x]))","A",3,2,24,0.08333,1,"{3502, 2633}"
113,1,85,0,0.0553903,"\int \frac{\cos ^5(c+d x)}{a+i a \tan (c+d x)} \, dx","Int[Cos[c + d*x]^5/(a + I*a*Tan[c + d*x]),x]","\frac{6 \sin ^5(c+d x)}{35 a d}-\frac{4 \sin ^3(c+d x)}{7 a d}+\frac{6 \sin (c+d x)}{7 a d}+\frac{i \cos ^5(c+d x)}{7 d (a+i a \tan (c+d x))}","\frac{6 \sin ^5(c+d x)}{35 a d}-\frac{4 \sin ^3(c+d x)}{7 a d}+\frac{6 \sin (c+d x)}{7 a d}+\frac{i \cos ^5(c+d x)}{7 d (a+i a \tan (c+d x))}",1,"(6*Sin[c + d*x])/(7*a*d) - (4*Sin[c + d*x]^3)/(7*a*d) + (6*Sin[c + d*x]^5)/(35*a*d) + ((I/7)*Cos[c + d*x]^5)/(d*(a + I*a*Tan[c + d*x]))","A",3,2,24,0.08333,1,"{3502, 2633}"
114,1,82,0,0.0625975,"\int \frac{\sec ^{10}(c+d x)}{(a+i a \tan (c+d x))^2} \, dx","Int[Sec[c + d*x]^10/(a + I*a*Tan[c + d*x])^2,x]","\frac{i (a-i a \tan (c+d x))^7}{7 a^9 d}-\frac{2 i (a-i a \tan (c+d x))^6}{3 a^8 d}+\frac{4 i (a-i a \tan (c+d x))^5}{5 a^7 d}","\frac{i (a-i a \tan (c+d x))^7}{7 a^9 d}-\frac{2 i (a-i a \tan (c+d x))^6}{3 a^8 d}+\frac{4 i (a-i a \tan (c+d x))^5}{5 a^7 d}",1,"(((4*I)/5)*(a - I*a*Tan[c + d*x])^5)/(a^7*d) - (((2*I)/3)*(a - I*a*Tan[c + d*x])^6)/(a^8*d) + ((I/7)*(a - I*a*Tan[c + d*x])^7)/(a^9*d)","A",3,2,24,0.08333,1,"{3487, 43}"
115,1,55,0,0.0505928,"\int \frac{\sec ^8(c+d x)}{(a+i a \tan (c+d x))^2} \, dx","Int[Sec[c + d*x]^8/(a + I*a*Tan[c + d*x])^2,x]","\frac{i (a-i a \tan (c+d x))^4}{2 a^6 d}-\frac{i (a-i a \tan (c+d x))^5}{5 a^7 d}","\frac{i (a-i a \tan (c+d x))^4}{2 a^6 d}-\frac{i (a-i a \tan (c+d x))^5}{5 a^7 d}",1,"((I/2)*(a - I*a*Tan[c + d*x])^4)/(a^6*d) - ((I/5)*(a - I*a*Tan[c + d*x])^5)/(a^7*d)","A",3,2,24,0.08333,1,"{3487, 43}"
116,1,27,0,0.0444558,"\int \frac{\sec ^6(c+d x)}{(a+i a \tan (c+d x))^2} \, dx","Int[Sec[c + d*x]^6/(a + I*a*Tan[c + d*x])^2,x]","\frac{i (a-i a \tan (c+d x))^3}{3 a^5 d}","\frac{i (a-i a \tan (c+d x))^3}{3 a^5 d}",1,"((I/3)*(a - I*a*Tan[c + d*x])^3)/(a^5*d)","A",2,2,24,0.08333,1,"{3487, 32}"
117,1,38,0,0.0487313,"\int \frac{\sec ^4(c+d x)}{(a+i a \tan (c+d x))^2} \, dx","Int[Sec[c + d*x]^4/(a + I*a*Tan[c + d*x])^2,x]","-\frac{\tan (c+d x)}{a^2 d}+\frac{2 i \log (\cos (c+d x))}{a^2 d}+\frac{2 x}{a^2}","-\frac{\tan (c+d x)}{a^2 d}+\frac{2 i \log (\cos (c+d x))}{a^2 d}+\frac{2 x}{a^2}",1,"(2*x)/a^2 + ((2*I)*Log[Cos[c + d*x]])/(a^2*d) - Tan[c + d*x]/(a^2*d)","A",3,2,24,0.08333,1,"{3487, 43}"
118,1,26,0,0.0432143,"\int \frac{\sec ^2(c+d x)}{(a+i a \tan (c+d x))^2} \, dx","Int[Sec[c + d*x]^2/(a + I*a*Tan[c + d*x])^2,x]","\frac{i}{d \left(a^2+i a^2 \tan (c+d x)\right)}","\frac{i}{d \left(a^2+i a^2 \tan (c+d x)\right)}",1,"I/(d*(a^2 + I*a^2*Tan[c + d*x]))","A",2,2,24,0.08333,1,"{3487, 32}"
119,1,61,0,0.0285386,"\int \frac{1}{(a+i a \tan (c+d x))^2} \, dx","Int[(a + I*a*Tan[c + d*x])^(-2),x]","\frac{i}{4 d \left(a^2+i a^2 \tan (c+d x)\right)}+\frac{x}{4 a^2}+\frac{i}{4 d (a+i a \tan (c+d x))^2}","\frac{i}{4 d \left(a^2+i a^2 \tan (c+d x)\right)}+\frac{x}{4 a^2}+\frac{i}{4 d (a+i a \tan (c+d x))^2}",1,"x/(4*a^2) + (I/4)/(d*(a + I*a*Tan[c + d*x])^2) + (I/4)/(d*(a^2 + I*a^2*Tan[c + d*x]))","A",3,2,15,0.1333,1,"{3479, 8}"
120,1,114,0,0.0814118,"\int \frac{\cos ^2(c+d x)}{(a+i a \tan (c+d x))^2} \, dx","Int[Cos[c + d*x]^2/(a + I*a*Tan[c + d*x])^2,x]","-\frac{i}{16 d \left(a^2-i a^2 \tan (c+d x)\right)}+\frac{3 i}{16 d \left(a^2+i a^2 \tan (c+d x)\right)}+\frac{x}{4 a^2}+\frac{i a}{12 d (a+i a \tan (c+d x))^3}+\frac{i}{8 d (a+i a \tan (c+d x))^2}","-\frac{i}{16 d \left(a^2-i a^2 \tan (c+d x)\right)}+\frac{3 i}{16 d \left(a^2+i a^2 \tan (c+d x)\right)}+\frac{x}{4 a^2}+\frac{i a}{12 d (a+i a \tan (c+d x))^3}+\frac{i}{8 d (a+i a \tan (c+d x))^2}",1,"x/(4*a^2) + ((I/12)*a)/(d*(a + I*a*Tan[c + d*x])^3) + (I/8)/(d*(a + I*a*Tan[c + d*x])^2) - (I/16)/(d*(a^2 - I*a^2*Tan[c + d*x])) + ((3*I)/16)/(d*(a^2 + I*a^2*Tan[c + d*x]))","A",4,3,24,0.1250,1,"{3487, 44, 206}"
121,1,165,0,0.1032332,"\int \frac{\cos ^4(c+d x)}{(a+i a \tan (c+d x))^2} \, dx","Int[Cos[c + d*x]^4/(a + I*a*Tan[c + d*x])^2,x]","\frac{i a^2}{32 d (a+i a \tan (c+d x))^4}-\frac{5 i}{64 d \left(a^2-i a^2 \tan (c+d x)\right)}+\frac{5 i}{32 d \left(a^2+i a^2 \tan (c+d x)\right)}+\frac{15 x}{64 a^2}+\frac{i a}{16 d (a+i a \tan (c+d x))^3}-\frac{i}{64 d (a-i a \tan (c+d x))^2}+\frac{3 i}{32 d (a+i a \tan (c+d x))^2}","\frac{i a^2}{32 d (a+i a \tan (c+d x))^4}-\frac{5 i}{64 d \left(a^2-i a^2 \tan (c+d x)\right)}+\frac{5 i}{32 d \left(a^2+i a^2 \tan (c+d x)\right)}+\frac{15 x}{64 a^2}+\frac{i a}{16 d (a+i a \tan (c+d x))^3}-\frac{i}{64 d (a-i a \tan (c+d x))^2}+\frac{3 i}{32 d (a+i a \tan (c+d x))^2}",1,"(15*x)/(64*a^2) - (I/64)/(d*(a - I*a*Tan[c + d*x])^2) + ((I/32)*a^2)/(d*(a + I*a*Tan[c + d*x])^4) + ((I/16)*a)/(d*(a + I*a*Tan[c + d*x])^3) + ((3*I)/32)/(d*(a + I*a*Tan[c + d*x])^2) - ((5*I)/64)/(d*(a^2 - I*a^2*Tan[c + d*x])) + ((5*I)/32)/(d*(a^2 + I*a^2*Tan[c + d*x]))","A",4,3,24,0.1250,1,"{3487, 44, 206}"
122,1,124,0,0.0814793,"\int \frac{\sec ^9(c+d x)}{(a+i a \tan (c+d x))^2} \, dx","Int[Sec[c + d*x]^9/(a + I*a*Tan[c + d*x])^2,x]","\frac{7 \tanh ^{-1}(\sin (c+d x))}{16 a^2 d}-\frac{2 i \sec ^7(c+d x)}{5 d \left(a^2+i a^2 \tan (c+d x)\right)}+\frac{7 \tan (c+d x) \sec ^5(c+d x)}{30 a^2 d}+\frac{7 \tan (c+d x) \sec ^3(c+d x)}{24 a^2 d}+\frac{7 \tan (c+d x) \sec (c+d x)}{16 a^2 d}","\frac{7 \tanh ^{-1}(\sin (c+d x))}{16 a^2 d}-\frac{2 i \sec ^7(c+d x)}{5 d \left(a^2+i a^2 \tan (c+d x)\right)}+\frac{7 \tan (c+d x) \sec ^5(c+d x)}{30 a^2 d}+\frac{7 \tan (c+d x) \sec ^3(c+d x)}{24 a^2 d}+\frac{7 \tan (c+d x) \sec (c+d x)}{16 a^2 d}",1,"(7*ArcTanh[Sin[c + d*x]])/(16*a^2*d) + (7*Sec[c + d*x]*Tan[c + d*x])/(16*a^2*d) + (7*Sec[c + d*x]^3*Tan[c + d*x])/(24*a^2*d) + (7*Sec[c + d*x]^5*Tan[c + d*x])/(30*a^2*d) - (((2*I)/5)*Sec[c + d*x]^7)/(d*(a^2 + I*a^2*Tan[c + d*x]))","A",5,3,24,0.1250,1,"{3500, 3768, 3770}"
123,1,100,0,0.0676607,"\int \frac{\sec ^7(c+d x)}{(a+i a \tan (c+d x))^2} \, dx","Int[Sec[c + d*x]^7/(a + I*a*Tan[c + d*x])^2,x]","\frac{5 \tanh ^{-1}(\sin (c+d x))}{8 a^2 d}-\frac{2 i \sec ^5(c+d x)}{3 d \left(a^2+i a^2 \tan (c+d x)\right)}+\frac{5 \tan (c+d x) \sec ^3(c+d x)}{12 a^2 d}+\frac{5 \tan (c+d x) \sec (c+d x)}{8 a^2 d}","\frac{5 \tanh ^{-1}(\sin (c+d x))}{8 a^2 d}-\frac{2 i \sec ^5(c+d x)}{3 d \left(a^2+i a^2 \tan (c+d x)\right)}+\frac{5 \tan (c+d x) \sec ^3(c+d x)}{12 a^2 d}+\frac{5 \tan (c+d x) \sec (c+d x)}{8 a^2 d}",1,"(5*ArcTanh[Sin[c + d*x]])/(8*a^2*d) + (5*Sec[c + d*x]*Tan[c + d*x])/(8*a^2*d) + (5*Sec[c + d*x]^3*Tan[c + d*x])/(12*a^2*d) - (((2*I)/3)*Sec[c + d*x]^5)/(d*(a^2 + I*a^2*Tan[c + d*x]))","A",4,3,24,0.1250,1,"{3500, 3768, 3770}"
124,1,74,0,0.0580909,"\int \frac{\sec ^5(c+d x)}{(a+i a \tan (c+d x))^2} \, dx","Int[Sec[c + d*x]^5/(a + I*a*Tan[c + d*x])^2,x]","\frac{3 \tanh ^{-1}(\sin (c+d x))}{2 a^2 d}-\frac{2 i \sec ^3(c+d x)}{d \left(a^2+i a^2 \tan (c+d x)\right)}+\frac{3 \tan (c+d x) \sec (c+d x)}{2 a^2 d}","\frac{3 \tanh ^{-1}(\sin (c+d x))}{2 a^2 d}-\frac{2 i \sec ^3(c+d x)}{d \left(a^2+i a^2 \tan (c+d x)\right)}+\frac{3 \tan (c+d x) \sec (c+d x)}{2 a^2 d}",1,"(3*ArcTanh[Sin[c + d*x]])/(2*a^2*d) + (3*Sec[c + d*x]*Tan[c + d*x])/(2*a^2*d) - ((2*I)*Sec[c + d*x]^3)/(d*(a^2 + I*a^2*Tan[c + d*x]))","A",3,3,24,0.1250,1,"{3500, 3768, 3770}"
125,1,48,0,0.0471635,"\int \frac{\sec ^3(c+d x)}{(a+i a \tan (c+d x))^2} \, dx","Int[Sec[c + d*x]^3/(a + I*a*Tan[c + d*x])^2,x]","-\frac{\tanh ^{-1}(\sin (c+d x))}{a^2 d}+\frac{2 i \sec (c+d x)}{d \left(a^2+i a^2 \tan (c+d x)\right)}","-\frac{\tanh ^{-1}(\sin (c+d x))}{a^2 d}+\frac{2 i \sec (c+d x)}{d \left(a^2+i a^2 \tan (c+d x)\right)}",1,"-(ArcTanh[Sin[c + d*x]]/(a^2*d)) + ((2*I)*Sec[c + d*x])/(d*(a^2 + I*a^2*Tan[c + d*x]))","A",2,2,24,0.08333,1,"{3500, 3770}"
126,1,65,0,0.0539423,"\int \frac{\sec (c+d x)}{(a+i a \tan (c+d x))^2} \, dx","Int[Sec[c + d*x]/(a + I*a*Tan[c + d*x])^2,x]","\frac{i \sec (c+d x)}{3 d \left(a^2+i a^2 \tan (c+d x)\right)}+\frac{i \sec (c+d x)}{3 d (a+i a \tan (c+d x))^2}","\frac{i \sec (c+d x)}{3 d \left(a^2+i a^2 \tan (c+d x)\right)}+\frac{i \sec (c+d x)}{3 d (a+i a \tan (c+d x))^2}",1,"((I/3)*Sec[c + d*x])/(d*(a + I*a*Tan[c + d*x])^2) + ((I/3)*Sec[c + d*x])/(d*(a^2 + I*a^2*Tan[c + d*x]))","A",2,2,22,0.09091,1,"{3502, 3488}"
127,1,71,0,0.048421,"\int \frac{\cos (c+d x)}{(a+i a \tan (c+d x))^2} \, dx","Int[Cos[c + d*x]/(a + I*a*Tan[c + d*x])^2,x]","-\frac{\sin ^3(c+d x)}{5 a^2 d}+\frac{3 \sin (c+d x)}{5 a^2 d}+\frac{2 i \cos ^3(c+d x)}{5 d \left(a^2+i a^2 \tan (c+d x)\right)}","-\frac{\sin ^3(c+d x)}{5 a^2 d}+\frac{3 \sin (c+d x)}{5 a^2 d}+\frac{2 i \cos ^3(c+d x)}{5 d \left(a^2+i a^2 \tan (c+d x)\right)}",1,"(3*Sin[c + d*x])/(5*a^2*d) - Sin[c + d*x]^3/(5*a^2*d) + (((2*I)/5)*Cos[c + d*x]^3)/(d*(a^2 + I*a^2*Tan[c + d*x]))","A",3,2,22,0.09091,1,"{3500, 2633}"
128,1,89,0,0.0585017,"\int \frac{\cos ^3(c+d x)}{(a+i a \tan (c+d x))^2} \, dx","Int[Cos[c + d*x]^3/(a + I*a*Tan[c + d*x])^2,x]","\frac{\sin ^5(c+d x)}{7 a^2 d}-\frac{10 \sin ^3(c+d x)}{21 a^2 d}+\frac{5 \sin (c+d x)}{7 a^2 d}+\frac{2 i \cos ^5(c+d x)}{7 d \left(a^2+i a^2 \tan (c+d x)\right)}","\frac{\sin ^5(c+d x)}{7 a^2 d}-\frac{10 \sin ^3(c+d x)}{21 a^2 d}+\frac{5 \sin (c+d x)}{7 a^2 d}+\frac{2 i \cos ^5(c+d x)}{7 d \left(a^2+i a^2 \tan (c+d x)\right)}",1,"(5*Sin[c + d*x])/(7*a^2*d) - (10*Sin[c + d*x]^3)/(21*a^2*d) + Sin[c + d*x]^5/(7*a^2*d) + (((2*I)/7)*Cos[c + d*x]^5)/(d*(a^2 + I*a^2*Tan[c + d*x]))","A",3,2,24,0.08333,1,"{3500, 2633}"
129,1,107,0,0.0615628,"\int \frac{\cos ^5(c+d x)}{(a+i a \tan (c+d x))^2} \, dx","Int[Cos[c + d*x]^5/(a + I*a*Tan[c + d*x])^2,x]","-\frac{\sin ^7(c+d x)}{9 a^2 d}+\frac{7 \sin ^5(c+d x)}{15 a^2 d}-\frac{7 \sin ^3(c+d x)}{9 a^2 d}+\frac{7 \sin (c+d x)}{9 a^2 d}+\frac{2 i \cos ^7(c+d x)}{9 d \left(a^2+i a^2 \tan (c+d x)\right)}","-\frac{\sin ^7(c+d x)}{9 a^2 d}+\frac{7 \sin ^5(c+d x)}{15 a^2 d}-\frac{7 \sin ^3(c+d x)}{9 a^2 d}+\frac{7 \sin (c+d x)}{9 a^2 d}+\frac{2 i \cos ^7(c+d x)}{9 d \left(a^2+i a^2 \tan (c+d x)\right)}",1,"(7*Sin[c + d*x])/(9*a^2*d) - (7*Sin[c + d*x]^3)/(9*a^2*d) + (7*Sin[c + d*x]^5)/(15*a^2*d) - Sin[c + d*x]^7/(9*a^2*d) + (((2*I)/9)*Cos[c + d*x]^7)/(d*(a^2 + I*a^2*Tan[c + d*x]))","A",3,2,24,0.08333,1,"{3500, 2633}"
130,1,109,0,0.0688227,"\int \frac{\sec ^{14}(c+d x)}{(a+i a \tan (c+d x))^3} \, dx","Int[Sec[c + d*x]^14/(a + I*a*Tan[c + d*x])^3,x]","-\frac{i (a-i a \tan (c+d x))^{10}}{10 a^{13} d}+\frac{2 i (a-i a \tan (c+d x))^9}{3 a^{12} d}-\frac{3 i (a-i a \tan (c+d x))^8}{2 a^{11} d}+\frac{8 i (a-i a \tan (c+d x))^7}{7 a^{10} d}","-\frac{i (a-i a \tan (c+d x))^{10}}{10 a^{13} d}+\frac{2 i (a-i a \tan (c+d x))^9}{3 a^{12} d}-\frac{3 i (a-i a \tan (c+d x))^8}{2 a^{11} d}+\frac{8 i (a-i a \tan (c+d x))^7}{7 a^{10} d}",1,"(((8*I)/7)*(a - I*a*Tan[c + d*x])^7)/(a^10*d) - (((3*I)/2)*(a - I*a*Tan[c + d*x])^8)/(a^11*d) + (((2*I)/3)*(a - I*a*Tan[c + d*x])^9)/(a^12*d) - ((I/10)*(a - I*a*Tan[c + d*x])^10)/(a^13*d)","A",3,2,24,0.08333,1,"{3487, 43}"
131,1,82,0,0.0613849,"\int \frac{\sec ^{12}(c+d x)}{(a+i a \tan (c+d x))^3} \, dx","Int[Sec[c + d*x]^12/(a + I*a*Tan[c + d*x])^3,x]","\frac{i (a-i a \tan (c+d x))^8}{8 a^{11} d}-\frac{4 i (a-i a \tan (c+d x))^7}{7 a^{10} d}+\frac{2 i (a-i a \tan (c+d x))^6}{3 a^9 d}","\frac{i (a-i a \tan (c+d x))^8}{8 a^{11} d}-\frac{4 i (a-i a \tan (c+d x))^7}{7 a^{10} d}+\frac{2 i (a-i a \tan (c+d x))^6}{3 a^9 d}",1,"(((2*I)/3)*(a - I*a*Tan[c + d*x])^6)/(a^9*d) - (((4*I)/7)*(a - I*a*Tan[c + d*x])^7)/(a^10*d) + ((I/8)*(a - I*a*Tan[c + d*x])^8)/(a^11*d)","A",3,2,24,0.08333,1,"{3487, 43}"
132,1,55,0,0.0473699,"\int \frac{\sec ^{10}(c+d x)}{(a+i a \tan (c+d x))^3} \, dx","Int[Sec[c + d*x]^10/(a + I*a*Tan[c + d*x])^3,x]","\frac{2 i (a-i a \tan (c+d x))^5}{5 a^8 d}-\frac{i (a-i a \tan (c+d x))^6}{6 a^9 d}","\frac{2 i (a-i a \tan (c+d x))^5}{5 a^8 d}-\frac{i (a-i a \tan (c+d x))^6}{6 a^9 d}",1,"(((2*I)/5)*(a - I*a*Tan[c + d*x])^5)/(a^8*d) - ((I/6)*(a - I*a*Tan[c + d*x])^6)/(a^9*d)","A",3,2,24,0.08333,1,"{3487, 43}"
133,1,27,0,0.039479,"\int \frac{\sec ^8(c+d x)}{(a+i a \tan (c+d x))^3} \, dx","Int[Sec[c + d*x]^8/(a + I*a*Tan[c + d*x])^3,x]","\frac{i (a-i a \tan (c+d x))^4}{4 a^7 d}","\frac{i (a-i a \tan (c+d x))^4}{4 a^7 d}",1,"((I/4)*(a - I*a*Tan[c + d*x])^4)/(a^7*d)","A",2,2,24,0.08333,1,"{3487, 32}"
134,1,58,0,0.0472475,"\int \frac{\sec ^6(c+d x)}{(a+i a \tan (c+d x))^3} \, dx","Int[Sec[c + d*x]^6/(a + I*a*Tan[c + d*x])^3,x]","\frac{i \tan ^2(c+d x)}{2 a^3 d}-\frac{3 \tan (c+d x)}{a^3 d}+\frac{4 i \log (\cos (c+d x))}{a^3 d}+\frac{4 x}{a^3}","\frac{i \tan ^2(c+d x)}{2 a^3 d}-\frac{3 \tan (c+d x)}{a^3 d}+\frac{4 i \log (\cos (c+d x))}{a^3 d}+\frac{4 x}{a^3}",1,"(4*x)/a^3 + ((4*I)*Log[Cos[c + d*x]])/(a^3*d) - (3*Tan[c + d*x])/(a^3*d) + ((I/2)*Tan[c + d*x]^2)/(a^3*d)","A",3,2,24,0.08333,1,"{3487, 43}"
135,1,50,0,0.0486496,"\int \frac{\sec ^4(c+d x)}{(a+i a \tan (c+d x))^3} \, dx","Int[Sec[c + d*x]^4/(a + I*a*Tan[c + d*x])^3,x]","\frac{2 i}{d \left(a^3+i a^3 \tan (c+d x)\right)}-\frac{i \log (\cos (c+d x))}{a^3 d}-\frac{x}{a^3}","\frac{2 i}{d \left(a^3+i a^3 \tan (c+d x)\right)}-\frac{i \log (\cos (c+d x))}{a^3 d}-\frac{x}{a^3}",1,"-(x/a^3) - (I*Log[Cos[c + d*x]])/(a^3*d) + (2*I)/(d*(a^3 + I*a^3*Tan[c + d*x]))","A",3,2,24,0.08333,1,"{3487, 43}"
136,1,27,0,0.0531279,"\int \frac{\sec ^2(c+d x)}{(a+i a \tan (c+d x))^3} \, dx","Int[Sec[c + d*x]^2/(a + I*a*Tan[c + d*x])^3,x]","\frac{i}{2 a d (a+i a \tan (c+d x))^2}","\frac{i}{2 a d (a+i a \tan (c+d x))^2}",1,"(I/2)/(a*d*(a + I*a*Tan[c + d*x])^2)","A",2,2,24,0.08333,1,"{3487, 32}"
137,1,88,0,0.0470442,"\int \frac{1}{(a+i a \tan (c+d x))^3} \, dx","Int[(a + I*a*Tan[c + d*x])^(-3),x]","\frac{i}{8 d \left(a^3+i a^3 \tan (c+d x)\right)}+\frac{x}{8 a^3}+\frac{i}{8 a d (a+i a \tan (c+d x))^2}+\frac{i}{6 d (a+i a \tan (c+d x))^3}","\frac{i}{8 d \left(a^3+i a^3 \tan (c+d x)\right)}+\frac{x}{8 a^3}+\frac{i}{8 a d (a+i a \tan (c+d x))^2}+\frac{i}{6 d (a+i a \tan (c+d x))^3}",1,"x/(8*a^3) + (I/6)/(d*(a + I*a*Tan[c + d*x])^3) + (I/8)/(a*d*(a + I*a*Tan[c + d*x])^2) + (I/8)/(d*(a^3 + I*a^3*Tan[c + d*x]))","A",4,2,15,0.1333,1,"{3479, 8}"
138,1,141,0,0.0861982,"\int \frac{\cos ^2(c+d x)}{(a+i a \tan (c+d x))^3} \, dx","Int[Cos[c + d*x]^2/(a + I*a*Tan[c + d*x])^3,x]","-\frac{i}{32 d \left(a^3-i a^3 \tan (c+d x)\right)}+\frac{i}{8 d \left(a^3+i a^3 \tan (c+d x)\right)}+\frac{5 x}{32 a^3}+\frac{i a}{16 d (a+i a \tan (c+d x))^4}+\frac{i}{12 d (a+i a \tan (c+d x))^3}+\frac{3 i}{32 a d (a+i a \tan (c+d x))^2}","-\frac{i}{32 d \left(a^3-i a^3 \tan (c+d x)\right)}+\frac{i}{8 d \left(a^3+i a^3 \tan (c+d x)\right)}+\frac{5 x}{32 a^3}+\frac{i a}{16 d (a+i a \tan (c+d x))^4}+\frac{i}{12 d (a+i a \tan (c+d x))^3}+\frac{3 i}{32 a d (a+i a \tan (c+d x))^2}",1,"(5*x)/(32*a^3) + ((I/16)*a)/(d*(a + I*a*Tan[c + d*x])^4) + (I/12)/(d*(a + I*a*Tan[c + d*x])^3) + ((3*I)/32)/(a*d*(a + I*a*Tan[c + d*x])^2) - (I/32)/(d*(a^3 - I*a^3*Tan[c + d*x])) + (I/8)/(d*(a^3 + I*a^3*Tan[c + d*x]))","A",4,3,24,0.1250,1,"{3487, 44, 206}"
139,1,195,0,0.1161336,"\int \frac{\cos ^4(c+d x)}{(a+i a \tan (c+d x))^3} \, dx","Int[Cos[c + d*x]^4/(a + I*a*Tan[c + d*x])^3,x]","\frac{i a^2}{40 d (a+i a \tan (c+d x))^5}-\frac{3 i}{64 d \left(a^3-i a^3 \tan (c+d x)\right)}+\frac{15 i}{128 d \left(a^3+i a^3 \tan (c+d x)\right)}+\frac{21 x}{128 a^3}+\frac{3 i a}{64 d (a+i a \tan (c+d x))^4}+\frac{i}{16 d (a+i a \tan (c+d x))^3}-\frac{i}{128 a d (a-i a \tan (c+d x))^2}+\frac{5 i}{64 a d (a+i a \tan (c+d x))^2}","\frac{i a^2}{40 d (a+i a \tan (c+d x))^5}-\frac{3 i}{64 d \left(a^3-i a^3 \tan (c+d x)\right)}+\frac{15 i}{128 d \left(a^3+i a^3 \tan (c+d x)\right)}+\frac{21 x}{128 a^3}+\frac{3 i a}{64 d (a+i a \tan (c+d x))^4}+\frac{i}{16 d (a+i a \tan (c+d x))^3}-\frac{i}{128 a d (a-i a \tan (c+d x))^2}+\frac{5 i}{64 a d (a+i a \tan (c+d x))^2}",1,"(21*x)/(128*a^3) - (I/128)/(a*d*(a - I*a*Tan[c + d*x])^2) + ((I/40)*a^2)/(d*(a + I*a*Tan[c + d*x])^5) + (((3*I)/64)*a)/(d*(a + I*a*Tan[c + d*x])^4) + (I/16)/(d*(a + I*a*Tan[c + d*x])^3) + ((5*I)/64)/(a*d*(a + I*a*Tan[c + d*x])^2) - ((3*I)/64)/(d*(a^3 - I*a^3*Tan[c + d*x])) + ((15*I)/128)/(d*(a^3 + I*a^3*Tan[c + d*x]))","A",4,3,24,0.1250,1,"{3487, 44, 206}"
140,1,119,0,0.1149831,"\int \frac{\sec ^9(c+d x)}{(a+i a \tan (c+d x))^3} \, dx","Int[Sec[c + d*x]^9/(a + I*a*Tan[c + d*x])^3,x]","-\frac{7 i \sec ^5(c+d x)}{15 a^3 d}+\frac{7 \tanh ^{-1}(\sin (c+d x))}{8 a^3 d}+\frac{7 \tan (c+d x) \sec ^3(c+d x)}{12 a^3 d}+\frac{7 \tan (c+d x) \sec (c+d x)}{8 a^3 d}-\frac{2 i \sec ^7(c+d x)}{3 a d (a+i a \tan (c+d x))^2}","-\frac{7 i \sec ^5(c+d x)}{15 a^3 d}+\frac{7 \tanh ^{-1}(\sin (c+d x))}{8 a^3 d}+\frac{7 \tan (c+d x) \sec ^3(c+d x)}{12 a^3 d}+\frac{7 \tan (c+d x) \sec (c+d x)}{8 a^3 d}-\frac{2 i \sec ^7(c+d x)}{3 a d (a+i a \tan (c+d x))^2}",1,"(7*ArcTanh[Sin[c + d*x]])/(8*a^3*d) - (((7*I)/15)*Sec[c + d*x]^5)/(a^3*d) + (7*Sec[c + d*x]*Tan[c + d*x])/(8*a^3*d) + (7*Sec[c + d*x]^3*Tan[c + d*x])/(12*a^3*d) - (((2*I)/3)*Sec[c + d*x]^7)/(a*d*(a + I*a*Tan[c + d*x])^2)","A",5,4,24,0.1667,1,"{3500, 3501, 3768, 3770}"
141,1,93,0,0.0981361,"\int \frac{\sec ^7(c+d x)}{(a+i a \tan (c+d x))^3} \, dx","Int[Sec[c + d*x]^7/(a + I*a*Tan[c + d*x])^3,x]","-\frac{5 i \sec ^3(c+d x)}{3 a^3 d}+\frac{5 \tanh ^{-1}(\sin (c+d x))}{2 a^3 d}+\frac{5 \tan (c+d x) \sec (c+d x)}{2 a^3 d}-\frac{2 i \sec ^5(c+d x)}{a d (a+i a \tan (c+d x))^2}","-\frac{5 i \sec ^3(c+d x)}{3 a^3 d}+\frac{5 \tanh ^{-1}(\sin (c+d x))}{2 a^3 d}+\frac{5 \tan (c+d x) \sec (c+d x)}{2 a^3 d}-\frac{2 i \sec ^5(c+d x)}{a d (a+i a \tan (c+d x))^2}",1,"(5*ArcTanh[Sin[c + d*x]])/(2*a^3*d) - (((5*I)/3)*Sec[c + d*x]^3)/(a^3*d) + (5*Sec[c + d*x]*Tan[c + d*x])/(2*a^3*d) - ((2*I)*Sec[c + d*x]^5)/(a*d*(a + I*a*Tan[c + d*x])^2)","A",4,4,24,0.1667,1,"{3500, 3501, 3768, 3770}"
142,1,65,0,0.0850484,"\int \frac{\sec ^5(c+d x)}{(a+i a \tan (c+d x))^3} \, dx","Int[Sec[c + d*x]^5/(a + I*a*Tan[c + d*x])^3,x]","\frac{3 i \sec (c+d x)}{a^3 d}-\frac{3 \tanh ^{-1}(\sin (c+d x))}{a^3 d}+\frac{2 i \sec ^3(c+d x)}{a d (a+i a \tan (c+d x))^2}","\frac{3 i \sec (c+d x)}{a^3 d}-\frac{3 \tanh ^{-1}(\sin (c+d x))}{a^3 d}+\frac{2 i \sec ^3(c+d x)}{a d (a+i a \tan (c+d x))^2}",1,"(-3*ArcTanh[Sin[c + d*x]])/(a^3*d) + ((3*I)*Sec[c + d*x])/(a^3*d) + ((2*I)*Sec[c + d*x]^3)/(a*d*(a + I*a*Tan[c + d*x])^2)","A",3,3,24,0.1250,1,"{3500, 3501, 3770}"
143,1,32,0,0.0372742,"\int \frac{\sec ^3(c+d x)}{(a+i a \tan (c+d x))^3} \, dx","Int[Sec[c + d*x]^3/(a + I*a*Tan[c + d*x])^3,x]","\frac{i \sec ^3(c+d x)}{3 d (a+i a \tan (c+d x))^3}","\frac{i \sec ^3(c+d x)}{3 d (a+i a \tan (c+d x))^3}",1,"((I/3)*Sec[c + d*x]^3)/(d*(a + I*a*Tan[c + d*x])^3)","A",1,1,24,0.04167,1,"{3488}"
144,1,98,0,0.0766288,"\int \frac{\sec (c+d x)}{(a+i a \tan (c+d x))^3} \, dx","Int[Sec[c + d*x]/(a + I*a*Tan[c + d*x])^3,x]","\frac{2 i \sec (c+d x)}{15 d \left(a^3+i a^3 \tan (c+d x)\right)}+\frac{2 i \sec (c+d x)}{15 a d (a+i a \tan (c+d x))^2}+\frac{i \sec (c+d x)}{5 d (a+i a \tan (c+d x))^3}","\frac{2 i \sec (c+d x)}{15 d \left(a^3+i a^3 \tan (c+d x)\right)}+\frac{2 i \sec (c+d x)}{15 a d (a+i a \tan (c+d x))^2}+\frac{i \sec (c+d x)}{5 d (a+i a \tan (c+d x))^3}",1,"((I/5)*Sec[c + d*x])/(d*(a + I*a*Tan[c + d*x])^3) + (((2*I)/15)*Sec[c + d*x])/(a*d*(a + I*a*Tan[c + d*x])^2) + (((2*I)/15)*Sec[c + d*x])/(d*(a^3 + I*a^3*Tan[c + d*x]))","A",3,2,22,0.09091,1,"{3502, 3488}"
145,1,101,0,0.0810969,"\int \frac{\cos (c+d x)}{(a+i a \tan (c+d x))^3} \, dx","Int[Cos[c + d*x]/(a + I*a*Tan[c + d*x])^3,x]","-\frac{4 \sin ^3(c+d x)}{35 a^3 d}+\frac{12 \sin (c+d x)}{35 a^3 d}+\frac{8 i \cos ^3(c+d x)}{35 d \left(a^3+i a^3 \tan (c+d x)\right)}+\frac{i \cos (c+d x)}{7 d (a+i a \tan (c+d x))^3}","-\frac{4 \sin ^3(c+d x)}{35 a^3 d}+\frac{12 \sin (c+d x)}{35 a^3 d}+\frac{8 i \cos ^3(c+d x)}{35 d \left(a^3+i a^3 \tan (c+d x)\right)}+\frac{i \cos (c+d x)}{7 d (a+i a \tan (c+d x))^3}",1,"(12*Sin[c + d*x])/(35*a^3*d) - (4*Sin[c + d*x]^3)/(35*a^3*d) + ((I/7)*Cos[c + d*x])/(d*(a + I*a*Tan[c + d*x])^3) + (((8*I)/35)*Cos[c + d*x]^3)/(d*(a^3 + I*a^3*Tan[c + d*x]))","A",4,3,22,0.1364,1,"{3502, 3500, 2633}"
146,1,121,0,0.1133803,"\int \frac{\cos ^3(c+d x)}{(a+i a \tan (c+d x))^3} \, dx","Int[Cos[c + d*x]^3/(a + I*a*Tan[c + d*x])^3,x]","\frac{2 \sin ^5(c+d x)}{21 a^3 d}-\frac{20 \sin ^3(c+d x)}{63 a^3 d}+\frac{10 \sin (c+d x)}{21 a^3 d}+\frac{4 i \cos ^5(c+d x)}{21 d \left(a^3+i a^3 \tan (c+d x)\right)}+\frac{i \cos ^3(c+d x)}{9 d (a+i a \tan (c+d x))^3}","\frac{2 \sin ^5(c+d x)}{21 a^3 d}-\frac{20 \sin ^3(c+d x)}{63 a^3 d}+\frac{10 \sin (c+d x)}{21 a^3 d}+\frac{4 i \cos ^5(c+d x)}{21 d \left(a^3+i a^3 \tan (c+d x)\right)}+\frac{i \cos ^3(c+d x)}{9 d (a+i a \tan (c+d x))^3}",1,"(10*Sin[c + d*x])/(21*a^3*d) - (20*Sin[c + d*x]^3)/(63*a^3*d) + (2*Sin[c + d*x]^5)/(21*a^3*d) + ((I/9)*Cos[c + d*x]^3)/(d*(a + I*a*Tan[c + d*x])^3) + (((4*I)/21)*Cos[c + d*x]^5)/(d*(a^3 + I*a^3*Tan[c + d*x]))","A",4,3,24,0.1250,1,"{3502, 3500, 2633}"
147,1,139,0,0.1166757,"\int \frac{\cos ^5(c+d x)}{(a+i a \tan (c+d x))^3} \, dx","Int[Cos[c + d*x]^5/(a + I*a*Tan[c + d*x])^3,x]","-\frac{8 \sin ^7(c+d x)}{99 a^3 d}+\frac{56 \sin ^5(c+d x)}{165 a^3 d}-\frac{56 \sin ^3(c+d x)}{99 a^3 d}+\frac{56 \sin (c+d x)}{99 a^3 d}+\frac{16 i \cos ^7(c+d x)}{99 d \left(a^3+i a^3 \tan (c+d x)\right)}+\frac{i \cos ^5(c+d x)}{11 d (a+i a \tan (c+d x))^3}","-\frac{8 \sin ^7(c+d x)}{99 a^3 d}+\frac{56 \sin ^5(c+d x)}{165 a^3 d}-\frac{56 \sin ^3(c+d x)}{99 a^3 d}+\frac{56 \sin (c+d x)}{99 a^3 d}+\frac{16 i \cos ^7(c+d x)}{99 d \left(a^3+i a^3 \tan (c+d x)\right)}+\frac{i \cos ^5(c+d x)}{11 d (a+i a \tan (c+d x))^3}",1,"(56*Sin[c + d*x])/(99*a^3*d) - (56*Sin[c + d*x]^3)/(99*a^3*d) + (56*Sin[c + d*x]^5)/(165*a^3*d) - (8*Sin[c + d*x]^7)/(99*a^3*d) + ((I/11)*Cos[c + d*x]^5)/(d*(a + I*a*Tan[c + d*x])^3) + (((16*I)/99)*Cos[c + d*x]^7)/(d*(a^3 + I*a^3*Tan[c + d*x]))","A",4,3,24,0.1250,1,"{3502, 3500, 2633}"
148,1,82,0,0.0636081,"\int \frac{\sec ^{14}(c+d x)}{(a+i a \tan (c+d x))^4} \, dx","Int[Sec[c + d*x]^14/(a + I*a*Tan[c + d*x])^4,x]","\frac{i (a-i a \tan (c+d x))^9}{9 a^{13} d}-\frac{i (a-i a \tan (c+d x))^8}{2 a^{12} d}+\frac{4 i (a-i a \tan (c+d x))^7}{7 a^{11} d}","\frac{i (a-i a \tan (c+d x))^9}{9 a^{13} d}-\frac{i (a-i a \tan (c+d x))^8}{2 a^{12} d}+\frac{4 i (a-i a \tan (c+d x))^7}{7 a^{11} d}",1,"(((4*I)/7)*(a - I*a*Tan[c + d*x])^7)/(a^11*d) - ((I/2)*(a - I*a*Tan[c + d*x])^8)/(a^12*d) + ((I/9)*(a - I*a*Tan[c + d*x])^9)/(a^13*d)","A",3,2,24,0.08333,1,"{3487, 43}"
149,1,55,0,0.0472249,"\int \frac{\sec ^{12}(c+d x)}{(a+i a \tan (c+d x))^4} \, dx","Int[Sec[c + d*x]^12/(a + I*a*Tan[c + d*x])^4,x]","\frac{i (a-i a \tan (c+d x))^6}{3 a^{10} d}-\frac{i (a-i a \tan (c+d x))^7}{7 a^{11} d}","\frac{i (a-i a \tan (c+d x))^6}{3 a^{10} d}-\frac{i (a-i a \tan (c+d x))^7}{7 a^{11} d}",1,"((I/3)*(a - I*a*Tan[c + d*x])^6)/(a^10*d) - ((I/7)*(a - I*a*Tan[c + d*x])^7)/(a^11*d)","A",3,2,24,0.08333,1,"{3487, 43}"
150,1,27,0,0.0400154,"\int \frac{\sec ^{10}(c+d x)}{(a+i a \tan (c+d x))^4} \, dx","Int[Sec[c + d*x]^10/(a + I*a*Tan[c + d*x])^4,x]","\frac{i (a-i a \tan (c+d x))^5}{5 a^9 d}","\frac{i (a-i a \tan (c+d x))^5}{5 a^9 d}",1,"((I/5)*(a - I*a*Tan[c + d*x])^5)/(a^9*d)","A",2,2,24,0.08333,1,"{3487, 32}"
151,1,90,0,0.0560963,"\int \frac{\sec ^8(c+d x)}{(a+i a \tan (c+d x))^4} \, dx","Int[Sec[c + d*x]^8/(a + I*a*Tan[c + d*x])^4,x]","-\frac{i (a-i a \tan (c+d x))^3}{3 a^7 d}-\frac{i (a-i a \tan (c+d x))^2}{a^6 d}-\frac{4 \tan (c+d x)}{a^4 d}+\frac{8 i \log (\cos (c+d x))}{a^4 d}+\frac{8 x}{a^4}","-\frac{i (a-i a \tan (c+d x))^3}{3 a^7 d}-\frac{i (a-i a \tan (c+d x))^2}{a^6 d}-\frac{4 \tan (c+d x)}{a^4 d}+\frac{8 i \log (\cos (c+d x))}{a^4 d}+\frac{8 x}{a^4}",1,"(8*x)/a^4 + ((8*I)*Log[Cos[c + d*x]])/(a^4*d) - (4*Tan[c + d*x])/(a^4*d) - (I*(a - I*a*Tan[c + d*x])^2)/(a^6*d) - ((I/3)*(a - I*a*Tan[c + d*x])^3)/(a^7*d)","A",3,2,24,0.08333,1,"{3487, 43}"
152,1,63,0,0.053086,"\int \frac{\sec ^6(c+d x)}{(a+i a \tan (c+d x))^4} \, dx","Int[Sec[c + d*x]^6/(a + I*a*Tan[c + d*x])^4,x]","\frac{\tan (c+d x)}{a^4 d}+\frac{4 i}{d \left(a^4+i a^4 \tan (c+d x)\right)}-\frac{4 i \log (\cos (c+d x))}{a^4 d}-\frac{4 x}{a^4}","\frac{\tan (c+d x)}{a^4 d}+\frac{4 i}{d \left(a^4+i a^4 \tan (c+d x)\right)}-\frac{4 i \log (\cos (c+d x))}{a^4 d}-\frac{4 x}{a^4}",1,"(-4*x)/a^4 - ((4*I)*Log[Cos[c + d*x]])/(a^4*d) + Tan[c + d*x]/(a^4*d) + (4*I)/(d*(a^4 + I*a^4*Tan[c + d*x]))","A",3,2,24,0.08333,1,"{3487, 43}"
153,1,29,0,0.0412489,"\int \frac{\sec ^4(c+d x)}{(a+i a \tan (c+d x))^4} \, dx","Int[Sec[c + d*x]^4/(a + I*a*Tan[c + d*x])^4,x]","\frac{\tan (c+d x)}{d \left(a^2+i a^2 \tan (c+d x)\right)^2}","\frac{\tan (c+d x)}{d \left(a^2+i a^2 \tan (c+d x)\right)^2}",1,"Tan[c + d*x]/(d*(a^2 + I*a^2*Tan[c + d*x])^2)","A",2,2,24,0.08333,1,"{3487, 34}"
154,1,27,0,0.039359,"\int \frac{\sec ^2(c+d x)}{(a+i a \tan (c+d x))^4} \, dx","Int[Sec[c + d*x]^2/(a + I*a*Tan[c + d*x])^4,x]","\frac{i}{3 a d (a+i a \tan (c+d x))^3}","\frac{i}{3 a d (a+i a \tan (c+d x))^3}",1,"(I/3)/(a*d*(a + I*a*Tan[c + d*x])^3)","A",2,2,24,0.08333,1,"{3487, 32}"
155,1,116,0,0.0620533,"\int \frac{1}{(a+i a \tan (c+d x))^4} \, dx","Int[(a + I*a*Tan[c + d*x])^(-4),x]","\frac{i}{16 d \left(a^4+i a^4 \tan (c+d x)\right)}+\frac{i}{16 d \left(a^2+i a^2 \tan (c+d x)\right)^2}+\frac{x}{16 a^4}+\frac{i}{12 a d (a+i a \tan (c+d x))^3}+\frac{i}{8 d (a+i a \tan (c+d x))^4}","\frac{i}{16 d \left(a^4+i a^4 \tan (c+d x)\right)}+\frac{i}{16 d \left(a^2+i a^2 \tan (c+d x)\right)^2}+\frac{x}{16 a^4}+\frac{i}{12 a d (a+i a \tan (c+d x))^3}+\frac{i}{8 d (a+i a \tan (c+d x))^4}",1,"x/(16*a^4) + (I/8)/(d*(a + I*a*Tan[c + d*x])^4) + (I/12)/(a*d*(a + I*a*Tan[c + d*x])^3) + (I/16)/(d*(a^2 + I*a^2*Tan[c + d*x])^2) + (I/16)/(d*(a^4 + I*a^4*Tan[c + d*x]))","A",5,2,15,0.1333,1,"{3479, 8}"
156,1,169,0,0.0964324,"\int \frac{\cos ^2(c+d x)}{(a+i a \tan (c+d x))^4} \, dx","Int[Cos[c + d*x]^2/(a + I*a*Tan[c + d*x])^4,x]","-\frac{i}{64 d \left(a^4-i a^4 \tan (c+d x)\right)}+\frac{5 i}{64 d \left(a^4+i a^4 \tan (c+d x)\right)}+\frac{i}{16 d \left(a^2+i a^2 \tan (c+d x)\right)^2}+\frac{3 x}{32 a^4}+\frac{i a}{20 d (a+i a \tan (c+d x))^5}+\frac{i}{16 d (a+i a \tan (c+d x))^4}+\frac{i}{16 a d (a+i a \tan (c+d x))^3}","-\frac{i}{64 d \left(a^4-i a^4 \tan (c+d x)\right)}+\frac{5 i}{64 d \left(a^4+i a^4 \tan (c+d x)\right)}+\frac{i}{16 d \left(a^2+i a^2 \tan (c+d x)\right)^2}+\frac{3 x}{32 a^4}+\frac{i a}{20 d (a+i a \tan (c+d x))^5}+\frac{i}{16 d (a+i a \tan (c+d x))^4}+\frac{i}{16 a d (a+i a \tan (c+d x))^3}",1,"(3*x)/(32*a^4) + ((I/20)*a)/(d*(a + I*a*Tan[c + d*x])^5) + (I/16)/(d*(a + I*a*Tan[c + d*x])^4) + (I/16)/(a*d*(a + I*a*Tan[c + d*x])^3) + (I/16)/(d*(a^2 + I*a^2*Tan[c + d*x])^2) - (I/64)/(d*(a^4 - I*a^4*Tan[c + d*x])) + ((5*I)/64)/(d*(a^4 + I*a^4*Tan[c + d*x]))","A",4,3,24,0.1250,1,"{3487, 44, 206}"
157,1,224,0,0.1248974,"\int \frac{\cos ^4(c+d x)}{(a+i a \tan (c+d x))^4} \, dx","Int[Cos[c + d*x]^4/(a + I*a*Tan[c + d*x])^4,x]","\frac{i a^2}{48 d (a+i a \tan (c+d x))^6}-\frac{7 i}{256 d \left(a^4-i a^4 \tan (c+d x)\right)}+\frac{21 i}{256 d \left(a^4+i a^4 \tan (c+d x)\right)}-\frac{i}{256 d \left(a^2-i a^2 \tan (c+d x)\right)^2}+\frac{15 i}{256 d \left(a^2+i a^2 \tan (c+d x)\right)^2}+\frac{7 x}{64 a^4}+\frac{3 i a}{80 d (a+i a \tan (c+d x))^5}+\frac{3 i}{64 d (a+i a \tan (c+d x))^4}+\frac{5 i}{96 a d (a+i a \tan (c+d x))^3}","\frac{i a^2}{48 d (a+i a \tan (c+d x))^6}-\frac{7 i}{256 d \left(a^4-i a^4 \tan (c+d x)\right)}+\frac{21 i}{256 d \left(a^4+i a^4 \tan (c+d x)\right)}-\frac{i}{256 d \left(a^2-i a^2 \tan (c+d x)\right)^2}+\frac{15 i}{256 d \left(a^2+i a^2 \tan (c+d x)\right)^2}+\frac{7 x}{64 a^4}+\frac{3 i a}{80 d (a+i a \tan (c+d x))^5}+\frac{3 i}{64 d (a+i a \tan (c+d x))^4}+\frac{5 i}{96 a d (a+i a \tan (c+d x))^3}",1,"(7*x)/(64*a^4) + ((I/48)*a^2)/(d*(a + I*a*Tan[c + d*x])^6) + (((3*I)/80)*a)/(d*(a + I*a*Tan[c + d*x])^5) + ((3*I)/64)/(d*(a + I*a*Tan[c + d*x])^4) + ((5*I)/96)/(a*d*(a + I*a*Tan[c + d*x])^3) - (I/256)/(d*(a^2 - I*a^2*Tan[c + d*x])^2) + ((15*I)/256)/(d*(a^2 + I*a^2*Tan[c + d*x])^2) - ((7*I)/256)/(d*(a^4 - I*a^4*Tan[c + d*x])) + ((21*I)/256)/(d*(a^4 + I*a^4*Tan[c + d*x]))","A",4,3,24,0.1250,1,"{3487, 44, 206}"
158,1,133,0,0.1143465,"\int \frac{\sec ^9(c+d x)}{(a+i a \tan (c+d x))^4} \, dx","Int[Sec[c + d*x]^9/(a + I*a*Tan[c + d*x])^4,x]","\frac{35 \tanh ^{-1}(\sin (c+d x))}{8 a^4 d}-\frac{14 i \sec ^5(c+d x)}{3 d \left(a^4+i a^4 \tan (c+d x)\right)}+\frac{35 \tan (c+d x) \sec ^3(c+d x)}{12 a^4 d}+\frac{35 \tan (c+d x) \sec (c+d x)}{8 a^4 d}-\frac{2 i \sec ^7(c+d x)}{a d (a+i a \tan (c+d x))^3}","\frac{35 \tanh ^{-1}(\sin (c+d x))}{8 a^4 d}-\frac{14 i \sec ^5(c+d x)}{3 d \left(a^4+i a^4 \tan (c+d x)\right)}+\frac{35 \tan (c+d x) \sec ^3(c+d x)}{12 a^4 d}+\frac{35 \tan (c+d x) \sec (c+d x)}{8 a^4 d}-\frac{2 i \sec ^7(c+d x)}{a d (a+i a \tan (c+d x))^3}",1,"(35*ArcTanh[Sin[c + d*x]])/(8*a^4*d) + (35*Sec[c + d*x]*Tan[c + d*x])/(8*a^4*d) + (35*Sec[c + d*x]^3*Tan[c + d*x])/(12*a^4*d) - ((2*I)*Sec[c + d*x]^7)/(a*d*(a + I*a*Tan[c + d*x])^3) - (((14*I)/3)*Sec[c + d*x]^5)/(d*(a^4 + I*a^4*Tan[c + d*x]))","A",5,3,24,0.1250,1,"{3500, 3768, 3770}"
159,1,107,0,0.1008981,"\int \frac{\sec ^7(c+d x)}{(a+i a \tan (c+d x))^4} \, dx","Int[Sec[c + d*x]^7/(a + I*a*Tan[c + d*x])^4,x]","-\frac{15 \tanh ^{-1}(\sin (c+d x))}{2 a^4 d}+\frac{10 i \sec ^3(c+d x)}{d \left(a^4+i a^4 \tan (c+d x)\right)}-\frac{15 \tan (c+d x) \sec (c+d x)}{2 a^4 d}+\frac{2 i \sec ^5(c+d x)}{a d (a+i a \tan (c+d x))^3}","-\frac{15 \tanh ^{-1}(\sin (c+d x))}{2 a^4 d}+\frac{10 i \sec ^3(c+d x)}{d \left(a^4+i a^4 \tan (c+d x)\right)}-\frac{15 \tan (c+d x) \sec (c+d x)}{2 a^4 d}+\frac{2 i \sec ^5(c+d x)}{a d (a+i a \tan (c+d x))^3}",1,"(-15*ArcTanh[Sin[c + d*x]])/(2*a^4*d) - (15*Sec[c + d*x]*Tan[c + d*x])/(2*a^4*d) + ((2*I)*Sec[c + d*x]^5)/(a*d*(a + I*a*Tan[c + d*x])^3) + ((10*I)*Sec[c + d*x]^3)/(d*(a^4 + I*a^4*Tan[c + d*x]))","A",4,3,24,0.1250,1,"{3500, 3768, 3770}"
160,1,82,0,0.0866693,"\int \frac{\sec ^5(c+d x)}{(a+i a \tan (c+d x))^4} \, dx","Int[Sec[c + d*x]^5/(a + I*a*Tan[c + d*x])^4,x]","\frac{\tanh ^{-1}(\sin (c+d x))}{a^4 d}-\frac{2 i \sec (c+d x)}{d \left(a^4+i a^4 \tan (c+d x)\right)}+\frac{2 i \sec ^3(c+d x)}{3 a d (a+i a \tan (c+d x))^3}","\frac{\tanh ^{-1}(\sin (c+d x))}{a^4 d}-\frac{2 i \sec (c+d x)}{d \left(a^4+i a^4 \tan (c+d x)\right)}+\frac{2 i \sec ^3(c+d x)}{3 a d (a+i a \tan (c+d x))^3}",1,"ArcTanh[Sin[c + d*x]]/(a^4*d) + (((2*I)/3)*Sec[c + d*x]^3)/(a*d*(a + I*a*Tan[c + d*x])^3) - ((2*I)*Sec[c + d*x])/(d*(a^4 + I*a^4*Tan[c + d*x]))","A",3,2,24,0.08333,1,"{3500, 3770}"
161,1,68,0,0.0793596,"\int \frac{\sec ^3(c+d x)}{(a+i a \tan (c+d x))^4} \, dx","Int[Sec[c + d*x]^3/(a + I*a*Tan[c + d*x])^4,x]","\frac{i \sec ^3(c+d x)}{15 a d (a+i a \tan (c+d x))^3}+\frac{i \sec ^3(c+d x)}{5 d (a+i a \tan (c+d x))^4}","\frac{i \sec ^3(c+d x)}{15 a d (a+i a \tan (c+d x))^3}+\frac{i \sec ^3(c+d x)}{5 d (a+i a \tan (c+d x))^4}",1,"((I/5)*Sec[c + d*x]^3)/(d*(a + I*a*Tan[c + d*x])^4) + ((I/15)*Sec[c + d*x]^3)/(a*d*(a + I*a*Tan[c + d*x])^3)","A",2,2,24,0.08333,1,"{3502, 3488}"
162,1,132,0,0.10815,"\int \frac{\sec (c+d x)}{(a+i a \tan (c+d x))^4} \, dx","Int[Sec[c + d*x]/(a + I*a*Tan[c + d*x])^4,x]","\frac{2 i \sec (c+d x)}{35 d \left(a^4+i a^4 \tan (c+d x)\right)}+\frac{2 i \sec (c+d x)}{35 d \left(a^2+i a^2 \tan (c+d x)\right)^2}+\frac{3 i \sec (c+d x)}{35 a d (a+i a \tan (c+d x))^3}+\frac{i \sec (c+d x)}{7 d (a+i a \tan (c+d x))^4}","\frac{2 i \sec (c+d x)}{35 d \left(a^4+i a^4 \tan (c+d x)\right)}+\frac{2 i \sec (c+d x)}{35 d \left(a^2+i a^2 \tan (c+d x)\right)^2}+\frac{3 i \sec (c+d x)}{35 a d (a+i a \tan (c+d x))^3}+\frac{i \sec (c+d x)}{7 d (a+i a \tan (c+d x))^4}",1,"((I/7)*Sec[c + d*x])/(d*(a + I*a*Tan[c + d*x])^4) + (((3*I)/35)*Sec[c + d*x])/(a*d*(a + I*a*Tan[c + d*x])^3) + (((2*I)/35)*Sec[c + d*x])/(d*(a^2 + I*a^2*Tan[c + d*x])^2) + (((2*I)/35)*Sec[c + d*x])/(d*(a^4 + I*a^4*Tan[c + d*x]))","A",4,2,22,0.09091,1,"{3502, 3488}"
163,1,134,0,0.1203341,"\int \frac{\cos (c+d x)}{(a+i a \tan (c+d x))^4} \, dx","Int[Cos[c + d*x]/(a + I*a*Tan[c + d*x])^4,x]","-\frac{4 \sin ^3(c+d x)}{63 a^4 d}+\frac{4 \sin (c+d x)}{21 a^4 d}+\frac{8 i \cos ^3(c+d x)}{63 d \left(a^4+i a^4 \tan (c+d x)\right)}+\frac{5 i \cos (c+d x)}{63 a d (a+i a \tan (c+d x))^3}+\frac{i \cos (c+d x)}{9 d (a+i a \tan (c+d x))^4}","-\frac{4 \sin ^3(c+d x)}{63 a^4 d}+\frac{4 \sin (c+d x)}{21 a^4 d}+\frac{8 i \cos ^3(c+d x)}{63 d \left(a^4+i a^4 \tan (c+d x)\right)}+\frac{5 i \cos (c+d x)}{63 a d (a+i a \tan (c+d x))^3}+\frac{i \cos (c+d x)}{9 d (a+i a \tan (c+d x))^4}",1,"(4*Sin[c + d*x])/(21*a^4*d) - (4*Sin[c + d*x]^3)/(63*a^4*d) + ((I/9)*Cos[c + d*x])/(d*(a + I*a*Tan[c + d*x])^4) + (((5*I)/63)*Cos[c + d*x])/(a*d*(a + I*a*Tan[c + d*x])^3) + (((8*I)/63)*Cos[c + d*x]^3)/(d*(a^4 + I*a^4*Tan[c + d*x]))","A",5,3,22,0.1364,1,"{3502, 3500, 2633}"
164,1,156,0,0.1475371,"\int \frac{\cos ^3(c+d x)}{(a+i a \tan (c+d x))^4} \, dx","Int[Cos[c + d*x]^3/(a + I*a*Tan[c + d*x])^4,x]","\frac{2 \sin ^5(c+d x)}{33 a^4 d}-\frac{20 \sin ^3(c+d x)}{99 a^4 d}+\frac{10 \sin (c+d x)}{33 a^4 d}+\frac{4 i \cos ^5(c+d x)}{33 d \left(a^4+i a^4 \tan (c+d x)\right)}+\frac{7 i \cos ^3(c+d x)}{99 a d (a+i a \tan (c+d x))^3}+\frac{i \cos ^3(c+d x)}{11 d (a+i a \tan (c+d x))^4}","\frac{2 \sin ^5(c+d x)}{33 a^4 d}-\frac{20 \sin ^3(c+d x)}{99 a^4 d}+\frac{10 \sin (c+d x)}{33 a^4 d}+\frac{4 i \cos ^5(c+d x)}{33 d \left(a^4+i a^4 \tan (c+d x)\right)}+\frac{7 i \cos ^3(c+d x)}{99 a d (a+i a \tan (c+d x))^3}+\frac{i \cos ^3(c+d x)}{11 d (a+i a \tan (c+d x))^4}",1,"(10*Sin[c + d*x])/(33*a^4*d) - (20*Sin[c + d*x]^3)/(99*a^4*d) + (2*Sin[c + d*x]^5)/(33*a^4*d) + ((I/11)*Cos[c + d*x]^3)/(d*(a + I*a*Tan[c + d*x])^4) + (((7*I)/99)*Cos[c + d*x]^3)/(a*d*(a + I*a*Tan[c + d*x])^3) + (((4*I)/33)*Cos[c + d*x]^5)/(d*(a^4 + I*a^4*Tan[c + d*x]))","A",5,3,24,0.1250,1,"{3502, 3500, 2633}"
165,1,174,0,0.158102,"\int \frac{\cos ^5(c+d x)}{(a+i a \tan (c+d x))^4} \, dx","Int[Cos[c + d*x]^5/(a + I*a*Tan[c + d*x])^4,x]","-\frac{8 \sin ^7(c+d x)}{143 a^4 d}+\frac{168 \sin ^5(c+d x)}{715 a^4 d}-\frac{56 \sin ^3(c+d x)}{143 a^4 d}+\frac{56 \sin (c+d x)}{143 a^4 d}+\frac{16 i \cos ^7(c+d x)}{143 d \left(a^4+i a^4 \tan (c+d x)\right)}+\frac{9 i \cos ^5(c+d x)}{143 a d (a+i a \tan (c+d x))^3}+\frac{i \cos ^5(c+d x)}{13 d (a+i a \tan (c+d x))^4}","-\frac{8 \sin ^7(c+d x)}{143 a^4 d}+\frac{168 \sin ^5(c+d x)}{715 a^4 d}-\frac{56 \sin ^3(c+d x)}{143 a^4 d}+\frac{56 \sin (c+d x)}{143 a^4 d}+\frac{16 i \cos ^7(c+d x)}{143 d \left(a^4+i a^4 \tan (c+d x)\right)}+\frac{9 i \cos ^5(c+d x)}{143 a d (a+i a \tan (c+d x))^3}+\frac{i \cos ^5(c+d x)}{13 d (a+i a \tan (c+d x))^4}",1,"(56*Sin[c + d*x])/(143*a^4*d) - (56*Sin[c + d*x]^3)/(143*a^4*d) + (168*Sin[c + d*x]^5)/(715*a^4*d) - (8*Sin[c + d*x]^7)/(143*a^4*d) + ((I/13)*Cos[c + d*x]^5)/(d*(a + I*a*Tan[c + d*x])^4) + (((9*I)/143)*Cos[c + d*x]^5)/(a*d*(a + I*a*Tan[c + d*x])^3) + (((16*I)/143)*Cos[c + d*x]^7)/(d*(a^4 + I*a^4*Tan[c + d*x]))","A",5,3,24,0.1250,1,"{3502, 3500, 2633}"
166,1,134,0,0.0792108,"\int \frac{\sec ^{14}(c+d x)}{(a+i a \tan (c+d x))^8} \, dx","Int[Sec[c + d*x]^14/(a + I*a*Tan[c + d*x])^8,x]","\frac{\tan ^5(c+d x)}{5 a^8 d}+\frac{2 i \tan ^4(c+d x)}{a^8 d}-\frac{10 \tan ^3(c+d x)}{a^8 d}-\frac{36 i \tan ^2(c+d x)}{a^8 d}+\frac{129 \tan (c+d x)}{a^8 d}+\frac{64 i}{d \left(a^8+i a^8 \tan (c+d x)\right)}-\frac{192 i \log (\cos (c+d x))}{a^8 d}-\frac{192 x}{a^8}","\frac{\tan ^5(c+d x)}{5 a^8 d}+\frac{2 i \tan ^4(c+d x)}{a^8 d}-\frac{10 \tan ^3(c+d x)}{a^8 d}-\frac{36 i \tan ^2(c+d x)}{a^8 d}+\frac{129 \tan (c+d x)}{a^8 d}+\frac{64 i}{d \left(a^8+i a^8 \tan (c+d x)\right)}-\frac{192 i \log (\cos (c+d x))}{a^8 d}-\frac{192 x}{a^8}",1,"(-192*x)/a^8 - ((192*I)*Log[Cos[c + d*x]])/(a^8*d) + (129*Tan[c + d*x])/(a^8*d) - ((36*I)*Tan[c + d*x]^2)/(a^8*d) - (10*Tan[c + d*x]^3)/(a^8*d) + ((2*I)*Tan[c + d*x]^4)/(a^8*d) + Tan[c + d*x]^5/(5*a^8*d) + (64*I)/(d*(a^8 + I*a^8*Tan[c + d*x]))","A",3,2,24,0.08333,1,"{3487, 43}"
167,1,126,0,0.0768581,"\int \frac{\sec ^{12}(c+d x)}{(a+i a \tan (c+d x))^8} \, dx","Int[Sec[c + d*x]^12/(a + I*a*Tan[c + d*x])^8,x]","\frac{\tan ^3(c+d x)}{3 a^8 d}+\frac{4 i \tan ^2(c+d x)}{a^8 d}-\frac{31 \tan (c+d x)}{a^8 d}-\frac{80 i}{d \left(a^8+i a^8 \tan (c+d x)\right)}+\frac{16 i}{d \left(a^4+i a^4 \tan (c+d x)\right)^2}+\frac{80 i \log (\cos (c+d x))}{a^8 d}+\frac{80 x}{a^8}","\frac{\tan ^3(c+d x)}{3 a^8 d}+\frac{4 i \tan ^2(c+d x)}{a^8 d}-\frac{31 \tan (c+d x)}{a^8 d}-\frac{80 i}{d \left(a^8+i a^8 \tan (c+d x)\right)}+\frac{16 i}{d \left(a^4+i a^4 \tan (c+d x)\right)^2}+\frac{80 i \log (\cos (c+d x))}{a^8 d}+\frac{80 x}{a^8}",1,"(80*x)/a^8 + ((80*I)*Log[Cos[c + d*x]])/(a^8*d) - (31*Tan[c + d*x])/(a^8*d) + ((4*I)*Tan[c + d*x]^2)/(a^8*d) + Tan[c + d*x]^3/(3*a^8*d) + (16*I)/(d*(a^4 + I*a^4*Tan[c + d*x])^2) - (80*I)/(d*(a^8 + I*a^8*Tan[c + d*x]))","A",3,2,24,0.08333,1,"{3487, 43}"
168,1,116,0,0.0682109,"\int \frac{\sec ^{10}(c+d x)}{(a+i a \tan (c+d x))^8} \, dx","Int[Sec[c + d*x]^10/(a + I*a*Tan[c + d*x])^8,x]","\frac{\tan (c+d x)}{a^8 d}+\frac{24 i}{d \left(a^8+i a^8 \tan (c+d x)\right)}-\frac{16 i}{d \left(a^4+i a^4 \tan (c+d x)\right)^2}+\frac{16 i}{3 a^5 d (a+i a \tan (c+d x))^3}-\frac{8 i \log (\cos (c+d x))}{a^8 d}-\frac{8 x}{a^8}","\frac{\tan (c+d x)}{a^8 d}+\frac{24 i}{d \left(a^8+i a^8 \tan (c+d x)\right)}-\frac{16 i}{d \left(a^4+i a^4 \tan (c+d x)\right)^2}+\frac{16 i}{3 a^5 d (a+i a \tan (c+d x))^3}-\frac{8 i \log (\cos (c+d x))}{a^8 d}-\frac{8 x}{a^8}",1,"(-8*x)/a^8 - ((8*I)*Log[Cos[c + d*x]])/(a^8*d) + Tan[c + d*x]/(a^8*d) + ((16*I)/3)/(a^5*d*(a + I*a*Tan[c + d*x])^3) - (16*I)/(d*(a^4 + I*a^4*Tan[c + d*x])^2) + (24*I)/(d*(a^8 + I*a^8*Tan[c + d*x]))","A",3,2,24,0.08333,1,"{3487, 43}"
169,1,43,0,0.0431671,"\int \frac{\sec ^8(c+d x)}{(a+i a \tan (c+d x))^8} \, dx","Int[Sec[c + d*x]^8/(a + I*a*Tan[c + d*x])^8,x]","\frac{i (a-i a \tan (c+d x))^4}{8 d \left(a^3+i a^3 \tan (c+d x)\right)^4}","\frac{i (a-i a \tan (c+d x))^4}{8 d \left(a^3+i a^3 \tan (c+d x)\right)^4}",1,"((I/8)*(a - I*a*Tan[c + d*x])^4)/(d*(a^3 + I*a^3*Tan[c + d*x])^4)","A",2,2,24,0.08333,1,"{3487, 37}"
170,1,81,0,0.0556106,"\int \frac{\sec ^6(c+d x)}{(a+i a \tan (c+d x))^8} \, dx","Int[Sec[c + d*x]^6/(a + I*a*Tan[c + d*x])^8,x]","\frac{i}{3 a^5 d (a+i a \tan (c+d x))^3}-\frac{i}{d \left(a^2+i a^2 \tan (c+d x)\right)^4}+\frac{4 i}{5 a^3 d (a+i a \tan (c+d x))^5}","\frac{i}{3 a^5 d (a+i a \tan (c+d x))^3}-\frac{i}{d \left(a^2+i a^2 \tan (c+d x)\right)^4}+\frac{4 i}{5 a^3 d (a+i a \tan (c+d x))^5}",1,"((4*I)/5)/(a^3*d*(a + I*a*Tan[c + d*x])^5) + (I/3)/(a^5*d*(a + I*a*Tan[c + d*x])^3) - I/(d*(a^2 + I*a^2*Tan[c + d*x])^4)","A",3,2,24,0.08333,1,"{3487, 43}"
171,1,55,0,0.0479161,"\int \frac{\sec ^4(c+d x)}{(a+i a \tan (c+d x))^8} \, dx","Int[Sec[c + d*x]^4/(a + I*a*Tan[c + d*x])^8,x]","\frac{i}{3 a^2 d (a+i a \tan (c+d x))^6}-\frac{i}{5 a^3 d (a+i a \tan (c+d x))^5}","\frac{i}{3 a^2 d (a+i a \tan (c+d x))^6}-\frac{i}{5 a^3 d (a+i a \tan (c+d x))^5}",1,"(I/3)/(a^2*d*(a + I*a*Tan[c + d*x])^6) - (I/5)/(a^3*d*(a + I*a*Tan[c + d*x])^5)","A",3,2,24,0.08333,1,"{3487, 43}"
172,1,27,0,0.0388354,"\int \frac{\sec ^2(c+d x)}{(a+i a \tan (c+d x))^8} \, dx","Int[Sec[c + d*x]^2/(a + I*a*Tan[c + d*x])^8,x]","\frac{i}{7 a d (a+i a \tan (c+d x))^7}","\frac{i}{7 a d (a+i a \tan (c+d x))^7}",1,"(I/7)/(a*d*(a + I*a*Tan[c + d*x])^7)","A",2,2,24,0.08333,1,"{3487, 32}"
173,1,229,0,0.1531161,"\int \frac{1}{(a+i a \tan (c+d x))^8} \, dx","Int[(a + I*a*Tan[c + d*x])^(-8),x]","\frac{i}{256 d \left(a^8+i a^8 \tan (c+d x)\right)}+\frac{i}{256 d \left(a^4+i a^4 \tan (c+d x)\right)^2}+\frac{i}{192 a^2 d \left(a^2+i a^2 \tan (c+d x)\right)^3}+\frac{i}{128 d \left(a^2+i a^2 \tan (c+d x)\right)^4}+\frac{i}{80 a^3 d (a+i a \tan (c+d x))^5}+\frac{i}{48 a^2 d (a+i a \tan (c+d x))^6}+\frac{x}{256 a^8}+\frac{i}{28 a d (a+i a \tan (c+d x))^7}+\frac{i}{16 d (a+i a \tan (c+d x))^8}","\frac{i}{256 d \left(a^8+i a^8 \tan (c+d x)\right)}+\frac{i}{256 d \left(a^4+i a^4 \tan (c+d x)\right)^2}+\frac{i}{192 a^2 d \left(a^2+i a^2 \tan (c+d x)\right)^3}+\frac{i}{128 d \left(a^2+i a^2 \tan (c+d x)\right)^4}+\frac{i}{80 a^3 d (a+i a \tan (c+d x))^5}+\frac{i}{48 a^2 d (a+i a \tan (c+d x))^6}+\frac{x}{256 a^8}+\frac{i}{28 a d (a+i a \tan (c+d x))^7}+\frac{i}{16 d (a+i a \tan (c+d x))^8}",1,"x/(256*a^8) + (I/16)/(d*(a + I*a*Tan[c + d*x])^8) + (I/28)/(a*d*(a + I*a*Tan[c + d*x])^7) + (I/48)/(a^2*d*(a + I*a*Tan[c + d*x])^6) + (I/80)/(a^3*d*(a + I*a*Tan[c + d*x])^5) + (I/128)/(d*(a^2 + I*a^2*Tan[c + d*x])^4) + (I/192)/(a^2*d*(a^2 + I*a^2*Tan[c + d*x])^3) + (I/256)/(d*(a^4 + I*a^4*Tan[c + d*x])^2) + (I/256)/(d*(a^8 + I*a^8*Tan[c + d*x]))","A",9,2,15,0.1333,1,"{3479, 8}"
174,1,278,0,0.1435765,"\int \frac{\cos ^2(c+d x)}{(a+i a \tan (c+d x))^8} \, dx","Int[Cos[c + d*x]^2/(a + I*a*Tan[c + d*x])^8,x]","-\frac{i}{1024 d \left(a^8-i a^8 \tan (c+d x)\right)}+\frac{9 i}{1024 d \left(a^8+i a^8 \tan (c+d x)\right)}+\frac{i}{128 d \left(a^4+i a^4 \tan (c+d x)\right)^2}+\frac{3 i}{256 d \left(a^2+i a^2 \tan (c+d x)\right)^4}+\frac{i}{48 a^2 d (a+i a \tan (c+d x))^6}+\frac{i}{64 a^3 d (a+i a \tan (c+d x))^5}+\frac{7 i}{768 a^5 d (a+i a \tan (c+d x))^3}+\frac{5 x}{512 a^8}+\frac{i a}{36 d (a+i a \tan (c+d x))^9}+\frac{i}{32 d (a+i a \tan (c+d x))^8}+\frac{3 i}{112 a d (a+i a \tan (c+d x))^7}","-\frac{i}{1024 d \left(a^8-i a^8 \tan (c+d x)\right)}+\frac{9 i}{1024 d \left(a^8+i a^8 \tan (c+d x)\right)}+\frac{i}{128 d \left(a^4+i a^4 \tan (c+d x)\right)^2}+\frac{3 i}{256 d \left(a^2+i a^2 \tan (c+d x)\right)^4}+\frac{i}{48 a^2 d (a+i a \tan (c+d x))^6}+\frac{i}{64 a^3 d (a+i a \tan (c+d x))^5}+\frac{7 i}{768 a^5 d (a+i a \tan (c+d x))^3}+\frac{5 x}{512 a^8}+\frac{i a}{36 d (a+i a \tan (c+d x))^9}+\frac{i}{32 d (a+i a \tan (c+d x))^8}+\frac{3 i}{112 a d (a+i a \tan (c+d x))^7}",1,"(5*x)/(512*a^8) + ((I/36)*a)/(d*(a + I*a*Tan[c + d*x])^9) + (I/32)/(d*(a + I*a*Tan[c + d*x])^8) + ((3*I)/112)/(a*d*(a + I*a*Tan[c + d*x])^7) + (I/48)/(a^2*d*(a + I*a*Tan[c + d*x])^6) + (I/64)/(a^3*d*(a + I*a*Tan[c + d*x])^5) + ((7*I)/768)/(a^5*d*(a + I*a*Tan[c + d*x])^3) + ((3*I)/256)/(d*(a^2 + I*a^2*Tan[c + d*x])^4) + (I/128)/(d*(a^4 + I*a^4*Tan[c + d*x])^2) - (I/1024)/(d*(a^8 - I*a^8*Tan[c + d*x])) + ((9*I)/1024)/(d*(a^8 + I*a^8*Tan[c + d*x]))","A",4,3,24,0.1250,1,"{3487, 44, 206}"
175,1,333,0,0.1807169,"\int \frac{\cos ^4(c+d x)}{(a+i a \tan (c+d x))^8} \, dx","Int[Cos[c + d*x]^4/(a + I*a*Tan[c + d*x])^8,x]","\frac{i a^2}{80 d (a+i a \tan (c+d x))^{10}}-\frac{11 i}{4096 d \left(a^8-i a^8 \tan (c+d x)\right)}+\frac{55 i}{4096 d \left(a^8+i a^8 \tan (c+d x)\right)}-\frac{i}{4096 d \left(a^4-i a^4 \tan (c+d x)\right)^2}+\frac{45 i}{4096 d \left(a^4+i a^4 \tan (c+d x)\right)^2}+\frac{7 i}{512 d \left(a^2+i a^2 \tan (c+d x)\right)^4}+\frac{5 i}{256 a^2 d (a+i a \tan (c+d x))^6}+\frac{21 i}{1280 a^3 d (a+i a \tan (c+d x))^5}+\frac{3 i}{256 a^5 d (a+i a \tan (c+d x))^3}+\frac{33 x}{2048 a^8}+\frac{i a}{48 d (a+i a \tan (c+d x))^9}+\frac{3 i}{128 d (a+i a \tan (c+d x))^8}+\frac{5 i}{224 a d (a+i a \tan (c+d x))^7}","\frac{i a^2}{80 d (a+i a \tan (c+d x))^{10}}-\frac{11 i}{4096 d \left(a^8-i a^8 \tan (c+d x)\right)}+\frac{55 i}{4096 d \left(a^8+i a^8 \tan (c+d x)\right)}-\frac{i}{4096 d \left(a^4-i a^4 \tan (c+d x)\right)^2}+\frac{45 i}{4096 d \left(a^4+i a^4 \tan (c+d x)\right)^2}+\frac{7 i}{512 d \left(a^2+i a^2 \tan (c+d x)\right)^4}+\frac{5 i}{256 a^2 d (a+i a \tan (c+d x))^6}+\frac{21 i}{1280 a^3 d (a+i a \tan (c+d x))^5}+\frac{3 i}{256 a^5 d (a+i a \tan (c+d x))^3}+\frac{33 x}{2048 a^8}+\frac{i a}{48 d (a+i a \tan (c+d x))^9}+\frac{3 i}{128 d (a+i a \tan (c+d x))^8}+\frac{5 i}{224 a d (a+i a \tan (c+d x))^7}",1,"(33*x)/(2048*a^8) + ((I/80)*a^2)/(d*(a + I*a*Tan[c + d*x])^10) + ((I/48)*a)/(d*(a + I*a*Tan[c + d*x])^9) + ((3*I)/128)/(d*(a + I*a*Tan[c + d*x])^8) + ((5*I)/224)/(a*d*(a + I*a*Tan[c + d*x])^7) + ((5*I)/256)/(a^2*d*(a + I*a*Tan[c + d*x])^6) + ((21*I)/1280)/(a^3*d*(a + I*a*Tan[c + d*x])^5) + ((3*I)/256)/(a^5*d*(a + I*a*Tan[c + d*x])^3) + ((7*I)/512)/(d*(a^2 + I*a^2*Tan[c + d*x])^4) - (I/4096)/(d*(a^4 - I*a^4*Tan[c + d*x])^2) + ((45*I)/4096)/(d*(a^4 + I*a^4*Tan[c + d*x])^2) - ((11*I)/4096)/(d*(a^8 - I*a^8*Tan[c + d*x])) + ((55*I)/4096)/(d*(a^8 + I*a^8*Tan[c + d*x]))","A",4,3,24,0.1250,1,"{3487, 44, 206}"
176,1,205,0,0.2169916,"\int \frac{\sec ^{13}(c+d x)}{(a+i a \tan (c+d x))^8} \, dx","Int[Sec[c + d*x]^13/(a + I*a*Tan[c + d*x])^8,x]","\frac{1155 \tanh ^{-1}(\sin (c+d x))}{8 a^8 d}-\frac{22 i \sec ^9(c+d x)}{3 a^3 d (a+i a \tan (c+d x))^5}-\frac{66 i \sec ^7(c+d x)}{a^2 d \left(a^2+i a^2 \tan (c+d x)\right)^3}-\frac{154 i \sec ^5(c+d x)}{d \left(a^8+i a^8 \tan (c+d x)\right)}+\frac{385 \tan (c+d x) \sec ^3(c+d x)}{4 a^8 d}+\frac{1155 \tan (c+d x) \sec (c+d x)}{8 a^8 d}+\frac{2 i \sec ^{11}(c+d x)}{3 a d (a+i a \tan (c+d x))^7}","\frac{1155 \tanh ^{-1}(\sin (c+d x))}{8 a^8 d}-\frac{22 i \sec ^9(c+d x)}{3 a^3 d (a+i a \tan (c+d x))^5}-\frac{66 i \sec ^7(c+d x)}{a^2 d \left(a^2+i a^2 \tan (c+d x)\right)^3}-\frac{154 i \sec ^5(c+d x)}{d \left(a^8+i a^8 \tan (c+d x)\right)}+\frac{385 \tan (c+d x) \sec ^3(c+d x)}{4 a^8 d}+\frac{1155 \tan (c+d x) \sec (c+d x)}{8 a^8 d}+\frac{2 i \sec ^{11}(c+d x)}{3 a d (a+i a \tan (c+d x))^7}",1,"(1155*ArcTanh[Sin[c + d*x]])/(8*a^8*d) + (1155*Sec[c + d*x]*Tan[c + d*x])/(8*a^8*d) + (385*Sec[c + d*x]^3*Tan[c + d*x])/(4*a^8*d) + (((2*I)/3)*Sec[c + d*x]^11)/(a*d*(a + I*a*Tan[c + d*x])^7) - (((22*I)/3)*Sec[c + d*x]^9)/(a^3*d*(a + I*a*Tan[c + d*x])^5) - ((66*I)*Sec[c + d*x]^7)/(a^2*d*(a^2 + I*a^2*Tan[c + d*x])^3) - ((154*I)*Sec[c + d*x]^5)/(d*(a^8 + I*a^8*Tan[c + d*x]))","A",7,3,24,0.1250,1,"{3500, 3768, 3770}"
177,1,183,0,0.200439,"\int \frac{\sec ^{11}(c+d x)}{(a+i a \tan (c+d x))^8} \, dx","Int[Sec[c + d*x]^11/(a + I*a*Tan[c + d*x])^8,x]","-\frac{63 \tanh ^{-1}(\sin (c+d x))}{2 a^8 d}-\frac{6 i \sec ^7(c+d x)}{5 a^3 d (a+i a \tan (c+d x))^5}+\frac{42 i \sec ^5(c+d x)}{5 a^2 d \left(a^2+i a^2 \tan (c+d x)\right)^3}+\frac{42 i \sec ^3(c+d x)}{d \left(a^8+i a^8 \tan (c+d x)\right)}-\frac{63 \tan (c+d x) \sec (c+d x)}{2 a^8 d}+\frac{2 i \sec ^9(c+d x)}{5 a d (a+i a \tan (c+d x))^7}","-\frac{63 \tanh ^{-1}(\sin (c+d x))}{2 a^8 d}-\frac{6 i \sec ^7(c+d x)}{5 a^3 d (a+i a \tan (c+d x))^5}+\frac{42 i \sec ^5(c+d x)}{5 a^2 d \left(a^2+i a^2 \tan (c+d x)\right)^3}+\frac{42 i \sec ^3(c+d x)}{d \left(a^8+i a^8 \tan (c+d x)\right)}-\frac{63 \tan (c+d x) \sec (c+d x)}{2 a^8 d}+\frac{2 i \sec ^9(c+d x)}{5 a d (a+i a \tan (c+d x))^7}",1,"(-63*ArcTanh[Sin[c + d*x]])/(2*a^8*d) - (63*Sec[c + d*x]*Tan[c + d*x])/(2*a^8*d) + (((2*I)/5)*Sec[c + d*x]^9)/(a*d*(a + I*a*Tan[c + d*x])^7) - (((6*I)/5)*Sec[c + d*x]^7)/(a^3*d*(a + I*a*Tan[c + d*x])^5) + (((42*I)/5)*Sec[c + d*x]^5)/(a^2*d*(a^2 + I*a^2*Tan[c + d*x])^3) + ((42*I)*Sec[c + d*x]^3)/(d*(a^8 + I*a^8*Tan[c + d*x]))","A",6,3,24,0.1250,1,"{3500, 3768, 3770}"
178,1,156,0,0.216498,"\int \frac{\sec ^9(c+d x)}{(a+i a \tan (c+d x))^8} \, dx","Int[Sec[c + d*x]^9/(a + I*a*Tan[c + d*x])^8,x]","\frac{\tanh ^{-1}(\sin (c+d x))}{a^8 d}-\frac{2 i \sec ^5(c+d x)}{5 a^3 d (a+i a \tan (c+d x))^5}+\frac{2 i \sec ^3(c+d x)}{3 a^2 d \left(a^2+i a^2 \tan (c+d x)\right)^3}-\frac{2 i \sec (c+d x)}{d \left(a^8+i a^8 \tan (c+d x)\right)}+\frac{2 i \sec ^7(c+d x)}{7 a d (a+i a \tan (c+d x))^7}","\frac{\tanh ^{-1}(\sin (c+d x))}{a^8 d}-\frac{2 i \sec ^5(c+d x)}{5 a^3 d (a+i a \tan (c+d x))^5}+\frac{2 i \sec ^3(c+d x)}{3 a^2 d \left(a^2+i a^2 \tan (c+d x)\right)^3}-\frac{2 i \sec (c+d x)}{d \left(a^8+i a^8 \tan (c+d x)\right)}+\frac{2 i \sec ^7(c+d x)}{7 a d (a+i a \tan (c+d x))^7}",1,"ArcTanh[Sin[c + d*x]]/(a^8*d) + (((2*I)/7)*Sec[c + d*x]^7)/(a*d*(a + I*a*Tan[c + d*x])^7) - (((2*I)/5)*Sec[c + d*x]^5)/(a^3*d*(a + I*a*Tan[c + d*x])^5) + (((2*I)/3)*Sec[c + d*x]^3)/(a^2*d*(a^2 + I*a^2*Tan[c + d*x])^3) - ((2*I)*Sec[c + d*x])/(d*(a^8 + I*a^8*Tan[c + d*x]))","A",5,2,24,0.08333,1,"{3500, 3770}"
179,1,68,0,0.0803466,"\int \frac{\sec ^7(c+d x)}{(a+i a \tan (c+d x))^8} \, dx","Int[Sec[c + d*x]^7/(a + I*a*Tan[c + d*x])^8,x]","\frac{i \sec ^7(c+d x)}{63 a d (a+i a \tan (c+d x))^7}+\frac{i \sec ^7(c+d x)}{9 d (a+i a \tan (c+d x))^8}","\frac{i \sec ^7(c+d x)}{63 a d (a+i a \tan (c+d x))^7}+\frac{i \sec ^7(c+d x)}{9 d (a+i a \tan (c+d x))^8}",1,"((I/9)*Sec[c + d*x]^7)/(d*(a + I*a*Tan[c + d*x])^8) + ((I/63)*Sec[c + d*x]^7)/(a*d*(a + I*a*Tan[c + d*x])^7)","A",2,2,24,0.08333,1,"{3502, 3488}"
180,1,138,0,0.1752953,"\int \frac{\sec ^5(c+d x)}{(a+i a \tan (c+d x))^8} \, dx","Int[Sec[c + d*x]^5/(a + I*a*Tan[c + d*x])^8,x]","\frac{2 i \sec ^5(c+d x)}{1155 a^3 d (a+i a \tan (c+d x))^5}+\frac{2 i \sec ^5(c+d x)}{231 a^2 d (a+i a \tan (c+d x))^6}+\frac{i \sec ^5(c+d x)}{33 a d (a+i a \tan (c+d x))^7}+\frac{i \sec ^5(c+d x)}{11 d (a+i a \tan (c+d x))^8}","\frac{2 i \sec ^5(c+d x)}{1155 a^3 d (a+i a \tan (c+d x))^5}+\frac{2 i \sec ^5(c+d x)}{231 a^2 d (a+i a \tan (c+d x))^6}+\frac{i \sec ^5(c+d x)}{33 a d (a+i a \tan (c+d x))^7}+\frac{i \sec ^5(c+d x)}{11 d (a+i a \tan (c+d x))^8}",1,"((I/11)*Sec[c + d*x]^5)/(d*(a + I*a*Tan[c + d*x])^8) + ((I/33)*Sec[c + d*x]^5)/(a*d*(a + I*a*Tan[c + d*x])^7) + (((2*I)/231)*Sec[c + d*x]^5)/(a^2*d*(a + I*a*Tan[c + d*x])^6) + (((2*I)/1155)*Sec[c + d*x]^5)/(a^3*d*(a + I*a*Tan[c + d*x])^5)","A",4,2,24,0.08333,1,"{3502, 3488}"
181,1,213,0,0.2758232,"\int \frac{\sec ^3(c+d x)}{(a+i a \tan (c+d x))^8} \, dx","Int[Sec[c + d*x]^3/(a + I*a*Tan[c + d*x])^8,x]","\frac{8 i \sec ^3(c+d x)}{9009 a^2 d \left(a^2+i a^2 \tan (c+d x)\right)^3}+\frac{8 i \sec ^3(c+d x)}{3003 d \left(a^2+i a^2 \tan (c+d x)\right)^4}+\frac{20 i \sec ^3(c+d x)}{3003 a^3 d (a+i a \tan (c+d x))^5}+\frac{20 i \sec ^3(c+d x)}{1287 a^2 d (a+i a \tan (c+d x))^6}+\frac{5 i \sec ^3(c+d x)}{143 a d (a+i a \tan (c+d x))^7}+\frac{i \sec ^3(c+d x)}{13 d (a+i a \tan (c+d x))^8}","\frac{8 i \sec ^3(c+d x)}{9009 a^2 d \left(a^2+i a^2 \tan (c+d x)\right)^3}+\frac{8 i \sec ^3(c+d x)}{3003 d \left(a^2+i a^2 \tan (c+d x)\right)^4}+\frac{20 i \sec ^3(c+d x)}{3003 a^3 d (a+i a \tan (c+d x))^5}+\frac{20 i \sec ^3(c+d x)}{1287 a^2 d (a+i a \tan (c+d x))^6}+\frac{5 i \sec ^3(c+d x)}{143 a d (a+i a \tan (c+d x))^7}+\frac{i \sec ^3(c+d x)}{13 d (a+i a \tan (c+d x))^8}",1,"((I/13)*Sec[c + d*x]^3)/(d*(a + I*a*Tan[c + d*x])^8) + (((5*I)/143)*Sec[c + d*x]^3)/(a*d*(a + I*a*Tan[c + d*x])^7) + (((20*I)/1287)*Sec[c + d*x]^3)/(a^2*d*(a + I*a*Tan[c + d*x])^6) + (((20*I)/3003)*Sec[c + d*x]^3)/(a^3*d*(a + I*a*Tan[c + d*x])^5) + (((8*I)/3003)*Sec[c + d*x]^3)/(d*(a^2 + I*a^2*Tan[c + d*x])^4) + (((8*I)/9009)*Sec[c + d*x]^3)/(a^2*d*(a^2 + I*a^2*Tan[c + d*x])^3)","A",6,2,24,0.08333,1,"{3502, 3488}"
182,1,269,0,0.2597541,"\int \frac{\sec (c+d x)}{(a+i a \tan (c+d x))^8} \, dx","Int[Sec[c + d*x]/(a + I*a*Tan[c + d*x])^8,x]","\frac{16 i \sec (c+d x)}{6435 d \left(a^8+i a^8 \tan (c+d x)\right)}+\frac{16 i \sec (c+d x)}{6435 d \left(a^4+i a^4 \tan (c+d x)\right)^2}+\frac{8 i \sec (c+d x)}{2145 a^2 d \left(a^2+i a^2 \tan (c+d x)\right)^3}+\frac{8 i \sec (c+d x)}{1287 d \left(a^2+i a^2 \tan (c+d x)\right)^4}+\frac{14 i \sec (c+d x)}{1287 a^3 d (a+i a \tan (c+d x))^5}+\frac{14 i \sec (c+d x)}{715 a^2 d (a+i a \tan (c+d x))^6}+\frac{7 i \sec (c+d x)}{195 a d (a+i a \tan (c+d x))^7}+\frac{i \sec (c+d x)}{15 d (a+i a \tan (c+d x))^8}","\frac{16 i \sec (c+d x)}{6435 d \left(a^8+i a^8 \tan (c+d x)\right)}+\frac{16 i \sec (c+d x)}{6435 d \left(a^4+i a^4 \tan (c+d x)\right)^2}+\frac{8 i \sec (c+d x)}{2145 a^2 d \left(a^2+i a^2 \tan (c+d x)\right)^3}+\frac{8 i \sec (c+d x)}{1287 d \left(a^2+i a^2 \tan (c+d x)\right)^4}+\frac{14 i \sec (c+d x)}{1287 a^3 d (a+i a \tan (c+d x))^5}+\frac{14 i \sec (c+d x)}{715 a^2 d (a+i a \tan (c+d x))^6}+\frac{7 i \sec (c+d x)}{195 a d (a+i a \tan (c+d x))^7}+\frac{i \sec (c+d x)}{15 d (a+i a \tan (c+d x))^8}",1,"((I/15)*Sec[c + d*x])/(d*(a + I*a*Tan[c + d*x])^8) + (((7*I)/195)*Sec[c + d*x])/(a*d*(a + I*a*Tan[c + d*x])^7) + (((14*I)/715)*Sec[c + d*x])/(a^2*d*(a + I*a*Tan[c + d*x])^6) + (((14*I)/1287)*Sec[c + d*x])/(a^3*d*(a + I*a*Tan[c + d*x])^5) + (((8*I)/1287)*Sec[c + d*x])/(d*(a^2 + I*a^2*Tan[c + d*x])^4) + (((8*I)/2145)*Sec[c + d*x])/(a^2*d*(a^2 + I*a^2*Tan[c + d*x])^3) + (((16*I)/6435)*Sec[c + d*x])/(d*(a^4 + I*a^4*Tan[c + d*x])^2) + (((16*I)/6435)*Sec[c + d*x])/(d*(a^8 + I*a^8*Tan[c + d*x]))","A",8,2,22,0.09091,1,"{3502, 3488}"
183,1,271,0,0.3120191,"\int \frac{\cos (c+d x)}{(a+i a \tan (c+d x))^8} \, dx","Int[Cos[c + d*x]/(a + I*a*Tan[c + d*x])^8,x]","-\frac{64 \sin ^3(c+d x)}{12155 a^8 d}+\frac{192 \sin (c+d x)}{12155 a^8 d}+\frac{128 i \cos ^3(c+d x)}{12155 d \left(a^8+i a^8 \tan (c+d x)\right)}+\frac{16 i \cos (c+d x)}{2431 a^2 d \left(a^2+i a^2 \tan (c+d x)\right)^3}+\frac{112 i \cos (c+d x)}{12155 d \left(a^2+i a^2 \tan (c+d x)\right)^4}+\frac{168 i \cos (c+d x)}{12155 a^3 d (a+i a \tan (c+d x))^5}+\frac{24 i \cos (c+d x)}{1105 a^2 d (a+i a \tan (c+d x))^6}+\frac{3 i \cos (c+d x)}{85 a d (a+i a \tan (c+d x))^7}+\frac{i \cos (c+d x)}{17 d (a+i a \tan (c+d x))^8}","-\frac{64 \sin ^3(c+d x)}{12155 a^8 d}+\frac{192 \sin (c+d x)}{12155 a^8 d}+\frac{128 i \cos ^3(c+d x)}{12155 d \left(a^8+i a^8 \tan (c+d x)\right)}+\frac{16 i \cos (c+d x)}{2431 a^2 d \left(a^2+i a^2 \tan (c+d x)\right)^3}+\frac{112 i \cos (c+d x)}{12155 d \left(a^2+i a^2 \tan (c+d x)\right)^4}+\frac{168 i \cos (c+d x)}{12155 a^3 d (a+i a \tan (c+d x))^5}+\frac{24 i \cos (c+d x)}{1105 a^2 d (a+i a \tan (c+d x))^6}+\frac{3 i \cos (c+d x)}{85 a d (a+i a \tan (c+d x))^7}+\frac{i \cos (c+d x)}{17 d (a+i a \tan (c+d x))^8}",1,"(192*Sin[c + d*x])/(12155*a^8*d) - (64*Sin[c + d*x]^3)/(12155*a^8*d) + ((I/17)*Cos[c + d*x])/(d*(a + I*a*Tan[c + d*x])^8) + (((3*I)/85)*Cos[c + d*x])/(a*d*(a + I*a*Tan[c + d*x])^7) + (((24*I)/1105)*Cos[c + d*x])/(a^2*d*(a + I*a*Tan[c + d*x])^6) + (((168*I)/12155)*Cos[c + d*x])/(a^3*d*(a + I*a*Tan[c + d*x])^5) + (((112*I)/12155)*Cos[c + d*x])/(d*(a^2 + I*a^2*Tan[c + d*x])^4) + (((16*I)/2431)*Cos[c + d*x])/(a^2*d*(a^2 + I*a^2*Tan[c + d*x])^3) + (((128*I)/12155)*Cos[c + d*x]^3)/(d*(a^8 + I*a^8*Tan[c + d*x]))","A",9,3,22,0.1364,1,"{3502, 3500, 2633}"
184,1,301,0,0.3840338,"\int \frac{\cos ^3(c+d x)}{(a+i a \tan (c+d x))^8} \, dx","Int[Cos[c + d*x]^3/(a + I*a*Tan[c + d*x])^8,x]","\frac{32 \sin ^5(c+d x)}{4199 a^8 d}-\frac{320 \sin ^3(c+d x)}{12597 a^8 d}+\frac{160 \sin (c+d x)}{4199 a^8 d}+\frac{64 i \cos ^5(c+d x)}{4199 d \left(a^8+i a^8 \tan (c+d x)\right)}+\frac{112 i \cos ^3(c+d x)}{12597 a^2 d \left(a^2+i a^2 \tan (c+d x)\right)^3}+\frac{48 i \cos ^3(c+d x)}{4199 d \left(a^2+i a^2 \tan (c+d x)\right)^4}+\frac{66 i \cos ^3(c+d x)}{4199 a^3 d (a+i a \tan (c+d x))^5}+\frac{22 i \cos ^3(c+d x)}{969 a^2 d (a+i a \tan (c+d x))^6}+\frac{11 i \cos ^3(c+d x)}{323 a d (a+i a \tan (c+d x))^7}+\frac{i \cos ^3(c+d x)}{19 d (a+i a \tan (c+d x))^8}","\frac{32 \sin ^5(c+d x)}{4199 a^8 d}-\frac{320 \sin ^3(c+d x)}{12597 a^8 d}+\frac{160 \sin (c+d x)}{4199 a^8 d}+\frac{64 i \cos ^5(c+d x)}{4199 d \left(a^8+i a^8 \tan (c+d x)\right)}+\frac{112 i \cos ^3(c+d x)}{12597 a^2 d \left(a^2+i a^2 \tan (c+d x)\right)^3}+\frac{48 i \cos ^3(c+d x)}{4199 d \left(a^2+i a^2 \tan (c+d x)\right)^4}+\frac{66 i \cos ^3(c+d x)}{4199 a^3 d (a+i a \tan (c+d x))^5}+\frac{22 i \cos ^3(c+d x)}{969 a^2 d (a+i a \tan (c+d x))^6}+\frac{11 i \cos ^3(c+d x)}{323 a d (a+i a \tan (c+d x))^7}+\frac{i \cos ^3(c+d x)}{19 d (a+i a \tan (c+d x))^8}",1,"(160*Sin[c + d*x])/(4199*a^8*d) - (320*Sin[c + d*x]^3)/(12597*a^8*d) + (32*Sin[c + d*x]^5)/(4199*a^8*d) + ((I/19)*Cos[c + d*x]^3)/(d*(a + I*a*Tan[c + d*x])^8) + (((11*I)/323)*Cos[c + d*x]^3)/(a*d*(a + I*a*Tan[c + d*x])^7) + (((22*I)/969)*Cos[c + d*x]^3)/(a^2*d*(a + I*a*Tan[c + d*x])^6) + (((66*I)/4199)*Cos[c + d*x]^3)/(a^3*d*(a + I*a*Tan[c + d*x])^5) + (((48*I)/4199)*Cos[c + d*x]^3)/(d*(a^2 + I*a^2*Tan[c + d*x])^4) + (((112*I)/12597)*Cos[c + d*x]^3)/(a^2*d*(a^2 + I*a^2*Tan[c + d*x])^3) + (((64*I)/4199)*Cos[c + d*x]^5)/(d*(a^8 + I*a^8*Tan[c + d*x]))","A",9,3,24,0.1250,1,"{3502, 3500, 2633}"
185,1,123,0,0.0905456,"\int (e \sec (c+d x))^{7/2} (a+i a \tan (c+d x)) \, dx","Int[(e*Sec[c + d*x])^(7/2)*(a + I*a*Tan[c + d*x]),x]","\frac{6 a e^3 \sin (c+d x) \sqrt{e \sec (c+d x)}}{5 d}-\frac{6 a e^4 E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{5 d \sqrt{\cos (c+d x)} \sqrt{e \sec (c+d x)}}+\frac{2 i a (e \sec (c+d x))^{7/2}}{7 d}+\frac{2 a e \sin (c+d x) (e \sec (c+d x))^{5/2}}{5 d}","\frac{6 a e^3 \sin (c+d x) \sqrt{e \sec (c+d x)}}{5 d}-\frac{6 a e^4 E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{5 d \sqrt{\cos (c+d x)} \sqrt{e \sec (c+d x)}}+\frac{2 i a (e \sec (c+d x))^{7/2}}{7 d}+\frac{2 a e \sin (c+d x) (e \sec (c+d x))^{5/2}}{5 d}",1,"(-6*a*e^4*EllipticE[(c + d*x)/2, 2])/(5*d*Sqrt[Cos[c + d*x]]*Sqrt[e*Sec[c + d*x]]) + (((2*I)/7)*a*(e*Sec[c + d*x])^(7/2))/d + (6*a*e^3*Sqrt[e*Sec[c + d*x]]*Sin[c + d*x])/(5*d) + (2*a*e*(e*Sec[c + d*x])^(5/2)*Sin[c + d*x])/(5*d)","A",5,4,26,0.1538,1,"{3486, 3768, 3771, 2639}"
186,1,94,0,0.060312,"\int (e \sec (c+d x))^{5/2} (a+i a \tan (c+d x)) \, dx","Int[(e*Sec[c + d*x])^(5/2)*(a + I*a*Tan[c + d*x]),x]","\frac{2 a e^2 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{e \sec (c+d x)}}{3 d}+\frac{2 i a (e \sec (c+d x))^{5/2}}{5 d}+\frac{2 a e \sin (c+d x) (e \sec (c+d x))^{3/2}}{3 d}","\frac{2 a e^2 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{e \sec (c+d x)}}{3 d}+\frac{2 i a (e \sec (c+d x))^{5/2}}{5 d}+\frac{2 a e \sin (c+d x) (e \sec (c+d x))^{3/2}}{3 d}",1,"(2*a*e^2*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2]*Sqrt[e*Sec[c + d*x]])/(3*d) + (((2*I)/5)*a*(e*Sec[c + d*x])^(5/2))/d + (2*a*e*(e*Sec[c + d*x])^(3/2)*Sin[c + d*x])/(3*d)","A",4,4,26,0.1538,1,"{3486, 3768, 3771, 2641}"
187,1,90,0,0.0605921,"\int (e \sec (c+d x))^{3/2} (a+i a \tan (c+d x)) \, dx","Int[(e*Sec[c + d*x])^(3/2)*(a + I*a*Tan[c + d*x]),x]","-\frac{2 a e^2 E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{d \sqrt{\cos (c+d x)} \sqrt{e \sec (c+d x)}}+\frac{2 i a (e \sec (c+d x))^{3/2}}{3 d}+\frac{2 a e \sin (c+d x) \sqrt{e \sec (c+d x)}}{d}","-\frac{2 a e^2 E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{d \sqrt{\cos (c+d x)} \sqrt{e \sec (c+d x)}}+\frac{2 i a (e \sec (c+d x))^{3/2}}{3 d}+\frac{2 a e \sin (c+d x) \sqrt{e \sec (c+d x)}}{d}",1,"(-2*a*e^2*EllipticE[(c + d*x)/2, 2])/(d*Sqrt[Cos[c + d*x]]*Sqrt[e*Sec[c + d*x]]) + (((2*I)/3)*a*(e*Sec[c + d*x])^(3/2))/d + (2*a*e*Sqrt[e*Sec[c + d*x]]*Sin[c + d*x])/d","A",4,4,26,0.1538,1,"{3486, 3768, 3771, 2639}"
188,1,60,0,0.0434359,"\int \sqrt{e \sec (c+d x)} (a+i a \tan (c+d x)) \, dx","Int[Sqrt[e*Sec[c + d*x]]*(a + I*a*Tan[c + d*x]),x]","\frac{2 a \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{e \sec (c+d x)}}{d}+\frac{2 i a \sqrt{e \sec (c+d x)}}{d}","\frac{2 a \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{e \sec (c+d x)}}{d}+\frac{2 i a \sqrt{e \sec (c+d x)}}{d}",1,"((2*I)*a*Sqrt[e*Sec[c + d*x]])/d + (2*a*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2]*Sqrt[e*Sec[c + d*x]])/d","A",3,3,26,0.1154,1,"{3486, 3771, 2641}"
189,1,60,0,0.0467685,"\int \frac{a+i a \tan (c+d x)}{\sqrt{e \sec (c+d x)}} \, dx","Int[(a + I*a*Tan[c + d*x])/Sqrt[e*Sec[c + d*x]],x]","\frac{2 a E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{d \sqrt{\cos (c+d x)} \sqrt{e \sec (c+d x)}}-\frac{2 i a}{d \sqrt{e \sec (c+d x)}}","\frac{2 a E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{d \sqrt{\cos (c+d x)} \sqrt{e \sec (c+d x)}}-\frac{2 i a}{d \sqrt{e \sec (c+d x)}}",1,"((-2*I)*a)/(d*Sqrt[e*Sec[c + d*x]]) + (2*a*EllipticE[(c + d*x)/2, 2])/(d*Sqrt[Cos[c + d*x]]*Sqrt[e*Sec[c + d*x]])","A",3,3,26,0.1154,1,"{3486, 3771, 2639}"
190,1,96,0,0.0680948,"\int \frac{a+i a \tan (c+d x)}{(e \sec (c+d x))^{3/2}} \, dx","Int[(a + I*a*Tan[c + d*x])/(e*Sec[c + d*x])^(3/2),x]","\frac{2 a \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{e \sec (c+d x)}}{3 d e^2}-\frac{2 i a}{3 d (e \sec (c+d x))^{3/2}}+\frac{2 a \sin (c+d x)}{3 d e \sqrt{e \sec (c+d x)}}","\frac{2 a \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{e \sec (c+d x)}}{3 d e^2}-\frac{2 i a}{3 d (e \sec (c+d x))^{3/2}}+\frac{2 a \sin (c+d x)}{3 d e \sqrt{e \sec (c+d x)}}",1,"(((-2*I)/3)*a)/(d*(e*Sec[c + d*x])^(3/2)) + (2*a*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2]*Sqrt[e*Sec[c + d*x]])/(3*d*e^2) + (2*a*Sin[c + d*x])/(3*d*e*Sqrt[e*Sec[c + d*x]])","A",4,4,26,0.1538,1,"{3486, 3769, 3771, 2641}"
191,1,96,0,0.0652379,"\int \frac{a+i a \tan (c+d x)}{(e \sec (c+d x))^{5/2}} \, dx","Int[(a + I*a*Tan[c + d*x])/(e*Sec[c + d*x])^(5/2),x]","\frac{6 a E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{5 d e^2 \sqrt{\cos (c+d x)} \sqrt{e \sec (c+d x)}}-\frac{2 i a}{5 d (e \sec (c+d x))^{5/2}}+\frac{2 a \sin (c+d x)}{5 d e (e \sec (c+d x))^{3/2}}","\frac{6 a E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{5 d e^2 \sqrt{\cos (c+d x)} \sqrt{e \sec (c+d x)}}-\frac{2 i a}{5 d (e \sec (c+d x))^{5/2}}+\frac{2 a \sin (c+d x)}{5 d e (e \sec (c+d x))^{3/2}}",1,"(((-2*I)/5)*a)/(d*(e*Sec[c + d*x])^(5/2)) + (6*a*EllipticE[(c + d*x)/2, 2])/(5*d*e^2*Sqrt[Cos[c + d*x]]*Sqrt[e*Sec[c + d*x]]) + (2*a*Sin[c + d*x])/(5*d*e*(e*Sec[c + d*x])^(3/2))","A",4,4,26,0.1538,1,"{3486, 3769, 3771, 2639}"
192,1,125,0,0.0823461,"\int \frac{a+i a \tan (c+d x)}{(e \sec (c+d x))^{7/2}} \, dx","Int[(a + I*a*Tan[c + d*x])/(e*Sec[c + d*x])^(7/2),x]","\frac{10 a \sin (c+d x)}{21 d e^3 \sqrt{e \sec (c+d x)}}+\frac{10 a \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{e \sec (c+d x)}}{21 d e^4}-\frac{2 i a}{7 d (e \sec (c+d x))^{7/2}}+\frac{2 a \sin (c+d x)}{7 d e (e \sec (c+d x))^{5/2}}","\frac{10 a \sin (c+d x)}{21 d e^3 \sqrt{e \sec (c+d x)}}+\frac{10 a \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{e \sec (c+d x)}}{21 d e^4}-\frac{2 i a}{7 d (e \sec (c+d x))^{7/2}}+\frac{2 a \sin (c+d x)}{7 d e (e \sec (c+d x))^{5/2}}",1,"(((-2*I)/7)*a)/(d*(e*Sec[c + d*x])^(7/2)) + (10*a*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2]*Sqrt[e*Sec[c + d*x]])/(21*d*e^4) + (2*a*Sin[c + d*x])/(7*d*e*(e*Sec[c + d*x])^(5/2)) + (10*a*Sin[c + d*x])/(21*d*e^3*Sqrt[e*Sec[c + d*x]])","A",5,4,26,0.1538,1,"{3486, 3769, 3771, 2641}"
193,1,138,0,0.1172029,"\int (e \sec (c+d x))^{3/2} (a+i a \tan (c+d x))^2 \, dx","Int[(e*Sec[c + d*x])^(3/2)*(a + I*a*Tan[c + d*x])^2,x]","-\frac{14 a^2 e^2 E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{5 d \sqrt{\cos (c+d x)} \sqrt{e \sec (c+d x)}}+\frac{14 i a^2 (e \sec (c+d x))^{3/2}}{15 d}+\frac{14 a^2 e \sin (c+d x) \sqrt{e \sec (c+d x)}}{5 d}+\frac{2 i \left(a^2+i a^2 \tan (c+d x)\right) (e \sec (c+d x))^{3/2}}{5 d}","-\frac{14 a^2 e^2 E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{5 d \sqrt{\cos (c+d x)} \sqrt{e \sec (c+d x)}}+\frac{14 i a^2 (e \sec (c+d x))^{3/2}}{15 d}+\frac{14 a^2 e \sin (c+d x) \sqrt{e \sec (c+d x)}}{5 d}+\frac{2 i \left(a^2+i a^2 \tan (c+d x)\right) (e \sec (c+d x))^{3/2}}{5 d}",1,"(-14*a^2*e^2*EllipticE[(c + d*x)/2, 2])/(5*d*Sqrt[Cos[c + d*x]]*Sqrt[e*Sec[c + d*x]]) + (((14*I)/15)*a^2*(e*Sec[c + d*x])^(3/2))/d + (14*a^2*e*Sqrt[e*Sec[c + d*x]]*Sin[c + d*x])/(5*d) + (((2*I)/5)*(e*Sec[c + d*x])^(3/2)*(a^2 + I*a^2*Tan[c + d*x]))/d","A",5,5,28,0.1786,1,"{3498, 3486, 3768, 3771, 2639}"
194,1,106,0,0.0894341,"\int \sqrt{e \sec (c+d x)} (a+i a \tan (c+d x))^2 \, dx","Int[Sqrt[e*Sec[c + d*x]]*(a + I*a*Tan[c + d*x])^2,x]","\frac{10 i a^2 \sqrt{e \sec (c+d x)}}{3 d}+\frac{2 i \left(a^2+i a^2 \tan (c+d x)\right) \sqrt{e \sec (c+d x)}}{3 d}+\frac{10 a^2 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{e \sec (c+d x)}}{3 d}","\frac{10 i a^2 \sqrt{e \sec (c+d x)}}{3 d}+\frac{2 i \left(a^2+i a^2 \tan (c+d x)\right) \sqrt{e \sec (c+d x)}}{3 d}+\frac{10 a^2 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{e \sec (c+d x)}}{3 d}",1,"(((10*I)/3)*a^2*Sqrt[e*Sec[c + d*x]])/d + (10*a^2*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2]*Sqrt[e*Sec[c + d*x]])/(3*d) + (((2*I)/3)*Sqrt[e*Sec[c + d*x]]*(a^2 + I*a^2*Tan[c + d*x]))/d","A",4,4,28,0.1429,1,"{3498, 3486, 3771, 2641}"
195,1,107,0,0.0806821,"\int \frac{(a+i a \tan (c+d x))^2}{\sqrt{e \sec (c+d x)}} \, dx","Int[(a + I*a*Tan[c + d*x])^2/Sqrt[e*Sec[c + d*x]],x]","-\frac{6 a^2 \sin (c+d x) \sqrt{e \sec (c+d x)}}{d e}-\frac{4 i \left(a^2+i a^2 \tan (c+d x)\right)}{d \sqrt{e \sec (c+d x)}}+\frac{6 a^2 E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{d \sqrt{\cos (c+d x)} \sqrt{e \sec (c+d x)}}","-\frac{6 a^2 \sin (c+d x) \sqrt{e \sec (c+d x)}}{d e}-\frac{4 i \left(a^2+i a^2 \tan (c+d x)\right)}{d \sqrt{e \sec (c+d x)}}+\frac{6 a^2 E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{d \sqrt{\cos (c+d x)} \sqrt{e \sec (c+d x)}}",1,"(6*a^2*EllipticE[(c + d*x)/2, 2])/(d*Sqrt[Cos[c + d*x]]*Sqrt[e*Sec[c + d*x]]) - (6*a^2*Sqrt[e*Sec[c + d*x]]*Sin[c + d*x])/(d*e) - ((4*I)*(a^2 + I*a^2*Tan[c + d*x]))/(d*Sqrt[e*Sec[c + d*x]])","A",4,4,28,0.1429,1,"{3496, 3768, 3771, 2639}"
196,1,85,0,0.0713038,"\int \frac{(a+i a \tan (c+d x))^2}{(e \sec (c+d x))^{3/2}} \, dx","Int[(a + I*a*Tan[c + d*x])^2/(e*Sec[c + d*x])^(3/2),x]","-\frac{2 a^2 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{e \sec (c+d x)}}{3 d e^2}-\frac{4 i \left(a^2+i a^2 \tan (c+d x)\right)}{3 d (e \sec (c+d x))^{3/2}}","-\frac{2 a^2 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{e \sec (c+d x)}}{3 d e^2}-\frac{4 i \left(a^2+i a^2 \tan (c+d x)\right)}{3 d (e \sec (c+d x))^{3/2}}",1,"(-2*a^2*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2]*Sqrt[e*Sec[c + d*x]])/(3*d*e^2) - (((4*I)/3)*(a^2 + I*a^2*Tan[c + d*x]))/(d*(e*Sec[c + d*x])^(3/2))","A",3,3,28,0.1071,1,"{3496, 3771, 2641}"
197,1,85,0,0.0715836,"\int \frac{(a+i a \tan (c+d x))^2}{(e \sec (c+d x))^{5/2}} \, dx","Int[(a + I*a*Tan[c + d*x])^2/(e*Sec[c + d*x])^(5/2),x]","\frac{2 a^2 E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{5 d e^2 \sqrt{\cos (c+d x)} \sqrt{e \sec (c+d x)}}-\frac{4 i \left(a^2+i a^2 \tan (c+d x)\right)}{5 d (e \sec (c+d x))^{5/2}}","\frac{2 a^2 E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{5 d e^2 \sqrt{\cos (c+d x)} \sqrt{e \sec (c+d x)}}-\frac{4 i \left(a^2+i a^2 \tan (c+d x)\right)}{5 d (e \sec (c+d x))^{5/2}}",1,"(2*a^2*EllipticE[(c + d*x)/2, 2])/(5*d*e^2*Sqrt[Cos[c + d*x]]*Sqrt[e*Sec[c + d*x]]) - (((4*I)/5)*(a^2 + I*a^2*Tan[c + d*x]))/(d*(e*Sec[c + d*x])^(5/2))","A",3,3,28,0.1071,1,"{3496, 3771, 2639}"
198,1,116,0,0.0873508,"\int \frac{(a+i a \tan (c+d x))^2}{(e \sec (c+d x))^{7/2}} \, dx","Int[(a + I*a*Tan[c + d*x])^2/(e*Sec[c + d*x])^(7/2),x]","\frac{2 a^2 \sin (c+d x)}{7 d e^3 \sqrt{e \sec (c+d x)}}+\frac{2 a^2 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{e \sec (c+d x)}}{7 d e^4}-\frac{4 i \left(a^2+i a^2 \tan (c+d x)\right)}{7 d (e \sec (c+d x))^{7/2}}","\frac{2 a^2 \sin (c+d x)}{7 d e^3 \sqrt{e \sec (c+d x)}}+\frac{2 a^2 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{e \sec (c+d x)}}{7 d e^4}-\frac{4 i \left(a^2+i a^2 \tan (c+d x)\right)}{7 d (e \sec (c+d x))^{7/2}}",1,"(2*a^2*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2]*Sqrt[e*Sec[c + d*x]])/(7*d*e^4) + (2*a^2*Sin[c + d*x])/(7*d*e^3*Sqrt[e*Sec[c + d*x]]) - (((4*I)/7)*(a^2 + I*a^2*Tan[c + d*x]))/(d*(e*Sec[c + d*x])^(7/2))","A",4,4,28,0.1429,1,"{3496, 3769, 3771, 2641}"
199,1,116,0,0.0871165,"\int \frac{(a+i a \tan (c+d x))^2}{(e \sec (c+d x))^{9/2}} \, dx","Int[(a + I*a*Tan[c + d*x])^2/(e*Sec[c + d*x])^(9/2),x]","\frac{2 a^2 \sin (c+d x)}{9 d e^3 (e \sec (c+d x))^{3/2}}+\frac{2 a^2 E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{3 d e^4 \sqrt{\cos (c+d x)} \sqrt{e \sec (c+d x)}}-\frac{4 i \left(a^2+i a^2 \tan (c+d x)\right)}{9 d (e \sec (c+d x))^{9/2}}","\frac{2 a^2 \sin (c+d x)}{9 d e^3 (e \sec (c+d x))^{3/2}}+\frac{2 a^2 E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{3 d e^4 \sqrt{\cos (c+d x)} \sqrt{e \sec (c+d x)}}-\frac{4 i \left(a^2+i a^2 \tan (c+d x)\right)}{9 d (e \sec (c+d x))^{9/2}}",1,"(2*a^2*EllipticE[(c + d*x)/2, 2])/(3*d*e^4*Sqrt[Cos[c + d*x]]*Sqrt[e*Sec[c + d*x]]) + (2*a^2*Sin[c + d*x])/(9*d*e^3*(e*Sec[c + d*x])^(3/2)) - (((4*I)/9)*(a^2 + I*a^2*Tan[c + d*x]))/(d*(e*Sec[c + d*x])^(9/2))","A",4,4,28,0.1429,1,"{3496, 3769, 3771, 2639}"
200,1,147,0,0.1055368,"\int \frac{(a+i a \tan (c+d x))^2}{(e \sec (c+d x))^{11/2}} \, dx","Int[(a + I*a*Tan[c + d*x])^2/(e*Sec[c + d*x])^(11/2),x]","\frac{10 a^2 \sin (c+d x)}{33 d e^5 \sqrt{e \sec (c+d x)}}+\frac{2 a^2 \sin (c+d x)}{11 d e^3 (e \sec (c+d x))^{5/2}}+\frac{10 a^2 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{e \sec (c+d x)}}{33 d e^6}-\frac{4 i \left(a^2+i a^2 \tan (c+d x)\right)}{11 d (e \sec (c+d x))^{11/2}}","\frac{10 a^2 \sin (c+d x)}{33 d e^5 \sqrt{e \sec (c+d x)}}+\frac{2 a^2 \sin (c+d x)}{11 d e^3 (e \sec (c+d x))^{5/2}}+\frac{10 a^2 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{e \sec (c+d x)}}{33 d e^6}-\frac{4 i \left(a^2+i a^2 \tan (c+d x)\right)}{11 d (e \sec (c+d x))^{11/2}}",1,"(10*a^2*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2]*Sqrt[e*Sec[c + d*x]])/(33*d*e^6) + (2*a^2*Sin[c + d*x])/(11*d*e^3*(e*Sec[c + d*x])^(5/2)) + (10*a^2*Sin[c + d*x])/(33*d*e^5*Sqrt[e*Sec[c + d*x]]) - (((4*I)/11)*(a^2 + I*a^2*Tan[c + d*x]))/(d*(e*Sec[c + d*x])^(11/2))","A",5,4,28,0.1429,1,"{3496, 3769, 3771, 2641}"
201,1,202,0,0.2013364,"\int (e \sec (c+d x))^{7/2} (a+i a \tan (c+d x))^3 \, dx","Int[(e*Sec[c + d*x])^(7/2)*(a + I*a*Tan[c + d*x])^3,x]","\frac{2 a^3 e^3 \sin (c+d x) \sqrt{e \sec (c+d x)}}{d}-\frac{2 a^3 e^4 E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{d \sqrt{\cos (c+d x)} \sqrt{e \sec (c+d x)}}+\frac{10 i a^3 (e \sec (c+d x))^{7/2}}{21 d}+\frac{2 a^3 e \sin (c+d x) (e \sec (c+d x))^{5/2}}{3 d}+\frac{10 i \left(a^3+i a^3 \tan (c+d x)\right) (e \sec (c+d x))^{7/2}}{33 d}+\frac{2 i a (a+i a \tan (c+d x))^2 (e \sec (c+d x))^{7/2}}{11 d}","\frac{2 a^3 e^3 \sin (c+d x) \sqrt{e \sec (c+d x)}}{d}-\frac{2 a^3 e^4 E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{d \sqrt{\cos (c+d x)} \sqrt{e \sec (c+d x)}}+\frac{10 i a^3 (e \sec (c+d x))^{7/2}}{21 d}+\frac{2 a^3 e \sin (c+d x) (e \sec (c+d x))^{5/2}}{3 d}+\frac{10 i \left(a^3+i a^3 \tan (c+d x)\right) (e \sec (c+d x))^{7/2}}{33 d}+\frac{2 i a (a+i a \tan (c+d x))^2 (e \sec (c+d x))^{7/2}}{11 d}",1,"(-2*a^3*e^4*EllipticE[(c + d*x)/2, 2])/(d*Sqrt[Cos[c + d*x]]*Sqrt[e*Sec[c + d*x]]) + (((10*I)/21)*a^3*(e*Sec[c + d*x])^(7/2))/d + (2*a^3*e^3*Sqrt[e*Sec[c + d*x]]*Sin[c + d*x])/d + (2*a^3*e*(e*Sec[c + d*x])^(5/2)*Sin[c + d*x])/(3*d) + (((2*I)/11)*a*(e*Sec[c + d*x])^(7/2)*(a + I*a*Tan[c + d*x])^2)/d + (((10*I)/33)*(e*Sec[c + d*x])^(7/2)*(a^3 + I*a^3*Tan[c + d*x]))/d","A",7,5,28,0.1786,1,"{3498, 3486, 3768, 3771, 2639}"
202,1,175,0,0.1877912,"\int (e \sec (c+d x))^{5/2} (a+i a \tan (c+d x))^3 \, dx","Int[(e*Sec[c + d*x])^(5/2)*(a + I*a*Tan[c + d*x])^3,x]","\frac{26 a^3 e^2 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{e \sec (c+d x)}}{21 d}+\frac{26 i a^3 (e \sec (c+d x))^{5/2}}{35 d}+\frac{26 a^3 e \sin (c+d x) (e \sec (c+d x))^{3/2}}{21 d}+\frac{26 i \left(a^3+i a^3 \tan (c+d x)\right) (e \sec (c+d x))^{5/2}}{63 d}+\frac{2 i a (a+i a \tan (c+d x))^2 (e \sec (c+d x))^{5/2}}{9 d}","\frac{26 a^3 e^2 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{e \sec (c+d x)}}{21 d}+\frac{26 i a^3 (e \sec (c+d x))^{5/2}}{35 d}+\frac{26 a^3 e \sin (c+d x) (e \sec (c+d x))^{3/2}}{21 d}+\frac{26 i \left(a^3+i a^3 \tan (c+d x)\right) (e \sec (c+d x))^{5/2}}{63 d}+\frac{2 i a (a+i a \tan (c+d x))^2 (e \sec (c+d x))^{5/2}}{9 d}",1,"(26*a^3*e^2*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2]*Sqrt[e*Sec[c + d*x]])/(21*d) + (((26*I)/35)*a^3*(e*Sec[c + d*x])^(5/2))/d + (26*a^3*e*(e*Sec[c + d*x])^(3/2)*Sin[c + d*x])/(21*d) + (((2*I)/9)*a*(e*Sec[c + d*x])^(5/2)*(a + I*a*Tan[c + d*x])^2)/d + (((26*I)/63)*(e*Sec[c + d*x])^(5/2)*(a^3 + I*a^3*Tan[c + d*x]))/d","A",6,5,28,0.1786,1,"{3498, 3486, 3768, 3771, 2641}"
203,1,175,0,0.1854266,"\int (e \sec (c+d x))^{3/2} (a+i a \tan (c+d x))^3 \, dx","Int[(e*Sec[c + d*x])^(3/2)*(a + I*a*Tan[c + d*x])^3,x]","-\frac{22 a^3 e^2 E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{5 d \sqrt{\cos (c+d x)} \sqrt{e \sec (c+d x)}}+\frac{22 i a^3 (e \sec (c+d x))^{3/2}}{15 d}+\frac{22 a^3 e \sin (c+d x) \sqrt{e \sec (c+d x)}}{5 d}+\frac{22 i \left(a^3+i a^3 \tan (c+d x)\right) (e \sec (c+d x))^{3/2}}{35 d}+\frac{2 i a (a+i a \tan (c+d x))^2 (e \sec (c+d x))^{3/2}}{7 d}","-\frac{22 a^3 e^2 E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{5 d \sqrt{\cos (c+d x)} \sqrt{e \sec (c+d x)}}+\frac{22 i a^3 (e \sec (c+d x))^{3/2}}{15 d}+\frac{22 a^3 e \sin (c+d x) \sqrt{e \sec (c+d x)}}{5 d}+\frac{22 i \left(a^3+i a^3 \tan (c+d x)\right) (e \sec (c+d x))^{3/2}}{35 d}+\frac{2 i a (a+i a \tan (c+d x))^2 (e \sec (c+d x))^{3/2}}{7 d}",1,"(-22*a^3*e^2*EllipticE[(c + d*x)/2, 2])/(5*d*Sqrt[Cos[c + d*x]]*Sqrt[e*Sec[c + d*x]]) + (((22*I)/15)*a^3*(e*Sec[c + d*x])^(3/2))/d + (22*a^3*e*Sqrt[e*Sec[c + d*x]]*Sin[c + d*x])/(5*d) + (((2*I)/7)*a*(e*Sec[c + d*x])^(3/2)*(a + I*a*Tan[c + d*x])^2)/d + (((22*I)/35)*(e*Sec[c + d*x])^(3/2)*(a^3 + I*a^3*Tan[c + d*x]))/d","A",6,5,28,0.1786,1,"{3498, 3486, 3768, 3771, 2639}"
204,1,139,0,0.1393443,"\int \sqrt{e \sec (c+d x)} (a+i a \tan (c+d x))^3 \, dx","Int[Sqrt[e*Sec[c + d*x]]*(a + I*a*Tan[c + d*x])^3,x]","\frac{6 i a^3 \sqrt{e \sec (c+d x)}}{d}+\frac{6 i \left(a^3+i a^3 \tan (c+d x)\right) \sqrt{e \sec (c+d x)}}{5 d}+\frac{6 a^3 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{e \sec (c+d x)}}{d}+\frac{2 i a (a+i a \tan (c+d x))^2 \sqrt{e \sec (c+d x)}}{5 d}","\frac{6 i a^3 \sqrt{e \sec (c+d x)}}{d}+\frac{6 i \left(a^3+i a^3 \tan (c+d x)\right) \sqrt{e \sec (c+d x)}}{5 d}+\frac{6 a^3 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{e \sec (c+d x)}}{d}+\frac{2 i a (a+i a \tan (c+d x))^2 \sqrt{e \sec (c+d x)}}{5 d}",1,"((6*I)*a^3*Sqrt[e*Sec[c + d*x]])/d + (6*a^3*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2]*Sqrt[e*Sec[c + d*x]])/d + (((2*I)/5)*a*Sqrt[e*Sec[c + d*x]]*(a + I*a*Tan[c + d*x])^2)/d + (((6*I)/5)*Sqrt[e*Sec[c + d*x]]*(a^3 + I*a^3*Tan[c + d*x]))/d","A",5,4,28,0.1429,1,"{3498, 3486, 3771, 2641}"
205,1,146,0,0.1336425,"\int \frac{(a+i a \tan (c+d x))^3}{\sqrt{e \sec (c+d x)}} \, dx","Int[(a + I*a*Tan[c + d*x])^3/Sqrt[e*Sec[c + d*x]],x]","-\frac{14 a^3 \sin (c+d x) \sqrt{e \sec (c+d x)}}{d e}-\frac{28 i \left(a^3+i a^3 \tan (c+d x)\right)}{3 d \sqrt{e \sec (c+d x)}}+\frac{14 a^3 E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{d \sqrt{\cos (c+d x)} \sqrt{e \sec (c+d x)}}+\frac{2 i a (a+i a \tan (c+d x))^2}{3 d \sqrt{e \sec (c+d x)}}","-\frac{26 i a^3}{3 d \sqrt{e \sec (c+d x)}}-\frac{2 i a^3 \tan ^2(c+d x)}{3 d \sqrt{e \sec (c+d x)}}-\frac{6 a^3 \tan (c+d x)}{d \sqrt{e \sec (c+d x)}}+\frac{14 a^3 E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{d \sqrt{\cos (c+d x)} \sqrt{e \sec (c+d x)}}",1,"(14*a^3*EllipticE[(c + d*x)/2, 2])/(d*Sqrt[Cos[c + d*x]]*Sqrt[e*Sec[c + d*x]]) - (14*a^3*Sqrt[e*Sec[c + d*x]]*Sin[c + d*x])/(d*e) + (((2*I)/3)*a*(a + I*a*Tan[c + d*x])^2)/(d*Sqrt[e*Sec[c + d*x]]) - (((28*I)/3)*(a^3 + I*a^3*Tan[c + d*x]))/(d*Sqrt[e*Sec[c + d*x]])","A",5,5,28,0.1786,1,"{3498, 3496, 3768, 3771, 2639}"
206,1,111,0,0.1024236,"\int \frac{(a+i a \tan (c+d x))^3}{(e \sec (c+d x))^{3/2}} \, dx","Int[(a + I*a*Tan[c + d*x])^3/(e*Sec[c + d*x])^(3/2),x]","-\frac{10 i a^3 \sqrt{e \sec (c+d x)}}{3 d e^2}-\frac{10 a^3 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{e \sec (c+d x)}}{3 d e^2}-\frac{4 i a (a+i a \tan (c+d x))^2}{3 d (e \sec (c+d x))^{3/2}}","-\frac{10 i a^3 \sqrt{e \sec (c+d x)}}{3 d e^2}-\frac{10 a^3 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{e \sec (c+d x)}}{3 d e^2}-\frac{4 i a (a+i a \tan (c+d x))^2}{3 d (e \sec (c+d x))^{3/2}}",1,"(((-10*I)/3)*a^3*Sqrt[e*Sec[c + d*x]])/(d*e^2) - (10*a^3*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2]*Sqrt[e*Sec[c + d*x]])/(3*d*e^2) - (((4*I)/3)*a*(a + I*a*Tan[c + d*x])^2)/(d*(e*Sec[c + d*x])^(3/2))","A",4,4,28,0.1429,1,"{3496, 3486, 3771, 2641}"
207,1,111,0,0.1011706,"\int \frac{(a+i a \tan (c+d x))^3}{(e \sec (c+d x))^{5/2}} \, dx","Int[(a + I*a*Tan[c + d*x])^3/(e*Sec[c + d*x])^(5/2),x]","\frac{6 i a^3}{5 d e^2 \sqrt{e \sec (c+d x)}}-\frac{6 a^3 E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{5 d e^2 \sqrt{\cos (c+d x)} \sqrt{e \sec (c+d x)}}-\frac{4 i a (a+i a \tan (c+d x))^2}{5 d (e \sec (c+d x))^{5/2}}","\frac{6 i a^3}{5 d e^2 \sqrt{e \sec (c+d x)}}-\frac{6 a^3 E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{5 d e^2 \sqrt{\cos (c+d x)} \sqrt{e \sec (c+d x)}}-\frac{4 i a (a+i a \tan (c+d x))^2}{5 d (e \sec (c+d x))^{5/2}}",1,"(((6*I)/5)*a^3)/(d*e^2*Sqrt[e*Sec[c + d*x]]) - (6*a^3*EllipticE[(c + d*x)/2, 2])/(5*d*e^2*Sqrt[Cos[c + d*x]]*Sqrt[e*Sec[c + d*x]]) - (((4*I)/5)*a*(a + I*a*Tan[c + d*x])^2)/(d*(e*Sec[c + d*x])^(5/2))","A",4,4,28,0.1429,1,"{3496, 3486, 3771, 2639}"
208,1,124,0,0.1265056,"\int \frac{(a+i a \tan (c+d x))^3}{(e \sec (c+d x))^{7/2}} \, dx","Int[(a + I*a*Tan[c + d*x])^3/(e*Sec[c + d*x])^(7/2),x]","-\frac{4 i \left(a^3+i a^3 \tan (c+d x)\right)}{21 d e^2 (e \sec (c+d x))^{3/2}}-\frac{2 a^3 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{e \sec (c+d x)}}{21 d e^4}-\frac{2 i (a+i a \tan (c+d x))^3}{7 d (e \sec (c+d x))^{7/2}}","-\frac{4 i \left(a^3+i a^3 \tan (c+d x)\right)}{21 d e^2 (e \sec (c+d x))^{3/2}}-\frac{2 a^3 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{e \sec (c+d x)}}{21 d e^4}-\frac{2 i (a+i a \tan (c+d x))^3}{7 d (e \sec (c+d x))^{7/2}}",1,"(-2*a^3*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2]*Sqrt[e*Sec[c + d*x]])/(21*d*e^4) - (((2*I)/7)*(a + I*a*Tan[c + d*x])^3)/(d*(e*Sec[c + d*x])^(7/2)) - (((4*I)/21)*(a^3 + I*a^3*Tan[c + d*x]))/(d*e^2*(e*Sec[c + d*x])^(3/2))","A",4,4,28,0.1429,1,"{3497, 3496, 3771, 2641}"
209,1,124,0,0.1265616,"\int \frac{(a+i a \tan (c+d x))^3}{(e \sec (c+d x))^{9/2}} \, dx","Int[(a + I*a*Tan[c + d*x])^3/(e*Sec[c + d*x])^(9/2),x]","-\frac{4 i \left(a^3+i a^3 \tan (c+d x)\right)}{15 d e^2 (e \sec (c+d x))^{5/2}}+\frac{2 a^3 E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{15 d e^4 \sqrt{\cos (c+d x)} \sqrt{e \sec (c+d x)}}-\frac{2 i (a+i a \tan (c+d x))^3}{9 d (e \sec (c+d x))^{9/2}}","-\frac{4 i \left(a^3+i a^3 \tan (c+d x)\right)}{15 d e^2 (e \sec (c+d x))^{5/2}}+\frac{2 a^3 E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{15 d e^4 \sqrt{\cos (c+d x)} \sqrt{e \sec (c+d x)}}-\frac{2 i (a+i a \tan (c+d x))^3}{9 d (e \sec (c+d x))^{9/2}}",1,"(2*a^3*EllipticE[(c + d*x)/2, 2])/(15*d*e^4*Sqrt[Cos[c + d*x]]*Sqrt[e*Sec[c + d*x]]) - (((2*I)/9)*(a + I*a*Tan[c + d*x])^3)/(d*(e*Sec[c + d*x])^(9/2)) - (((4*I)/15)*(a^3 + I*a^3*Tan[c + d*x]))/(d*e^2*(e*Sec[c + d*x])^(5/2))","A",4,4,28,0.1429,1,"{3497, 3496, 3771, 2639}"
210,1,155,0,0.1546899,"\int \frac{(a+i a \tan (c+d x))^3}{(e \sec (c+d x))^{11/2}} \, dx","Int[(a + I*a*Tan[c + d*x])^3/(e*Sec[c + d*x])^(11/2),x]","\frac{10 a^3 \sin (c+d x)}{77 d e^5 \sqrt{e \sec (c+d x)}}-\frac{20 i \left(a^3+i a^3 \tan (c+d x)\right)}{77 d e^2 (e \sec (c+d x))^{7/2}}+\frac{10 a^3 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{e \sec (c+d x)}}{77 d e^6}-\frac{2 i (a+i a \tan (c+d x))^3}{11 d (e \sec (c+d x))^{11/2}}","\frac{10 a^3 \sin (c+d x)}{77 d e^5 \sqrt{e \sec (c+d x)}}-\frac{20 i \left(a^3+i a^3 \tan (c+d x)\right)}{77 d e^2 (e \sec (c+d x))^{7/2}}+\frac{10 a^3 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{e \sec (c+d x)}}{77 d e^6}-\frac{2 i (a+i a \tan (c+d x))^3}{11 d (e \sec (c+d x))^{11/2}}",1,"(10*a^3*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2]*Sqrt[e*Sec[c + d*x]])/(77*d*e^6) + (10*a^3*Sin[c + d*x])/(77*d*e^5*Sqrt[e*Sec[c + d*x]]) - (((2*I)/11)*(a + I*a*Tan[c + d*x])^3)/(d*(e*Sec[c + d*x])^(11/2)) - (((20*I)/77)*(a^3 + I*a^3*Tan[c + d*x]))/(d*e^2*(e*Sec[c + d*x])^(7/2))","A",5,5,28,0.1786,1,"{3497, 3496, 3769, 3771, 2641}"
211,1,155,0,0.1479788,"\int \frac{(a+i a \tan (c+d x))^3}{(e \sec (c+d x))^{13/2}} \, dx","Int[(a + I*a*Tan[c + d*x])^3/(e*Sec[c + d*x])^(13/2),x]","\frac{14 a^3 \sin (c+d x)}{117 d e^5 (e \sec (c+d x))^{3/2}}-\frac{28 i \left(a^3+i a^3 \tan (c+d x)\right)}{117 d e^2 (e \sec (c+d x))^{9/2}}+\frac{14 a^3 E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{39 d e^6 \sqrt{\cos (c+d x)} \sqrt{e \sec (c+d x)}}-\frac{2 i (a+i a \tan (c+d x))^3}{13 d (e \sec (c+d x))^{13/2}}","\frac{14 a^3 \sin (c+d x)}{117 d e^5 (e \sec (c+d x))^{3/2}}-\frac{28 i \left(a^3+i a^3 \tan (c+d x)\right)}{117 d e^2 (e \sec (c+d x))^{9/2}}+\frac{14 a^3 E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{39 d e^6 \sqrt{\cos (c+d x)} \sqrt{e \sec (c+d x)}}-\frac{2 i (a+i a \tan (c+d x))^3}{13 d (e \sec (c+d x))^{13/2}}",1,"(14*a^3*EllipticE[(c + d*x)/2, 2])/(39*d*e^6*Sqrt[Cos[c + d*x]]*Sqrt[e*Sec[c + d*x]]) + (14*a^3*Sin[c + d*x])/(117*d*e^5*(e*Sec[c + d*x])^(3/2)) - (((2*I)/13)*(a + I*a*Tan[c + d*x])^3)/(d*(e*Sec[c + d*x])^(13/2)) - (((28*I)/117)*(a^3 + I*a^3*Tan[c + d*x]))/(d*e^2*(e*Sec[c + d*x])^(9/2))","A",5,5,28,0.1786,1,"{3497, 3496, 3769, 3771, 2639}"
212,1,186,0,0.1733924,"\int \frac{(a+i a \tan (c+d x))^3}{(e \sec (c+d x))^{15/2}} \, dx","Int[(a + I*a*Tan[c + d*x])^3/(e*Sec[c + d*x])^(15/2),x]","\frac{2 a^3 \sin (c+d x)}{11 d e^7 \sqrt{e \sec (c+d x)}}+\frac{6 a^3 \sin (c+d x)}{55 d e^5 (e \sec (c+d x))^{5/2}}-\frac{12 i \left(a^3+i a^3 \tan (c+d x)\right)}{55 d e^2 (e \sec (c+d x))^{11/2}}+\frac{2 a^3 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{e \sec (c+d x)}}{11 d e^8}-\frac{2 i (a+i a \tan (c+d x))^3}{15 d (e \sec (c+d x))^{15/2}}","\frac{2 a^3 \sin (c+d x)}{11 d e^7 \sqrt{e \sec (c+d x)}}+\frac{6 a^3 \sin (c+d x)}{55 d e^5 (e \sec (c+d x))^{5/2}}-\frac{12 i \left(a^3+i a^3 \tan (c+d x)\right)}{55 d e^2 (e \sec (c+d x))^{11/2}}+\frac{2 a^3 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{e \sec (c+d x)}}{11 d e^8}-\frac{2 i (a+i a \tan (c+d x))^3}{15 d (e \sec (c+d x))^{15/2}}",1,"(2*a^3*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2]*Sqrt[e*Sec[c + d*x]])/(11*d*e^8) + (6*a^3*Sin[c + d*x])/(55*d*e^5*(e*Sec[c + d*x])^(5/2)) + (2*a^3*Sin[c + d*x])/(11*d*e^7*Sqrt[e*Sec[c + d*x]]) - (((2*I)/15)*(a + I*a*Tan[c + d*x])^3)/(d*(e*Sec[c + d*x])^(15/2)) - (((12*I)/55)*(a^3 + I*a^3*Tan[c + d*x]))/(d*e^2*(e*Sec[c + d*x])^(11/2))","A",6,5,28,0.1786,1,"{3497, 3496, 3769, 3771, 2641}"
213,1,215,0,0.2569756,"\int (e \sec (c+d x))^{3/2} (a+i a \tan (c+d x))^4 \, dx","Int[(e*Sec[c + d*x])^(3/2)*(a + I*a*Tan[c + d*x])^4,x]","-\frac{22 a^4 e^2 E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{3 d \sqrt{\cos (c+d x)} \sqrt{e \sec (c+d x)}}+\frac{22 i a^4 (e \sec (c+d x))^{3/2}}{9 d}+\frac{22 a^4 e \sin (c+d x) \sqrt{e \sec (c+d x)}}{3 d}+\frac{10 i \left(a^2+i a^2 \tan (c+d x)\right)^2 (e \sec (c+d x))^{3/2}}{21 d}+\frac{22 i \left(a^4+i a^4 \tan (c+d x)\right) (e \sec (c+d x))^{3/2}}{21 d}+\frac{2 i a (a+i a \tan (c+d x))^3 (e \sec (c+d x))^{3/2}}{9 d}","-\frac{22 a^4 e^2 E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{3 d \sqrt{\cos (c+d x)} \sqrt{e \sec (c+d x)}}+\frac{22 i a^4 (e \sec (c+d x))^{3/2}}{9 d}+\frac{22 a^4 e \sin (c+d x) \sqrt{e \sec (c+d x)}}{3 d}+\frac{10 i \left(a^2+i a^2 \tan (c+d x)\right)^2 (e \sec (c+d x))^{3/2}}{21 d}+\frac{22 i \left(a^4+i a^4 \tan (c+d x)\right) (e \sec (c+d x))^{3/2}}{21 d}+\frac{2 i a (a+i a \tan (c+d x))^3 (e \sec (c+d x))^{3/2}}{9 d}",1,"(-22*a^4*e^2*EllipticE[(c + d*x)/2, 2])/(3*d*Sqrt[Cos[c + d*x]]*Sqrt[e*Sec[c + d*x]]) + (((22*I)/9)*a^4*(e*Sec[c + d*x])^(3/2))/d + (22*a^4*e*Sqrt[e*Sec[c + d*x]]*Sin[c + d*x])/(3*d) + (((2*I)/9)*a*(e*Sec[c + d*x])^(3/2)*(a + I*a*Tan[c + d*x])^3)/d + (((10*I)/21)*(e*Sec[c + d*x])^(3/2)*(a^2 + I*a^2*Tan[c + d*x])^2)/d + (((22*I)/21)*(e*Sec[c + d*x])^(3/2)*(a^4 + I*a^4*Tan[c + d*x]))/d","A",7,5,28,0.1786,1,"{3498, 3486, 3768, 3771, 2639}"
214,1,183,0,0.2015632,"\int \sqrt{e \sec (c+d x)} (a+i a \tan (c+d x))^4 \, dx","Int[Sqrt[e*Sec[c + d*x]]*(a + I*a*Tan[c + d*x])^4,x]","\frac{78 i a^4 \sqrt{e \sec (c+d x)}}{7 d}+\frac{26 i \left(a^2+i a^2 \tan (c+d x)\right)^2 \sqrt{e \sec (c+d x)}}{35 d}+\frac{78 i \left(a^4+i a^4 \tan (c+d x)\right) \sqrt{e \sec (c+d x)}}{35 d}+\frac{78 a^4 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{e \sec (c+d x)}}{7 d}+\frac{2 i a (a+i a \tan (c+d x))^3 \sqrt{e \sec (c+d x)}}{7 d}","\frac{78 i a^4 \sqrt{e \sec (c+d x)}}{7 d}+\frac{26 i \left(a^2+i a^2 \tan (c+d x)\right)^2 \sqrt{e \sec (c+d x)}}{35 d}+\frac{78 i \left(a^4+i a^4 \tan (c+d x)\right) \sqrt{e \sec (c+d x)}}{35 d}+\frac{78 a^4 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{e \sec (c+d x)}}{7 d}+\frac{2 i a (a+i a \tan (c+d x))^3 \sqrt{e \sec (c+d x)}}{7 d}",1,"(((78*I)/7)*a^4*Sqrt[e*Sec[c + d*x]])/d + (78*a^4*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2]*Sqrt[e*Sec[c + d*x]])/(7*d) + (((2*I)/7)*a*Sqrt[e*Sec[c + d*x]]*(a + I*a*Tan[c + d*x])^3)/d + (((26*I)/35)*Sqrt[e*Sec[c + d*x]]*(a^2 + I*a^2*Tan[c + d*x])^2)/d + (((78*I)/35)*Sqrt[e*Sec[c + d*x]]*(a^4 + I*a^4*Tan[c + d*x]))/d","A",6,4,28,0.1429,1,"{3498, 3486, 3771, 2641}"
215,1,178,0,0.1863388,"\int \frac{(a+i a \tan (c+d x))^4}{\sqrt{e \sec (c+d x)}} \, dx","Int[(a + I*a*Tan[c + d*x])^4/Sqrt[e*Sec[c + d*x]],x]","-\frac{154 i a^4 (e \sec (c+d x))^{3/2}}{15 d e^2}-\frac{22 i \left(a^4+i a^4 \tan (c+d x)\right) (e \sec (c+d x))^{3/2}}{5 d e^2}-\frac{154 a^4 \sin (c+d x) \sqrt{e \sec (c+d x)}}{5 d e}+\frac{154 a^4 E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{5 d \sqrt{\cos (c+d x)} \sqrt{e \sec (c+d x)}}-\frac{4 i a (a+i a \tan (c+d x))^3}{d \sqrt{e \sec (c+d x)}}","-\frac{154 i a^4 (e \sec (c+d x))^{3/2}}{15 d e^2}-\frac{22 i \left(a^4+i a^4 \tan (c+d x)\right) (e \sec (c+d x))^{3/2}}{5 d e^2}-\frac{154 a^4 \sin (c+d x) \sqrt{e \sec (c+d x)}}{5 d e}+\frac{154 a^4 E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{5 d \sqrt{\cos (c+d x)} \sqrt{e \sec (c+d x)}}-\frac{4 i a (a+i a \tan (c+d x))^3}{d \sqrt{e \sec (c+d x)}}",1,"(154*a^4*EllipticE[(c + d*x)/2, 2])/(5*d*Sqrt[Cos[c + d*x]]*Sqrt[e*Sec[c + d*x]]) - (((154*I)/15)*a^4*(e*Sec[c + d*x])^(3/2))/(d*e^2) - (154*a^4*Sqrt[e*Sec[c + d*x]]*Sin[c + d*x])/(5*d*e) - ((4*I)*a*(a + I*a*Tan[c + d*x])^3)/(d*Sqrt[e*Sec[c + d*x]]) - (((22*I)/5)*(e*Sec[c + d*x])^(3/2)*(a^4 + I*a^4*Tan[c + d*x]))/(d*e^2)","A",6,6,28,0.2143,1,"{3496, 3498, 3486, 3768, 3771, 2639}"
216,1,146,0,0.1490205,"\int \frac{(a+i a \tan (c+d x))^4}{(e \sec (c+d x))^{3/2}} \, dx","Int[(a + I*a*Tan[c + d*x])^4/(e*Sec[c + d*x])^(3/2),x]","-\frac{10 i a^4 \sqrt{e \sec (c+d x)}}{d e^2}-\frac{2 i \left(a^4+i a^4 \tan (c+d x)\right) \sqrt{e \sec (c+d x)}}{d e^2}-\frac{10 a^4 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{e \sec (c+d x)}}{d e^2}-\frac{4 i a (a+i a \tan (c+d x))^3}{3 d (e \sec (c+d x))^{3/2}}","-\frac{10 i a^4 \sqrt{e \sec (c+d x)}}{d e^2}-\frac{2 i \left(a^4+i a^4 \tan (c+d x)\right) \sqrt{e \sec (c+d x)}}{d e^2}-\frac{10 a^4 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{e \sec (c+d x)}}{d e^2}-\frac{4 i a (a+i a \tan (c+d x))^3}{3 d (e \sec (c+d x))^{3/2}}",1,"((-10*I)*a^4*Sqrt[e*Sec[c + d*x]])/(d*e^2) - (10*a^4*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2]*Sqrt[e*Sec[c + d*x]])/(d*e^2) - (((4*I)/3)*a*(a + I*a*Tan[c + d*x])^3)/(d*(e*Sec[c + d*x])^(3/2)) - ((2*I)*Sqrt[e*Sec[c + d*x]]*(a^4 + I*a^4*Tan[c + d*x]))/(d*e^2)","A",5,5,28,0.1786,1,"{3496, 3498, 3486, 3771, 2641}"
217,1,156,0,0.1387279,"\int \frac{(a+i a \tan (c+d x))^4}{(e \sec (c+d x))^{5/2}} \, dx","Int[(a + I*a*Tan[c + d*x])^4/(e*Sec[c + d*x])^(5/2),x]","\frac{42 a^4 \sin (c+d x) \sqrt{e \sec (c+d x)}}{5 d e^3}+\frac{28 i \left(a^4+i a^4 \tan (c+d x)\right)}{5 d e^2 \sqrt{e \sec (c+d x)}}-\frac{42 a^4 E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{5 d e^2 \sqrt{\cos (c+d x)} \sqrt{e \sec (c+d x)}}-\frac{4 i a (a+i a \tan (c+d x))^3}{5 d (e \sec (c+d x))^{5/2}}","\frac{42 a^4 \sin (c+d x) \sqrt{e \sec (c+d x)}}{5 d e^3}+\frac{28 i \left(a^4+i a^4 \tan (c+d x)\right)}{5 d e^2 \sqrt{e \sec (c+d x)}}-\frac{42 a^4 E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{5 d e^2 \sqrt{\cos (c+d x)} \sqrt{e \sec (c+d x)}}-\frac{4 i a (a+i a \tan (c+d x))^3}{5 d (e \sec (c+d x))^{5/2}}",1,"(-42*a^4*EllipticE[(c + d*x)/2, 2])/(5*d*e^2*Sqrt[Cos[c + d*x]]*Sqrt[e*Sec[c + d*x]]) + (42*a^4*Sqrt[e*Sec[c + d*x]]*Sin[c + d*x])/(5*d*e^3) - (((4*I)/5)*a*(a + I*a*Tan[c + d*x])^3)/(d*(e*Sec[c + d*x])^(5/2)) + (((28*I)/5)*(a^4 + I*a^4*Tan[c + d*x]))/(d*e^2*Sqrt[e*Sec[c + d*x]])","A",5,4,28,0.1429,1,"{3496, 3768, 3771, 2639}"
218,1,125,0,0.1339247,"\int \frac{(a+i a \tan (c+d x))^4}{(e \sec (c+d x))^{7/2}} \, dx","Int[(a + I*a*Tan[c + d*x])^4/(e*Sec[c + d*x])^(7/2),x]","\frac{20 i \left(a^4+i a^4 \tan (c+d x)\right)}{21 d e^2 (e \sec (c+d x))^{3/2}}+\frac{10 a^4 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{e \sec (c+d x)}}{21 d e^4}-\frac{4 i a (a+i a \tan (c+d x))^3}{7 d (e \sec (c+d x))^{7/2}}","\frac{20 i \left(a^4+i a^4 \tan (c+d x)\right)}{21 d e^2 (e \sec (c+d x))^{3/2}}+\frac{10 a^4 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{e \sec (c+d x)}}{21 d e^4}-\frac{4 i a (a+i a \tan (c+d x))^3}{7 d (e \sec (c+d x))^{7/2}}",1,"(10*a^4*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2]*Sqrt[e*Sec[c + d*x]])/(21*d*e^4) - (((4*I)/7)*a*(a + I*a*Tan[c + d*x])^3)/(d*(e*Sec[c + d*x])^(7/2)) + (((20*I)/21)*(a^4 + I*a^4*Tan[c + d*x]))/(d*e^2*(e*Sec[c + d*x])^(3/2))","A",4,3,28,0.1071,1,"{3496, 3771, 2641}"
219,1,125,0,0.1313848,"\int \frac{(a+i a \tan (c+d x))^4}{(e \sec (c+d x))^{9/2}} \, dx","Int[(a + I*a*Tan[c + d*x])^4/(e*Sec[c + d*x])^(9/2),x]","\frac{4 i \left(a^4+i a^4 \tan (c+d x)\right)}{15 d e^2 (e \sec (c+d x))^{5/2}}-\frac{2 a^4 E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{15 d e^4 \sqrt{\cos (c+d x)} \sqrt{e \sec (c+d x)}}-\frac{4 i a (a+i a \tan (c+d x))^3}{9 d (e \sec (c+d x))^{9/2}}","\frac{4 i \left(a^4+i a^4 \tan (c+d x)\right)}{15 d e^2 (e \sec (c+d x))^{5/2}}-\frac{2 a^4 E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{15 d e^4 \sqrt{\cos (c+d x)} \sqrt{e \sec (c+d x)}}-\frac{4 i a (a+i a \tan (c+d x))^3}{9 d (e \sec (c+d x))^{9/2}}",1,"(-2*a^4*EllipticE[(c + d*x)/2, 2])/(15*d*e^4*Sqrt[Cos[c + d*x]]*Sqrt[e*Sec[c + d*x]]) - (((4*I)/9)*a*(a + I*a*Tan[c + d*x])^3)/(d*(e*Sec[c + d*x])^(9/2)) + (((4*I)/15)*(a^4 + I*a^4*Tan[c + d*x]))/(d*e^2*(e*Sec[c + d*x])^(5/2))","A",4,3,28,0.1071,1,"{3496, 3771, 2639}"
220,1,156,0,0.1470227,"\int \frac{(a+i a \tan (c+d x))^4}{(e \sec (c+d x))^{11/2}} \, dx","Int[(a + I*a*Tan[c + d*x])^4/(e*Sec[c + d*x])^(11/2),x]","-\frac{2 a^4 \sin (c+d x)}{77 d e^5 \sqrt{e \sec (c+d x)}}+\frac{4 i \left(a^4+i a^4 \tan (c+d x)\right)}{77 d e^2 (e \sec (c+d x))^{7/2}}-\frac{2 a^4 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{e \sec (c+d x)}}{77 d e^6}-\frac{4 i a (a+i a \tan (c+d x))^3}{11 d (e \sec (c+d x))^{11/2}}","-\frac{2 a^4 \sin (c+d x)}{77 d e^5 \sqrt{e \sec (c+d x)}}+\frac{4 i \left(a^4+i a^4 \tan (c+d x)\right)}{77 d e^2 (e \sec (c+d x))^{7/2}}-\frac{2 a^4 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{e \sec (c+d x)}}{77 d e^6}-\frac{4 i a (a+i a \tan (c+d x))^3}{11 d (e \sec (c+d x))^{11/2}}",1,"(-2*a^4*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2]*Sqrt[e*Sec[c + d*x]])/(77*d*e^6) - (2*a^4*Sin[c + d*x])/(77*d*e^5*Sqrt[e*Sec[c + d*x]]) - (((4*I)/11)*a*(a + I*a*Tan[c + d*x])^3)/(d*(e*Sec[c + d*x])^(11/2)) + (((4*I)/77)*(a^4 + I*a^4*Tan[c + d*x]))/(d*e^2*(e*Sec[c + d*x])^(7/2))","A",5,4,28,0.1429,1,"{3496, 3769, 3771, 2641}"
221,1,156,0,0.1465844,"\int \frac{(a+i a \tan (c+d x))^4}{(e \sec (c+d x))^{13/2}} \, dx","Int[(a + I*a*Tan[c + d*x])^4/(e*Sec[c + d*x])^(13/2),x]","\frac{2 a^4 \sin (c+d x)}{117 d e^5 (e \sec (c+d x))^{3/2}}-\frac{4 i \left(a^4+i a^4 \tan (c+d x)\right)}{117 d e^2 (e \sec (c+d x))^{9/2}}+\frac{2 a^4 E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{39 d e^6 \sqrt{\cos (c+d x)} \sqrt{e \sec (c+d x)}}-\frac{4 i a (a+i a \tan (c+d x))^3}{13 d (e \sec (c+d x))^{13/2}}","\frac{2 a^4 \sin (c+d x)}{117 d e^5 (e \sec (c+d x))^{3/2}}-\frac{4 i \left(a^4+i a^4 \tan (c+d x)\right)}{117 d e^2 (e \sec (c+d x))^{9/2}}+\frac{2 a^4 E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{39 d e^6 \sqrt{\cos (c+d x)} \sqrt{e \sec (c+d x)}}-\frac{4 i a (a+i a \tan (c+d x))^3}{13 d (e \sec (c+d x))^{13/2}}",1,"(2*a^4*EllipticE[(c + d*x)/2, 2])/(39*d*e^6*Sqrt[Cos[c + d*x]]*Sqrt[e*Sec[c + d*x]]) + (2*a^4*Sin[c + d*x])/(117*d*e^5*(e*Sec[c + d*x])^(3/2)) - (((4*I)/13)*a*(a + I*a*Tan[c + d*x])^3)/(d*(e*Sec[c + d*x])^(13/2)) - (((4*I)/117)*(a^4 + I*a^4*Tan[c + d*x]))/(d*e^2*(e*Sec[c + d*x])^(9/2))","A",5,4,28,0.1429,1,"{3496, 3769, 3771, 2639}"
222,1,187,0,0.1665631,"\int \frac{(a+i a \tan (c+d x))^4}{(e \sec (c+d x))^{15/2}} \, dx","Int[(a + I*a*Tan[c + d*x])^4/(e*Sec[c + d*x])^(15/2),x]","\frac{2 a^4 \sin (c+d x)}{33 d e^7 \sqrt{e \sec (c+d x)}}+\frac{2 a^4 \sin (c+d x)}{55 d e^5 (e \sec (c+d x))^{5/2}}-\frac{4 i \left(a^4+i a^4 \tan (c+d x)\right)}{55 d e^2 (e \sec (c+d x))^{11/2}}+\frac{2 a^4 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{e \sec (c+d x)}}{33 d e^8}-\frac{4 i a (a+i a \tan (c+d x))^3}{15 d (e \sec (c+d x))^{15/2}}","\frac{2 a^4 \sin (c+d x)}{33 d e^7 \sqrt{e \sec (c+d x)}}+\frac{2 a^4 \sin (c+d x)}{55 d e^5 (e \sec (c+d x))^{5/2}}-\frac{4 i \left(a^4+i a^4 \tan (c+d x)\right)}{55 d e^2 (e \sec (c+d x))^{11/2}}+\frac{2 a^4 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{e \sec (c+d x)}}{33 d e^8}-\frac{4 i a (a+i a \tan (c+d x))^3}{15 d (e \sec (c+d x))^{15/2}}",1,"(2*a^4*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2]*Sqrt[e*Sec[c + d*x]])/(33*d*e^8) + (2*a^4*Sin[c + d*x])/(55*d*e^5*(e*Sec[c + d*x])^(5/2)) + (2*a^4*Sin[c + d*x])/(33*d*e^7*Sqrt[e*Sec[c + d*x]]) - (((4*I)/15)*a*(a + I*a*Tan[c + d*x])^3)/(d*(e*Sec[c + d*x])^(15/2)) - (((4*I)/55)*(a^4 + I*a^4*Tan[c + d*x]))/(d*e^2*(e*Sec[c + d*x])^(11/2))","A",6,4,28,0.1429,1,"{3496, 3769, 3771, 2641}"
223,1,136,0,0.1081598,"\int \frac{(e \sec (c+d x))^{11/2}}{a+i a \tan (c+d x)} \, dx","Int[(e*Sec[c + d*x])^(11/2)/(a + I*a*Tan[c + d*x]),x]","-\frac{2 i e^2 (e \sec (c+d x))^{7/2}}{7 a d}+\frac{6 e^5 \sin (c+d x) \sqrt{e \sec (c+d x)}}{5 a d}+\frac{2 e^3 \sin (c+d x) (e \sec (c+d x))^{5/2}}{5 a d}-\frac{6 e^6 E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{5 a d \sqrt{\cos (c+d x)} \sqrt{e \sec (c+d x)}}","-\frac{2 i e^2 (e \sec (c+d x))^{7/2}}{7 a d}+\frac{6 e^5 \sin (c+d x) \sqrt{e \sec (c+d x)}}{5 a d}+\frac{2 e^3 \sin (c+d x) (e \sec (c+d x))^{5/2}}{5 a d}-\frac{6 e^6 E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{5 a d \sqrt{\cos (c+d x)} \sqrt{e \sec (c+d x)}}",1,"(-6*e^6*EllipticE[(c + d*x)/2, 2])/(5*a*d*Sqrt[Cos[c + d*x]]*Sqrt[e*Sec[c + d*x]]) - (((2*I)/7)*e^2*(e*Sec[c + d*x])^(7/2))/(a*d) + (6*e^5*Sqrt[e*Sec[c + d*x]]*Sin[c + d*x])/(5*a*d) + (2*e^3*(e*Sec[c + d*x])^(5/2)*Sin[c + d*x])/(5*a*d)","A",5,4,28,0.1429,1,"{3501, 3768, 3771, 2639}"
224,1,105,0,0.0891565,"\int \frac{(e \sec (c+d x))^{9/2}}{a+i a \tan (c+d x)} \, dx","Int[(e*Sec[c + d*x])^(9/2)/(a + I*a*Tan[c + d*x]),x]","-\frac{2 i e^2 (e \sec (c+d x))^{5/2}}{5 a d}+\frac{2 e^3 \sin (c+d x) (e \sec (c+d x))^{3/2}}{3 a d}+\frac{2 e^4 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{e \sec (c+d x)}}{3 a d}","-\frac{2 i e^2 (e \sec (c+d x))^{5/2}}{5 a d}+\frac{2 e^3 \sin (c+d x) (e \sec (c+d x))^{3/2}}{3 a d}+\frac{2 e^4 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{e \sec (c+d x)}}{3 a d}",1,"(2*e^4*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2]*Sqrt[e*Sec[c + d*x]])/(3*a*d) - (((2*I)/5)*e^2*(e*Sec[c + d*x])^(5/2))/(a*d) + (2*e^3*(e*Sec[c + d*x])^(3/2)*Sin[c + d*x])/(3*a*d)","A",4,4,28,0.1429,1,"{3501, 3768, 3771, 2641}"
225,1,101,0,0.0878165,"\int \frac{(e \sec (c+d x))^{7/2}}{a+i a \tan (c+d x)} \, dx","Int[(e*Sec[c + d*x])^(7/2)/(a + I*a*Tan[c + d*x]),x]","-\frac{2 i e^2 (e \sec (c+d x))^{3/2}}{3 a d}+\frac{2 e^3 \sin (c+d x) \sqrt{e \sec (c+d x)}}{a d}-\frac{2 e^4 E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{a d \sqrt{\cos (c+d x)} \sqrt{e \sec (c+d x)}}","-\frac{2 i e^2 (e \sec (c+d x))^{3/2}}{3 a d}+\frac{2 e^3 \sin (c+d x) \sqrt{e \sec (c+d x)}}{a d}-\frac{2 e^4 E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{a d \sqrt{\cos (c+d x)} \sqrt{e \sec (c+d x)}}",1,"(-2*e^4*EllipticE[(c + d*x)/2, 2])/(a*d*Sqrt[Cos[c + d*x]]*Sqrt[e*Sec[c + d*x]]) - (((2*I)/3)*e^2*(e*Sec[c + d*x])^(3/2))/(a*d) + (2*e^3*Sqrt[e*Sec[c + d*x]]*Sin[c + d*x])/(a*d)","A",4,4,28,0.1429,1,"{3501, 3768, 3771, 2639}"
226,1,70,0,0.0736854,"\int \frac{(e \sec (c+d x))^{5/2}}{a+i a \tan (c+d x)} \, dx","Int[(e*Sec[c + d*x])^(5/2)/(a + I*a*Tan[c + d*x]),x]","\frac{2 e^2 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{e \sec (c+d x)}}{a d}-\frac{2 i e^2 \sqrt{e \sec (c+d x)}}{a d}","\frac{2 e^2 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{e \sec (c+d x)}}{a d}-\frac{2 i e^2 \sqrt{e \sec (c+d x)}}{a d}",1,"((-2*I)*e^2*Sqrt[e*Sec[c + d*x]])/(a*d) + (2*e^2*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2]*Sqrt[e*Sec[c + d*x]])/(a*d)","A",3,3,28,0.1071,1,"{3501, 3771, 2641}"
227,1,70,0,0.0728845,"\int \frac{(e \sec (c+d x))^{3/2}}{a+i a \tan (c+d x)} \, dx","Int[(e*Sec[c + d*x])^(3/2)/(a + I*a*Tan[c + d*x]),x]","\frac{2 e^2 E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{a d \sqrt{\cos (c+d x)} \sqrt{e \sec (c+d x)}}+\frac{2 i e^2}{a d \sqrt{e \sec (c+d x)}}","\frac{2 e^2 E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{a d \sqrt{\cos (c+d x)} \sqrt{e \sec (c+d x)}}+\frac{2 i e^2}{a d \sqrt{e \sec (c+d x)}}",1,"((2*I)*e^2)/(a*d*Sqrt[e*Sec[c + d*x]]) + (2*e^2*EllipticE[(c + d*x)/2, 2])/(a*d*Sqrt[Cos[c + d*x]]*Sqrt[e*Sec[c + d*x]])","A",3,3,28,0.1071,1,"{3501, 3771, 2639}"
228,1,80,0,0.0666296,"\int \frac{\sqrt{e \sec (c+d x)}}{a+i a \tan (c+d x)} \, dx","Int[Sqrt[e*Sec[c + d*x]]/(a + I*a*Tan[c + d*x]),x]","\frac{2 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{e \sec (c+d x)}}{3 a d}+\frac{2 i \sqrt{e \sec (c+d x)}}{3 d (a+i a \tan (c+d x))}","\frac{2 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{e \sec (c+d x)}}{3 a d}+\frac{2 i \sqrt{e \sec (c+d x)}}{3 d (a+i a \tan (c+d x))}",1,"(2*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2]*Sqrt[e*Sec[c + d*x]])/(3*a*d) + (((2*I)/3)*Sqrt[e*Sec[c + d*x]])/(d*(a + I*a*Tan[c + d*x]))","A",3,3,28,0.1071,1,"{3502, 3771, 2641}"
229,1,80,0,0.0696769,"\int \frac{1}{\sqrt{e \sec (c+d x)} (a+i a \tan (c+d x))} \, dx","Int[1/(Sqrt[e*Sec[c + d*x]]*(a + I*a*Tan[c + d*x])),x]","\frac{6 E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{5 a d \sqrt{\cos (c+d x)} \sqrt{e \sec (c+d x)}}+\frac{2 i}{5 d (a+i a \tan (c+d x)) \sqrt{e \sec (c+d x)}}","\frac{6 E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{5 a d \sqrt{\cos (c+d x)} \sqrt{e \sec (c+d x)}}+\frac{2 i}{5 d (a+i a \tan (c+d x)) \sqrt{e \sec (c+d x)}}",1,"(6*EllipticE[(c + d*x)/2, 2])/(5*a*d*Sqrt[Cos[c + d*x]]*Sqrt[e*Sec[c + d*x]]) + ((2*I)/5)/(d*Sqrt[e*Sec[c + d*x]]*(a + I*a*Tan[c + d*x]))","A",3,3,28,0.1071,1,"{3502, 3771, 2639}"
230,1,114,0,0.0930508,"\int \frac{1}{(e \sec (c+d x))^{3/2} (a+i a \tan (c+d x))} \, dx","Int[1/((e*Sec[c + d*x])^(3/2)*(a + I*a*Tan[c + d*x])),x]","\frac{10 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{e \sec (c+d x)}}{21 a d e^2}+\frac{10 \sin (c+d x)}{21 a d e \sqrt{e \sec (c+d x)}}+\frac{2 i}{7 d (a+i a \tan (c+d x)) (e \sec (c+d x))^{3/2}}","\frac{10 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{e \sec (c+d x)}}{21 a d e^2}+\frac{10 \sin (c+d x)}{21 a d e \sqrt{e \sec (c+d x)}}+\frac{2 i}{7 d (a+i a \tan (c+d x)) (e \sec (c+d x))^{3/2}}",1,"(10*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2]*Sqrt[e*Sec[c + d*x]])/(21*a*d*e^2) + (10*Sin[c + d*x])/(21*a*d*e*Sqrt[e*Sec[c + d*x]]) + ((2*I)/7)/(d*(e*Sec[c + d*x])^(3/2)*(a + I*a*Tan[c + d*x]))","A",4,4,28,0.1429,1,"{3502, 3769, 3771, 2641}"
231,1,114,0,0.0919698,"\int \frac{1}{(e \sec (c+d x))^{5/2} (a+i a \tan (c+d x))} \, dx","Int[1/((e*Sec[c + d*x])^(5/2)*(a + I*a*Tan[c + d*x])),x]","\frac{14 E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{15 a d e^2 \sqrt{\cos (c+d x)} \sqrt{e \sec (c+d x)}}+\frac{14 \sin (c+d x)}{45 a d e (e \sec (c+d x))^{3/2}}+\frac{2 i}{9 d (a+i a \tan (c+d x)) (e \sec (c+d x))^{5/2}}","\frac{14 E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{15 a d e^2 \sqrt{\cos (c+d x)} \sqrt{e \sec (c+d x)}}+\frac{14 \sin (c+d x)}{45 a d e (e \sec (c+d x))^{3/2}}+\frac{2 i}{9 d (a+i a \tan (c+d x)) (e \sec (c+d x))^{5/2}}",1,"(14*EllipticE[(c + d*x)/2, 2])/(15*a*d*e^2*Sqrt[Cos[c + d*x]]*Sqrt[e*Sec[c + d*x]]) + (14*Sin[c + d*x])/(45*a*d*e*(e*Sec[c + d*x])^(3/2)) + ((2*I)/9)/(d*(e*Sec[c + d*x])^(5/2)*(a + I*a*Tan[c + d*x]))","A",4,4,28,0.1429,1,"{3502, 3769, 3771, 2639}"
232,1,145,0,0.1094972,"\int \frac{1}{(e \sec (c+d x))^{7/2} (a+i a \tan (c+d x))} \, dx","Int[1/((e*Sec[c + d*x])^(7/2)*(a + I*a*Tan[c + d*x])),x]","\frac{30 \sin (c+d x)}{77 a d e^3 \sqrt{e \sec (c+d x)}}+\frac{30 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{e \sec (c+d x)}}{77 a d e^4}+\frac{18 \sin (c+d x)}{77 a d e (e \sec (c+d x))^{5/2}}+\frac{2 i}{11 d (a+i a \tan (c+d x)) (e \sec (c+d x))^{7/2}}","\frac{30 \sin (c+d x)}{77 a d e^3 \sqrt{e \sec (c+d x)}}+\frac{30 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{e \sec (c+d x)}}{77 a d e^4}+\frac{18 \sin (c+d x)}{77 a d e (e \sec (c+d x))^{5/2}}+\frac{2 i}{11 d (a+i a \tan (c+d x)) (e \sec (c+d x))^{7/2}}",1,"(30*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2]*Sqrt[e*Sec[c + d*x]])/(77*a*d*e^4) + (18*Sin[c + d*x])/(77*a*d*e*(e*Sec[c + d*x])^(5/2)) + (30*Sin[c + d*x])/(77*a*d*e^3*Sqrt[e*Sec[c + d*x]]) + ((2*I)/11)/(d*(e*Sec[c + d*x])^(7/2)*(a + I*a*Tan[c + d*x]))","A",5,4,28,0.1429,1,"{3502, 3769, 3771, 2641}"
233,1,183,0,0.1272741,"\int \frac{(e \sec (c+d x))^{15/2}}{(a+i a \tan (c+d x))^2} \, dx","Int[(e*Sec[c + d*x])^(15/2)/(a + I*a*Tan[c + d*x])^2,x]","\frac{22 e^7 \sin (c+d x) \sqrt{e \sec (c+d x)}}{15 a^2 d}+\frac{22 e^5 \sin (c+d x) (e \sec (c+d x))^{5/2}}{45 a^2 d}+\frac{22 e^3 \sin (c+d x) (e \sec (c+d x))^{9/2}}{63 a^2 d}-\frac{4 i e^2 (e \sec (c+d x))^{11/2}}{7 d \left(a^2+i a^2 \tan (c+d x)\right)}-\frac{22 e^8 E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{15 a^2 d \sqrt{\cos (c+d x)} \sqrt{e \sec (c+d x)}}","\frac{22 e^7 \sin (c+d x) \sqrt{e \sec (c+d x)}}{15 a^2 d}+\frac{22 e^5 \sin (c+d x) (e \sec (c+d x))^{5/2}}{45 a^2 d}+\frac{22 e^3 \sin (c+d x) (e \sec (c+d x))^{9/2}}{63 a^2 d}-\frac{4 i e^2 (e \sec (c+d x))^{11/2}}{7 d \left(a^2+i a^2 \tan (c+d x)\right)}-\frac{22 e^8 E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{15 a^2 d \sqrt{\cos (c+d x)} \sqrt{e \sec (c+d x)}}",1,"(-22*e^8*EllipticE[(c + d*x)/2, 2])/(15*a^2*d*Sqrt[Cos[c + d*x]]*Sqrt[e*Sec[c + d*x]]) + (22*e^7*Sqrt[e*Sec[c + d*x]]*Sin[c + d*x])/(15*a^2*d) + (22*e^5*(e*Sec[c + d*x])^(5/2)*Sin[c + d*x])/(45*a^2*d) + (22*e^3*(e*Sec[c + d*x])^(9/2)*Sin[c + d*x])/(63*a^2*d) - (((4*I)/7)*e^2*(e*Sec[c + d*x])^(11/2))/(d*(a^2 + I*a^2*Tan[c + d*x]))","A",6,4,28,0.1429,1,"{3500, 3768, 3771, 2639}"
234,1,152,0,0.1088686,"\int \frac{(e \sec (c+d x))^{13/2}}{(a+i a \tan (c+d x))^2} \, dx","Int[(e*Sec[c + d*x])^(13/2)/(a + I*a*Tan[c + d*x])^2,x]","\frac{6 e^5 \sin (c+d x) (e \sec (c+d x))^{3/2}}{7 a^2 d}+\frac{18 e^3 \sin (c+d x) (e \sec (c+d x))^{7/2}}{35 a^2 d}-\frac{4 i e^2 (e \sec (c+d x))^{9/2}}{5 d \left(a^2+i a^2 \tan (c+d x)\right)}+\frac{6 e^6 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{e \sec (c+d x)}}{7 a^2 d}","\frac{6 e^5 \sin (c+d x) (e \sec (c+d x))^{3/2}}{7 a^2 d}+\frac{18 e^3 \sin (c+d x) (e \sec (c+d x))^{7/2}}{35 a^2 d}-\frac{4 i e^2 (e \sec (c+d x))^{9/2}}{5 d \left(a^2+i a^2 \tan (c+d x)\right)}+\frac{6 e^6 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{e \sec (c+d x)}}{7 a^2 d}",1,"(6*e^6*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2]*Sqrt[e*Sec[c + d*x]])/(7*a^2*d) + (6*e^5*(e*Sec[c + d*x])^(3/2)*Sin[c + d*x])/(7*a^2*d) + (18*e^3*(e*Sec[c + d*x])^(7/2)*Sin[c + d*x])/(35*a^2*d) - (((4*I)/5)*e^2*(e*Sec[c + d*x])^(9/2))/(d*(a^2 + I*a^2*Tan[c + d*x]))","A",5,4,28,0.1429,1,"{3500, 3768, 3771, 2641}"
235,1,152,0,0.1074005,"\int \frac{(e \sec (c+d x))^{11/2}}{(a+i a \tan (c+d x))^2} \, dx","Int[(e*Sec[c + d*x])^(11/2)/(a + I*a*Tan[c + d*x])^2,x]","\frac{14 e^5 \sin (c+d x) \sqrt{e \sec (c+d x)}}{5 a^2 d}+\frac{14 e^3 \sin (c+d x) (e \sec (c+d x))^{5/2}}{15 a^2 d}-\frac{4 i e^2 (e \sec (c+d x))^{7/2}}{3 d \left(a^2+i a^2 \tan (c+d x)\right)}-\frac{14 e^6 E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{5 a^2 d \sqrt{\cos (c+d x)} \sqrt{e \sec (c+d x)}}","\frac{14 e^5 \sin (c+d x) \sqrt{e \sec (c+d x)}}{5 a^2 d}+\frac{14 e^3 \sin (c+d x) (e \sec (c+d x))^{5/2}}{15 a^2 d}-\frac{4 i e^2 (e \sec (c+d x))^{7/2}}{3 d \left(a^2+i a^2 \tan (c+d x)\right)}-\frac{14 e^6 E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{5 a^2 d \sqrt{\cos (c+d x)} \sqrt{e \sec (c+d x)}}",1,"(-14*e^6*EllipticE[(c + d*x)/2, 2])/(5*a^2*d*Sqrt[Cos[c + d*x]]*Sqrt[e*Sec[c + d*x]]) + (14*e^5*Sqrt[e*Sec[c + d*x]]*Sin[c + d*x])/(5*a^2*d) + (14*e^3*(e*Sec[c + d*x])^(5/2)*Sin[c + d*x])/(15*a^2*d) - (((4*I)/3)*e^2*(e*Sec[c + d*x])^(7/2))/(d*(a^2 + I*a^2*Tan[c + d*x]))","A",5,4,28,0.1429,1,"{3500, 3768, 3771, 2639}"
236,1,119,0,0.0889732,"\int \frac{(e \sec (c+d x))^{9/2}}{(a+i a \tan (c+d x))^2} \, dx","Int[(e*Sec[c + d*x])^(9/2)/(a + I*a*Tan[c + d*x])^2,x]","\frac{10 e^3 \sin (c+d x) (e \sec (c+d x))^{3/2}}{3 a^2 d}-\frac{4 i e^2 (e \sec (c+d x))^{5/2}}{d \left(a^2+i a^2 \tan (c+d x)\right)}+\frac{10 e^4 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{e \sec (c+d x)}}{3 a^2 d}","\frac{10 e^3 \sin (c+d x) (e \sec (c+d x))^{3/2}}{3 a^2 d}-\frac{4 i e^2 (e \sec (c+d x))^{5/2}}{d \left(a^2+i a^2 \tan (c+d x)\right)}+\frac{10 e^4 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{e \sec (c+d x)}}{3 a^2 d}",1,"(10*e^4*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2]*Sqrt[e*Sec[c + d*x]])/(3*a^2*d) + (10*e^3*(e*Sec[c + d*x])^(3/2)*Sin[c + d*x])/(3*a^2*d) - ((4*I)*e^2*(e*Sec[c + d*x])^(5/2))/(d*(a^2 + I*a^2*Tan[c + d*x]))","A",4,4,28,0.1429,1,"{3500, 3768, 3771, 2641}"
237,1,115,0,0.0888349,"\int \frac{(e \sec (c+d x))^{7/2}}{(a+i a \tan (c+d x))^2} \, dx","Int[(e*Sec[c + d*x])^(7/2)/(a + I*a*Tan[c + d*x])^2,x]","-\frac{6 e^3 \sin (c+d x) \sqrt{e \sec (c+d x)}}{a^2 d}+\frac{4 i e^2 (e \sec (c+d x))^{3/2}}{d \left(a^2+i a^2 \tan (c+d x)\right)}+\frac{6 e^4 E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{a^2 d \sqrt{\cos (c+d x)} \sqrt{e \sec (c+d x)}}","-\frac{6 e^3 \sin (c+d x) \sqrt{e \sec (c+d x)}}{a^2 d}+\frac{4 i e^2 (e \sec (c+d x))^{3/2}}{d \left(a^2+i a^2 \tan (c+d x)\right)}+\frac{6 e^4 E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{a^2 d \sqrt{\cos (c+d x)} \sqrt{e \sec (c+d x)}}",1,"(6*e^4*EllipticE[(c + d*x)/2, 2])/(a^2*d*Sqrt[Cos[c + d*x]]*Sqrt[e*Sec[c + d*x]]) - (6*e^3*Sqrt[e*Sec[c + d*x]]*Sin[c + d*x])/(a^2*d) + ((4*I)*e^2*(e*Sec[c + d*x])^(3/2))/(d*(a^2 + I*a^2*Tan[c + d*x]))","A",4,4,28,0.1429,1,"{3500, 3768, 3771, 2639}"
238,1,90,0,0.073417,"\int \frac{(e \sec (c+d x))^{5/2}}{(a+i a \tan (c+d x))^2} \, dx","Int[(e*Sec[c + d*x])^(5/2)/(a + I*a*Tan[c + d*x])^2,x]","-\frac{2 e^2 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{e \sec (c+d x)}}{3 a^2 d}+\frac{4 i e^2 \sqrt{e \sec (c+d x)}}{3 d \left(a^2+i a^2 \tan (c+d x)\right)}","-\frac{2 e^2 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{e \sec (c+d x)}}{3 a^2 d}+\frac{4 i e^2 \sqrt{e \sec (c+d x)}}{3 d \left(a^2+i a^2 \tan (c+d x)\right)}",1,"(-2*e^2*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2]*Sqrt[e*Sec[c + d*x]])/(3*a^2*d) + (((4*I)/3)*e^2*Sqrt[e*Sec[c + d*x]])/(d*(a^2 + I*a^2*Tan[c + d*x]))","A",3,3,28,0.1071,1,"{3500, 3771, 2641}"
239,1,90,0,0.0746756,"\int \frac{(e \sec (c+d x))^{3/2}}{(a+i a \tan (c+d x))^2} \, dx","Int[(e*Sec[c + d*x])^(3/2)/(a + I*a*Tan[c + d*x])^2,x]","\frac{2 e^2 E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{5 a^2 d \sqrt{\cos (c+d x)} \sqrt{e \sec (c+d x)}}+\frac{4 i e^2}{5 d \left(a^2+i a^2 \tan (c+d x)\right) \sqrt{e \sec (c+d x)}}","\frac{2 e^2 E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{5 a^2 d \sqrt{\cos (c+d x)} \sqrt{e \sec (c+d x)}}+\frac{4 i e^2}{5 d \left(a^2+i a^2 \tan (c+d x)\right) \sqrt{e \sec (c+d x)}}",1,"(2*e^2*EllipticE[(c + d*x)/2, 2])/(5*a^2*d*Sqrt[Cos[c + d*x]]*Sqrt[e*Sec[c + d*x]]) + (((4*I)/5)*e^2)/(d*Sqrt[e*Sec[c + d*x]]*(a^2 + I*a^2*Tan[c + d*x]))","A",3,3,28,0.1071,1,"{3500, 3771, 2639}"
240,1,116,0,0.0832255,"\int \frac{\sqrt{e \sec (c+d x)}}{(a+i a \tan (c+d x))^2} \, dx","Int[Sqrt[e*Sec[c + d*x]]/(a + I*a*Tan[c + d*x])^2,x]","\frac{4 i e^2}{7 d \left(a^2+i a^2 \tan (c+d x)\right) (e \sec (c+d x))^{3/2}}+\frac{2 e \sin (c+d x)}{7 a^2 d \sqrt{e \sec (c+d x)}}+\frac{2 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{e \sec (c+d x)}}{7 a^2 d}","\frac{4 i e^2}{7 d \left(a^2+i a^2 \tan (c+d x)\right) (e \sec (c+d x))^{3/2}}+\frac{2 e \sin (c+d x)}{7 a^2 d \sqrt{e \sec (c+d x)}}+\frac{2 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{e \sec (c+d x)}}{7 a^2 d}",1,"(2*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2]*Sqrt[e*Sec[c + d*x]])/(7*a^2*d) + (2*e*Sin[c + d*x])/(7*a^2*d*Sqrt[e*Sec[c + d*x]]) + (((4*I)/7)*e^2)/(d*(e*Sec[c + d*x])^(3/2)*(a^2 + I*a^2*Tan[c + d*x]))","A",4,4,28,0.1429,1,"{3500, 3769, 3771, 2641}"
241,1,116,0,0.0843109,"\int \frac{1}{\sqrt{e \sec (c+d x)} (a+i a \tan (c+d x))^2} \, dx","Int[1/(Sqrt[e*Sec[c + d*x]]*(a + I*a*Tan[c + d*x])^2),x]","\frac{4 i e^2}{9 d \left(a^2+i a^2 \tan (c+d x)\right) (e \sec (c+d x))^{5/2}}+\frac{2 e \sin (c+d x)}{9 a^2 d (e \sec (c+d x))^{3/2}}+\frac{2 E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{3 a^2 d \sqrt{\cos (c+d x)} \sqrt{e \sec (c+d x)}}","\frac{4 i e^2}{9 d \left(a^2+i a^2 \tan (c+d x)\right) (e \sec (c+d x))^{5/2}}+\frac{2 e \sin (c+d x)}{9 a^2 d (e \sec (c+d x))^{3/2}}+\frac{2 E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{3 a^2 d \sqrt{\cos (c+d x)} \sqrt{e \sec (c+d x)}}",1,"(2*EllipticE[(c + d*x)/2, 2])/(3*a^2*d*Sqrt[Cos[c + d*x]]*Sqrt[e*Sec[c + d*x]]) + (2*e*Sin[c + d*x])/(9*a^2*d*(e*Sec[c + d*x])^(3/2)) + (((4*I)/9)*e^2)/(d*(e*Sec[c + d*x])^(5/2)*(a^2 + I*a^2*Tan[c + d*x]))","A",4,4,28,0.1429,1,"{3500, 3769, 3771, 2639}"
242,1,150,0,0.1099875,"\int \frac{1}{(e \sec (c+d x))^{3/2} (a+i a \tan (c+d x))^2} \, dx","Int[1/((e*Sec[c + d*x])^(3/2)*(a + I*a*Tan[c + d*x])^2),x]","\frac{4 i e^2}{11 d \left(a^2+i a^2 \tan (c+d x)\right) (e \sec (c+d x))^{7/2}}+\frac{10 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{e \sec (c+d x)}}{33 a^2 d e^2}+\frac{2 e \sin (c+d x)}{11 a^2 d (e \sec (c+d x))^{5/2}}+\frac{10 \sin (c+d x)}{33 a^2 d e \sqrt{e \sec (c+d x)}}","\frac{4 i e^2}{11 d \left(a^2+i a^2 \tan (c+d x)\right) (e \sec (c+d x))^{7/2}}+\frac{10 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{e \sec (c+d x)}}{33 a^2 d e^2}+\frac{2 e \sin (c+d x)}{11 a^2 d (e \sec (c+d x))^{5/2}}+\frac{10 \sin (c+d x)}{33 a^2 d e \sqrt{e \sec (c+d x)}}",1,"(10*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2]*Sqrt[e*Sec[c + d*x]])/(33*a^2*d*e^2) + (2*e*Sin[c + d*x])/(11*a^2*d*(e*Sec[c + d*x])^(5/2)) + (10*Sin[c + d*x])/(33*a^2*d*e*Sqrt[e*Sec[c + d*x]]) + (((4*I)/11)*e^2)/(d*(e*Sec[c + d*x])^(7/2)*(a^2 + I*a^2*Tan[c + d*x]))","A",5,4,28,0.1429,1,"{3500, 3769, 3771, 2641}"
243,1,150,0,0.1092954,"\int \frac{1}{(e \sec (c+d x))^{5/2} (a+i a \tan (c+d x))^2} \, dx","Int[1/((e*Sec[c + d*x])^(5/2)*(a + I*a*Tan[c + d*x])^2),x]","\frac{4 i e^2}{13 d \left(a^2+i a^2 \tan (c+d x)\right) (e \sec (c+d x))^{9/2}}+\frac{42 E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{65 a^2 d e^2 \sqrt{\cos (c+d x)} \sqrt{e \sec (c+d x)}}+\frac{2 e \sin (c+d x)}{13 a^2 d (e \sec (c+d x))^{7/2}}+\frac{14 \sin (c+d x)}{65 a^2 d e (e \sec (c+d x))^{3/2}}","\frac{4 i e^2}{13 d \left(a^2+i a^2 \tan (c+d x)\right) (e \sec (c+d x))^{9/2}}+\frac{42 E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{65 a^2 d e^2 \sqrt{\cos (c+d x)} \sqrt{e \sec (c+d x)}}+\frac{2 e \sin (c+d x)}{13 a^2 d (e \sec (c+d x))^{7/2}}+\frac{14 \sin (c+d x)}{65 a^2 d e (e \sec (c+d x))^{3/2}}",1,"(42*EllipticE[(c + d*x)/2, 2])/(65*a^2*d*e^2*Sqrt[Cos[c + d*x]]*Sqrt[e*Sec[c + d*x]]) + (2*e*Sin[c + d*x])/(13*a^2*d*(e*Sec[c + d*x])^(7/2)) + (14*Sin[c + d*x])/(65*a^2*d*e*(e*Sec[c + d*x])^(3/2)) + (((4*I)/13)*e^2)/(d*(e*Sec[c + d*x])^(9/2)*(a^2 + I*a^2*Tan[c + d*x]))","A",5,4,28,0.1429,1,"{3500, 3769, 3771, 2639}"
244,1,181,0,0.1306218,"\int \frac{1}{(e \sec (c+d x))^{7/2} (a+i a \tan (c+d x))^2} \, dx","Int[1/((e*Sec[c + d*x])^(7/2)*(a + I*a*Tan[c + d*x])^2),x]","\frac{2 \sin (c+d x)}{7 a^2 d e^3 \sqrt{e \sec (c+d x)}}+\frac{4 i e^2}{15 d \left(a^2+i a^2 \tan (c+d x)\right) (e \sec (c+d x))^{11/2}}+\frac{2 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{e \sec (c+d x)}}{7 a^2 d e^4}+\frac{2 e \sin (c+d x)}{15 a^2 d (e \sec (c+d x))^{9/2}}+\frac{6 \sin (c+d x)}{35 a^2 d e (e \sec (c+d x))^{5/2}}","\frac{2 \sin (c+d x)}{7 a^2 d e^3 \sqrt{e \sec (c+d x)}}+\frac{4 i e^2}{15 d \left(a^2+i a^2 \tan (c+d x)\right) (e \sec (c+d x))^{11/2}}+\frac{2 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{e \sec (c+d x)}}{7 a^2 d e^4}+\frac{2 e \sin (c+d x)}{15 a^2 d (e \sec (c+d x))^{9/2}}+\frac{6 \sin (c+d x)}{35 a^2 d e (e \sec (c+d x))^{5/2}}",1,"(2*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2]*Sqrt[e*Sec[c + d*x]])/(7*a^2*d*e^4) + (2*e*Sin[c + d*x])/(15*a^2*d*(e*Sec[c + d*x])^(9/2)) + (6*Sin[c + d*x])/(35*a^2*d*e*(e*Sec[c + d*x])^(5/2)) + (2*Sin[c + d*x])/(7*a^2*d*e^3*Sqrt[e*Sec[c + d*x]]) + (((4*I)/15)*e^2)/(d*(e*Sec[c + d*x])^(11/2)*(a^2 + I*a^2*Tan[c + d*x]))","A",6,4,28,0.1429,1,"{3500, 3769, 3771, 2641}"
245,1,178,0,0.1704918,"\int \frac{(e \sec (c+d x))^{15/2}}{(a+i a \tan (c+d x))^3} \, dx","Int[(e*Sec[c + d*x])^(15/2)/(a + I*a*Tan[c + d*x])^3,x]","-\frac{22 i e^4 (e \sec (c+d x))^{7/2}}{21 a^3 d}+\frac{22 e^7 \sin (c+d x) \sqrt{e \sec (c+d x)}}{5 a^3 d}+\frac{22 e^5 \sin (c+d x) (e \sec (c+d x))^{5/2}}{15 a^3 d}-\frac{22 e^8 E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{5 a^3 d \sqrt{\cos (c+d x)} \sqrt{e \sec (c+d x)}}-\frac{4 i e^2 (e \sec (c+d x))^{11/2}}{3 a d (a+i a \tan (c+d x))^2}","-\frac{22 i e^4 (e \sec (c+d x))^{7/2}}{21 a^3 d}+\frac{22 e^7 \sin (c+d x) \sqrt{e \sec (c+d x)}}{5 a^3 d}+\frac{22 e^5 \sin (c+d x) (e \sec (c+d x))^{5/2}}{15 a^3 d}-\frac{22 e^8 E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{5 a^3 d \sqrt{\cos (c+d x)} \sqrt{e \sec (c+d x)}}-\frac{4 i e^2 (e \sec (c+d x))^{11/2}}{3 a d (a+i a \tan (c+d x))^2}",1,"(-22*e^8*EllipticE[(c + d*x)/2, 2])/(5*a^3*d*Sqrt[Cos[c + d*x]]*Sqrt[e*Sec[c + d*x]]) - (((22*I)/21)*e^4*(e*Sec[c + d*x])^(7/2))/(a^3*d) + (22*e^7*Sqrt[e*Sec[c + d*x]]*Sin[c + d*x])/(5*a^3*d) + (22*e^5*(e*Sec[c + d*x])^(5/2)*Sin[c + d*x])/(15*a^3*d) - (((4*I)/3)*e^2*(e*Sec[c + d*x])^(11/2))/(a*d*(a + I*a*Tan[c + d*x])^2)","A",6,5,28,0.1786,1,"{3500, 3501, 3768, 3771, 2639}"
246,1,141,0,0.1504561,"\int \frac{(e \sec (c+d x))^{13/2}}{(a+i a \tan (c+d x))^3} \, dx","Int[(e*Sec[c + d*x])^(13/2)/(a + I*a*Tan[c + d*x])^3,x]","-\frac{18 i e^4 (e \sec (c+d x))^{5/2}}{5 a^3 d}+\frac{6 e^5 \sin (c+d x) (e \sec (c+d x))^{3/2}}{a^3 d}+\frac{6 e^6 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{e \sec (c+d x)}}{a^3 d}-\frac{4 i e^2 (e \sec (c+d x))^{9/2}}{a d (a+i a \tan (c+d x))^2}","-\frac{18 i e^4 (e \sec (c+d x))^{5/2}}{5 a^3 d}+\frac{6 e^5 \sin (c+d x) (e \sec (c+d x))^{3/2}}{a^3 d}+\frac{6 e^6 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{e \sec (c+d x)}}{a^3 d}-\frac{4 i e^2 (e \sec (c+d x))^{9/2}}{a d (a+i a \tan (c+d x))^2}",1,"(6*e^6*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2]*Sqrt[e*Sec[c + d*x]])/(a^3*d) - (((18*I)/5)*e^4*(e*Sec[c + d*x])^(5/2))/(a^3*d) + (6*e^5*(e*Sec[c + d*x])^(3/2)*Sin[c + d*x])/(a^3*d) - ((4*I)*e^2*(e*Sec[c + d*x])^(9/2))/(a*d*(a + I*a*Tan[c + d*x])^2)","A",5,5,28,0.1786,1,"{3500, 3501, 3768, 3771, 2641}"
247,1,141,0,0.1493902,"\int \frac{(e \sec (c+d x))^{11/2}}{(a+i a \tan (c+d x))^3} \, dx","Int[(e*Sec[c + d*x])^(11/2)/(a + I*a*Tan[c + d*x])^3,x]","\frac{14 i e^4 (e \sec (c+d x))^{3/2}}{3 a^3 d}-\frac{14 e^5 \sin (c+d x) \sqrt{e \sec (c+d x)}}{a^3 d}+\frac{14 e^6 E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{a^3 d \sqrt{\cos (c+d x)} \sqrt{e \sec (c+d x)}}+\frac{4 i e^2 (e \sec (c+d x))^{7/2}}{a d (a+i a \tan (c+d x))^2}","\frac{14 i e^4 (e \sec (c+d x))^{3/2}}{3 a^3 d}-\frac{14 e^5 \sin (c+d x) \sqrt{e \sec (c+d x)}}{a^3 d}+\frac{14 e^6 E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{a^3 d \sqrt{\cos (c+d x)} \sqrt{e \sec (c+d x)}}+\frac{4 i e^2 (e \sec (c+d x))^{7/2}}{a d (a+i a \tan (c+d x))^2}",1,"(14*e^6*EllipticE[(c + d*x)/2, 2])/(a^3*d*Sqrt[Cos[c + d*x]]*Sqrt[e*Sec[c + d*x]]) + (((14*I)/3)*e^4*(e*Sec[c + d*x])^(3/2))/(a^3*d) - (14*e^5*Sqrt[e*Sec[c + d*x]]*Sin[c + d*x])/(a^3*d) + ((4*I)*e^2*(e*Sec[c + d*x])^(7/2))/(a*d*(a + I*a*Tan[c + d*x])^2)","A",5,5,28,0.1786,1,"{3500, 3501, 3768, 3771, 2639}"
248,1,116,0,0.1339406,"\int \frac{(e \sec (c+d x))^{9/2}}{(a+i a \tan (c+d x))^3} \, dx","Int[(e*Sec[c + d*x])^(9/2)/(a + I*a*Tan[c + d*x])^3,x]","\frac{10 i e^4 \sqrt{e \sec (c+d x)}}{3 a^3 d}-\frac{10 e^4 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{e \sec (c+d x)}}{3 a^3 d}+\frac{4 i e^2 (e \sec (c+d x))^{5/2}}{3 a d (a+i a \tan (c+d x))^2}","\frac{10 i e^4 \sqrt{e \sec (c+d x)}}{3 a^3 d}-\frac{10 e^4 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{e \sec (c+d x)}}{3 a^3 d}+\frac{4 i e^2 (e \sec (c+d x))^{5/2}}{3 a d (a+i a \tan (c+d x))^2}",1,"(((10*I)/3)*e^4*Sqrt[e*Sec[c + d*x]])/(a^3*d) - (10*e^4*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2]*Sqrt[e*Sec[c + d*x]])/(3*a^3*d) + (((4*I)/3)*e^2*(e*Sec[c + d*x])^(5/2))/(a*d*(a + I*a*Tan[c + d*x])^2)","A",4,4,28,0.1429,1,"{3500, 3501, 3771, 2641}"
249,1,116,0,0.1320583,"\int \frac{(e \sec (c+d x))^{7/2}}{(a+i a \tan (c+d x))^3} \, dx","Int[(e*Sec[c + d*x])^(7/2)/(a + I*a*Tan[c + d*x])^3,x]","-\frac{6 i e^4}{5 a^3 d \sqrt{e \sec (c+d x)}}-\frac{6 e^4 E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{5 a^3 d \sqrt{\cos (c+d x)} \sqrt{e \sec (c+d x)}}+\frac{4 i e^2 (e \sec (c+d x))^{3/2}}{5 a d (a+i a \tan (c+d x))^2}","-\frac{6 i e^4}{5 a^3 d \sqrt{e \sec (c+d x)}}-\frac{6 e^4 E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{5 a^3 d \sqrt{\cos (c+d x)} \sqrt{e \sec (c+d x)}}+\frac{4 i e^2 (e \sec (c+d x))^{3/2}}{5 a d (a+i a \tan (c+d x))^2}",1,"(((-6*I)/5)*e^4)/(a^3*d*Sqrt[e*Sec[c + d*x]]) - (6*e^4*EllipticE[(c + d*x)/2, 2])/(5*a^3*d*Sqrt[Cos[c + d*x]]*Sqrt[e*Sec[c + d*x]]) + (((4*I)/5)*e^2*(e*Sec[c + d*x])^(3/2))/(a*d*(a + I*a*Tan[c + d*x])^2)","A",4,4,28,0.1429,1,"{3500, 3501, 3771, 2639}"
250,1,132,0,0.1273769,"\int \frac{(e \sec (c+d x))^{5/2}}{(a+i a \tan (c+d x))^3} \, dx","Int[(e*Sec[c + d*x])^(5/2)/(a + I*a*Tan[c + d*x])^3,x]","-\frac{2 i e^2 \sqrt{e \sec (c+d x)}}{21 d \left(a^3+i a^3 \tan (c+d x)\right)}-\frac{2 e^2 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{e \sec (c+d x)}}{21 a^3 d}+\frac{4 i e^2 \sqrt{e \sec (c+d x)}}{7 a d (a+i a \tan (c+d x))^2}","-\frac{2 i e^2 \sqrt{e \sec (c+d x)}}{21 d \left(a^3+i a^3 \tan (c+d x)\right)}-\frac{2 e^2 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{e \sec (c+d x)}}{21 a^3 d}+\frac{4 i e^2 \sqrt{e \sec (c+d x)}}{7 a d (a+i a \tan (c+d x))^2}",1,"(-2*e^2*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2]*Sqrt[e*Sec[c + d*x]])/(21*a^3*d) + (((4*I)/7)*e^2*Sqrt[e*Sec[c + d*x]])/(a*d*(a + I*a*Tan[c + d*x])^2) - (((2*I)/21)*e^2*Sqrt[e*Sec[c + d*x]])/(d*(a^3 + I*a^3*Tan[c + d*x]))","A",4,4,28,0.1429,1,"{3500, 3502, 3771, 2641}"
251,1,132,0,0.1289759,"\int \frac{(e \sec (c+d x))^{3/2}}{(a+i a \tan (c+d x))^3} \, dx","Int[(e*Sec[c + d*x])^(3/2)/(a + I*a*Tan[c + d*x])^3,x]","\frac{2 i e^2}{45 d \left(a^3+i a^3 \tan (c+d x)\right) \sqrt{e \sec (c+d x)}}+\frac{2 e^2 E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{15 a^3 d \sqrt{\cos (c+d x)} \sqrt{e \sec (c+d x)}}+\frac{4 i e^2}{9 a d (a+i a \tan (c+d x))^2 \sqrt{e \sec (c+d x)}}","\frac{2 i e^2}{45 d \left(a^3+i a^3 \tan (c+d x)\right) \sqrt{e \sec (c+d x)}}+\frac{2 e^2 E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{15 a^3 d \sqrt{\cos (c+d x)} \sqrt{e \sec (c+d x)}}+\frac{4 i e^2}{9 a d (a+i a \tan (c+d x))^2 \sqrt{e \sec (c+d x)}}",1,"(2*e^2*EllipticE[(c + d*x)/2, 2])/(15*a^3*d*Sqrt[Cos[c + d*x]]*Sqrt[e*Sec[c + d*x]]) + (((4*I)/9)*e^2)/(a*d*Sqrt[e*Sec[c + d*x]]*(a + I*a*Tan[c + d*x])^2) + (((2*I)/45)*e^2)/(d*Sqrt[e*Sec[c + d*x]]*(a^3 + I*a^3*Tan[c + d*x]))","A",4,4,28,0.1429,1,"{3500, 3502, 3771, 2639}"
252,1,152,0,0.1398766,"\int \frac{\sqrt{e \sec (c+d x)}}{(a+i a \tan (c+d x))^3} \, dx","Int[Sqrt[e*Sec[c + d*x]]/(a + I*a*Tan[c + d*x])^3,x]","\frac{20 i e^2}{77 d \left(a^3+i a^3 \tan (c+d x)\right) (e \sec (c+d x))^{3/2}}+\frac{10 e \sin (c+d x)}{77 a^3 d \sqrt{e \sec (c+d x)}}+\frac{10 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{e \sec (c+d x)}}{77 a^3 d}+\frac{2 i \sqrt{e \sec (c+d x)}}{11 d (a+i a \tan (c+d x))^3}","\frac{20 i e^2}{77 d \left(a^3+i a^3 \tan (c+d x)\right) (e \sec (c+d x))^{3/2}}+\frac{10 e \sin (c+d x)}{77 a^3 d \sqrt{e \sec (c+d x)}}+\frac{10 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{e \sec (c+d x)}}{77 a^3 d}+\frac{2 i \sqrt{e \sec (c+d x)}}{11 d (a+i a \tan (c+d x))^3}",1,"(10*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2]*Sqrt[e*Sec[c + d*x]])/(77*a^3*d) + (10*e*Sin[c + d*x])/(77*a^3*d*Sqrt[e*Sec[c + d*x]]) + (((2*I)/11)*Sqrt[e*Sec[c + d*x]])/(d*(a + I*a*Tan[c + d*x])^3) + (((20*I)/77)*e^2)/(d*(e*Sec[c + d*x])^(3/2)*(a^3 + I*a^3*Tan[c + d*x]))","A",5,5,28,0.1786,1,"{3502, 3500, 3769, 3771, 2641}"
253,1,152,0,0.1445621,"\int \frac{1}{\sqrt{e \sec (c+d x)} (a+i a \tan (c+d x))^3} \, dx","Int[1/(Sqrt[e*Sec[c + d*x]]*(a + I*a*Tan[c + d*x])^3),x]","\frac{28 i e^2}{117 d \left(a^3+i a^3 \tan (c+d x)\right) (e \sec (c+d x))^{5/2}}+\frac{14 e \sin (c+d x)}{117 a^3 d (e \sec (c+d x))^{3/2}}+\frac{14 E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{39 a^3 d \sqrt{\cos (c+d x)} \sqrt{e \sec (c+d x)}}+\frac{2 i}{13 d (a+i a \tan (c+d x))^3 \sqrt{e \sec (c+d x)}}","\frac{28 i e^2}{117 d \left(a^3+i a^3 \tan (c+d x)\right) (e \sec (c+d x))^{5/2}}+\frac{14 e \sin (c+d x)}{117 a^3 d (e \sec (c+d x))^{3/2}}+\frac{14 E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{39 a^3 d \sqrt{\cos (c+d x)} \sqrt{e \sec (c+d x)}}+\frac{2 i}{13 d (a+i a \tan (c+d x))^3 \sqrt{e \sec (c+d x)}}",1,"(14*EllipticE[(c + d*x)/2, 2])/(39*a^3*d*Sqrt[Cos[c + d*x]]*Sqrt[e*Sec[c + d*x]]) + (14*e*Sin[c + d*x])/(117*a^3*d*(e*Sec[c + d*x])^(3/2)) + ((2*I)/13)/(d*Sqrt[e*Sec[c + d*x]]*(a + I*a*Tan[c + d*x])^3) + (((28*I)/117)*e^2)/(d*(e*Sec[c + d*x])^(5/2)*(a^3 + I*a^3*Tan[c + d*x]))","A",5,5,28,0.1786,1,"{3502, 3500, 3769, 3771, 2639}"
254,1,186,0,0.1816895,"\int \frac{1}{(e \sec (c+d x))^{3/2} (a+i a \tan (c+d x))^3} \, dx","Int[1/((e*Sec[c + d*x])^(3/2)*(a + I*a*Tan[c + d*x])^3),x]","\frac{12 i e^2}{55 d \left(a^3+i a^3 \tan (c+d x)\right) (e \sec (c+d x))^{7/2}}+\frac{2 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{e \sec (c+d x)}}{11 a^3 d e^2}+\frac{6 e \sin (c+d x)}{55 a^3 d (e \sec (c+d x))^{5/2}}+\frac{2 \sin (c+d x)}{11 a^3 d e \sqrt{e \sec (c+d x)}}+\frac{2 i}{15 d (a+i a \tan (c+d x))^3 (e \sec (c+d x))^{3/2}}","\frac{12 i e^2}{55 d \left(a^3+i a^3 \tan (c+d x)\right) (e \sec (c+d x))^{7/2}}+\frac{2 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{e \sec (c+d x)}}{11 a^3 d e^2}+\frac{6 e \sin (c+d x)}{55 a^3 d (e \sec (c+d x))^{5/2}}+\frac{2 \sin (c+d x)}{11 a^3 d e \sqrt{e \sec (c+d x)}}+\frac{2 i}{15 d (a+i a \tan (c+d x))^3 (e \sec (c+d x))^{3/2}}",1,"(2*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2]*Sqrt[e*Sec[c + d*x]])/(11*a^3*d*e^2) + (6*e*Sin[c + d*x])/(55*a^3*d*(e*Sec[c + d*x])^(5/2)) + (2*Sin[c + d*x])/(11*a^3*d*e*Sqrt[e*Sec[c + d*x]]) + ((2*I)/15)/(d*(e*Sec[c + d*x])^(3/2)*(a + I*a*Tan[c + d*x])^3) + (((12*I)/55)*e^2)/(d*(e*Sec[c + d*x])^(7/2)*(a^3 + I*a^3*Tan[c + d*x]))","A",6,5,28,0.1786,1,"{3502, 3500, 3769, 3771, 2641}"
255,1,192,0,0.1749346,"\int \frac{(e \sec (c+d x))^{15/2}}{(a+i a \tan (c+d x))^4} \, dx","Int[(e*Sec[c + d*x])^(15/2)/(a + I*a*Tan[c + d*x])^4,x]","-\frac{154 e^7 \sin (c+d x) \sqrt{e \sec (c+d x)}}{5 a^4 d}-\frac{154 e^5 \sin (c+d x) (e \sec (c+d x))^{5/2}}{15 a^4 d}+\frac{44 i e^4 (e \sec (c+d x))^{7/2}}{3 d \left(a^4+i a^4 \tan (c+d x)\right)}+\frac{154 e^8 E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{5 a^4 d \sqrt{\cos (c+d x)} \sqrt{e \sec (c+d x)}}+\frac{4 i e^2 (e \sec (c+d x))^{11/2}}{a d (a+i a \tan (c+d x))^3}","-\frac{154 e^7 \sin (c+d x) \sqrt{e \sec (c+d x)}}{5 a^4 d}-\frac{154 e^5 \sin (c+d x) (e \sec (c+d x))^{5/2}}{15 a^4 d}+\frac{44 i e^4 (e \sec (c+d x))^{7/2}}{3 d \left(a^4+i a^4 \tan (c+d x)\right)}+\frac{154 e^8 E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{5 a^4 d \sqrt{\cos (c+d x)} \sqrt{e \sec (c+d x)}}+\frac{4 i e^2 (e \sec (c+d x))^{11/2}}{a d (a+i a \tan (c+d x))^3}",1,"(154*e^8*EllipticE[(c + d*x)/2, 2])/(5*a^4*d*Sqrt[Cos[c + d*x]]*Sqrt[e*Sec[c + d*x]]) - (154*e^7*Sqrt[e*Sec[c + d*x]]*Sin[c + d*x])/(5*a^4*d) - (154*e^5*(e*Sec[c + d*x])^(5/2)*Sin[c + d*x])/(15*a^4*d) + ((4*I)*e^2*(e*Sec[c + d*x])^(11/2))/(a*d*(a + I*a*Tan[c + d*x])^3) + (((44*I)/3)*e^4*(e*Sec[c + d*x])^(7/2))/(d*(a^4 + I*a^4*Tan[c + d*x]))","A",6,4,28,0.1429,1,"{3500, 3768, 3771, 2639}"
256,1,157,0,0.1547509,"\int \frac{(e \sec (c+d x))^{13/2}}{(a+i a \tan (c+d x))^4} \, dx","Int[(e*Sec[c + d*x])^(13/2)/(a + I*a*Tan[c + d*x])^4,x]","-\frac{10 e^5 \sin (c+d x) (e \sec (c+d x))^{3/2}}{a^4 d}+\frac{12 i e^4 (e \sec (c+d x))^{5/2}}{d \left(a^4+i a^4 \tan (c+d x)\right)}-\frac{10 e^6 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{e \sec (c+d x)}}{a^4 d}+\frac{4 i e^2 (e \sec (c+d x))^{9/2}}{3 a d (a+i a \tan (c+d x))^3}","-\frac{10 e^5 \sin (c+d x) (e \sec (c+d x))^{3/2}}{a^4 d}+\frac{12 i e^4 (e \sec (c+d x))^{5/2}}{d \left(a^4+i a^4 \tan (c+d x)\right)}-\frac{10 e^6 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{e \sec (c+d x)}}{a^4 d}+\frac{4 i e^2 (e \sec (c+d x))^{9/2}}{3 a d (a+i a \tan (c+d x))^3}",1,"(-10*e^6*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2]*Sqrt[e*Sec[c + d*x]])/(a^4*d) - (10*e^5*(e*Sec[c + d*x])^(3/2)*Sin[c + d*x])/(a^4*d) + (((4*I)/3)*e^2*(e*Sec[c + d*x])^(9/2))/(a*d*(a + I*a*Tan[c + d*x])^3) + ((12*I)*e^4*(e*Sec[c + d*x])^(5/2))/(d*(a^4 + I*a^4*Tan[c + d*x]))","A",5,4,28,0.1429,1,"{3500, 3768, 3771, 2641}"
257,1,163,0,0.1542515,"\int \frac{(e \sec (c+d x))^{11/2}}{(a+i a \tan (c+d x))^4} \, dx","Int[(e*Sec[c + d*x])^(11/2)/(a + I*a*Tan[c + d*x])^4,x]","\frac{42 e^5 \sin (c+d x) \sqrt{e \sec (c+d x)}}{5 a^4 d}-\frac{28 i e^4 (e \sec (c+d x))^{3/2}}{5 d \left(a^4+i a^4 \tan (c+d x)\right)}-\frac{42 e^6 E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{5 a^4 d \sqrt{\cos (c+d x)} \sqrt{e \sec (c+d x)}}+\frac{4 i e^2 (e \sec (c+d x))^{7/2}}{5 a d (a+i a \tan (c+d x))^3}","\frac{42 e^5 \sin (c+d x) \sqrt{e \sec (c+d x)}}{5 a^4 d}-\frac{28 i e^4 (e \sec (c+d x))^{3/2}}{5 d \left(a^4+i a^4 \tan (c+d x)\right)}-\frac{42 e^6 E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{5 a^4 d \sqrt{\cos (c+d x)} \sqrt{e \sec (c+d x)}}+\frac{4 i e^2 (e \sec (c+d x))^{7/2}}{5 a d (a+i a \tan (c+d x))^3}",1,"(-42*e^6*EllipticE[(c + d*x)/2, 2])/(5*a^4*d*Sqrt[Cos[c + d*x]]*Sqrt[e*Sec[c + d*x]]) + (42*e^5*Sqrt[e*Sec[c + d*x]]*Sin[c + d*x])/(5*a^4*d) + (((4*I)/5)*e^2*(e*Sec[c + d*x])^(7/2))/(a*d*(a + I*a*Tan[c + d*x])^3) - (((28*I)/5)*e^4*(e*Sec[c + d*x])^(3/2))/(d*(a^4 + I*a^4*Tan[c + d*x]))","A",5,4,28,0.1429,1,"{3500, 3768, 3771, 2639}"
258,1,132,0,0.1374372,"\int \frac{(e \sec (c+d x))^{9/2}}{(a+i a \tan (c+d x))^4} \, dx","Int[(e*Sec[c + d*x])^(9/2)/(a + I*a*Tan[c + d*x])^4,x]","-\frac{20 i e^4 \sqrt{e \sec (c+d x)}}{21 d \left(a^4+i a^4 \tan (c+d x)\right)}+\frac{10 e^4 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{e \sec (c+d x)}}{21 a^4 d}+\frac{4 i e^2 (e \sec (c+d x))^{5/2}}{7 a d (a+i a \tan (c+d x))^3}","-\frac{20 i e^4 \sqrt{e \sec (c+d x)}}{21 d \left(a^4+i a^4 \tan (c+d x)\right)}+\frac{10 e^4 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{e \sec (c+d x)}}{21 a^4 d}+\frac{4 i e^2 (e \sec (c+d x))^{5/2}}{7 a d (a+i a \tan (c+d x))^3}",1,"(10*e^4*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2]*Sqrt[e*Sec[c + d*x]])/(21*a^4*d) + (((4*I)/7)*e^2*(e*Sec[c + d*x])^(5/2))/(a*d*(a + I*a*Tan[c + d*x])^3) - (((20*I)/21)*e^4*Sqrt[e*Sec[c + d*x]])/(d*(a^4 + I*a^4*Tan[c + d*x]))","A",4,3,28,0.1071,1,"{3500, 3771, 2641}"
259,1,132,0,0.1377486,"\int \frac{(e \sec (c+d x))^{7/2}}{(a+i a \tan (c+d x))^4} \, dx","Int[(e*Sec[c + d*x])^(7/2)/(a + I*a*Tan[c + d*x])^4,x]","-\frac{4 i e^4}{15 d \left(a^4+i a^4 \tan (c+d x)\right) \sqrt{e \sec (c+d x)}}-\frac{2 e^4 E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{15 a^4 d \sqrt{\cos (c+d x)} \sqrt{e \sec (c+d x)}}+\frac{4 i e^2 (e \sec (c+d x))^{3/2}}{9 a d (a+i a \tan (c+d x))^3}","-\frac{4 i e^4}{15 d \left(a^4+i a^4 \tan (c+d x)\right) \sqrt{e \sec (c+d x)}}-\frac{2 e^4 E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{15 a^4 d \sqrt{\cos (c+d x)} \sqrt{e \sec (c+d x)}}+\frac{4 i e^2 (e \sec (c+d x))^{3/2}}{9 a d (a+i a \tan (c+d x))^3}",1,"(-2*e^4*EllipticE[(c + d*x)/2, 2])/(15*a^4*d*Sqrt[Cos[c + d*x]]*Sqrt[e*Sec[c + d*x]]) + (((4*I)/9)*e^2*(e*Sec[c + d*x])^(3/2))/(a*d*(a + I*a*Tan[c + d*x])^3) - (((4*I)/15)*e^4)/(d*Sqrt[e*Sec[c + d*x]]*(a^4 + I*a^4*Tan[c + d*x]))","A",4,3,28,0.1071,1,"{3500, 3771, 2639}"
260,1,163,0,0.1438272,"\int \frac{(e \sec (c+d x))^{5/2}}{(a+i a \tan (c+d x))^4} \, dx","Int[(e*Sec[c + d*x])^(5/2)/(a + I*a*Tan[c + d*x])^4,x]","-\frac{2 e^3 \sin (c+d x)}{77 a^4 d \sqrt{e \sec (c+d x)}}-\frac{4 i e^4}{77 d \left(a^4+i a^4 \tan (c+d x)\right) (e \sec (c+d x))^{3/2}}-\frac{2 e^2 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{e \sec (c+d x)}}{77 a^4 d}+\frac{4 i e^2 \sqrt{e \sec (c+d x)}}{11 a d (a+i a \tan (c+d x))^3}","-\frac{2 e^3 \sin (c+d x)}{77 a^4 d \sqrt{e \sec (c+d x)}}-\frac{4 i e^4}{77 d \left(a^4+i a^4 \tan (c+d x)\right) (e \sec (c+d x))^{3/2}}-\frac{2 e^2 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{e \sec (c+d x)}}{77 a^4 d}+\frac{4 i e^2 \sqrt{e \sec (c+d x)}}{11 a d (a+i a \tan (c+d x))^3}",1,"(-2*e^2*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2]*Sqrt[e*Sec[c + d*x]])/(77*a^4*d) - (2*e^3*Sin[c + d*x])/(77*a^4*d*Sqrt[e*Sec[c + d*x]]) + (((4*I)/11)*e^2*Sqrt[e*Sec[c + d*x]])/(a*d*(a + I*a*Tan[c + d*x])^3) - (((4*I)/77)*e^4)/(d*(e*Sec[c + d*x])^(3/2)*(a^4 + I*a^4*Tan[c + d*x]))","A",5,4,28,0.1429,1,"{3500, 3769, 3771, 2641}"
261,1,163,0,0.1462644,"\int \frac{(e \sec (c+d x))^{3/2}}{(a+i a \tan (c+d x))^4} \, dx","Int[(e*Sec[c + d*x])^(3/2)/(a + I*a*Tan[c + d*x])^4,x]","\frac{2 e^3 \sin (c+d x)}{117 a^4 d (e \sec (c+d x))^{3/2}}+\frac{4 i e^4}{117 d \left(a^4+i a^4 \tan (c+d x)\right) (e \sec (c+d x))^{5/2}}+\frac{2 e^2 E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{39 a^4 d \sqrt{\cos (c+d x)} \sqrt{e \sec (c+d x)}}+\frac{4 i e^2}{13 a d (a+i a \tan (c+d x))^3 \sqrt{e \sec (c+d x)}}","\frac{2 e^3 \sin (c+d x)}{117 a^4 d (e \sec (c+d x))^{3/2}}+\frac{4 i e^4}{117 d \left(a^4+i a^4 \tan (c+d x)\right) (e \sec (c+d x))^{5/2}}+\frac{2 e^2 E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{39 a^4 d \sqrt{\cos (c+d x)} \sqrt{e \sec (c+d x)}}+\frac{4 i e^2}{13 a d (a+i a \tan (c+d x))^3 \sqrt{e \sec (c+d x)}}",1,"(2*e^2*EllipticE[(c + d*x)/2, 2])/(39*a^4*d*Sqrt[Cos[c + d*x]]*Sqrt[e*Sec[c + d*x]]) + (2*e^3*Sin[c + d*x])/(117*a^4*d*(e*Sec[c + d*x])^(3/2)) + (((4*I)/13)*e^2)/(a*d*Sqrt[e*Sec[c + d*x]]*(a + I*a*Tan[c + d*x])^3) + (((4*I)/117)*e^4)/(d*(e*Sec[c + d*x])^(5/2)*(a^4 + I*a^4*Tan[c + d*x]))","A",5,4,28,0.1429,1,"{3500, 3769, 3771, 2639}"
262,1,191,0,0.1917233,"\int \frac{\sqrt{e \sec (c+d x)}}{(a+i a \tan (c+d x))^4} \, dx","Int[Sqrt[e*Sec[c + d*x]]/(a + I*a*Tan[c + d*x])^4,x]","\frac{4 i e^2}{33 d \left(a^4+i a^4 \tan (c+d x)\right) (e \sec (c+d x))^{3/2}}+\frac{2 e \sin (c+d x)}{33 a^4 d \sqrt{e \sec (c+d x)}}+\frac{2 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{e \sec (c+d x)}}{33 a^4 d}+\frac{14 i \sqrt{e \sec (c+d x)}}{165 a d (a+i a \tan (c+d x))^3}+\frac{2 i \sqrt{e \sec (c+d x)}}{15 d (a+i a \tan (c+d x))^4}","\frac{4 i e^2}{33 d \left(a^4+i a^4 \tan (c+d x)\right) (e \sec (c+d x))^{3/2}}+\frac{2 e \sin (c+d x)}{33 a^4 d \sqrt{e \sec (c+d x)}}+\frac{2 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{e \sec (c+d x)}}{33 a^4 d}+\frac{14 i \sqrt{e \sec (c+d x)}}{165 a d (a+i a \tan (c+d x))^3}+\frac{2 i \sqrt{e \sec (c+d x)}}{15 d (a+i a \tan (c+d x))^4}",1,"(2*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2]*Sqrt[e*Sec[c + d*x]])/(33*a^4*d) + (2*e*Sin[c + d*x])/(33*a^4*d*Sqrt[e*Sec[c + d*x]]) + (((2*I)/15)*Sqrt[e*Sec[c + d*x]])/(d*(a + I*a*Tan[c + d*x])^4) + (((14*I)/165)*Sqrt[e*Sec[c + d*x]])/(a*d*(a + I*a*Tan[c + d*x])^3) + (((4*I)/33)*e^2)/(d*(e*Sec[c + d*x])^(3/2)*(a^4 + I*a^4*Tan[c + d*x]))","A",6,5,28,0.1786,1,"{3502, 3500, 3769, 3771, 2641}"
263,1,69,0,0.1660155,"\int (d \sec (e+f x))^{5/3} (a+i a \tan (e+f x)) \, dx","Int[(d*Sec[e + f*x])^(5/3)*(a + I*a*Tan[e + f*x]),x]","\frac{6 i 2^{5/6} a (d \sec (e+f x))^{5/3} \text{Hypergeometric2F1}\left(-\frac{5}{6},\frac{5}{6},\frac{11}{6},\frac{1}{2} (1-i \tan (e+f x))\right)}{5 f (1+i \tan (e+f x))^{5/6}}","\frac{6 i 2^{5/6} a (d \sec (e+f x))^{5/3} \text{Hypergeometric2F1}\left(-\frac{5}{6},\frac{5}{6},\frac{11}{6},\frac{1}{2} (1-i \tan (e+f x))\right)}{5 f (1+i \tan (e+f x))^{5/6}}",1,"(((6*I)/5)*2^(5/6)*a*Hypergeometric2F1[-5/6, 5/6, 11/6, (1 - I*Tan[e + f*x])/2]*(d*Sec[e + f*x])^(5/3))/(f*(1 + I*Tan[e + f*x])^(5/6))","A",4,4,26,0.1538,1,"{3505, 3523, 70, 69}"
264,1,67,0,0.1467196,"\int \sqrt[3]{d \sec (e+f x)} (a+i a \tan (e+f x)) \, dx","Int[(d*Sec[e + f*x])^(1/3)*(a + I*a*Tan[e + f*x]),x]","\frac{6 i \sqrt[6]{2} a \sqrt[3]{d \sec (e+f x)} \text{Hypergeometric2F1}\left(-\frac{1}{6},\frac{1}{6},\frac{7}{6},\frac{1}{2} (1-i \tan (e+f x))\right)}{f \sqrt[6]{1+i \tan (e+f x)}}","\frac{6 i \sqrt[6]{2} a \sqrt[3]{d \sec (e+f x)} \text{Hypergeometric2F1}\left(-\frac{1}{6},\frac{1}{6},\frac{7}{6},\frac{1}{2} (1-i \tan (e+f x))\right)}{f \sqrt[6]{1+i \tan (e+f x)}}",1,"((6*I)*2^(1/6)*a*Hypergeometric2F1[-1/6, 1/6, 7/6, (1 - I*Tan[e + f*x])/2]*(d*Sec[e + f*x])^(1/3))/(f*(1 + I*Tan[e + f*x])^(1/6))","A",4,4,26,0.1538,1,"{3505, 3523, 70, 69}"
265,1,67,0,0.1544737,"\int \frac{a+i a \tan (e+f x)}{\sqrt[3]{d \sec (e+f x)}} \, dx","Int[(a + I*a*Tan[e + f*x])/(d*Sec[e + f*x])^(1/3),x]","-\frac{3 i 2^{5/6} a \sqrt[6]{1+i \tan (e+f x)} \text{Hypergeometric2F1}\left(-\frac{1}{6},\frac{1}{6},\frac{5}{6},\frac{1}{2} (1-i \tan (e+f x))\right)}{f \sqrt[3]{d \sec (e+f x)}}","-\frac{3 i 2^{5/6} a \sqrt[6]{1+i \tan (e+f x)} \text{Hypergeometric2F1}\left(-\frac{1}{6},\frac{1}{6},\frac{5}{6},\frac{1}{2} (1-i \tan (e+f x))\right)}{f \sqrt[3]{d \sec (e+f x)}}",1,"((-3*I)*2^(5/6)*a*Hypergeometric2F1[-1/6, 1/6, 5/6, (1 - I*Tan[e + f*x])/2]*(1 + I*Tan[e + f*x])^(1/6))/(f*(d*Sec[e + f*x])^(1/3))","A",4,4,26,0.1538,1,"{3505, 3523, 70, 69}"
266,1,69,0,0.1522349,"\int \frac{a+i a \tan (e+f x)}{(d \sec (e+f x))^{5/3}} \, dx","Int[(a + I*a*Tan[e + f*x])/(d*Sec[e + f*x])^(5/3),x]","-\frac{3 i \sqrt[6]{2} a (1+i \tan (e+f x))^{5/6} \text{Hypergeometric2F1}\left(-\frac{5}{6},\frac{5}{6},\frac{1}{6},\frac{1}{2} (1-i \tan (e+f x))\right)}{5 f (d \sec (e+f x))^{5/3}}","-\frac{3 i \sqrt[6]{2} a (1+i \tan (e+f x))^{5/6} \text{Hypergeometric2F1}\left(-\frac{5}{6},\frac{5}{6},\frac{1}{6},\frac{1}{2} (1-i \tan (e+f x))\right)}{5 f (d \sec (e+f x))^{5/3}}",1,"(((-3*I)/5)*2^(1/6)*a*Hypergeometric2F1[-5/6, 5/6, 1/6, (1 - I*Tan[e + f*x])/2]*(1 + I*Tan[e + f*x])^(5/6))/(f*(d*Sec[e + f*x])^(5/3))","A",4,4,26,0.1538,1,"{3505, 3523, 70, 69}"
267,1,71,0,0.1766463,"\int (d \sec (e+f x))^{5/3} (a+i a \tan (e+f x))^2 \, dx","Int[(d*Sec[e + f*x])^(5/3)*(a + I*a*Tan[e + f*x])^2,x]","\frac{12 i 2^{5/6} a^2 (d \sec (e+f x))^{5/3} \text{Hypergeometric2F1}\left(-\frac{11}{6},\frac{5}{6},\frac{11}{6},\frac{1}{2} (1-i \tan (e+f x))\right)}{5 f (1+i \tan (e+f x))^{5/6}}","\frac{12 i 2^{5/6} a^2 (d \sec (e+f x))^{5/3} \text{Hypergeometric2F1}\left(-\frac{11}{6},\frac{5}{6},\frac{11}{6},\frac{1}{2} (1-i \tan (e+f x))\right)}{5 f (1+i \tan (e+f x))^{5/6}}",1,"(((12*I)/5)*2^(5/6)*a^2*Hypergeometric2F1[-11/6, 5/6, 11/6, (1 - I*Tan[e + f*x])/2]*(d*Sec[e + f*x])^(5/3))/(f*(1 + I*Tan[e + f*x])^(5/6))","A",4,4,28,0.1429,1,"{3505, 3523, 70, 69}"
268,1,69,0,0.1576429,"\int \sqrt[3]{d \sec (e+f x)} (a+i a \tan (e+f x))^2 \, dx","Int[(d*Sec[e + f*x])^(1/3)*(a + I*a*Tan[e + f*x])^2,x]","\frac{12 i \sqrt[6]{2} a^2 \sqrt[3]{d \sec (e+f x)} \text{Hypergeometric2F1}\left(-\frac{7}{6},\frac{1}{6},\frac{7}{6},\frac{1}{2} (1-i \tan (e+f x))\right)}{f \sqrt[6]{1+i \tan (e+f x)}}","\frac{12 i \sqrt[6]{2} a^2 \sqrt[3]{d \sec (e+f x)} \text{Hypergeometric2F1}\left(-\frac{7}{6},\frac{1}{6},\frac{7}{6},\frac{1}{2} (1-i \tan (e+f x))\right)}{f \sqrt[6]{1+i \tan (e+f x)}}",1,"((12*I)*2^(1/6)*a^2*Hypergeometric2F1[-7/6, 1/6, 7/6, (1 - I*Tan[e + f*x])/2]*(d*Sec[e + f*x])^(1/3))/(f*(1 + I*Tan[e + f*x])^(1/6))","A",4,4,28,0.1429,1,"{3505, 3523, 70, 69}"
269,1,83,0,0.165748,"\int \frac{(a+i a \tan (e+f x))^2}{\sqrt[3]{d \sec (e+f x)}} \, dx","Int[(a + I*a*Tan[e + f*x])^2/(d*Sec[e + f*x])^(1/3),x]","-\frac{6 i 2^{5/6} \left(a^2+i a^2 \tan (e+f x)\right) \text{Hypergeometric2F1}\left(-\frac{5}{6},-\frac{1}{6},\frac{5}{6},\frac{1}{2} (1-i \tan (e+f x))\right)}{f (1+i \tan (e+f x))^{5/6} \sqrt[3]{d \sec (e+f x)}}","-\frac{6 i 2^{5/6} \left(a^2+i a^2 \tan (e+f x)\right) \text{Hypergeometric2F1}\left(-\frac{5}{6},-\frac{1}{6},\frac{5}{6},\frac{1}{2} (1-i \tan (e+f x))\right)}{f (1+i \tan (e+f x))^{5/6} \sqrt[3]{d \sec (e+f x)}}",1,"((-6*I)*2^(5/6)*Hypergeometric2F1[-5/6, -1/6, 5/6, (1 - I*Tan[e + f*x])/2]*(a^2 + I*a^2*Tan[e + f*x]))/(f*(d*Sec[e + f*x])^(1/3)*(1 + I*Tan[e + f*x])^(5/6))","A",4,4,28,0.1429,1,"{3505, 3523, 70, 69}"
270,1,85,0,0.1803326,"\int \frac{(a+i a \tan (e+f x))^2}{(d \sec (e+f x))^{5/3}} \, dx","Int[(a + I*a*Tan[e + f*x])^2/(d*Sec[e + f*x])^(5/3),x]","-\frac{6 i \sqrt[6]{2} \left(a^2+i a^2 \tan (e+f x)\right) \text{Hypergeometric2F1}\left(-\frac{5}{6},-\frac{1}{6},\frac{1}{6},\frac{1}{2} (1-i \tan (e+f x))\right)}{5 f \sqrt[6]{1+i \tan (e+f x)} (d \sec (e+f x))^{5/3}}","-\frac{6 i \sqrt[6]{2} \left(a^2+i a^2 \tan (e+f x)\right) \text{Hypergeometric2F1}\left(-\frac{5}{6},-\frac{1}{6},\frac{1}{6},\frac{1}{2} (1-i \tan (e+f x))\right)}{5 f \sqrt[6]{1+i \tan (e+f x)} (d \sec (e+f x))^{5/3}}",1,"(((-6*I)/5)*2^(1/6)*Hypergeometric2F1[-5/6, -1/6, 1/6, (1 - I*Tan[e + f*x])/2]*(a^2 + I*a^2*Tan[e + f*x]))/(f*(d*Sec[e + f*x])^(5/3)*(1 + I*Tan[e + f*x])^(1/6))","A",4,4,28,0.1429,1,"{3505, 3523, 70, 69}"
271,1,83,0,0.1750582,"\int \frac{(d \sec (e+f x))^{5/3}}{a+i a \tan (e+f x)} \, dx","Int[(d*Sec[e + f*x])^(5/3)/(a + I*a*Tan[e + f*x]),x]","\frac{3 i \sqrt[6]{1+i \tan (e+f x)} (d \sec (e+f x))^{5/3} \text{Hypergeometric2F1}\left(\frac{5}{6},\frac{7}{6},\frac{11}{6},\frac{1}{2} (1-i \tan (e+f x))\right)}{5 \sqrt[6]{2} f (a+i a \tan (e+f x))}","\frac{3 i \sqrt[6]{1+i \tan (e+f x)} (d \sec (e+f x))^{5/3} \text{Hypergeometric2F1}\left(\frac{5}{6},\frac{7}{6},\frac{11}{6},\frac{1}{2} (1-i \tan (e+f x))\right)}{5 \sqrt[6]{2} f (a+i a \tan (e+f x))}",1,"(((3*I)/5)*Hypergeometric2F1[5/6, 7/6, 11/6, (1 - I*Tan[e + f*x])/2]*(d*Sec[e + f*x])^(5/3)*(1 + I*Tan[e + f*x])^(1/6))/(2^(1/6)*f*(a + I*a*Tan[e + f*x]))","A",4,4,28,0.1429,1,"{3505, 3523, 70, 69}"
272,1,81,0,0.1693889,"\int \frac{\sqrt[3]{d \sec (e+f x)}}{a+i a \tan (e+f x)} \, dx","Int[(d*Sec[e + f*x])^(1/3)/(a + I*a*Tan[e + f*x]),x]","\frac{3 i (1+i \tan (e+f x))^{5/6} \sqrt[3]{d \sec (e+f x)} \text{Hypergeometric2F1}\left(\frac{1}{6},\frac{11}{6},\frac{7}{6},\frac{1}{2} (1-i \tan (e+f x))\right)}{2^{5/6} f (a+i a \tan (e+f x))}","\frac{3 i (1+i \tan (e+f x))^{5/6} \sqrt[3]{d \sec (e+f x)} \text{Hypergeometric2F1}\left(\frac{1}{6},\frac{11}{6},\frac{7}{6},\frac{1}{2} (1-i \tan (e+f x))\right)}{2^{5/6} f (a+i a \tan (e+f x))}",1,"((3*I)*Hypergeometric2F1[1/6, 11/6, 7/6, (1 - I*Tan[e + f*x])/2]*(d*Sec[e + f*x])^(1/3)*(1 + I*Tan[e + f*x])^(5/6))/(2^(5/6)*f*(a + I*a*Tan[e + f*x]))","A",4,4,28,0.1429,1,"{3505, 3523, 70, 69}"
273,1,71,0,0.183121,"\int \frac{1}{\sqrt[3]{d \sec (e+f x)} (a+i a \tan (e+f x))} \, dx","Int[1/((d*Sec[e + f*x])^(1/3)*(a + I*a*Tan[e + f*x])),x]","-\frac{3 i \sqrt[6]{1+i \tan (e+f x)} \text{Hypergeometric2F1}\left(-\frac{1}{6},\frac{13}{6},\frac{5}{6},\frac{1}{2} (1-i \tan (e+f x))\right)}{2 \sqrt[6]{2} a f \sqrt[3]{d \sec (e+f x)}}","-\frac{3 i \sqrt[6]{1+i \tan (e+f x)} \text{Hypergeometric2F1}\left(-\frac{1}{6},\frac{13}{6},\frac{5}{6},\frac{1}{2} (1-i \tan (e+f x))\right)}{2 \sqrt[6]{2} a f \sqrt[3]{d \sec (e+f x)}}",1,"(((-3*I)/2)*Hypergeometric2F1[-1/6, 13/6, 5/6, (1 - I*Tan[e + f*x])/2]*(1 + I*Tan[e + f*x])^(1/6))/(2^(1/6)*a*f*(d*Sec[e + f*x])^(1/3))","A",4,4,28,0.1429,1,"{3505, 3523, 70, 69}"
274,1,71,0,0.2090701,"\int \frac{1}{(d \sec (e+f x))^{5/3} (a+i a \tan (e+f x))} \, dx","Int[1/((d*Sec[e + f*x])^(5/3)*(a + I*a*Tan[e + f*x])),x]","-\frac{3 i (1+i \tan (e+f x))^{5/6} \text{Hypergeometric2F1}\left(-\frac{5}{6},\frac{17}{6},\frac{1}{6},\frac{1}{2} (1-i \tan (e+f x))\right)}{10\ 2^{5/6} a f (d \sec (e+f x))^{5/3}}","-\frac{3 i (1+i \tan (e+f x))^{5/6} \text{Hypergeometric2F1}\left(-\frac{5}{6},\frac{17}{6},\frac{1}{6},\frac{1}{2} (1-i \tan (e+f x))\right)}{10\ 2^{5/6} a f (d \sec (e+f x))^{5/3}}",1,"(((-3*I)/10)*Hypergeometric2F1[-5/6, 17/6, 1/6, (1 - I*Tan[e + f*x])/2]*(1 + I*Tan[e + f*x])^(5/6))/(2^(5/6)*a*f*(d*Sec[e + f*x])^(5/3))","A",4,4,28,0.1429,1,"{3505, 3523, 70, 69}"
275,1,87,0,0.1853383,"\int \frac{(d \sec (e+f x))^{5/3}}{(a+i a \tan (e+f x))^2} \, dx","Int[(d*Sec[e + f*x])^(5/3)/(a + I*a*Tan[e + f*x])^2,x]","\frac{3 i \sqrt[6]{1+i \tan (e+f x)} (d \sec (e+f x))^{5/3} \text{Hypergeometric2F1}\left(\frac{5}{6},\frac{13}{6},\frac{11}{6},\frac{1}{2} (1-i \tan (e+f x))\right)}{10 \sqrt[6]{2} f \left(a^2+i a^2 \tan (e+f x)\right)}","\frac{3 i \sqrt[6]{1+i \tan (e+f x)} (d \sec (e+f x))^{5/3} \text{Hypergeometric2F1}\left(\frac{5}{6},\frac{13}{6},\frac{11}{6},\frac{1}{2} (1-i \tan (e+f x))\right)}{10 \sqrt[6]{2} f \left(a^2+i a^2 \tan (e+f x)\right)}",1,"(((3*I)/10)*Hypergeometric2F1[5/6, 13/6, 11/6, (1 - I*Tan[e + f*x])/2]*(d*Sec[e + f*x])^(5/3)*(1 + I*Tan[e + f*x])^(1/6))/(2^(1/6)*f*(a^2 + I*a^2*Tan[e + f*x]))","A",4,4,28,0.1429,1,"{3505, 3523, 70, 69}"
276,1,87,0,0.1703165,"\int \frac{\sqrt[3]{d \sec (e+f x)}}{(a+i a \tan (e+f x))^2} \, dx","Int[(d*Sec[e + f*x])^(1/3)/(a + I*a*Tan[e + f*x])^2,x]","\frac{3 i (1+i \tan (e+f x))^{5/6} \sqrt[3]{d \sec (e+f x)} \text{Hypergeometric2F1}\left(\frac{1}{6},\frac{17}{6},\frac{7}{6},\frac{1}{2} (1-i \tan (e+f x))\right)}{2\ 2^{5/6} f \left(a^2+i a^2 \tan (e+f x)\right)}","\frac{3 i (1+i \tan (e+f x))^{5/6} \sqrt[3]{d \sec (e+f x)} \text{Hypergeometric2F1}\left(\frac{1}{6},\frac{17}{6},\frac{7}{6},\frac{1}{2} (1-i \tan (e+f x))\right)}{2\ 2^{5/6} f \left(a^2+i a^2 \tan (e+f x)\right)}",1,"(((3*I)/2)*Hypergeometric2F1[1/6, 17/6, 7/6, (1 - I*Tan[e + f*x])/2]*(d*Sec[e + f*x])^(1/3)*(1 + I*Tan[e + f*x])^(5/6))/(2^(5/6)*f*(a^2 + I*a^2*Tan[e + f*x]))","A",4,4,28,0.1429,1,"{3505, 3523, 70, 69}"
277,1,71,0,0.1798467,"\int \frac{1}{\sqrt[3]{d \sec (e+f x)} (a+i a \tan (e+f x))^2} \, dx","Int[1/((d*Sec[e + f*x])^(1/3)*(a + I*a*Tan[e + f*x])^2),x]","-\frac{3 i \sqrt[6]{1+i \tan (e+f x)} \text{Hypergeometric2F1}\left(-\frac{1}{6},\frac{19}{6},\frac{5}{6},\frac{1}{2} (1-i \tan (e+f x))\right)}{4 \sqrt[6]{2} a^2 f \sqrt[3]{d \sec (e+f x)}}","-\frac{3 i \sqrt[6]{1+i \tan (e+f x)} \text{Hypergeometric2F1}\left(-\frac{1}{6},\frac{19}{6},\frac{5}{6},\frac{1}{2} (1-i \tan (e+f x))\right)}{4 \sqrt[6]{2} a^2 f \sqrt[3]{d \sec (e+f x)}}",1,"(((-3*I)/4)*Hypergeometric2F1[-1/6, 19/6, 5/6, (1 - I*Tan[e + f*x])/2]*(1 + I*Tan[e + f*x])^(1/6))/(2^(1/6)*a^2*f*(d*Sec[e + f*x])^(1/3))","A",4,4,28,0.1429,1,"{3505, 3523, 70, 69}"
278,1,71,0,0.190183,"\int \frac{1}{(d \sec (e+f x))^{5/3} (a+i a \tan (e+f x))^2} \, dx","Int[1/((d*Sec[e + f*x])^(5/3)*(a + I*a*Tan[e + f*x])^2),x]","-\frac{3 i (1+i \tan (e+f x))^{5/6} \text{Hypergeometric2F1}\left(-\frac{5}{6},\frac{23}{6},\frac{1}{6},\frac{1}{2} (1-i \tan (e+f x))\right)}{20\ 2^{5/6} a^2 f (d \sec (e+f x))^{5/3}}","-\frac{3 i (1+i \tan (e+f x))^{5/6} \text{Hypergeometric2F1}\left(-\frac{5}{6},\frac{23}{6},\frac{1}{6},\frac{1}{2} (1-i \tan (e+f x))\right)}{20\ 2^{5/6} a^2 f (d \sec (e+f x))^{5/3}}",1,"(((-3*I)/20)*Hypergeometric2F1[-5/6, 23/6, 1/6, (1 - I*Tan[e + f*x])/2]*(1 + I*Tan[e + f*x])^(5/6))/(2^(5/6)*a^2*f*(d*Sec[e + f*x])^(5/3))","A",4,4,28,0.1429,1,"{3505, 3523, 70, 69}"
279,1,117,0,0.0754535,"\int \sec ^8(c+d x) \sqrt{a+i a \tan (c+d x)} \, dx","Int[Sec[c + d*x]^8*Sqrt[a + I*a*Tan[c + d*x]],x]","\frac{2 i (a+i a \tan (c+d x))^{15/2}}{15 a^7 d}-\frac{12 i (a+i a \tan (c+d x))^{13/2}}{13 a^6 d}+\frac{24 i (a+i a \tan (c+d x))^{11/2}}{11 a^5 d}-\frac{16 i (a+i a \tan (c+d x))^{9/2}}{9 a^4 d}","\frac{2 i (a+i a \tan (c+d x))^{15/2}}{15 a^7 d}-\frac{12 i (a+i a \tan (c+d x))^{13/2}}{13 a^6 d}+\frac{24 i (a+i a \tan (c+d x))^{11/2}}{11 a^5 d}-\frac{16 i (a+i a \tan (c+d x))^{9/2}}{9 a^4 d}",1,"(((-16*I)/9)*(a + I*a*Tan[c + d*x])^(9/2))/(a^4*d) + (((24*I)/11)*(a + I*a*Tan[c + d*x])^(11/2))/(a^5*d) - (((12*I)/13)*(a + I*a*Tan[c + d*x])^(13/2))/(a^6*d) + (((2*I)/15)*(a + I*a*Tan[c + d*x])^(15/2))/(a^7*d)","A",3,2,26,0.07692,1,"{3487, 43}"
280,1,88,0,0.0690455,"\int \sec ^6(c+d x) \sqrt{a+i a \tan (c+d x)} \, dx","Int[Sec[c + d*x]^6*Sqrt[a + I*a*Tan[c + d*x]],x]","-\frac{2 i (a+i a \tan (c+d x))^{11/2}}{11 a^5 d}+\frac{8 i (a+i a \tan (c+d x))^{9/2}}{9 a^4 d}-\frac{8 i (a+i a \tan (c+d x))^{7/2}}{7 a^3 d}","-\frac{2 i (a+i a \tan (c+d x))^{11/2}}{11 a^5 d}+\frac{8 i (a+i a \tan (c+d x))^{9/2}}{9 a^4 d}-\frac{8 i (a+i a \tan (c+d x))^{7/2}}{7 a^3 d}",1,"(((-8*I)/7)*(a + I*a*Tan[c + d*x])^(7/2))/(a^3*d) + (((8*I)/9)*(a + I*a*Tan[c + d*x])^(9/2))/(a^4*d) - (((2*I)/11)*(a + I*a*Tan[c + d*x])^(11/2))/(a^5*d)","A",3,2,26,0.07692,1,"{3487, 43}"
281,1,59,0,0.0622915,"\int \sec ^4(c+d x) \sqrt{a+i a \tan (c+d x)} \, dx","Int[Sec[c + d*x]^4*Sqrt[a + I*a*Tan[c + d*x]],x]","\frac{2 i (a+i a \tan (c+d x))^{7/2}}{7 a^3 d}-\frac{4 i (a+i a \tan (c+d x))^{5/2}}{5 a^2 d}","\frac{2 i (a+i a \tan (c+d x))^{7/2}}{7 a^3 d}-\frac{4 i (a+i a \tan (c+d x))^{5/2}}{5 a^2 d}",1,"(((-4*I)/5)*(a + I*a*Tan[c + d*x])^(5/2))/(a^2*d) + (((2*I)/7)*(a + I*a*Tan[c + d*x])^(7/2))/(a^3*d)","A",3,2,26,0.07692,1,"{3487, 43}"
282,1,29,0,0.0556067,"\int \sec ^2(c+d x) \sqrt{a+i a \tan (c+d x)} \, dx","Int[Sec[c + d*x]^2*Sqrt[a + I*a*Tan[c + d*x]],x]","-\frac{2 i (a+i a \tan (c+d x))^{3/2}}{3 a d}","-\frac{2 i (a+i a \tan (c+d x))^{3/2}}{3 a d}",1,"(((-2*I)/3)*(a + I*a*Tan[c + d*x])^(3/2))/(a*d)","A",2,2,26,0.07692,1,"{3487, 32}"
283,1,120,0,0.0981145,"\int \cos ^2(c+d x) \sqrt{a+i a \tan (c+d x)} \, dx","Int[Cos[c + d*x]^2*Sqrt[a + I*a*Tan[c + d*x]],x]","-\frac{i a^2}{2 d (a-i a \tan (c+d x)) \sqrt{a+i a \tan (c+d x)}}+\frac{3 i a}{4 d \sqrt{a+i a \tan (c+d x)}}-\frac{3 i \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{4 \sqrt{2} d}","-\frac{i a^2}{2 d (a-i a \tan (c+d x)) \sqrt{a+i a \tan (c+d x)}}+\frac{3 i a}{4 d \sqrt{a+i a \tan (c+d x)}}-\frac{3 i \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{4 \sqrt{2} d}",1,"(((-3*I)/4)*Sqrt[a]*ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/(Sqrt[2]*Sqrt[a])])/(Sqrt[2]*d) + (((3*I)/4)*a)/(d*Sqrt[a + I*a*Tan[c + d*x]]) - ((I/2)*a^2)/(d*(a - I*a*Tan[c + d*x])*Sqrt[a + I*a*Tan[c + d*x]])","A",5,4,26,0.1538,1,"{3487, 51, 63, 206}"
284,1,193,0,0.1120874,"\int \cos ^4(c+d x) \sqrt{a+i a \tan (c+d x)} \, dx","Int[Cos[c + d*x]^4*Sqrt[a + I*a*Tan[c + d*x]],x]","-\frac{i a^4}{4 d (a-i a \tan (c+d x))^2 (a+i a \tan (c+d x))^{3/2}}-\frac{7 i a^3}{16 d (a-i a \tan (c+d x)) (a+i a \tan (c+d x))^{3/2}}+\frac{35 i a^2}{96 d (a+i a \tan (c+d x))^{3/2}}+\frac{35 i a}{64 d \sqrt{a+i a \tan (c+d x)}}-\frac{35 i \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{64 \sqrt{2} d}","-\frac{i a^4}{4 d (a-i a \tan (c+d x))^2 (a+i a \tan (c+d x))^{3/2}}-\frac{7 i a^3}{16 d (a-i a \tan (c+d x)) (a+i a \tan (c+d x))^{3/2}}+\frac{35 i a^2}{96 d (a+i a \tan (c+d x))^{3/2}}+\frac{35 i a}{64 d \sqrt{a+i a \tan (c+d x)}}-\frac{35 i \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{64 \sqrt{2} d}",1,"(((-35*I)/64)*Sqrt[a]*ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/(Sqrt[2]*Sqrt[a])])/(Sqrt[2]*d) + (((35*I)/96)*a^2)/(d*(a + I*a*Tan[c + d*x])^(3/2)) - ((I/4)*a^4)/(d*(a - I*a*Tan[c + d*x])^2*(a + I*a*Tan[c + d*x])^(3/2)) - (((7*I)/16)*a^3)/(d*(a - I*a*Tan[c + d*x])*(a + I*a*Tan[c + d*x])^(3/2)) + (((35*I)/64)*a)/(d*Sqrt[a + I*a*Tan[c + d*x]])","A",7,4,26,0.1538,1,"{3487, 51, 63, 206}"
285,1,266,0,0.1419503,"\int \cos ^6(c+d x) \sqrt{a+i a \tan (c+d x)} \, dx","Int[Cos[c + d*x]^6*Sqrt[a + I*a*Tan[c + d*x]],x]","-\frac{i a^6}{6 d (a-i a \tan (c+d x))^3 (a+i a \tan (c+d x))^{5/2}}-\frac{11 i a^5}{48 d (a-i a \tan (c+d x))^2 (a+i a \tan (c+d x))^{5/2}}-\frac{33 i a^4}{64 d (a-i a \tan (c+d x)) (a+i a \tan (c+d x))^{5/2}}+\frac{231 i a^3}{640 d (a+i a \tan (c+d x))^{5/2}}+\frac{77 i a^2}{256 d (a+i a \tan (c+d x))^{3/2}}+\frac{231 i a}{512 d \sqrt{a+i a \tan (c+d x)}}-\frac{231 i \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{512 \sqrt{2} d}","-\frac{i a^6}{6 d (a-i a \tan (c+d x))^3 (a+i a \tan (c+d x))^{5/2}}-\frac{11 i a^5}{48 d (a-i a \tan (c+d x))^2 (a+i a \tan (c+d x))^{5/2}}-\frac{33 i a^4}{64 d (a-i a \tan (c+d x)) (a+i a \tan (c+d x))^{5/2}}+\frac{231 i a^3}{640 d (a+i a \tan (c+d x))^{5/2}}+\frac{77 i a^2}{256 d (a+i a \tan (c+d x))^{3/2}}+\frac{231 i a}{512 d \sqrt{a+i a \tan (c+d x)}}-\frac{231 i \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{512 \sqrt{2} d}",1,"(((-231*I)/512)*Sqrt[a]*ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/(Sqrt[2]*Sqrt[a])])/(Sqrt[2]*d) + (((231*I)/640)*a^3)/(d*(a + I*a*Tan[c + d*x])^(5/2)) - ((I/6)*a^6)/(d*(a - I*a*Tan[c + d*x])^3*(a + I*a*Tan[c + d*x])^(5/2)) - (((11*I)/48)*a^5)/(d*(a - I*a*Tan[c + d*x])^2*(a + I*a*Tan[c + d*x])^(5/2)) - (((33*I)/64)*a^4)/(d*(a - I*a*Tan[c + d*x])*(a + I*a*Tan[c + d*x])^(5/2)) + (((77*I)/256)*a^2)/(d*(a + I*a*Tan[c + d*x])^(3/2)) + (((231*I)/512)*a)/(d*Sqrt[a + I*a*Tan[c + d*x]])","A",9,4,26,0.1538,1,"{3487, 51, 63, 206}"
286,1,147,0,0.2498422,"\int \sec ^7(c+d x) \sqrt{a+i a \tan (c+d x)} \, dx","Int[Sec[c + d*x]^7*Sqrt[a + I*a*Tan[c + d*x]],x]","\frac{24 i a^2 \sec ^7(c+d x)}{143 d (a+i a \tan (c+d x))^{3/2}}+\frac{64 i a^3 \sec ^7(c+d x)}{429 d (a+i a \tan (c+d x))^{5/2}}+\frac{256 i a^4 \sec ^7(c+d x)}{3003 d (a+i a \tan (c+d x))^{7/2}}+\frac{2 i a \sec ^7(c+d x)}{13 d \sqrt{a+i a \tan (c+d x)}}","\frac{24 i a^2 \sec ^7(c+d x)}{143 d (a+i a \tan (c+d x))^{3/2}}+\frac{64 i a^3 \sec ^7(c+d x)}{429 d (a+i a \tan (c+d x))^{5/2}}+\frac{256 i a^4 \sec ^7(c+d x)}{3003 d (a+i a \tan (c+d x))^{7/2}}+\frac{2 i a \sec ^7(c+d x)}{13 d \sqrt{a+i a \tan (c+d x)}}",1,"(((256*I)/3003)*a^4*Sec[c + d*x]^7)/(d*(a + I*a*Tan[c + d*x])^(7/2)) + (((64*I)/429)*a^3*Sec[c + d*x]^7)/(d*(a + I*a*Tan[c + d*x])^(5/2)) + (((24*I)/143)*a^2*Sec[c + d*x]^7)/(d*(a + I*a*Tan[c + d*x])^(3/2)) + (((2*I)/13)*a*Sec[c + d*x]^7)/(d*Sqrt[a + I*a*Tan[c + d*x]])","A",4,2,26,0.07692,1,"{3494, 3493}"
287,1,110,0,0.1778708,"\int \sec ^5(c+d x) \sqrt{a+i a \tan (c+d x)} \, dx","Int[Sec[c + d*x]^5*Sqrt[a + I*a*Tan[c + d*x]],x]","\frac{16 i a^2 \sec ^5(c+d x)}{63 d (a+i a \tan (c+d x))^{3/2}}+\frac{64 i a^3 \sec ^5(c+d x)}{315 d (a+i a \tan (c+d x))^{5/2}}+\frac{2 i a \sec ^5(c+d x)}{9 d \sqrt{a+i a \tan (c+d x)}}","\frac{16 i a^2 \sec ^5(c+d x)}{63 d (a+i a \tan (c+d x))^{3/2}}+\frac{64 i a^3 \sec ^5(c+d x)}{315 d (a+i a \tan (c+d x))^{5/2}}+\frac{2 i a \sec ^5(c+d x)}{9 d \sqrt{a+i a \tan (c+d x)}}",1,"(((64*I)/315)*a^3*Sec[c + d*x]^5)/(d*(a + I*a*Tan[c + d*x])^(5/2)) + (((16*I)/63)*a^2*Sec[c + d*x]^5)/(d*(a + I*a*Tan[c + d*x])^(3/2)) + (((2*I)/9)*a*Sec[c + d*x]^5)/(d*Sqrt[a + I*a*Tan[c + d*x]])","A",3,2,26,0.07692,1,"{3494, 3493}"
288,1,73,0,0.1074285,"\int \sec ^3(c+d x) \sqrt{a+i a \tan (c+d x)} \, dx","Int[Sec[c + d*x]^3*Sqrt[a + I*a*Tan[c + d*x]],x]","\frac{8 i a^2 \sec ^3(c+d x)}{15 d (a+i a \tan (c+d x))^{3/2}}+\frac{2 i a \sec ^3(c+d x)}{5 d \sqrt{a+i a \tan (c+d x)}}","\frac{8 i a^2 \sec ^3(c+d x)}{15 d (a+i a \tan (c+d x))^{3/2}}+\frac{2 i a \sec ^3(c+d x)}{5 d \sqrt{a+i a \tan (c+d x)}}",1,"(((8*I)/15)*a^2*Sec[c + d*x]^3)/(d*(a + I*a*Tan[c + d*x])^(3/2)) + (((2*I)/5)*a*Sec[c + d*x]^3)/(d*Sqrt[a + I*a*Tan[c + d*x]])","A",2,2,26,0.07692,1,"{3494, 3493}"
289,1,31,0,0.0281013,"\int \sec (c+d x) \sqrt{a+i a \tan (c+d x)} \, dx","Int[Sec[c + d*x]*Sqrt[a + I*a*Tan[c + d*x]],x]","\frac{2 i a \sec (c+d x)}{d \sqrt{a+i a \tan (c+d x)}}","\frac{2 i a \sec (c+d x)}{d \sqrt{a+i a \tan (c+d x)}}",1,"((2*I)*a*Sec[c + d*x])/(d*Sqrt[a + I*a*Tan[c + d*x]])","A",1,1,24,0.04167,1,"{3493}"
290,1,83,0,0.0937708,"\int \cos (c+d x) \sqrt{a+i a \tan (c+d x)} \, dx","Int[Cos[c + d*x]*Sqrt[a + I*a*Tan[c + d*x]],x]","\frac{i \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a} \sec (c+d x)}{\sqrt{2} \sqrt{a+i a \tan (c+d x)}}\right)}{\sqrt{2} d}-\frac{i \cos (c+d x) \sqrt{a+i a \tan (c+d x)}}{d}","\frac{i \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a} \sec (c+d x)}{\sqrt{2} \sqrt{a+i a \tan (c+d x)}}\right)}{\sqrt{2} d}-\frac{i \cos (c+d x) \sqrt{a+i a \tan (c+d x)}}{d}",1,"(I*Sqrt[a]*ArcTanh[(Sqrt[a]*Sec[c + d*x])/(Sqrt[2]*Sqrt[a + I*a*Tan[c + d*x]])])/(Sqrt[2]*d) - (I*Cos[c + d*x]*Sqrt[a + I*a*Tan[c + d*x]])/d","A",3,3,24,0.1250,1,"{3490, 3489, 206}"
291,1,154,0,0.2231281,"\int \cos ^3(c+d x) \sqrt{a+i a \tan (c+d x)} \, dx","Int[Cos[c + d*x]^3*Sqrt[a + I*a*Tan[c + d*x]],x]","-\frac{i \cos ^3(c+d x) \sqrt{a+i a \tan (c+d x)}}{3 d}-\frac{5 i \cos (c+d x) \sqrt{a+i a \tan (c+d x)}}{8 d}+\frac{5 i a \cos (c+d x)}{12 d \sqrt{a+i a \tan (c+d x)}}+\frac{5 i \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a} \sec (c+d x)}{\sqrt{2} \sqrt{a+i a \tan (c+d x)}}\right)}{8 \sqrt{2} d}","-\frac{i \cos ^3(c+d x) \sqrt{a+i a \tan (c+d x)}}{3 d}-\frac{5 i \cos (c+d x) \sqrt{a+i a \tan (c+d x)}}{8 d}+\frac{5 i a \cos (c+d x)}{12 d \sqrt{a+i a \tan (c+d x)}}+\frac{5 i \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a} \sec (c+d x)}{\sqrt{2} \sqrt{a+i a \tan (c+d x)}}\right)}{8 \sqrt{2} d}",1,"(((5*I)/8)*Sqrt[a]*ArcTanh[(Sqrt[a]*Sec[c + d*x])/(Sqrt[2]*Sqrt[a + I*a*Tan[c + d*x]])])/(Sqrt[2]*d) + (((5*I)/12)*a*Cos[c + d*x])/(d*Sqrt[a + I*a*Tan[c + d*x]]) - (((5*I)/8)*Cos[c + d*x]*Sqrt[a + I*a*Tan[c + d*x]])/d - ((I/3)*Cos[c + d*x]^3*Sqrt[a + I*a*Tan[c + d*x]])/d","A",5,5,26,0.1923,1,"{3497, 3502, 3490, 3489, 206}"
292,1,223,0,0.3909307,"\int \cos ^5(c+d x) \sqrt{a+i a \tan (c+d x)} \, dx","Int[Cos[c + d*x]^5*Sqrt[a + I*a*Tan[c + d*x]],x]","-\frac{i \cos ^5(c+d x) \sqrt{a+i a \tan (c+d x)}}{5 d}-\frac{21 i \cos ^3(c+d x) \sqrt{a+i a \tan (c+d x)}}{80 d}+\frac{9 i a \cos ^3(c+d x)}{40 d \sqrt{a+i a \tan (c+d x)}}-\frac{63 i \cos (c+d x) \sqrt{a+i a \tan (c+d x)}}{128 d}+\frac{21 i a \cos (c+d x)}{64 d \sqrt{a+i a \tan (c+d x)}}+\frac{63 i \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a} \sec (c+d x)}{\sqrt{2} \sqrt{a+i a \tan (c+d x)}}\right)}{128 \sqrt{2} d}","-\frac{i \cos ^5(c+d x) \sqrt{a+i a \tan (c+d x)}}{5 d}-\frac{21 i \cos ^3(c+d x) \sqrt{a+i a \tan (c+d x)}}{80 d}+\frac{9 i a \cos ^3(c+d x)}{40 d \sqrt{a+i a \tan (c+d x)}}-\frac{63 i \cos (c+d x) \sqrt{a+i a \tan (c+d x)}}{128 d}+\frac{21 i a \cos (c+d x)}{64 d \sqrt{a+i a \tan (c+d x)}}+\frac{63 i \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a} \sec (c+d x)}{\sqrt{2} \sqrt{a+i a \tan (c+d x)}}\right)}{128 \sqrt{2} d}",1,"(((63*I)/128)*Sqrt[a]*ArcTanh[(Sqrt[a]*Sec[c + d*x])/(Sqrt[2]*Sqrt[a + I*a*Tan[c + d*x]])])/(Sqrt[2]*d) + (((21*I)/64)*a*Cos[c + d*x])/(d*Sqrt[a + I*a*Tan[c + d*x]]) + (((9*I)/40)*a*Cos[c + d*x]^3)/(d*Sqrt[a + I*a*Tan[c + d*x]]) - (((63*I)/128)*Cos[c + d*x]*Sqrt[a + I*a*Tan[c + d*x]])/d - (((21*I)/80)*Cos[c + d*x]^3*Sqrt[a + I*a*Tan[c + d*x]])/d - ((I/5)*Cos[c + d*x]^5*Sqrt[a + I*a*Tan[c + d*x]])/d","A",7,5,26,0.1923,1,"{3497, 3502, 3490, 3489, 206}"
293,1,117,0,0.0893523,"\int \sec ^8(c+d x) (a+i a \tan (c+d x))^{3/2} \, dx","Int[Sec[c + d*x]^8*(a + I*a*Tan[c + d*x])^(3/2),x]","\frac{2 i (a+i a \tan (c+d x))^{17/2}}{17 a^7 d}-\frac{4 i (a+i a \tan (c+d x))^{15/2}}{5 a^6 d}+\frac{24 i (a+i a \tan (c+d x))^{13/2}}{13 a^5 d}-\frac{16 i (a+i a \tan (c+d x))^{11/2}}{11 a^4 d}","\frac{2 i (a+i a \tan (c+d x))^{17/2}}{17 a^7 d}-\frac{4 i (a+i a \tan (c+d x))^{15/2}}{5 a^6 d}+\frac{24 i (a+i a \tan (c+d x))^{13/2}}{13 a^5 d}-\frac{16 i (a+i a \tan (c+d x))^{11/2}}{11 a^4 d}",1,"(((-16*I)/11)*(a + I*a*Tan[c + d*x])^(11/2))/(a^4*d) + (((24*I)/13)*(a + I*a*Tan[c + d*x])^(13/2))/(a^5*d) - (((4*I)/5)*(a + I*a*Tan[c + d*x])^(15/2))/(a^6*d) + (((2*I)/17)*(a + I*a*Tan[c + d*x])^(17/2))/(a^7*d)","A",3,2,26,0.07692,1,"{3487, 43}"
294,1,88,0,0.0768244,"\int \sec ^6(c+d x) (a+i a \tan (c+d x))^{3/2} \, dx","Int[Sec[c + d*x]^6*(a + I*a*Tan[c + d*x])^(3/2),x]","-\frac{2 i (a+i a \tan (c+d x))^{13/2}}{13 a^5 d}+\frac{8 i (a+i a \tan (c+d x))^{11/2}}{11 a^4 d}-\frac{8 i (a+i a \tan (c+d x))^{9/2}}{9 a^3 d}","-\frac{2 i (a+i a \tan (c+d x))^{13/2}}{13 a^5 d}+\frac{8 i (a+i a \tan (c+d x))^{11/2}}{11 a^4 d}-\frac{8 i (a+i a \tan (c+d x))^{9/2}}{9 a^3 d}",1,"(((-8*I)/9)*(a + I*a*Tan[c + d*x])^(9/2))/(a^3*d) + (((8*I)/11)*(a + I*a*Tan[c + d*x])^(11/2))/(a^4*d) - (((2*I)/13)*(a + I*a*Tan[c + d*x])^(13/2))/(a^5*d)","A",3,2,26,0.07692,1,"{3487, 43}"
295,1,59,0,0.0687435,"\int \sec ^4(c+d x) (a+i a \tan (c+d x))^{3/2} \, dx","Int[Sec[c + d*x]^4*(a + I*a*Tan[c + d*x])^(3/2),x]","\frac{2 i (a+i a \tan (c+d x))^{9/2}}{9 a^3 d}-\frac{4 i (a+i a \tan (c+d x))^{7/2}}{7 a^2 d}","\frac{2 i (a+i a \tan (c+d x))^{9/2}}{9 a^3 d}-\frac{4 i (a+i a \tan (c+d x))^{7/2}}{7 a^2 d}",1,"(((-4*I)/7)*(a + I*a*Tan[c + d*x])^(7/2))/(a^2*d) + (((2*I)/9)*(a + I*a*Tan[c + d*x])^(9/2))/(a^3*d)","A",3,2,26,0.07692,1,"{3487, 43}"
296,1,29,0,0.060965,"\int \sec ^2(c+d x) (a+i a \tan (c+d x))^{3/2} \, dx","Int[Sec[c + d*x]^2*(a + I*a*Tan[c + d*x])^(3/2),x]","-\frac{2 i (a+i a \tan (c+d x))^{5/2}}{5 a d}","-\frac{2 i (a+i a \tan (c+d x))^{5/2}}{5 a d}",1,"(((-2*I)/5)*(a + I*a*Tan[c + d*x])^(5/2))/(a*d)","A",2,2,26,0.07692,1,"{3487, 32}"
297,1,93,0,0.0834103,"\int \cos ^2(c+d x) (a+i a \tan (c+d x))^{3/2} \, dx","Int[Cos[c + d*x]^2*(a + I*a*Tan[c + d*x])^(3/2),x]","-\frac{i a^2 \sqrt{a+i a \tan (c+d x)}}{2 d (a-i a \tan (c+d x))}-\frac{i a^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{2 \sqrt{2} d}","-\frac{i a^2 \sqrt{a+i a \tan (c+d x)}}{2 d (a-i a \tan (c+d x))}-\frac{i a^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{2 \sqrt{2} d}",1,"((-I/2)*a^(3/2)*ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/(Sqrt[2]*Sqrt[a])])/(Sqrt[2]*d) - ((I/2)*a^2*Sqrt[a + I*a*Tan[c + d*x]])/(d*(a - I*a*Tan[c + d*x]))","A",4,4,26,0.1538,1,"{3487, 51, 63, 206}"
298,1,166,0,0.105757,"\int \cos ^4(c+d x) (a+i a \tan (c+d x))^{3/2} \, dx","Int[Cos[c + d*x]^4*(a + I*a*Tan[c + d*x])^(3/2),x]","-\frac{i a^4}{4 d (a-i a \tan (c+d x))^2 \sqrt{a+i a \tan (c+d x)}}-\frac{5 i a^3}{16 d (a-i a \tan (c+d x)) \sqrt{a+i a \tan (c+d x)}}+\frac{15 i a^2}{32 d \sqrt{a+i a \tan (c+d x)}}-\frac{15 i a^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{32 \sqrt{2} d}","-\frac{i a^4}{4 d (a-i a \tan (c+d x))^2 \sqrt{a+i a \tan (c+d x)}}-\frac{5 i a^3}{16 d (a-i a \tan (c+d x)) \sqrt{a+i a \tan (c+d x)}}+\frac{15 i a^2}{32 d \sqrt{a+i a \tan (c+d x)}}-\frac{15 i a^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{32 \sqrt{2} d}",1,"(((-15*I)/32)*a^(3/2)*ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/(Sqrt[2]*Sqrt[a])])/(Sqrt[2]*d) + (((15*I)/32)*a^2)/(d*Sqrt[a + I*a*Tan[c + d*x]]) - ((I/4)*a^4)/(d*(a - I*a*Tan[c + d*x])^2*Sqrt[a + I*a*Tan[c + d*x]]) - (((5*I)/16)*a^3)/(d*(a - I*a*Tan[c + d*x])*Sqrt[a + I*a*Tan[c + d*x]])","A",6,4,26,0.1538,1,"{3487, 51, 63, 206}"
299,1,239,0,0.1343444,"\int \cos ^6(c+d x) (a+i a \tan (c+d x))^{3/2} \, dx","Int[Cos[c + d*x]^6*(a + I*a*Tan[c + d*x])^(3/2),x]","-\frac{i a^6}{6 d (a-i a \tan (c+d x))^3 (a+i a \tan (c+d x))^{3/2}}-\frac{3 i a^5}{16 d (a-i a \tan (c+d x))^2 (a+i a \tan (c+d x))^{3/2}}-\frac{21 i a^4}{64 d (a-i a \tan (c+d x)) (a+i a \tan (c+d x))^{3/2}}+\frac{35 i a^3}{128 d (a+i a \tan (c+d x))^{3/2}}+\frac{105 i a^2}{256 d \sqrt{a+i a \tan (c+d x)}}-\frac{105 i a^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{256 \sqrt{2} d}","-\frac{i a^6}{6 d (a-i a \tan (c+d x))^3 (a+i a \tan (c+d x))^{3/2}}-\frac{3 i a^5}{16 d (a-i a \tan (c+d x))^2 (a+i a \tan (c+d x))^{3/2}}-\frac{21 i a^4}{64 d (a-i a \tan (c+d x)) (a+i a \tan (c+d x))^{3/2}}+\frac{35 i a^3}{128 d (a+i a \tan (c+d x))^{3/2}}+\frac{105 i a^2}{256 d \sqrt{a+i a \tan (c+d x)}}-\frac{105 i a^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{256 \sqrt{2} d}",1,"(((-105*I)/256)*a^(3/2)*ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/(Sqrt[2]*Sqrt[a])])/(Sqrt[2]*d) + (((35*I)/128)*a^3)/(d*(a + I*a*Tan[c + d*x])^(3/2)) - ((I/6)*a^6)/(d*(a - I*a*Tan[c + d*x])^3*(a + I*a*Tan[c + d*x])^(3/2)) - (((3*I)/16)*a^5)/(d*(a - I*a*Tan[c + d*x])^2*(a + I*a*Tan[c + d*x])^(3/2)) - (((21*I)/64)*a^4)/(d*(a - I*a*Tan[c + d*x])*(a + I*a*Tan[c + d*x])^(3/2)) + (((105*I)/256)*a^2)/(d*Sqrt[a + I*a*Tan[c + d*x]])","A",8,4,26,0.1538,1,"{3487, 51, 63, 206}"
300,1,147,0,0.2407225,"\int \sec ^5(c+d x) (a+i a \tan (c+d x))^{3/2} \, dx","Int[Sec[c + d*x]^5*(a + I*a*Tan[c + d*x])^(3/2),x]","\frac{8 i a^2 \sec ^5(c+d x)}{33 d \sqrt{a+i a \tan (c+d x)}}+\frac{64 i a^3 \sec ^5(c+d x)}{231 d (a+i a \tan (c+d x))^{3/2}}+\frac{256 i a^4 \sec ^5(c+d x)}{1155 d (a+i a \tan (c+d x))^{5/2}}+\frac{2 i a \sec ^5(c+d x) \sqrt{a+i a \tan (c+d x)}}{11 d}","\frac{8 i a^2 \sec ^5(c+d x)}{33 d \sqrt{a+i a \tan (c+d x)}}+\frac{64 i a^3 \sec ^5(c+d x)}{231 d (a+i a \tan (c+d x))^{3/2}}+\frac{256 i a^4 \sec ^5(c+d x)}{1155 d (a+i a \tan (c+d x))^{5/2}}+\frac{2 i a \sec ^5(c+d x) \sqrt{a+i a \tan (c+d x)}}{11 d}",1,"(((256*I)/1155)*a^4*Sec[c + d*x]^5)/(d*(a + I*a*Tan[c + d*x])^(5/2)) + (((64*I)/231)*a^3*Sec[c + d*x]^5)/(d*(a + I*a*Tan[c + d*x])^(3/2)) + (((8*I)/33)*a^2*Sec[c + d*x]^5)/(d*Sqrt[a + I*a*Tan[c + d*x]]) + (((2*I)/11)*a*Sec[c + d*x]^5*Sqrt[a + I*a*Tan[c + d*x]])/d","A",4,2,26,0.07692,1,"{3494, 3493}"
301,1,110,0,0.1766913,"\int \sec ^3(c+d x) (a+i a \tan (c+d x))^{3/2} \, dx","Int[Sec[c + d*x]^3*(a + I*a*Tan[c + d*x])^(3/2),x]","\frac{16 i a^2 \sec ^3(c+d x)}{35 d \sqrt{a+i a \tan (c+d x)}}+\frac{64 i a^3 \sec ^3(c+d x)}{105 d (a+i a \tan (c+d x))^{3/2}}+\frac{2 i a \sec ^3(c+d x) \sqrt{a+i a \tan (c+d x)}}{7 d}","\frac{16 i a^2 \sec ^3(c+d x)}{35 d \sqrt{a+i a \tan (c+d x)}}+\frac{64 i a^3 \sec ^3(c+d x)}{105 d (a+i a \tan (c+d x))^{3/2}}+\frac{2 i a \sec ^3(c+d x) \sqrt{a+i a \tan (c+d x)}}{7 d}",1,"(((64*I)/105)*a^3*Sec[c + d*x]^3)/(d*(a + I*a*Tan[c + d*x])^(3/2)) + (((16*I)/35)*a^2*Sec[c + d*x]^3)/(d*Sqrt[a + I*a*Tan[c + d*x]]) + (((2*I)/7)*a*Sec[c + d*x]^3*Sqrt[a + I*a*Tan[c + d*x]])/d","A",3,2,26,0.07692,1,"{3494, 3493}"
302,1,69,0,0.0643351,"\int \sec (c+d x) (a+i a \tan (c+d x))^{3/2} \, dx","Int[Sec[c + d*x]*(a + I*a*Tan[c + d*x])^(3/2),x]","\frac{8 i a^2 \sec (c+d x)}{3 d \sqrt{a+i a \tan (c+d x)}}+\frac{2 i a \sec (c+d x) \sqrt{a+i a \tan (c+d x)}}{3 d}","\frac{8 i a^2 \sec (c+d x)}{3 d \sqrt{a+i a \tan (c+d x)}}+\frac{2 i a \sec (c+d x) \sqrt{a+i a \tan (c+d x)}}{3 d}",1,"(((8*I)/3)*a^2*Sec[c + d*x])/(d*Sqrt[a + I*a*Tan[c + d*x]]) + (((2*I)/3)*a*Sec[c + d*x]*Sqrt[a + I*a*Tan[c + d*x]])/d","A",2,2,24,0.08333,1,"{3494, 3493}"
303,1,31,0,0.0490911,"\int \cos (c+d x) (a+i a \tan (c+d x))^{3/2} \, dx","Int[Cos[c + d*x]*(a + I*a*Tan[c + d*x])^(3/2),x]","-\frac{2 i a \cos (c+d x) \sqrt{a+i a \tan (c+d x)}}{d}","-\frac{2 i a \cos (c+d x) \sqrt{a+i a \tan (c+d x)}}{d}",1,"((-2*I)*a*Cos[c + d*x]*Sqrt[a + I*a*Tan[c + d*x]])/d","A",1,1,24,0.04167,1,"{3493}"
304,1,122,0,0.1494188,"\int \cos ^3(c+d x) (a+i a \tan (c+d x))^{3/2} \, dx","Int[Cos[c + d*x]^3*(a + I*a*Tan[c + d*x])^(3/2),x]","\frac{i a^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a} \sec (c+d x)}{\sqrt{2} \sqrt{a+i a \tan (c+d x)}}\right)}{2 \sqrt{2} d}-\frac{i \cos ^3(c+d x) (a+i a \tan (c+d x))^{3/2}}{3 d}-\frac{i a \cos (c+d x) \sqrt{a+i a \tan (c+d x)}}{2 d}","\frac{i a^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a} \sec (c+d x)}{\sqrt{2} \sqrt{a+i a \tan (c+d x)}}\right)}{2 \sqrt{2} d}-\frac{i \cos ^3(c+d x) (a+i a \tan (c+d x))^{3/2}}{3 d}-\frac{i a \cos (c+d x) \sqrt{a+i a \tan (c+d x)}}{2 d}",1,"((I/2)*a^(3/2)*ArcTanh[(Sqrt[a]*Sec[c + d*x])/(Sqrt[2]*Sqrt[a + I*a*Tan[c + d*x]])])/(Sqrt[2]*d) - ((I/2)*a*Cos[c + d*x]*Sqrt[a + I*a*Tan[c + d*x]])/d - ((I/3)*Cos[c + d*x]^3*(a + I*a*Tan[c + d*x])^(3/2))/d","A",4,3,26,0.1154,1,"{3490, 3489, 206}"
305,1,192,0,0.2700184,"\int \cos ^5(c+d x) (a+i a \tan (c+d x))^{3/2} \, dx","Int[Cos[c + d*x]^5*(a + I*a*Tan[c + d*x])^(3/2),x]","\frac{7 i a^2 \cos (c+d x)}{24 d \sqrt{a+i a \tan (c+d x)}}+\frac{7 i a^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a} \sec (c+d x)}{\sqrt{2} \sqrt{a+i a \tan (c+d x)}}\right)}{16 \sqrt{2} d}-\frac{i \cos ^5(c+d x) (a+i a \tan (c+d x))^{3/2}}{5 d}-\frac{7 i a \cos ^3(c+d x) \sqrt{a+i a \tan (c+d x)}}{30 d}-\frac{7 i a \cos (c+d x) \sqrt{a+i a \tan (c+d x)}}{16 d}","\frac{7 i a^2 \cos (c+d x)}{24 d \sqrt{a+i a \tan (c+d x)}}+\frac{7 i a^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a} \sec (c+d x)}{\sqrt{2} \sqrt{a+i a \tan (c+d x)}}\right)}{16 \sqrt{2} d}-\frac{i \cos ^5(c+d x) (a+i a \tan (c+d x))^{3/2}}{5 d}-\frac{7 i a \cos ^3(c+d x) \sqrt{a+i a \tan (c+d x)}}{30 d}-\frac{7 i a \cos (c+d x) \sqrt{a+i a \tan (c+d x)}}{16 d}",1,"(((7*I)/16)*a^(3/2)*ArcTanh[(Sqrt[a]*Sec[c + d*x])/(Sqrt[2]*Sqrt[a + I*a*Tan[c + d*x]])])/(Sqrt[2]*d) + (((7*I)/24)*a^2*Cos[c + d*x])/(d*Sqrt[a + I*a*Tan[c + d*x]]) - (((7*I)/16)*a*Cos[c + d*x]*Sqrt[a + I*a*Tan[c + d*x]])/d - (((7*I)/30)*a*Cos[c + d*x]^3*Sqrt[a + I*a*Tan[c + d*x]])/d - ((I/5)*Cos[c + d*x]^5*(a + I*a*Tan[c + d*x])^(3/2))/d","A",6,5,26,0.1923,1,"{3497, 3502, 3490, 3489, 206}"
306,1,117,0,0.0860853,"\int \sec ^8(c+d x) (a+i a \tan (c+d x))^{5/2} \, dx","Int[Sec[c + d*x]^8*(a + I*a*Tan[c + d*x])^(5/2),x]","\frac{2 i (a+i a \tan (c+d x))^{19/2}}{19 a^7 d}-\frac{12 i (a+i a \tan (c+d x))^{17/2}}{17 a^6 d}+\frac{8 i (a+i a \tan (c+d x))^{15/2}}{5 a^5 d}-\frac{16 i (a+i a \tan (c+d x))^{13/2}}{13 a^4 d}","\frac{2 i (a+i a \tan (c+d x))^{19/2}}{19 a^7 d}-\frac{12 i (a+i a \tan (c+d x))^{17/2}}{17 a^6 d}+\frac{8 i (a+i a \tan (c+d x))^{15/2}}{5 a^5 d}-\frac{16 i (a+i a \tan (c+d x))^{13/2}}{13 a^4 d}",1,"(((-16*I)/13)*(a + I*a*Tan[c + d*x])^(13/2))/(a^4*d) + (((8*I)/5)*(a + I*a*Tan[c + d*x])^(15/2))/(a^5*d) - (((12*I)/17)*(a + I*a*Tan[c + d*x])^(17/2))/(a^6*d) + (((2*I)/19)*(a + I*a*Tan[c + d*x])^(19/2))/(a^7*d)","A",3,2,26,0.07692,1,"{3487, 43}"
307,1,88,0,0.0771402,"\int \sec ^6(c+d x) (a+i a \tan (c+d x))^{5/2} \, dx","Int[Sec[c + d*x]^6*(a + I*a*Tan[c + d*x])^(5/2),x]","-\frac{2 i (a+i a \tan (c+d x))^{15/2}}{15 a^5 d}+\frac{8 i (a+i a \tan (c+d x))^{13/2}}{13 a^4 d}-\frac{8 i (a+i a \tan (c+d x))^{11/2}}{11 a^3 d}","-\frac{2 i (a+i a \tan (c+d x))^{15/2}}{15 a^5 d}+\frac{8 i (a+i a \tan (c+d x))^{13/2}}{13 a^4 d}-\frac{8 i (a+i a \tan (c+d x))^{11/2}}{11 a^3 d}",1,"(((-8*I)/11)*(a + I*a*Tan[c + d*x])^(11/2))/(a^3*d) + (((8*I)/13)*(a + I*a*Tan[c + d*x])^(13/2))/(a^4*d) - (((2*I)/15)*(a + I*a*Tan[c + d*x])^(15/2))/(a^5*d)","A",3,2,26,0.07692,1,"{3487, 43}"
308,1,59,0,0.0705784,"\int \sec ^4(c+d x) (a+i a \tan (c+d x))^{5/2} \, dx","Int[Sec[c + d*x]^4*(a + I*a*Tan[c + d*x])^(5/2),x]","\frac{2 i (a+i a \tan (c+d x))^{11/2}}{11 a^3 d}-\frac{4 i (a+i a \tan (c+d x))^{9/2}}{9 a^2 d}","\frac{2 i (a+i a \tan (c+d x))^{11/2}}{11 a^3 d}-\frac{4 i (a+i a \tan (c+d x))^{9/2}}{9 a^2 d}",1,"(((-4*I)/9)*(a + I*a*Tan[c + d*x])^(9/2))/(a^2*d) + (((2*I)/11)*(a + I*a*Tan[c + d*x])^(11/2))/(a^3*d)","A",3,2,26,0.07692,1,"{3487, 43}"
309,1,29,0,0.0628827,"\int \sec ^2(c+d x) (a+i a \tan (c+d x))^{5/2} \, dx","Int[Sec[c + d*x]^2*(a + I*a*Tan[c + d*x])^(5/2),x]","-\frac{2 i (a+i a \tan (c+d x))^{7/2}}{7 a d}","-\frac{2 i (a+i a \tan (c+d x))^{7/2}}{7 a d}",1,"(((-2*I)/7)*(a + I*a*Tan[c + d*x])^(7/2))/(a*d)","A",2,2,26,0.07692,1,"{3487, 32}"
310,1,89,0,0.0827533,"\int \cos ^2(c+d x) (a+i a \tan (c+d x))^{5/2} \, dx","Int[Cos[c + d*x]^2*(a + I*a*Tan[c + d*x])^(5/2),x]","\frac{i a^{5/2} \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{\sqrt{2} d}-\frac{i a^3 \sqrt{a+i a \tan (c+d x)}}{d (a-i a \tan (c+d x))}","\frac{i a^{5/2} \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{\sqrt{2} d}-\frac{i a^3 \sqrt{a+i a \tan (c+d x)}}{d (a-i a \tan (c+d x))}",1,"(I*a^(5/2)*ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/(Sqrt[2]*Sqrt[a])])/(Sqrt[2]*d) - (I*a^3*Sqrt[a + I*a*Tan[c + d*x]])/(d*(a - I*a*Tan[c + d*x]))","A",4,4,26,0.1538,1,"{3487, 47, 63, 206}"
311,1,137,0,0.0949402,"\int \cos ^4(c+d x) (a+i a \tan (c+d x))^{5/2} \, dx","Int[Cos[c + d*x]^4*(a + I*a*Tan[c + d*x])^(5/2),x]","-\frac{i a^4 \sqrt{a+i a \tan (c+d x)}}{4 d (a-i a \tan (c+d x))^2}-\frac{3 i a^3 \sqrt{a+i a \tan (c+d x)}}{16 d (a-i a \tan (c+d x))}-\frac{3 i a^{5/2} \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{16 \sqrt{2} d}","-\frac{i a^4 \sqrt{a+i a \tan (c+d x)}}{4 d (a-i a \tan (c+d x))^2}-\frac{3 i a^3 \sqrt{a+i a \tan (c+d x)}}{16 d (a-i a \tan (c+d x))}-\frac{3 i a^{5/2} \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{16 \sqrt{2} d}",1,"(((-3*I)/16)*a^(5/2)*ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/(Sqrt[2]*Sqrt[a])])/(Sqrt[2]*d) - ((I/4)*a^4*Sqrt[a + I*a*Tan[c + d*x]])/(d*(a - I*a*Tan[c + d*x])^2) - (((3*I)/16)*a^3*Sqrt[a + I*a*Tan[c + d*x]])/(d*(a - I*a*Tan[c + d*x]))","A",5,4,26,0.1538,1,"{3487, 51, 63, 206}"
312,1,210,0,0.1198645,"\int \cos ^6(c+d x) (a+i a \tan (c+d x))^{5/2} \, dx","Int[Cos[c + d*x]^6*(a + I*a*Tan[c + d*x])^(5/2),x]","-\frac{i a^6}{6 d (a-i a \tan (c+d x))^3 \sqrt{a+i a \tan (c+d x)}}-\frac{7 i a^5}{48 d (a-i a \tan (c+d x))^2 \sqrt{a+i a \tan (c+d x)}}-\frac{35 i a^4}{192 d (a-i a \tan (c+d x)) \sqrt{a+i a \tan (c+d x)}}+\frac{35 i a^3}{128 d \sqrt{a+i a \tan (c+d x)}}-\frac{35 i a^{5/2} \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{128 \sqrt{2} d}","-\frac{i a^6}{6 d (a-i a \tan (c+d x))^3 \sqrt{a+i a \tan (c+d x)}}-\frac{7 i a^5}{48 d (a-i a \tan (c+d x))^2 \sqrt{a+i a \tan (c+d x)}}-\frac{35 i a^4}{192 d (a-i a \tan (c+d x)) \sqrt{a+i a \tan (c+d x)}}+\frac{35 i a^3}{128 d \sqrt{a+i a \tan (c+d x)}}-\frac{35 i a^{5/2} \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{128 \sqrt{2} d}",1,"(((-35*I)/128)*a^(5/2)*ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/(Sqrt[2]*Sqrt[a])])/(Sqrt[2]*d) + (((35*I)/128)*a^3)/(d*Sqrt[a + I*a*Tan[c + d*x]]) - ((I/6)*a^6)/(d*(a - I*a*Tan[c + d*x])^3*Sqrt[a + I*a*Tan[c + d*x]]) - (((7*I)/48)*a^5)/(d*(a - I*a*Tan[c + d*x])^2*Sqrt[a + I*a*Tan[c + d*x]]) - (((35*I)/192)*a^4)/(d*(a - I*a*Tan[c + d*x])*Sqrt[a + I*a*Tan[c + d*x]])","A",7,4,26,0.1538,1,"{3487, 51, 63, 206}"
313,1,147,0,0.2404491,"\int \sec ^3(c+d x) (a+i a \tan (c+d x))^{5/2} \, dx","Int[Sec[c + d*x]^3*(a + I*a*Tan[c + d*x])^(5/2),x]","\frac{256 i a^4 \sec ^3(c+d x)}{315 d (a+i a \tan (c+d x))^{3/2}}+\frac{64 i a^3 \sec ^3(c+d x)}{105 d \sqrt{a+i a \tan (c+d x)}}+\frac{8 i a^2 \sec ^3(c+d x) \sqrt{a+i a \tan (c+d x)}}{21 d}+\frac{2 i a \sec ^3(c+d x) (a+i a \tan (c+d x))^{3/2}}{9 d}","\frac{256 i a^4 \sec ^3(c+d x)}{315 d (a+i a \tan (c+d x))^{3/2}}+\frac{64 i a^3 \sec ^3(c+d x)}{105 d \sqrt{a+i a \tan (c+d x)}}+\frac{8 i a^2 \sec ^3(c+d x) \sqrt{a+i a \tan (c+d x)}}{21 d}+\frac{2 i a \sec ^3(c+d x) (a+i a \tan (c+d x))^{3/2}}{9 d}",1,"(((256*I)/315)*a^4*Sec[c + d*x]^3)/(d*(a + I*a*Tan[c + d*x])^(3/2)) + (((64*I)/105)*a^3*Sec[c + d*x]^3)/(d*Sqrt[a + I*a*Tan[c + d*x]]) + (((8*I)/21)*a^2*Sec[c + d*x]^3*Sqrt[a + I*a*Tan[c + d*x]])/d + (((2*I)/9)*a*Sec[c + d*x]^3*(a + I*a*Tan[c + d*x])^(3/2))/d","A",4,2,26,0.07692,1,"{3494, 3493}"
314,1,104,0,0.1012825,"\int \sec (c+d x) (a+i a \tan (c+d x))^{5/2} \, dx","Int[Sec[c + d*x]*(a + I*a*Tan[c + d*x])^(5/2),x]","\frac{64 i a^3 \sec (c+d x)}{15 d \sqrt{a+i a \tan (c+d x)}}+\frac{16 i a^2 \sec (c+d x) \sqrt{a+i a \tan (c+d x)}}{15 d}+\frac{2 i a \sec (c+d x) (a+i a \tan (c+d x))^{3/2}}{5 d}","\frac{64 i a^3 \sec (c+d x)}{15 d \sqrt{a+i a \tan (c+d x)}}+\frac{16 i a^2 \sec (c+d x) \sqrt{a+i a \tan (c+d x)}}{15 d}+\frac{2 i a \sec (c+d x) (a+i a \tan (c+d x))^{3/2}}{5 d}",1,"(((64*I)/15)*a^3*Sec[c + d*x])/(d*Sqrt[a + I*a*Tan[c + d*x]]) + (((16*I)/15)*a^2*Sec[c + d*x]*Sqrt[a + I*a*Tan[c + d*x]])/d + (((2*I)/5)*a*Sec[c + d*x]*(a + I*a*Tan[c + d*x])^(3/2))/d","A",3,2,24,0.08333,1,"{3494, 3493}"
315,1,65,0,0.0966806,"\int \cos (c+d x) (a+i a \tan (c+d x))^{5/2} \, dx","Int[Cos[c + d*x]*(a + I*a*Tan[c + d*x])^(5/2),x]","\frac{2 i a \cos (c+d x) (a+i a \tan (c+d x))^{3/2}}{d}-\frac{8 i a^2 \cos (c+d x) \sqrt{a+i a \tan (c+d x)}}{d}","\frac{2 i a \cos (c+d x) (a+i a \tan (c+d x))^{3/2}}{d}-\frac{8 i a^2 \cos (c+d x) \sqrt{a+i a \tan (c+d x)}}{d}",1,"((-8*I)*a^2*Cos[c + d*x]*Sqrt[a + I*a*Tan[c + d*x]])/d + ((2*I)*a*Cos[c + d*x]*(a + I*a*Tan[c + d*x])^(3/2))/d","A",2,2,24,0.08333,1,"{3494, 3493}"
316,1,35,0,0.0598799,"\int \cos ^3(c+d x) (a+i a \tan (c+d x))^{5/2} \, dx","Int[Cos[c + d*x]^3*(a + I*a*Tan[c + d*x])^(5/2),x]","-\frac{2 i a \cos ^3(c+d x) (a+i a \tan (c+d x))^{3/2}}{3 d}","-\frac{2 i a \cos ^3(c+d x) (a+i a \tan (c+d x))^{3/2}}{3 d}",1,"(((-2*I)/3)*a*Cos[c + d*x]^3*(a + I*a*Tan[c + d*x])^(3/2))/d","A",1,1,26,0.03846,1,"{3493}"
317,1,159,0,0.2179167,"\int \cos ^5(c+d x) (a+i a \tan (c+d x))^{5/2} \, dx","Int[Cos[c + d*x]^5*(a + I*a*Tan[c + d*x])^(5/2),x]","-\frac{i a^2 \cos (c+d x) \sqrt{a+i a \tan (c+d x)}}{4 d}+\frac{i a^{5/2} \tanh ^{-1}\left(\frac{\sqrt{a} \sec (c+d x)}{\sqrt{2} \sqrt{a+i a \tan (c+d x)}}\right)}{4 \sqrt{2} d}-\frac{i \cos ^5(c+d x) (a+i a \tan (c+d x))^{5/2}}{5 d}-\frac{i a \cos ^3(c+d x) (a+i a \tan (c+d x))^{3/2}}{6 d}","-\frac{i a^2 \cos (c+d x) \sqrt{a+i a \tan (c+d x)}}{4 d}+\frac{i a^{5/2} \tanh ^{-1}\left(\frac{\sqrt{a} \sec (c+d x)}{\sqrt{2} \sqrt{a+i a \tan (c+d x)}}\right)}{4 \sqrt{2} d}-\frac{i \cos ^5(c+d x) (a+i a \tan (c+d x))^{5/2}}{5 d}-\frac{i a \cos ^3(c+d x) (a+i a \tan (c+d x))^{3/2}}{6 d}",1,"((I/4)*a^(5/2)*ArcTanh[(Sqrt[a]*Sec[c + d*x])/(Sqrt[2]*Sqrt[a + I*a*Tan[c + d*x]])])/(Sqrt[2]*d) - ((I/4)*a^2*Cos[c + d*x]*Sqrt[a + I*a*Tan[c + d*x]])/d - ((I/6)*a*Cos[c + d*x]^3*(a + I*a*Tan[c + d*x])^(3/2))/d - ((I/5)*Cos[c + d*x]^5*(a + I*a*Tan[c + d*x])^(5/2))/d","A",5,3,26,0.1154,1,"{3490, 3489, 206}"
318,1,231,0,0.3388961,"\int \cos ^7(c+d x) (a+i a \tan (c+d x))^{5/2} \, dx","Int[Cos[c + d*x]^7*(a + I*a*Tan[c + d*x])^(5/2),x]","-\frac{3 i a^2 \cos ^3(c+d x) \sqrt{a+i a \tan (c+d x)}}{20 d}-\frac{9 i a^2 \cos (c+d x) \sqrt{a+i a \tan (c+d x)}}{32 d}+\frac{3 i a^3 \cos (c+d x)}{16 d \sqrt{a+i a \tan (c+d x)}}+\frac{9 i a^{5/2} \tanh ^{-1}\left(\frac{\sqrt{a} \sec (c+d x)}{\sqrt{2} \sqrt{a+i a \tan (c+d x)}}\right)}{32 \sqrt{2} d}-\frac{i \cos ^7(c+d x) (a+i a \tan (c+d x))^{5/2}}{7 d}-\frac{9 i a \cos ^5(c+d x) (a+i a \tan (c+d x))^{3/2}}{70 d}","-\frac{3 i a^2 \cos ^3(c+d x) \sqrt{a+i a \tan (c+d x)}}{20 d}-\frac{9 i a^2 \cos (c+d x) \sqrt{a+i a \tan (c+d x)}}{32 d}+\frac{3 i a^3 \cos (c+d x)}{16 d \sqrt{a+i a \tan (c+d x)}}+\frac{9 i a^{5/2} \tanh ^{-1}\left(\frac{\sqrt{a} \sec (c+d x)}{\sqrt{2} \sqrt{a+i a \tan (c+d x)}}\right)}{32 \sqrt{2} d}-\frac{i \cos ^7(c+d x) (a+i a \tan (c+d x))^{5/2}}{7 d}-\frac{9 i a \cos ^5(c+d x) (a+i a \tan (c+d x))^{3/2}}{70 d}",1,"(((9*I)/32)*a^(5/2)*ArcTanh[(Sqrt[a]*Sec[c + d*x])/(Sqrt[2]*Sqrt[a + I*a*Tan[c + d*x]])])/(Sqrt[2]*d) + (((3*I)/16)*a^3*Cos[c + d*x])/(d*Sqrt[a + I*a*Tan[c + d*x]]) - (((9*I)/32)*a^2*Cos[c + d*x]*Sqrt[a + I*a*Tan[c + d*x]])/d - (((3*I)/20)*a^2*Cos[c + d*x]^3*Sqrt[a + I*a*Tan[c + d*x]])/d - (((9*I)/70)*a*Cos[c + d*x]^5*(a + I*a*Tan[c + d*x])^(3/2))/d - ((I/7)*Cos[c + d*x]^7*(a + I*a*Tan[c + d*x])^(5/2))/d","A",7,5,26,0.1923,1,"{3497, 3502, 3490, 3489, 206}"
319,1,117,0,0.0839321,"\int \sec ^8(c+d x) (a+i a \tan (c+d x))^{7/2} \, dx","Int[Sec[c + d*x]^8*(a + I*a*Tan[c + d*x])^(7/2),x]","\frac{2 i (a+i a \tan (c+d x))^{21/2}}{21 a^7 d}-\frac{12 i (a+i a \tan (c+d x))^{19/2}}{19 a^6 d}+\frac{24 i (a+i a \tan (c+d x))^{17/2}}{17 a^5 d}-\frac{16 i (a+i a \tan (c+d x))^{15/2}}{15 a^4 d}","\frac{2 i (a+i a \tan (c+d x))^{21/2}}{21 a^7 d}-\frac{12 i (a+i a \tan (c+d x))^{19/2}}{19 a^6 d}+\frac{24 i (a+i a \tan (c+d x))^{17/2}}{17 a^5 d}-\frac{16 i (a+i a \tan (c+d x))^{15/2}}{15 a^4 d}",1,"(((-16*I)/15)*(a + I*a*Tan[c + d*x])^(15/2))/(a^4*d) + (((24*I)/17)*(a + I*a*Tan[c + d*x])^(17/2))/(a^5*d) - (((12*I)/19)*(a + I*a*Tan[c + d*x])^(19/2))/(a^6*d) + (((2*I)/21)*(a + I*a*Tan[c + d*x])^(21/2))/(a^7*d)","A",3,2,26,0.07692,1,"{3487, 43}"
320,1,88,0,0.0766982,"\int \sec ^6(c+d x) (a+i a \tan (c+d x))^{7/2} \, dx","Int[Sec[c + d*x]^6*(a + I*a*Tan[c + d*x])^(7/2),x]","-\frac{2 i (a+i a \tan (c+d x))^{17/2}}{17 a^5 d}+\frac{8 i (a+i a \tan (c+d x))^{15/2}}{15 a^4 d}-\frac{8 i (a+i a \tan (c+d x))^{13/2}}{13 a^3 d}","-\frac{2 i (a+i a \tan (c+d x))^{17/2}}{17 a^5 d}+\frac{8 i (a+i a \tan (c+d x))^{15/2}}{15 a^4 d}-\frac{8 i (a+i a \tan (c+d x))^{13/2}}{13 a^3 d}",1,"(((-8*I)/13)*(a + I*a*Tan[c + d*x])^(13/2))/(a^3*d) + (((8*I)/15)*(a + I*a*Tan[c + d*x])^(15/2))/(a^4*d) - (((2*I)/17)*(a + I*a*Tan[c + d*x])^(17/2))/(a^5*d)","A",3,2,26,0.07692,1,"{3487, 43}"
321,1,59,0,0.0679677,"\int \sec ^4(c+d x) (a+i a \tan (c+d x))^{7/2} \, dx","Int[Sec[c + d*x]^4*(a + I*a*Tan[c + d*x])^(7/2),x]","\frac{2 i (a+i a \tan (c+d x))^{13/2}}{13 a^3 d}-\frac{4 i (a+i a \tan (c+d x))^{11/2}}{11 a^2 d}","\frac{2 i (a+i a \tan (c+d x))^{13/2}}{13 a^3 d}-\frac{4 i (a+i a \tan (c+d x))^{11/2}}{11 a^2 d}",1,"(((-4*I)/11)*(a + I*a*Tan[c + d*x])^(11/2))/(a^2*d) + (((2*I)/13)*(a + I*a*Tan[c + d*x])^(13/2))/(a^3*d)","A",3,2,26,0.07692,1,"{3487, 43}"
322,1,29,0,0.0615514,"\int \sec ^2(c+d x) (a+i a \tan (c+d x))^{7/2} \, dx","Int[Sec[c + d*x]^2*(a + I*a*Tan[c + d*x])^(7/2),x]","-\frac{2 i (a+i a \tan (c+d x))^{9/2}}{9 a d}","-\frac{2 i (a+i a \tan (c+d x))^{9/2}}{9 a d}",1,"(((-2*I)/9)*(a + I*a*Tan[c + d*x])^(9/2))/(a*d)","A",2,2,26,0.07692,1,"{3487, 32}"
323,1,116,0,0.0884955,"\int \cos ^2(c+d x) (a+i a \tan (c+d x))^{7/2} \, dx","Int[Cos[c + d*x]^2*(a + I*a*Tan[c + d*x])^(7/2),x]","-\frac{i a^3 (a+i a \tan (c+d x))^{3/2}}{d (a-i a \tan (c+d x))}-\frac{3 i a^3 \sqrt{a+i a \tan (c+d x)}}{d}+\frac{3 i \sqrt{2} a^{7/2} \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{d}","-\frac{i a^3 (a+i a \tan (c+d x))^{3/2}}{d (a-i a \tan (c+d x))}-\frac{3 i a^3 \sqrt{a+i a \tan (c+d x)}}{d}+\frac{3 i \sqrt{2} a^{7/2} \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{d}",1,"((3*I)*Sqrt[2]*a^(7/2)*ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/(Sqrt[2]*Sqrt[a])])/d - ((3*I)*a^3*Sqrt[a + I*a*Tan[c + d*x]])/d - (I*a^3*(a + I*a*Tan[c + d*x])^(3/2))/(d*(a - I*a*Tan[c + d*x]))","A",5,5,26,0.1923,1,"{3487, 47, 50, 63, 206}"
324,1,137,0,0.0937976,"\int \cos ^4(c+d x) (a+i a \tan (c+d x))^{7/2} \, dx","Int[Cos[c + d*x]^4*(a + I*a*Tan[c + d*x])^(7/2),x]","-\frac{i a^5 \sqrt{a+i a \tan (c+d x)}}{2 d (a-i a \tan (c+d x))^2}+\frac{i a^4 \sqrt{a+i a \tan (c+d x)}}{8 d (a-i a \tan (c+d x))}+\frac{i a^{7/2} \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{8 \sqrt{2} d}","-\frac{i a^5 \sqrt{a+i a \tan (c+d x)}}{2 d (a-i a \tan (c+d x))^2}+\frac{i a^4 \sqrt{a+i a \tan (c+d x)}}{8 d (a-i a \tan (c+d x))}+\frac{i a^{7/2} \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{8 \sqrt{2} d}",1,"((I/8)*a^(7/2)*ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/(Sqrt[2]*Sqrt[a])])/(Sqrt[2]*d) - ((I/2)*a^5*Sqrt[a + I*a*Tan[c + d*x]])/(d*(a - I*a*Tan[c + d*x])^2) + ((I/8)*a^4*Sqrt[a + I*a*Tan[c + d*x]])/(d*(a - I*a*Tan[c + d*x]))","A",5,5,26,0.1923,1,"{3487, 47, 51, 63, 206}"
325,1,181,0,0.1083354,"\int \cos ^6(c+d x) (a+i a \tan (c+d x))^{7/2} \, dx","Int[Cos[c + d*x]^6*(a + I*a*Tan[c + d*x])^(7/2),x]","-\frac{i a^6 \sqrt{a+i a \tan (c+d x)}}{6 d (a-i a \tan (c+d x))^3}-\frac{5 i a^5 \sqrt{a+i a \tan (c+d x)}}{48 d (a-i a \tan (c+d x))^2}-\frac{5 i a^4 \sqrt{a+i a \tan (c+d x)}}{64 d (a-i a \tan (c+d x))}-\frac{5 i a^{7/2} \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{64 \sqrt{2} d}","-\frac{i a^6 \sqrt{a+i a \tan (c+d x)}}{6 d (a-i a \tan (c+d x))^3}-\frac{5 i a^5 \sqrt{a+i a \tan (c+d x)}}{48 d (a-i a \tan (c+d x))^2}-\frac{5 i a^4 \sqrt{a+i a \tan (c+d x)}}{64 d (a-i a \tan (c+d x))}-\frac{5 i a^{7/2} \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{64 \sqrt{2} d}",1,"(((-5*I)/64)*a^(7/2)*ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/(Sqrt[2]*Sqrt[a])])/(Sqrt[2]*d) - ((I/6)*a^6*Sqrt[a + I*a*Tan[c + d*x]])/(d*(a - I*a*Tan[c + d*x])^3) - (((5*I)/48)*a^5*Sqrt[a + I*a*Tan[c + d*x]])/(d*(a - I*a*Tan[c + d*x])^2) - (((5*I)/64)*a^4*Sqrt[a + I*a*Tan[c + d*x]])/(d*(a - I*a*Tan[c + d*x]))","A",6,4,26,0.1538,1,"{3487, 51, 63, 206}"
326,1,139,0,0.1399049,"\int \sec (c+d x) (a+i a \tan (c+d x))^{7/2} \, dx","Int[Sec[c + d*x]*(a + I*a*Tan[c + d*x])^(7/2),x]","\frac{256 i a^4 \sec (c+d x)}{35 d \sqrt{a+i a \tan (c+d x)}}+\frac{64 i a^3 \sec (c+d x) \sqrt{a+i a \tan (c+d x)}}{35 d}+\frac{24 i a^2 \sec (c+d x) (a+i a \tan (c+d x))^{3/2}}{35 d}+\frac{2 i a \sec (c+d x) (a+i a \tan (c+d x))^{5/2}}{7 d}","\frac{256 i a^4 \sec (c+d x)}{35 d \sqrt{a+i a \tan (c+d x)}}+\frac{64 i a^3 \sec (c+d x) \sqrt{a+i a \tan (c+d x)}}{35 d}+\frac{24 i a^2 \sec (c+d x) (a+i a \tan (c+d x))^{3/2}}{35 d}+\frac{2 i a \sec (c+d x) (a+i a \tan (c+d x))^{5/2}}{7 d}",1,"(((256*I)/35)*a^4*Sec[c + d*x])/(d*Sqrt[a + I*a*Tan[c + d*x]]) + (((64*I)/35)*a^3*Sec[c + d*x]*Sqrt[a + I*a*Tan[c + d*x]])/d + (((24*I)/35)*a^2*Sec[c + d*x]*(a + I*a*Tan[c + d*x])^(3/2))/d + (((2*I)/7)*a*Sec[c + d*x]*(a + I*a*Tan[c + d*x])^(5/2))/d","A",4,2,24,0.08333,1,"{3494, 3493}"
327,1,104,0,0.1534741,"\int \cos (c+d x) (a+i a \tan (c+d x))^{7/2} \, dx","Int[Cos[c + d*x]*(a + I*a*Tan[c + d*x])^(7/2),x]","-\frac{64 i a^3 \cos (c+d x) \sqrt{a+i a \tan (c+d x)}}{3 d}+\frac{16 i a^2 \cos (c+d x) (a+i a \tan (c+d x))^{3/2}}{3 d}+\frac{2 i a \cos (c+d x) (a+i a \tan (c+d x))^{5/2}}{3 d}","-\frac{64 i a^3 \cos (c+d x) \sqrt{a+i a \tan (c+d x)}}{3 d}+\frac{16 i a^2 \cos (c+d x) (a+i a \tan (c+d x))^{3/2}}{3 d}+\frac{2 i a \cos (c+d x) (a+i a \tan (c+d x))^{5/2}}{3 d}",1,"(((-64*I)/3)*a^3*Cos[c + d*x]*Sqrt[a + I*a*Tan[c + d*x]])/d + (((16*I)/3)*a^2*Cos[c + d*x]*(a + I*a*Tan[c + d*x])^(3/2))/d + (((2*I)/3)*a*Cos[c + d*x]*(a + I*a*Tan[c + d*x])^(5/2))/d","A",3,2,24,0.08333,1,"{3494, 3493}"
328,1,71,0,0.1219747,"\int \cos ^3(c+d x) (a+i a \tan (c+d x))^{7/2} \, dx","Int[Cos[c + d*x]^3*(a + I*a*Tan[c + d*x])^(7/2),x]","\frac{8 i a^2 \cos ^3(c+d x) (a+i a \tan (c+d x))^{3/2}}{3 d}-\frac{2 i a \cos ^3(c+d x) (a+i a \tan (c+d x))^{5/2}}{d}","\frac{8 i a^2 \cos ^3(c+d x) (a+i a \tan (c+d x))^{3/2}}{3 d}-\frac{2 i a \cos ^3(c+d x) (a+i a \tan (c+d x))^{5/2}}{d}",1,"(((8*I)/3)*a^2*Cos[c + d*x]^3*(a + I*a*Tan[c + d*x])^(3/2))/d - ((2*I)*a*Cos[c + d*x]^3*(a + I*a*Tan[c + d*x])^(5/2))/d","A",2,2,26,0.07692,1,"{3494, 3493}"
329,1,35,0,0.0586437,"\int \cos ^5(c+d x) (a+i a \tan (c+d x))^{7/2} \, dx","Int[Cos[c + d*x]^5*(a + I*a*Tan[c + d*x])^(7/2),x]","-\frac{2 i a \cos ^5(c+d x) (a+i a \tan (c+d x))^{5/2}}{5 d}","-\frac{2 i a \cos ^5(c+d x) (a+i a \tan (c+d x))^{5/2}}{5 d}",1,"(((-2*I)/5)*a*Cos[c + d*x]^5*(a + I*a*Tan[c + d*x])^(5/2))/d","A",1,1,26,0.03846,1,"{3493}"
330,1,196,0,0.2866472,"\int \cos ^7(c+d x) (a+i a \tan (c+d x))^{7/2} \, dx","Int[Cos[c + d*x]^7*(a + I*a*Tan[c + d*x])^(7/2),x]","-\frac{i a^2 \cos ^3(c+d x) (a+i a \tan (c+d x))^{3/2}}{12 d}-\frac{i a^3 \cos (c+d x) \sqrt{a+i a \tan (c+d x)}}{8 d}+\frac{i a^{7/2} \tanh ^{-1}\left(\frac{\sqrt{a} \sec (c+d x)}{\sqrt{2} \sqrt{a+i a \tan (c+d x)}}\right)}{8 \sqrt{2} d}-\frac{i \cos ^7(c+d x) (a+i a \tan (c+d x))^{7/2}}{7 d}-\frac{i a \cos ^5(c+d x) (a+i a \tan (c+d x))^{5/2}}{10 d}","-\frac{i a^2 \cos ^3(c+d x) (a+i a \tan (c+d x))^{3/2}}{12 d}-\frac{i a^3 \cos (c+d x) \sqrt{a+i a \tan (c+d x)}}{8 d}+\frac{i a^{7/2} \tanh ^{-1}\left(\frac{\sqrt{a} \sec (c+d x)}{\sqrt{2} \sqrt{a+i a \tan (c+d x)}}\right)}{8 \sqrt{2} d}-\frac{i \cos ^7(c+d x) (a+i a \tan (c+d x))^{7/2}}{7 d}-\frac{i a \cos ^5(c+d x) (a+i a \tan (c+d x))^{5/2}}{10 d}",1,"((I/8)*a^(7/2)*ArcTanh[(Sqrt[a]*Sec[c + d*x])/(Sqrt[2]*Sqrt[a + I*a*Tan[c + d*x]])])/(Sqrt[2]*d) - ((I/8)*a^3*Cos[c + d*x]*Sqrt[a + I*a*Tan[c + d*x]])/d - ((I/12)*a^2*Cos[c + d*x]^3*(a + I*a*Tan[c + d*x])^(3/2))/d - ((I/10)*a*Cos[c + d*x]^5*(a + I*a*Tan[c + d*x])^(5/2))/d - ((I/7)*Cos[c + d*x]^7*(a + I*a*Tan[c + d*x])^(7/2))/d","A",6,3,26,0.1154,1,"{3490, 3489, 206}"
331,1,268,0,0.4114374,"\int \cos ^9(c+d x) (a+i a \tan (c+d x))^{7/2} \, dx","Int[Cos[c + d*x]^9*(a + I*a*Tan[c + d*x])^(7/2),x]","-\frac{11 i a^2 \cos ^5(c+d x) (a+i a \tan (c+d x))^{3/2}}{140 d}-\frac{11 i a^3 \cos ^3(c+d x) \sqrt{a+i a \tan (c+d x)}}{120 d}-\frac{11 i a^3 \cos (c+d x) \sqrt{a+i a \tan (c+d x)}}{64 d}+\frac{11 i a^4 \cos (c+d x)}{96 d \sqrt{a+i a \tan (c+d x)}}+\frac{11 i a^{7/2} \tanh ^{-1}\left(\frac{\sqrt{a} \sec (c+d x)}{\sqrt{2} \sqrt{a+i a \tan (c+d x)}}\right)}{64 \sqrt{2} d}-\frac{i \cos ^9(c+d x) (a+i a \tan (c+d x))^{7/2}}{9 d}-\frac{11 i a \cos ^7(c+d x) (a+i a \tan (c+d x))^{5/2}}{126 d}","-\frac{11 i a^2 \cos ^5(c+d x) (a+i a \tan (c+d x))^{3/2}}{140 d}-\frac{11 i a^3 \cos ^3(c+d x) \sqrt{a+i a \tan (c+d x)}}{120 d}-\frac{11 i a^3 \cos (c+d x) \sqrt{a+i a \tan (c+d x)}}{64 d}+\frac{11 i a^4 \cos (c+d x)}{96 d \sqrt{a+i a \tan (c+d x)}}+\frac{11 i a^{7/2} \tanh ^{-1}\left(\frac{\sqrt{a} \sec (c+d x)}{\sqrt{2} \sqrt{a+i a \tan (c+d x)}}\right)}{64 \sqrt{2} d}-\frac{i \cos ^9(c+d x) (a+i a \tan (c+d x))^{7/2}}{9 d}-\frac{11 i a \cos ^7(c+d x) (a+i a \tan (c+d x))^{5/2}}{126 d}",1,"(((11*I)/64)*a^(7/2)*ArcTanh[(Sqrt[a]*Sec[c + d*x])/(Sqrt[2]*Sqrt[a + I*a*Tan[c + d*x]])])/(Sqrt[2]*d) + (((11*I)/96)*a^4*Cos[c + d*x])/(d*Sqrt[a + I*a*Tan[c + d*x]]) - (((11*I)/64)*a^3*Cos[c + d*x]*Sqrt[a + I*a*Tan[c + d*x]])/d - (((11*I)/120)*a^3*Cos[c + d*x]^3*Sqrt[a + I*a*Tan[c + d*x]])/d - (((11*I)/140)*a^2*Cos[c + d*x]^5*(a + I*a*Tan[c + d*x])^(3/2))/d - (((11*I)/126)*a*Cos[c + d*x]^7*(a + I*a*Tan[c + d*x])^(5/2))/d - ((I/9)*Cos[c + d*x]^9*(a + I*a*Tan[c + d*x])^(7/2))/d","A",8,5,26,0.1923,1,"{3497, 3502, 3490, 3489, 206}"
332,1,342,0,0.5646103,"\int \cos ^{11}(c+d x) (a+i a \tan (c+d x))^{7/2} \, dx","Int[Cos[c + d*x]^11*(a + I*a*Tan[c + d*x])^(7/2),x]","-\frac{65 i a^2 \cos ^7(c+d x) (a+i a \tan (c+d x))^{3/2}}{924 d}-\frac{13 i a^3 \cos ^5(c+d x) \sqrt{a+i a \tan (c+d x)}}{168 d}-\frac{13 i a^3 \cos ^3(c+d x) \sqrt{a+i a \tan (c+d x)}}{128 d}+\frac{39 i a^4 \cos ^3(c+d x)}{448 d \sqrt{a+i a \tan (c+d x)}}-\frac{195 i a^3 \cos (c+d x) \sqrt{a+i a \tan (c+d x)}}{1024 d}+\frac{65 i a^4 \cos (c+d x)}{512 d \sqrt{a+i a \tan (c+d x)}}+\frac{195 i a^{7/2} \tanh ^{-1}\left(\frac{\sqrt{a} \sec (c+d x)}{\sqrt{2} \sqrt{a+i a \tan (c+d x)}}\right)}{1024 \sqrt{2} d}-\frac{i \cos ^{11}(c+d x) (a+i a \tan (c+d x))^{7/2}}{11 d}-\frac{5 i a \cos ^9(c+d x) (a+i a \tan (c+d x))^{5/2}}{66 d}","-\frac{65 i a^2 \cos ^7(c+d x) (a+i a \tan (c+d x))^{3/2}}{924 d}-\frac{13 i a^3 \cos ^5(c+d x) \sqrt{a+i a \tan (c+d x)}}{168 d}-\frac{13 i a^3 \cos ^3(c+d x) \sqrt{a+i a \tan (c+d x)}}{128 d}+\frac{39 i a^4 \cos ^3(c+d x)}{448 d \sqrt{a+i a \tan (c+d x)}}-\frac{195 i a^3 \cos (c+d x) \sqrt{a+i a \tan (c+d x)}}{1024 d}+\frac{65 i a^4 \cos (c+d x)}{512 d \sqrt{a+i a \tan (c+d x)}}+\frac{195 i a^{7/2} \tanh ^{-1}\left(\frac{\sqrt{a} \sec (c+d x)}{\sqrt{2} \sqrt{a+i a \tan (c+d x)}}\right)}{1024 \sqrt{2} d}-\frac{i \cos ^{11}(c+d x) (a+i a \tan (c+d x))^{7/2}}{11 d}-\frac{5 i a \cos ^9(c+d x) (a+i a \tan (c+d x))^{5/2}}{66 d}",1,"(((195*I)/1024)*a^(7/2)*ArcTanh[(Sqrt[a]*Sec[c + d*x])/(Sqrt[2]*Sqrt[a + I*a*Tan[c + d*x]])])/(Sqrt[2]*d) + (((65*I)/512)*a^4*Cos[c + d*x])/(d*Sqrt[a + I*a*Tan[c + d*x]]) + (((39*I)/448)*a^4*Cos[c + d*x]^3)/(d*Sqrt[a + I*a*Tan[c + d*x]]) - (((195*I)/1024)*a^3*Cos[c + d*x]*Sqrt[a + I*a*Tan[c + d*x]])/d - (((13*I)/128)*a^3*Cos[c + d*x]^3*Sqrt[a + I*a*Tan[c + d*x]])/d - (((13*I)/168)*a^3*Cos[c + d*x]^5*Sqrt[a + I*a*Tan[c + d*x]])/d - (((65*I)/924)*a^2*Cos[c + d*x]^7*(a + I*a*Tan[c + d*x])^(3/2))/d - (((5*I)/66)*a*Cos[c + d*x]^9*(a + I*a*Tan[c + d*x])^(5/2))/d - ((I/11)*Cos[c + d*x]^11*(a + I*a*Tan[c + d*x])^(7/2))/d","A",10,5,26,0.1923,1,"{3497, 3502, 3490, 3489, 206}"
333,1,117,0,0.0797237,"\int \frac{\sec ^8(c+d x)}{\sqrt{a+i a \tan (c+d x)}} \, dx","Int[Sec[c + d*x]^8/Sqrt[a + I*a*Tan[c + d*x]],x]","\frac{2 i (a+i a \tan (c+d x))^{13/2}}{13 a^7 d}-\frac{12 i (a+i a \tan (c+d x))^{11/2}}{11 a^6 d}+\frac{8 i (a+i a \tan (c+d x))^{9/2}}{3 a^5 d}-\frac{16 i (a+i a \tan (c+d x))^{7/2}}{7 a^4 d}","\frac{2 i (a+i a \tan (c+d x))^{13/2}}{13 a^7 d}-\frac{12 i (a+i a \tan (c+d x))^{11/2}}{11 a^6 d}+\frac{8 i (a+i a \tan (c+d x))^{9/2}}{3 a^5 d}-\frac{16 i (a+i a \tan (c+d x))^{7/2}}{7 a^4 d}",1,"(((-16*I)/7)*(a + I*a*Tan[c + d*x])^(7/2))/(a^4*d) + (((8*I)/3)*(a + I*a*Tan[c + d*x])^(9/2))/(a^5*d) - (((12*I)/11)*(a + I*a*Tan[c + d*x])^(11/2))/(a^6*d) + (((2*I)/13)*(a + I*a*Tan[c + d*x])^(13/2))/(a^7*d)","A",3,2,26,0.07692,1,"{3487, 43}"
334,1,88,0,0.0720852,"\int \frac{\sec ^6(c+d x)}{\sqrt{a+i a \tan (c+d x)}} \, dx","Int[Sec[c + d*x]^6/Sqrt[a + I*a*Tan[c + d*x]],x]","-\frac{2 i (a+i a \tan (c+d x))^{9/2}}{9 a^5 d}+\frac{8 i (a+i a \tan (c+d x))^{7/2}}{7 a^4 d}-\frac{8 i (a+i a \tan (c+d x))^{5/2}}{5 a^3 d}","-\frac{2 i (a+i a \tan (c+d x))^{9/2}}{9 a^5 d}+\frac{8 i (a+i a \tan (c+d x))^{7/2}}{7 a^4 d}-\frac{8 i (a+i a \tan (c+d x))^{5/2}}{5 a^3 d}",1,"(((-8*I)/5)*(a + I*a*Tan[c + d*x])^(5/2))/(a^3*d) + (((8*I)/7)*(a + I*a*Tan[c + d*x])^(7/2))/(a^4*d) - (((2*I)/9)*(a + I*a*Tan[c + d*x])^(9/2))/(a^5*d)","A",3,2,26,0.07692,1,"{3487, 43}"
335,1,59,0,0.0643235,"\int \frac{\sec ^4(c+d x)}{\sqrt{a+i a \tan (c+d x)}} \, dx","Int[Sec[c + d*x]^4/Sqrt[a + I*a*Tan[c + d*x]],x]","\frac{2 i (a+i a \tan (c+d x))^{5/2}}{5 a^3 d}-\frac{4 i (a+i a \tan (c+d x))^{3/2}}{3 a^2 d}","\frac{2 i (a+i a \tan (c+d x))^{5/2}}{5 a^3 d}-\frac{4 i (a+i a \tan (c+d x))^{3/2}}{3 a^2 d}",1,"(((-4*I)/3)*(a + I*a*Tan[c + d*x])^(3/2))/(a^2*d) + (((2*I)/5)*(a + I*a*Tan[c + d*x])^(5/2))/(a^3*d)","A",3,2,26,0.07692,1,"{3487, 43}"
336,1,27,0,0.0566053,"\int \frac{\sec ^2(c+d x)}{\sqrt{a+i a \tan (c+d x)}} \, dx","Int[Sec[c + d*x]^2/Sqrt[a + I*a*Tan[c + d*x]],x]","-\frac{2 i \sqrt{a+i a \tan (c+d x)}}{a d}","-\frac{2 i \sqrt{a+i a \tan (c+d x)}}{a d}",1,"((-2*I)*Sqrt[a + I*a*Tan[c + d*x]])/(a*d)","A",2,2,26,0.07692,1,"{3487, 32}"
337,1,146,0,0.0981909,"\int \frac{\cos ^2(c+d x)}{\sqrt{a+i a \tan (c+d x)}} \, dx","Int[Cos[c + d*x]^2/Sqrt[a + I*a*Tan[c + d*x]],x]","-\frac{i a^2}{2 d (a-i a \tan (c+d x)) (a+i a \tan (c+d x))^{3/2}}+\frac{5 i a}{12 d (a+i a \tan (c+d x))^{3/2}}+\frac{5 i}{8 d \sqrt{a+i a \tan (c+d x)}}-\frac{5 i \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{8 \sqrt{2} \sqrt{a} d}","-\frac{i a^2}{2 d (a-i a \tan (c+d x)) (a+i a \tan (c+d x))^{3/2}}+\frac{5 i a}{12 d (a+i a \tan (c+d x))^{3/2}}+\frac{5 i}{8 d \sqrt{a+i a \tan (c+d x)}}-\frac{5 i \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{8 \sqrt{2} \sqrt{a} d}",1,"(((-5*I)/8)*ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/(Sqrt[2]*Sqrt[a])])/(Sqrt[2]*Sqrt[a]*d) + (((5*I)/12)*a)/(d*(a + I*a*Tan[c + d*x])^(3/2)) - ((I/2)*a^2)/(d*(a - I*a*Tan[c + d*x])*(a + I*a*Tan[c + d*x])^(3/2)) + ((5*I)/8)/(d*Sqrt[a + I*a*Tan[c + d*x]])","A",6,4,26,0.1538,1,"{3487, 51, 63, 206}"
338,1,219,0,0.1240196,"\int \frac{\cos ^4(c+d x)}{\sqrt{a+i a \tan (c+d x)}} \, dx","Int[Cos[c + d*x]^4/Sqrt[a + I*a*Tan[c + d*x]],x]","-\frac{i a^4}{4 d (a-i a \tan (c+d x))^2 (a+i a \tan (c+d x))^{5/2}}-\frac{9 i a^3}{16 d (a-i a \tan (c+d x)) (a+i a \tan (c+d x))^{5/2}}+\frac{63 i a^2}{160 d (a+i a \tan (c+d x))^{5/2}}+\frac{21 i a}{64 d (a+i a \tan (c+d x))^{3/2}}+\frac{63 i}{128 d \sqrt{a+i a \tan (c+d x)}}-\frac{63 i \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{128 \sqrt{2} \sqrt{a} d}","-\frac{i a^4}{4 d (a-i a \tan (c+d x))^2 (a+i a \tan (c+d x))^{5/2}}-\frac{9 i a^3}{16 d (a-i a \tan (c+d x)) (a+i a \tan (c+d x))^{5/2}}+\frac{63 i a^2}{160 d (a+i a \tan (c+d x))^{5/2}}+\frac{21 i a}{64 d (a+i a \tan (c+d x))^{3/2}}+\frac{63 i}{128 d \sqrt{a+i a \tan (c+d x)}}-\frac{63 i \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{128 \sqrt{2} \sqrt{a} d}",1,"(((-63*I)/128)*ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/(Sqrt[2]*Sqrt[a])])/(Sqrt[2]*Sqrt[a]*d) + (((63*I)/160)*a^2)/(d*(a + I*a*Tan[c + d*x])^(5/2)) - ((I/4)*a^4)/(d*(a - I*a*Tan[c + d*x])^2*(a + I*a*Tan[c + d*x])^(5/2)) - (((9*I)/16)*a^3)/(d*(a - I*a*Tan[c + d*x])*(a + I*a*Tan[c + d*x])^(5/2)) + (((21*I)/64)*a)/(d*(a + I*a*Tan[c + d*x])^(3/2)) + ((63*I)/128)/(d*Sqrt[a + I*a*Tan[c + d*x]])","A",8,4,26,0.1538,1,"{3487, 51, 63, 206}"
339,1,292,0,0.1534315,"\int \frac{\cos ^6(c+d x)}{\sqrt{a+i a \tan (c+d x)}} \, dx","Int[Cos[c + d*x]^6/Sqrt[a + I*a*Tan[c + d*x]],x]","-\frac{i a^6}{6 d (a-i a \tan (c+d x))^3 (a+i a \tan (c+d x))^{7/2}}-\frac{13 i a^5}{48 d (a-i a \tan (c+d x))^2 (a+i a \tan (c+d x))^{7/2}}-\frac{143 i a^4}{192 d (a-i a \tan (c+d x)) (a+i a \tan (c+d x))^{7/2}}+\frac{429 i a^3}{896 d (a+i a \tan (c+d x))^{7/2}}+\frac{429 i a^2}{1280 d (a+i a \tan (c+d x))^{5/2}}+\frac{143 i a}{512 d (a+i a \tan (c+d x))^{3/2}}+\frac{429 i}{1024 d \sqrt{a+i a \tan (c+d x)}}-\frac{429 i \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{1024 \sqrt{2} \sqrt{a} d}","-\frac{i a^6}{6 d (a-i a \tan (c+d x))^3 (a+i a \tan (c+d x))^{7/2}}-\frac{13 i a^5}{48 d (a-i a \tan (c+d x))^2 (a+i a \tan (c+d x))^{7/2}}-\frac{143 i a^4}{192 d (a-i a \tan (c+d x)) (a+i a \tan (c+d x))^{7/2}}+\frac{429 i a^3}{896 d (a+i a \tan (c+d x))^{7/2}}+\frac{429 i a^2}{1280 d (a+i a \tan (c+d x))^{5/2}}+\frac{143 i a}{512 d (a+i a \tan (c+d x))^{3/2}}+\frac{429 i}{1024 d \sqrt{a+i a \tan (c+d x)}}-\frac{429 i \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{1024 \sqrt{2} \sqrt{a} d}",1,"(((-429*I)/1024)*ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/(Sqrt[2]*Sqrt[a])])/(Sqrt[2]*Sqrt[a]*d) + (((429*I)/896)*a^3)/(d*(a + I*a*Tan[c + d*x])^(7/2)) - ((I/6)*a^6)/(d*(a - I*a*Tan[c + d*x])^3*(a + I*a*Tan[c + d*x])^(7/2)) - (((13*I)/48)*a^5)/(d*(a - I*a*Tan[c + d*x])^2*(a + I*a*Tan[c + d*x])^(7/2)) - (((143*I)/192)*a^4)/(d*(a - I*a*Tan[c + d*x])*(a + I*a*Tan[c + d*x])^(7/2)) + (((429*I)/1280)*a^2)/(d*(a + I*a*Tan[c + d*x])^(5/2)) + (((143*I)/512)*a)/(d*(a + I*a*Tan[c + d*x])^(3/2)) + ((429*I)/1024)/(d*Sqrt[a + I*a*Tan[c + d*x]])","A",10,4,26,0.1538,1,"{3487, 51, 63, 206}"
340,1,147,0,0.2584643,"\int \frac{\sec ^9(c+d x)}{\sqrt{a+i a \tan (c+d x)}} \, dx","Int[Sec[c + d*x]^9/Sqrt[a + I*a*Tan[c + d*x]],x]","\frac{8 i a^2 \sec ^9(c+d x)}{65 d (a+i a \tan (c+d x))^{5/2}}+\frac{64 i a^3 \sec ^9(c+d x)}{715 d (a+i a \tan (c+d x))^{7/2}}+\frac{256 i a^4 \sec ^9(c+d x)}{6435 d (a+i a \tan (c+d x))^{9/2}}+\frac{2 i a \sec ^9(c+d x)}{15 d (a+i a \tan (c+d x))^{3/2}}","\frac{8 i a^2 \sec ^9(c+d x)}{65 d (a+i a \tan (c+d x))^{5/2}}+\frac{64 i a^3 \sec ^9(c+d x)}{715 d (a+i a \tan (c+d x))^{7/2}}+\frac{256 i a^4 \sec ^9(c+d x)}{6435 d (a+i a \tan (c+d x))^{9/2}}+\frac{2 i a \sec ^9(c+d x)}{15 d (a+i a \tan (c+d x))^{3/2}}",1,"(((256*I)/6435)*a^4*Sec[c + d*x]^9)/(d*(a + I*a*Tan[c + d*x])^(9/2)) + (((64*I)/715)*a^3*Sec[c + d*x]^9)/(d*(a + I*a*Tan[c + d*x])^(7/2)) + (((8*I)/65)*a^2*Sec[c + d*x]^9)/(d*(a + I*a*Tan[c + d*x])^(5/2)) + (((2*I)/15)*a*Sec[c + d*x]^9)/(d*(a + I*a*Tan[c + d*x])^(3/2))","A",4,2,26,0.07692,1,"{3494, 3493}"
341,1,110,0,0.1870323,"\int \frac{\sec ^7(c+d x)}{\sqrt{a+i a \tan (c+d x)}} \, dx","Int[Sec[c + d*x]^7/Sqrt[a + I*a*Tan[c + d*x]],x]","\frac{16 i a^2 \sec ^7(c+d x)}{99 d (a+i a \tan (c+d x))^{5/2}}+\frac{64 i a^3 \sec ^7(c+d x)}{693 d (a+i a \tan (c+d x))^{7/2}}+\frac{2 i a \sec ^7(c+d x)}{11 d (a+i a \tan (c+d x))^{3/2}}","\frac{16 i a^2 \sec ^7(c+d x)}{99 d (a+i a \tan (c+d x))^{5/2}}+\frac{64 i a^3 \sec ^7(c+d x)}{693 d (a+i a \tan (c+d x))^{7/2}}+\frac{2 i a \sec ^7(c+d x)}{11 d (a+i a \tan (c+d x))^{3/2}}",1,"(((64*I)/693)*a^3*Sec[c + d*x]^7)/(d*(a + I*a*Tan[c + d*x])^(7/2)) + (((16*I)/99)*a^2*Sec[c + d*x]^7)/(d*(a + I*a*Tan[c + d*x])^(5/2)) + (((2*I)/11)*a*Sec[c + d*x]^7)/(d*(a + I*a*Tan[c + d*x])^(3/2))","A",3,2,26,0.07692,1,"{3494, 3493}"
342,1,73,0,0.1180176,"\int \frac{\sec ^5(c+d x)}{\sqrt{a+i a \tan (c+d x)}} \, dx","Int[Sec[c + d*x]^5/Sqrt[a + I*a*Tan[c + d*x]],x]","\frac{8 i a^2 \sec ^5(c+d x)}{35 d (a+i a \tan (c+d x))^{5/2}}+\frac{2 i a \sec ^5(c+d x)}{7 d (a+i a \tan (c+d x))^{3/2}}","\frac{8 i a^2 \sec ^5(c+d x)}{35 d (a+i a \tan (c+d x))^{5/2}}+\frac{2 i a \sec ^5(c+d x)}{7 d (a+i a \tan (c+d x))^{3/2}}",1,"(((8*I)/35)*a^2*Sec[c + d*x]^5)/(d*(a + I*a*Tan[c + d*x])^(5/2)) + (((2*I)/7)*a*Sec[c + d*x]^5)/(d*(a + I*a*Tan[c + d*x])^(3/2))","A",2,2,26,0.07692,1,"{3494, 3493}"
343,1,35,0,0.0544807,"\int \frac{\sec ^3(c+d x)}{\sqrt{a+i a \tan (c+d x)}} \, dx","Int[Sec[c + d*x]^3/Sqrt[a + I*a*Tan[c + d*x]],x]","\frac{2 i a \sec ^3(c+d x)}{3 d (a+i a \tan (c+d x))^{3/2}}","\frac{2 i a \sec ^3(c+d x)}{3 d (a+i a \tan (c+d x))^{3/2}}",1,"(((2*I)/3)*a*Sec[c + d*x]^3)/(d*(a + I*a*Tan[c + d*x])^(3/2))","A",1,1,26,0.03846,1,"{3493}"
344,1,52,0,0.0410734,"\int \frac{\sec (c+d x)}{\sqrt{a+i a \tan (c+d x)}} \, dx","Int[Sec[c + d*x]/Sqrt[a + I*a*Tan[c + d*x]],x]","\frac{i \sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{a} \sec (c+d x)}{\sqrt{2} \sqrt{a+i a \tan (c+d x)}}\right)}{\sqrt{a} d}","\frac{i \sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{a} \sec (c+d x)}{\sqrt{2} \sqrt{a+i a \tan (c+d x)}}\right)}{\sqrt{a} d}",1,"(I*Sqrt[2]*ArcTanh[(Sqrt[a]*Sec[c + d*x])/(Sqrt[2]*Sqrt[a + I*a*Tan[c + d*x]])])/(Sqrt[a]*d)","A",2,2,24,0.08333,1,"{3489, 206}"
345,1,122,0,0.1335043,"\int \frac{\cos (c+d x)}{\sqrt{a+i a \tan (c+d x)}} \, dx","Int[Cos[c + d*x]/Sqrt[a + I*a*Tan[c + d*x]],x]","-\frac{3 i \cos (c+d x) \sqrt{a+i a \tan (c+d x)}}{4 a d}+\frac{i \cos (c+d x)}{2 d \sqrt{a+i a \tan (c+d x)}}+\frac{3 i \tanh ^{-1}\left(\frac{\sqrt{a} \sec (c+d x)}{\sqrt{2} \sqrt{a+i a \tan (c+d x)}}\right)}{4 \sqrt{2} \sqrt{a} d}","-\frac{3 i \cos (c+d x) \sqrt{a+i a \tan (c+d x)}}{4 a d}+\frac{i \cos (c+d x)}{2 d \sqrt{a+i a \tan (c+d x)}}+\frac{3 i \tanh ^{-1}\left(\frac{\sqrt{a} \sec (c+d x)}{\sqrt{2} \sqrt{a+i a \tan (c+d x)}}\right)}{4 \sqrt{2} \sqrt{a} d}",1,"(((3*I)/4)*ArcTanh[(Sqrt[a]*Sec[c + d*x])/(Sqrt[2]*Sqrt[a + I*a*Tan[c + d*x]])])/(Sqrt[2]*Sqrt[a]*d) + ((I/2)*Cos[c + d*x])/(d*Sqrt[a + I*a*Tan[c + d*x]]) - (((3*I)/4)*Cos[c + d*x]*Sqrt[a + I*a*Tan[c + d*x]])/(a*d)","A",4,4,24,0.1667,1,"{3502, 3490, 3489, 206}"
346,1,193,0,0.2661552,"\int \frac{\cos ^3(c+d x)}{\sqrt{a+i a \tan (c+d x)}} \, dx","Int[Cos[c + d*x]^3/Sqrt[a + I*a*Tan[c + d*x]],x]","-\frac{7 i \cos ^3(c+d x) \sqrt{a+i a \tan (c+d x)}}{24 a d}+\frac{i \cos ^3(c+d x)}{4 d \sqrt{a+i a \tan (c+d x)}}-\frac{35 i \cos (c+d x) \sqrt{a+i a \tan (c+d x)}}{64 a d}+\frac{35 i \cos (c+d x)}{96 d \sqrt{a+i a \tan (c+d x)}}+\frac{35 i \tanh ^{-1}\left(\frac{\sqrt{a} \sec (c+d x)}{\sqrt{2} \sqrt{a+i a \tan (c+d x)}}\right)}{64 \sqrt{2} \sqrt{a} d}","-\frac{7 i \cos ^3(c+d x) \sqrt{a+i a \tan (c+d x)}}{24 a d}+\frac{i \cos ^3(c+d x)}{4 d \sqrt{a+i a \tan (c+d x)}}-\frac{35 i \cos (c+d x) \sqrt{a+i a \tan (c+d x)}}{64 a d}+\frac{35 i \cos (c+d x)}{96 d \sqrt{a+i a \tan (c+d x)}}+\frac{35 i \tanh ^{-1}\left(\frac{\sqrt{a} \sec (c+d x)}{\sqrt{2} \sqrt{a+i a \tan (c+d x)}}\right)}{64 \sqrt{2} \sqrt{a} d}",1,"(((35*I)/64)*ArcTanh[(Sqrt[a]*Sec[c + d*x])/(Sqrt[2]*Sqrt[a + I*a*Tan[c + d*x]])])/(Sqrt[2]*Sqrt[a]*d) + (((35*I)/96)*Cos[c + d*x])/(d*Sqrt[a + I*a*Tan[c + d*x]]) + ((I/4)*Cos[c + d*x]^3)/(d*Sqrt[a + I*a*Tan[c + d*x]]) - (((35*I)/64)*Cos[c + d*x]*Sqrt[a + I*a*Tan[c + d*x]])/(a*d) - (((7*I)/24)*Cos[c + d*x]^3*Sqrt[a + I*a*Tan[c + d*x]])/(a*d)","A",6,5,26,0.1923,1,"{3502, 3497, 3490, 3489, 206}"
347,1,117,0,0.0869304,"\int \frac{\sec ^8(c+d x)}{(a+i a \tan (c+d x))^{3/2}} \, dx","Int[Sec[c + d*x]^8/(a + I*a*Tan[c + d*x])^(3/2),x]","\frac{2 i (a+i a \tan (c+d x))^{11/2}}{11 a^7 d}-\frac{4 i (a+i a \tan (c+d x))^{9/2}}{3 a^6 d}+\frac{24 i (a+i a \tan (c+d x))^{7/2}}{7 a^5 d}-\frac{16 i (a+i a \tan (c+d x))^{5/2}}{5 a^4 d}","\frac{2 i (a+i a \tan (c+d x))^{11/2}}{11 a^7 d}-\frac{4 i (a+i a \tan (c+d x))^{9/2}}{3 a^6 d}+\frac{24 i (a+i a \tan (c+d x))^{7/2}}{7 a^5 d}-\frac{16 i (a+i a \tan (c+d x))^{5/2}}{5 a^4 d}",1,"(((-16*I)/5)*(a + I*a*Tan[c + d*x])^(5/2))/(a^4*d) + (((24*I)/7)*(a + I*a*Tan[c + d*x])^(7/2))/(a^5*d) - (((4*I)/3)*(a + I*a*Tan[c + d*x])^(9/2))/(a^6*d) + (((2*I)/11)*(a + I*a*Tan[c + d*x])^(11/2))/(a^7*d)","A",3,2,26,0.07692,1,"{3487, 43}"
348,1,88,0,0.078767,"\int \frac{\sec ^6(c+d x)}{(a+i a \tan (c+d x))^{3/2}} \, dx","Int[Sec[c + d*x]^6/(a + I*a*Tan[c + d*x])^(3/2),x]","-\frac{2 i (a+i a \tan (c+d x))^{7/2}}{7 a^5 d}+\frac{8 i (a+i a \tan (c+d x))^{5/2}}{5 a^4 d}-\frac{8 i (a+i a \tan (c+d x))^{3/2}}{3 a^3 d}","-\frac{2 i (a+i a \tan (c+d x))^{7/2}}{7 a^5 d}+\frac{8 i (a+i a \tan (c+d x))^{5/2}}{5 a^4 d}-\frac{8 i (a+i a \tan (c+d x))^{3/2}}{3 a^3 d}",1,"(((-8*I)/3)*(a + I*a*Tan[c + d*x])^(3/2))/(a^3*d) + (((8*I)/5)*(a + I*a*Tan[c + d*x])^(5/2))/(a^4*d) - (((2*I)/7)*(a + I*a*Tan[c + d*x])^(7/2))/(a^5*d)","A",3,2,26,0.07692,1,"{3487, 43}"
349,1,57,0,0.0716966,"\int \frac{\sec ^4(c+d x)}{(a+i a \tan (c+d x))^{3/2}} \, dx","Int[Sec[c + d*x]^4/(a + I*a*Tan[c + d*x])^(3/2),x]","\frac{2 i (a+i a \tan (c+d x))^{3/2}}{3 a^3 d}-\frac{4 i \sqrt{a+i a \tan (c+d x)}}{a^2 d}","\frac{2 i (a+i a \tan (c+d x))^{3/2}}{3 a^3 d}-\frac{4 i \sqrt{a+i a \tan (c+d x)}}{a^2 d}",1,"((-4*I)*Sqrt[a + I*a*Tan[c + d*x]])/(a^2*d) + (((2*I)/3)*(a + I*a*Tan[c + d*x])^(3/2))/(a^3*d)","A",3,2,26,0.07692,1,"{3487, 43}"
350,1,27,0,0.0646933,"\int \frac{\sec ^2(c+d x)}{(a+i a \tan (c+d x))^{3/2}} \, dx","Int[Sec[c + d*x]^2/(a + I*a*Tan[c + d*x])^(3/2),x]","\frac{2 i}{a d \sqrt{a+i a \tan (c+d x)}}","\frac{2 i}{a d \sqrt{a+i a \tan (c+d x)}}",1,"(2*I)/(a*d*Sqrt[a + I*a*Tan[c + d*x]])","A",2,2,26,0.07692,1,"{3487, 32}"
351,1,175,0,0.1184181,"\int \frac{\cos ^2(c+d x)}{(a+i a \tan (c+d x))^{3/2}} \, dx","Int[Cos[c + d*x]^2/(a + I*a*Tan[c + d*x])^(3/2),x]","-\frac{i a^2}{2 d (a-i a \tan (c+d x)) (a+i a \tan (c+d x))^{5/2}}-\frac{7 i \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{16 \sqrt{2} a^{3/2} d}+\frac{7 i a}{20 d (a+i a \tan (c+d x))^{5/2}}+\frac{7 i}{24 d (a+i a \tan (c+d x))^{3/2}}+\frac{7 i}{16 a d \sqrt{a+i a \tan (c+d x)}}","-\frac{i a^2}{2 d (a-i a \tan (c+d x)) (a+i a \tan (c+d x))^{5/2}}-\frac{7 i \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{16 \sqrt{2} a^{3/2} d}+\frac{7 i a}{20 d (a+i a \tan (c+d x))^{5/2}}+\frac{7 i}{24 d (a+i a \tan (c+d x))^{3/2}}+\frac{7 i}{16 a d \sqrt{a+i a \tan (c+d x)}}",1,"(((-7*I)/16)*ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/(Sqrt[2]*Sqrt[a])])/(Sqrt[2]*a^(3/2)*d) + (((7*I)/20)*a)/(d*(a + I*a*Tan[c + d*x])^(5/2)) - ((I/2)*a^2)/(d*(a - I*a*Tan[c + d*x])*(a + I*a*Tan[c + d*x])^(5/2)) + ((7*I)/24)/(d*(a + I*a*Tan[c + d*x])^(3/2)) + ((7*I)/16)/(a*d*Sqrt[a + I*a*Tan[c + d*x]])","A",7,4,26,0.1538,1,"{3487, 51, 63, 206}"
352,1,248,0,0.1437861,"\int \frac{\cos ^4(c+d x)}{(a+i a \tan (c+d x))^{3/2}} \, dx","Int[Cos[c + d*x]^4/(a + I*a*Tan[c + d*x])^(3/2),x]","-\frac{i a^4}{4 d (a-i a \tan (c+d x))^2 (a+i a \tan (c+d x))^{7/2}}-\frac{11 i a^3}{16 d (a-i a \tan (c+d x)) (a+i a \tan (c+d x))^{7/2}}+\frac{99 i a^2}{224 d (a+i a \tan (c+d x))^{7/2}}-\frac{99 i \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{256 \sqrt{2} a^{3/2} d}+\frac{99 i a}{320 d (a+i a \tan (c+d x))^{5/2}}+\frac{33 i}{128 d (a+i a \tan (c+d x))^{3/2}}+\frac{99 i}{256 a d \sqrt{a+i a \tan (c+d x)}}","-\frac{i a^4}{4 d (a-i a \tan (c+d x))^2 (a+i a \tan (c+d x))^{7/2}}-\frac{11 i a^3}{16 d (a-i a \tan (c+d x)) (a+i a \tan (c+d x))^{7/2}}+\frac{99 i a^2}{224 d (a+i a \tan (c+d x))^{7/2}}-\frac{99 i \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{256 \sqrt{2} a^{3/2} d}+\frac{99 i a}{320 d (a+i a \tan (c+d x))^{5/2}}+\frac{33 i}{128 d (a+i a \tan (c+d x))^{3/2}}+\frac{99 i}{256 a d \sqrt{a+i a \tan (c+d x)}}",1,"(((-99*I)/256)*ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/(Sqrt[2]*Sqrt[a])])/(Sqrt[2]*a^(3/2)*d) + (((99*I)/224)*a^2)/(d*(a + I*a*Tan[c + d*x])^(7/2)) - ((I/4)*a^4)/(d*(a - I*a*Tan[c + d*x])^2*(a + I*a*Tan[c + d*x])^(7/2)) - (((11*I)/16)*a^3)/(d*(a - I*a*Tan[c + d*x])*(a + I*a*Tan[c + d*x])^(7/2)) + (((99*I)/320)*a)/(d*(a + I*a*Tan[c + d*x])^(5/2)) + ((33*I)/128)/(d*(a + I*a*Tan[c + d*x])^(3/2)) + ((99*I)/256)/(a*d*Sqrt[a + I*a*Tan[c + d*x]])","A",9,4,26,0.1538,1,"{3487, 51, 63, 206}"
353,1,321,0,0.1800611,"\int \frac{\cos ^6(c+d x)}{(a+i a \tan (c+d x))^{3/2}} \, dx","Int[Cos[c + d*x]^6/(a + I*a*Tan[c + d*x])^(3/2),x]","-\frac{i a^6}{6 d (a-i a \tan (c+d x))^3 (a+i a \tan (c+d x))^{9/2}}-\frac{5 i a^5}{16 d (a-i a \tan (c+d x))^2 (a+i a \tan (c+d x))^{9/2}}-\frac{65 i a^4}{64 d (a-i a \tan (c+d x)) (a+i a \tan (c+d x))^{9/2}}+\frac{715 i a^3}{1152 d (a+i a \tan (c+d x))^{9/2}}+\frac{715 i a^2}{1792 d (a+i a \tan (c+d x))^{7/2}}-\frac{715 i \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{2048 \sqrt{2} a^{3/2} d}+\frac{143 i a}{512 d (a+i a \tan (c+d x))^{5/2}}+\frac{715 i}{3072 d (a+i a \tan (c+d x))^{3/2}}+\frac{715 i}{2048 a d \sqrt{a+i a \tan (c+d x)}}","-\frac{i a^6}{6 d (a-i a \tan (c+d x))^3 (a+i a \tan (c+d x))^{9/2}}-\frac{5 i a^5}{16 d (a-i a \tan (c+d x))^2 (a+i a \tan (c+d x))^{9/2}}-\frac{65 i a^4}{64 d (a-i a \tan (c+d x)) (a+i a \tan (c+d x))^{9/2}}+\frac{715 i a^3}{1152 d (a+i a \tan (c+d x))^{9/2}}+\frac{715 i a^2}{1792 d (a+i a \tan (c+d x))^{7/2}}-\frac{715 i \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{2048 \sqrt{2} a^{3/2} d}+\frac{143 i a}{512 d (a+i a \tan (c+d x))^{5/2}}+\frac{715 i}{3072 d (a+i a \tan (c+d x))^{3/2}}+\frac{715 i}{2048 a d \sqrt{a+i a \tan (c+d x)}}",1,"(((-715*I)/2048)*ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/(Sqrt[2]*Sqrt[a])])/(Sqrt[2]*a^(3/2)*d) + (((715*I)/1152)*a^3)/(d*(a + I*a*Tan[c + d*x])^(9/2)) - ((I/6)*a^6)/(d*(a - I*a*Tan[c + d*x])^3*(a + I*a*Tan[c + d*x])^(9/2)) - (((5*I)/16)*a^5)/(d*(a - I*a*Tan[c + d*x])^2*(a + I*a*Tan[c + d*x])^(9/2)) - (((65*I)/64)*a^4)/(d*(a - I*a*Tan[c + d*x])*(a + I*a*Tan[c + d*x])^(9/2)) + (((715*I)/1792)*a^2)/(d*(a + I*a*Tan[c + d*x])^(7/2)) + (((143*I)/512)*a)/(d*(a + I*a*Tan[c + d*x])^(5/2)) + ((715*I)/3072)/(d*(a + I*a*Tan[c + d*x])^(3/2)) + ((715*I)/2048)/(a*d*Sqrt[a + I*a*Tan[c + d*x]])","A",11,4,26,0.1538,1,"{3487, 51, 63, 206}"
354,1,147,0,0.2623617,"\int \frac{\sec ^{11}(c+d x)}{(a+i a \tan (c+d x))^{3/2}} \, dx","Int[Sec[c + d*x]^11/(a + I*a*Tan[c + d*x])^(3/2),x]","\frac{8 i a^2 \sec ^{11}(c+d x)}{85 d (a+i a \tan (c+d x))^{7/2}}+\frac{64 i a^3 \sec ^{11}(c+d x)}{1105 d (a+i a \tan (c+d x))^{9/2}}+\frac{256 i a^4 \sec ^{11}(c+d x)}{12155 d (a+i a \tan (c+d x))^{11/2}}+\frac{2 i a \sec ^{11}(c+d x)}{17 d (a+i a \tan (c+d x))^{5/2}}","\frac{8 i a^2 \sec ^{11}(c+d x)}{85 d (a+i a \tan (c+d x))^{7/2}}+\frac{64 i a^3 \sec ^{11}(c+d x)}{1105 d (a+i a \tan (c+d x))^{9/2}}+\frac{256 i a^4 \sec ^{11}(c+d x)}{12155 d (a+i a \tan (c+d x))^{11/2}}+\frac{2 i a \sec ^{11}(c+d x)}{17 d (a+i a \tan (c+d x))^{5/2}}",1,"(((256*I)/12155)*a^4*Sec[c + d*x]^11)/(d*(a + I*a*Tan[c + d*x])^(11/2)) + (((64*I)/1105)*a^3*Sec[c + d*x]^11)/(d*(a + I*a*Tan[c + d*x])^(9/2)) + (((8*I)/85)*a^2*Sec[c + d*x]^11)/(d*(a + I*a*Tan[c + d*x])^(7/2)) + (((2*I)/17)*a*Sec[c + d*x]^11)/(d*(a + I*a*Tan[c + d*x])^(5/2))","A",4,2,26,0.07692,1,"{3494, 3493}"
355,1,110,0,0.1910729,"\int \frac{\sec ^9(c+d x)}{(a+i a \tan (c+d x))^{3/2}} \, dx","Int[Sec[c + d*x]^9/(a + I*a*Tan[c + d*x])^(3/2),x]","\frac{16 i a^2 \sec ^9(c+d x)}{143 d (a+i a \tan (c+d x))^{7/2}}+\frac{64 i a^3 \sec ^9(c+d x)}{1287 d (a+i a \tan (c+d x))^{9/2}}+\frac{2 i a \sec ^9(c+d x)}{13 d (a+i a \tan (c+d x))^{5/2}}","\frac{16 i a^2 \sec ^9(c+d x)}{143 d (a+i a \tan (c+d x))^{7/2}}+\frac{64 i a^3 \sec ^9(c+d x)}{1287 d (a+i a \tan (c+d x))^{9/2}}+\frac{2 i a \sec ^9(c+d x)}{13 d (a+i a \tan (c+d x))^{5/2}}",1,"(((64*I)/1287)*a^3*Sec[c + d*x]^9)/(d*(a + I*a*Tan[c + d*x])^(9/2)) + (((16*I)/143)*a^2*Sec[c + d*x]^9)/(d*(a + I*a*Tan[c + d*x])^(7/2)) + (((2*I)/13)*a*Sec[c + d*x]^9)/(d*(a + I*a*Tan[c + d*x])^(5/2))","A",3,2,26,0.07692,1,"{3494, 3493}"
356,1,73,0,0.1289311,"\int \frac{\sec ^7(c+d x)}{(a+i a \tan (c+d x))^{3/2}} \, dx","Int[Sec[c + d*x]^7/(a + I*a*Tan[c + d*x])^(3/2),x]","\frac{8 i a^2 \sec ^7(c+d x)}{63 d (a+i a \tan (c+d x))^{7/2}}+\frac{2 i a \sec ^7(c+d x)}{9 d (a+i a \tan (c+d x))^{5/2}}","\frac{8 i a^2 \sec ^7(c+d x)}{63 d (a+i a \tan (c+d x))^{7/2}}+\frac{2 i a \sec ^7(c+d x)}{9 d (a+i a \tan (c+d x))^{5/2}}",1,"(((8*I)/63)*a^2*Sec[c + d*x]^7)/(d*(a + I*a*Tan[c + d*x])^(7/2)) + (((2*I)/9)*a*Sec[c + d*x]^7)/(d*(a + I*a*Tan[c + d*x])^(5/2))","A",2,2,26,0.07692,1,"{3494, 3493}"
357,1,35,0,0.0615494,"\int \frac{\sec ^5(c+d x)}{(a+i a \tan (c+d x))^{3/2}} \, dx","Int[Sec[c + d*x]^5/(a + I*a*Tan[c + d*x])^(3/2),x]","\frac{2 i a \sec ^5(c+d x)}{5 d (a+i a \tan (c+d x))^{5/2}}","\frac{2 i a \sec ^5(c+d x)}{5 d (a+i a \tan (c+d x))^{5/2}}",1,"(((2*I)/5)*a*Sec[c + d*x]^5)/(d*(a + I*a*Tan[c + d*x])^(5/2))","A",1,1,26,0.03846,1,"{3493}"
358,1,86,0,0.1015636,"\int \frac{\sec ^3(c+d x)}{(a+i a \tan (c+d x))^{3/2}} \, dx","Int[Sec[c + d*x]^3/(a + I*a*Tan[c + d*x])^(3/2),x]","\frac{2 i \sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{a} \sec (c+d x)}{\sqrt{2} \sqrt{a+i a \tan (c+d x)}}\right)}{a^{3/2} d}-\frac{2 i \sec (c+d x)}{a d \sqrt{a+i a \tan (c+d x)}}","\frac{2 i \sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{a} \sec (c+d x)}{\sqrt{2} \sqrt{a+i a \tan (c+d x)}}\right)}{a^{3/2} d}-\frac{2 i \sec (c+d x)}{a d \sqrt{a+i a \tan (c+d x)}}",1,"((2*I)*Sqrt[2]*ArcTanh[(Sqrt[a]*Sec[c + d*x])/(Sqrt[2]*Sqrt[a + I*a*Tan[c + d*x]])])/(a^(3/2)*d) - ((2*I)*Sec[c + d*x])/(a*d*Sqrt[a + I*a*Tan[c + d*x]])","A",3,3,26,0.1154,1,"{3491, 3489, 206}"
359,1,87,0,0.0752919,"\int \frac{\sec (c+d x)}{(a+i a \tan (c+d x))^{3/2}} \, dx","Int[Sec[c + d*x]/(a + I*a*Tan[c + d*x])^(3/2),x]","\frac{i \tanh ^{-1}\left(\frac{\sqrt{a} \sec (c+d x)}{\sqrt{2} \sqrt{a+i a \tan (c+d x)}}\right)}{2 \sqrt{2} a^{3/2} d}+\frac{i \sec (c+d x)}{2 d (a+i a \tan (c+d x))^{3/2}}","\frac{i \tanh ^{-1}\left(\frac{\sqrt{a} \sec (c+d x)}{\sqrt{2} \sqrt{a+i a \tan (c+d x)}}\right)}{2 \sqrt{2} a^{3/2} d}+\frac{i \sec (c+d x)}{2 d (a+i a \tan (c+d x))^{3/2}}",1,"((I/2)*ArcTanh[(Sqrt[a]*Sec[c + d*x])/(Sqrt[2]*Sqrt[a + I*a*Tan[c + d*x]])])/(Sqrt[2]*a^(3/2)*d) + ((I/2)*Sec[c + d*x])/(d*(a + I*a*Tan[c + d*x])^(3/2))","A",3,3,24,0.1250,1,"{3502, 3489, 206}"
360,1,157,0,0.1924106,"\int \frac{\cos (c+d x)}{(a+i a \tan (c+d x))^{3/2}} \, dx","Int[Cos[c + d*x]/(a + I*a*Tan[c + d*x])^(3/2),x]","-\frac{15 i \cos (c+d x) \sqrt{a+i a \tan (c+d x)}}{32 a^2 d}+\frac{15 i \tanh ^{-1}\left(\frac{\sqrt{a} \sec (c+d x)}{\sqrt{2} \sqrt{a+i a \tan (c+d x)}}\right)}{32 \sqrt{2} a^{3/2} d}+\frac{5 i \cos (c+d x)}{16 a d \sqrt{a+i a \tan (c+d x)}}+\frac{i \cos (c+d x)}{4 d (a+i a \tan (c+d x))^{3/2}}","-\frac{15 i \cos (c+d x) \sqrt{a+i a \tan (c+d x)}}{32 a^2 d}+\frac{15 i \tanh ^{-1}\left(\frac{\sqrt{a} \sec (c+d x)}{\sqrt{2} \sqrt{a+i a \tan (c+d x)}}\right)}{32 \sqrt{2} a^{3/2} d}+\frac{5 i \cos (c+d x)}{16 a d \sqrt{a+i a \tan (c+d x)}}+\frac{i \cos (c+d x)}{4 d (a+i a \tan (c+d x))^{3/2}}",1,"(((15*I)/32)*ArcTanh[(Sqrt[a]*Sec[c + d*x])/(Sqrt[2]*Sqrt[a + I*a*Tan[c + d*x]])])/(Sqrt[2]*a^(3/2)*d) + ((I/4)*Cos[c + d*x])/(d*(a + I*a*Tan[c + d*x])^(3/2)) + (((5*I)/16)*Cos[c + d*x])/(a*d*Sqrt[a + I*a*Tan[c + d*x]]) - (((15*I)/32)*Cos[c + d*x]*Sqrt[a + I*a*Tan[c + d*x]])/(a^2*d)","A",5,4,24,0.1667,1,"{3502, 3490, 3489, 206}"
361,1,233,0,0.3372511,"\int \frac{\cos ^3(c+d x)}{(a+i a \tan (c+d x))^{3/2}} \, dx","Int[Cos[c + d*x]^3/(a + I*a*Tan[c + d*x])^(3/2),x]","-\frac{7 i \cos ^3(c+d x) \sqrt{a+i a \tan (c+d x)}}{32 a^2 d}-\frac{105 i \cos (c+d x) \sqrt{a+i a \tan (c+d x)}}{256 a^2 d}+\frac{105 i \tanh ^{-1}\left(\frac{\sqrt{a} \sec (c+d x)}{\sqrt{2} \sqrt{a+i a \tan (c+d x)}}\right)}{256 \sqrt{2} a^{3/2} d}+\frac{3 i \cos ^3(c+d x)}{16 a d \sqrt{a+i a \tan (c+d x)}}+\frac{i \cos ^3(c+d x)}{6 d (a+i a \tan (c+d x))^{3/2}}+\frac{35 i \cos (c+d x)}{128 a d \sqrt{a+i a \tan (c+d x)}}","-\frac{7 i \cos ^3(c+d x) \sqrt{a+i a \tan (c+d x)}}{32 a^2 d}-\frac{105 i \cos (c+d x) \sqrt{a+i a \tan (c+d x)}}{256 a^2 d}+\frac{105 i \tanh ^{-1}\left(\frac{\sqrt{a} \sec (c+d x)}{\sqrt{2} \sqrt{a+i a \tan (c+d x)}}\right)}{256 \sqrt{2} a^{3/2} d}+\frac{3 i \cos ^3(c+d x)}{16 a d \sqrt{a+i a \tan (c+d x)}}+\frac{i \cos ^3(c+d x)}{6 d (a+i a \tan (c+d x))^{3/2}}+\frac{35 i \cos (c+d x)}{128 a d \sqrt{a+i a \tan (c+d x)}}",1,"(((105*I)/256)*ArcTanh[(Sqrt[a]*Sec[c + d*x])/(Sqrt[2]*Sqrt[a + I*a*Tan[c + d*x]])])/(Sqrt[2]*a^(3/2)*d) + ((I/6)*Cos[c + d*x]^3)/(d*(a + I*a*Tan[c + d*x])^(3/2)) + (((35*I)/128)*Cos[c + d*x])/(a*d*Sqrt[a + I*a*Tan[c + d*x]]) + (((3*I)/16)*Cos[c + d*x]^3)/(a*d*Sqrt[a + I*a*Tan[c + d*x]]) - (((105*I)/256)*Cos[c + d*x]*Sqrt[a + I*a*Tan[c + d*x]])/(a^2*d) - (((7*I)/32)*Cos[c + d*x]^3*Sqrt[a + I*a*Tan[c + d*x]])/(a^2*d)","A",7,5,26,0.1923,1,"{3502, 3497, 3490, 3489, 206}"
362,1,146,0,0.0931937,"\int \frac{\sec ^{10}(c+d x)}{(a+i a \tan (c+d x))^{5/2}} \, dx","Int[Sec[c + d*x]^10/(a + I*a*Tan[c + d*x])^(5/2),x]","-\frac{2 i (a+i a \tan (c+d x))^{13/2}}{13 a^9 d}+\frac{16 i (a+i a \tan (c+d x))^{11/2}}{11 a^8 d}-\frac{16 i (a+i a \tan (c+d x))^{9/2}}{3 a^7 d}+\frac{64 i (a+i a \tan (c+d x))^{7/2}}{7 a^6 d}-\frac{32 i (a+i a \tan (c+d x))^{5/2}}{5 a^5 d}","-\frac{2 i (a+i a \tan (c+d x))^{13/2}}{13 a^9 d}+\frac{16 i (a+i a \tan (c+d x))^{11/2}}{11 a^8 d}-\frac{16 i (a+i a \tan (c+d x))^{9/2}}{3 a^7 d}+\frac{64 i (a+i a \tan (c+d x))^{7/2}}{7 a^6 d}-\frac{32 i (a+i a \tan (c+d x))^{5/2}}{5 a^5 d}",1,"(((-32*I)/5)*(a + I*a*Tan[c + d*x])^(5/2))/(a^5*d) + (((64*I)/7)*(a + I*a*Tan[c + d*x])^(7/2))/(a^6*d) - (((16*I)/3)*(a + I*a*Tan[c + d*x])^(9/2))/(a^7*d) + (((16*I)/11)*(a + I*a*Tan[c + d*x])^(11/2))/(a^8*d) - (((2*I)/13)*(a + I*a*Tan[c + d*x])^(13/2))/(a^9*d)","A",3,2,26,0.07692,1,"{3487, 43}"
363,1,117,0,0.0856808,"\int \frac{\sec ^8(c+d x)}{(a+i a \tan (c+d x))^{5/2}} \, dx","Int[Sec[c + d*x]^8/(a + I*a*Tan[c + d*x])^(5/2),x]","\frac{2 i (a+i a \tan (c+d x))^{9/2}}{9 a^7 d}-\frac{12 i (a+i a \tan (c+d x))^{7/2}}{7 a^6 d}+\frac{24 i (a+i a \tan (c+d x))^{5/2}}{5 a^5 d}-\frac{16 i (a+i a \tan (c+d x))^{3/2}}{3 a^4 d}","\frac{2 i (a+i a \tan (c+d x))^{9/2}}{9 a^7 d}-\frac{12 i (a+i a \tan (c+d x))^{7/2}}{7 a^6 d}+\frac{24 i (a+i a \tan (c+d x))^{5/2}}{5 a^5 d}-\frac{16 i (a+i a \tan (c+d x))^{3/2}}{3 a^4 d}",1,"(((-16*I)/3)*(a + I*a*Tan[c + d*x])^(3/2))/(a^4*d) + (((24*I)/5)*(a + I*a*Tan[c + d*x])^(5/2))/(a^5*d) - (((12*I)/7)*(a + I*a*Tan[c + d*x])^(7/2))/(a^6*d) + (((2*I)/9)*(a + I*a*Tan[c + d*x])^(9/2))/(a^7*d)","A",3,2,26,0.07692,1,"{3487, 43}"
364,1,86,0,0.0793853,"\int \frac{\sec ^6(c+d x)}{(a+i a \tan (c+d x))^{5/2}} \, dx","Int[Sec[c + d*x]^6/(a + I*a*Tan[c + d*x])^(5/2),x]","-\frac{2 i (a+i a \tan (c+d x))^{5/2}}{5 a^5 d}+\frac{8 i (a+i a \tan (c+d x))^{3/2}}{3 a^4 d}-\frac{8 i \sqrt{a+i a \tan (c+d x)}}{a^3 d}","-\frac{2 i (a+i a \tan (c+d x))^{5/2}}{5 a^5 d}+\frac{8 i (a+i a \tan (c+d x))^{3/2}}{3 a^4 d}-\frac{8 i \sqrt{a+i a \tan (c+d x)}}{a^3 d}",1,"((-8*I)*Sqrt[a + I*a*Tan[c + d*x]])/(a^3*d) + (((8*I)/3)*(a + I*a*Tan[c + d*x])^(3/2))/(a^4*d) - (((2*I)/5)*(a + I*a*Tan[c + d*x])^(5/2))/(a^5*d)","A",3,2,26,0.07692,1,"{3487, 43}"
365,1,55,0,0.0701862,"\int \frac{\sec ^4(c+d x)}{(a+i a \tan (c+d x))^{5/2}} \, dx","Int[Sec[c + d*x]^4/(a + I*a*Tan[c + d*x])^(5/2),x]","\frac{2 i \sqrt{a+i a \tan (c+d x)}}{a^3 d}+\frac{4 i}{a^2 d \sqrt{a+i a \tan (c+d x)}}","\frac{2 i \sqrt{a+i a \tan (c+d x)}}{a^3 d}+\frac{4 i}{a^2 d \sqrt{a+i a \tan (c+d x)}}",1,"(4*I)/(a^2*d*Sqrt[a + I*a*Tan[c + d*x]]) + ((2*I)*Sqrt[a + I*a*Tan[c + d*x]])/(a^3*d)","A",3,2,26,0.07692,1,"{3487, 43}"
366,1,29,0,0.0628563,"\int \frac{\sec ^2(c+d x)}{(a+i a \tan (c+d x))^{5/2}} \, dx","Int[Sec[c + d*x]^2/(a + I*a*Tan[c + d*x])^(5/2),x]","\frac{2 i}{3 a d (a+i a \tan (c+d x))^{3/2}}","\frac{2 i}{3 a d (a+i a \tan (c+d x))^{3/2}}",1,"((2*I)/3)/(a*d*(a + I*a*Tan[c + d*x])^(3/2))","A",2,2,26,0.07692,1,"{3487, 32}"
367,1,204,0,0.1267729,"\int \frac{\cos ^2(c+d x)}{(a+i a \tan (c+d x))^{5/2}} \, dx","Int[Cos[c + d*x]^2/(a + I*a*Tan[c + d*x])^(5/2),x]","-\frac{i a^2}{2 d (a-i a \tan (c+d x)) (a+i a \tan (c+d x))^{7/2}}+\frac{9 i}{32 a^2 d \sqrt{a+i a \tan (c+d x)}}-\frac{9 i \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{32 \sqrt{2} a^{5/2} d}+\frac{9 i a}{28 d (a+i a \tan (c+d x))^{7/2}}+\frac{9 i}{40 d (a+i a \tan (c+d x))^{5/2}}+\frac{3 i}{16 a d (a+i a \tan (c+d x))^{3/2}}","-\frac{i a^2}{2 d (a-i a \tan (c+d x)) (a+i a \tan (c+d x))^{7/2}}+\frac{9 i}{32 a^2 d \sqrt{a+i a \tan (c+d x)}}-\frac{9 i \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{32 \sqrt{2} a^{5/2} d}+\frac{9 i a}{28 d (a+i a \tan (c+d x))^{7/2}}+\frac{9 i}{40 d (a+i a \tan (c+d x))^{5/2}}+\frac{3 i}{16 a d (a+i a \tan (c+d x))^{3/2}}",1,"(((-9*I)/32)*ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/(Sqrt[2]*Sqrt[a])])/(Sqrt[2]*a^(5/2)*d) + (((9*I)/28)*a)/(d*(a + I*a*Tan[c + d*x])^(7/2)) - ((I/2)*a^2)/(d*(a - I*a*Tan[c + d*x])*(a + I*a*Tan[c + d*x])^(7/2)) + ((9*I)/40)/(d*(a + I*a*Tan[c + d*x])^(5/2)) + ((3*I)/16)/(a*d*(a + I*a*Tan[c + d*x])^(3/2)) + ((9*I)/32)/(a^2*d*Sqrt[a + I*a*Tan[c + d*x]])","A",8,4,26,0.1538,1,"{3487, 51, 63, 206}"
368,1,277,0,0.1571665,"\int \frac{\cos ^4(c+d x)}{(a+i a \tan (c+d x))^{5/2}} \, dx","Int[Cos[c + d*x]^4/(a + I*a*Tan[c + d*x])^(5/2),x]","-\frac{i a^4}{4 d (a-i a \tan (c+d x))^2 (a+i a \tan (c+d x))^{9/2}}-\frac{13 i a^3}{16 d (a-i a \tan (c+d x)) (a+i a \tan (c+d x))^{9/2}}+\frac{143 i a^2}{288 d (a+i a \tan (c+d x))^{9/2}}+\frac{143 i}{512 a^2 d \sqrt{a+i a \tan (c+d x)}}-\frac{143 i \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{512 \sqrt{2} a^{5/2} d}+\frac{143 i a}{448 d (a+i a \tan (c+d x))^{7/2}}+\frac{143 i}{640 d (a+i a \tan (c+d x))^{5/2}}+\frac{143 i}{768 a d (a+i a \tan (c+d x))^{3/2}}","-\frac{i a^4}{4 d (a-i a \tan (c+d x))^2 (a+i a \tan (c+d x))^{9/2}}-\frac{13 i a^3}{16 d (a-i a \tan (c+d x)) (a+i a \tan (c+d x))^{9/2}}+\frac{143 i a^2}{288 d (a+i a \tan (c+d x))^{9/2}}+\frac{143 i}{512 a^2 d \sqrt{a+i a \tan (c+d x)}}-\frac{143 i \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{512 \sqrt{2} a^{5/2} d}+\frac{143 i a}{448 d (a+i a \tan (c+d x))^{7/2}}+\frac{143 i}{640 d (a+i a \tan (c+d x))^{5/2}}+\frac{143 i}{768 a d (a+i a \tan (c+d x))^{3/2}}",1,"(((-143*I)/512)*ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/(Sqrt[2]*Sqrt[a])])/(Sqrt[2]*a^(5/2)*d) + (((143*I)/288)*a^2)/(d*(a + I*a*Tan[c + d*x])^(9/2)) - ((I/4)*a^4)/(d*(a - I*a*Tan[c + d*x])^2*(a + I*a*Tan[c + d*x])^(9/2)) - (((13*I)/16)*a^3)/(d*(a - I*a*Tan[c + d*x])*(a + I*a*Tan[c + d*x])^(9/2)) + (((143*I)/448)*a)/(d*(a + I*a*Tan[c + d*x])^(7/2)) + ((143*I)/640)/(d*(a + I*a*Tan[c + d*x])^(5/2)) + ((143*I)/768)/(a*d*(a + I*a*Tan[c + d*x])^(3/2)) + ((143*I)/512)/(a^2*d*Sqrt[a + I*a*Tan[c + d*x]])","A",10,4,26,0.1538,1,"{3487, 51, 63, 206}"
369,1,147,0,0.2654076,"\int \frac{\sec ^{13}(c+d x)}{(a+i a \tan (c+d x))^{5/2}} \, dx","Int[Sec[c + d*x]^13/(a + I*a*Tan[c + d*x])^(5/2),x]","\frac{24 i a^2 \sec ^{13}(c+d x)}{323 d (a+i a \tan (c+d x))^{9/2}}+\frac{64 i a^3 \sec ^{13}(c+d x)}{1615 d (a+i a \tan (c+d x))^{11/2}}+\frac{256 i a^4 \sec ^{13}(c+d x)}{20995 d (a+i a \tan (c+d x))^{13/2}}+\frac{2 i a \sec ^{13}(c+d x)}{19 d (a+i a \tan (c+d x))^{7/2}}","\frac{24 i a^2 \sec ^{13}(c+d x)}{323 d (a+i a \tan (c+d x))^{9/2}}+\frac{64 i a^3 \sec ^{13}(c+d x)}{1615 d (a+i a \tan (c+d x))^{11/2}}+\frac{256 i a^4 \sec ^{13}(c+d x)}{20995 d (a+i a \tan (c+d x))^{13/2}}+\frac{2 i a \sec ^{13}(c+d x)}{19 d (a+i a \tan (c+d x))^{7/2}}",1,"(((256*I)/20995)*a^4*Sec[c + d*x]^13)/(d*(a + I*a*Tan[c + d*x])^(13/2)) + (((64*I)/1615)*a^3*Sec[c + d*x]^13)/(d*(a + I*a*Tan[c + d*x])^(11/2)) + (((24*I)/323)*a^2*Sec[c + d*x]^13)/(d*(a + I*a*Tan[c + d*x])^(9/2)) + (((2*I)/19)*a*Sec[c + d*x]^13)/(d*(a + I*a*Tan[c + d*x])^(7/2))","A",4,2,26,0.07692,1,"{3494, 3493}"
370,1,110,0,0.1928439,"\int \frac{\sec ^{11}(c+d x)}{(a+i a \tan (c+d x))^{5/2}} \, dx","Int[Sec[c + d*x]^11/(a + I*a*Tan[c + d*x])^(5/2),x]","\frac{16 i a^2 \sec ^{11}(c+d x)}{195 d (a+i a \tan (c+d x))^{9/2}}+\frac{64 i a^3 \sec ^{11}(c+d x)}{2145 d (a+i a \tan (c+d x))^{11/2}}+\frac{2 i a \sec ^{11}(c+d x)}{15 d (a+i a \tan (c+d x))^{7/2}}","\frac{16 i a^2 \sec ^{11}(c+d x)}{195 d (a+i a \tan (c+d x))^{9/2}}+\frac{64 i a^3 \sec ^{11}(c+d x)}{2145 d (a+i a \tan (c+d x))^{11/2}}+\frac{2 i a \sec ^{11}(c+d x)}{15 d (a+i a \tan (c+d x))^{7/2}}",1,"(((64*I)/2145)*a^3*Sec[c + d*x]^11)/(d*(a + I*a*Tan[c + d*x])^(11/2)) + (((16*I)/195)*a^2*Sec[c + d*x]^11)/(d*(a + I*a*Tan[c + d*x])^(9/2)) + (((2*I)/15)*a*Sec[c + d*x]^11)/(d*(a + I*a*Tan[c + d*x])^(7/2))","A",3,2,26,0.07692,1,"{3494, 3493}"
371,1,73,0,0.1255385,"\int \frac{\sec ^9(c+d x)}{(a+i a \tan (c+d x))^{5/2}} \, dx","Int[Sec[c + d*x]^9/(a + I*a*Tan[c + d*x])^(5/2),x]","\frac{8 i a^2 \sec ^9(c+d x)}{99 d (a+i a \tan (c+d x))^{9/2}}+\frac{2 i a \sec ^9(c+d x)}{11 d (a+i a \tan (c+d x))^{7/2}}","\frac{8 i a^2 \sec ^9(c+d x)}{99 d (a+i a \tan (c+d x))^{9/2}}+\frac{2 i a \sec ^9(c+d x)}{11 d (a+i a \tan (c+d x))^{7/2}}",1,"(((8*I)/99)*a^2*Sec[c + d*x]^9)/(d*(a + I*a*Tan[c + d*x])^(9/2)) + (((2*I)/11)*a*Sec[c + d*x]^9)/(d*(a + I*a*Tan[c + d*x])^(7/2))","A",2,2,26,0.07692,1,"{3494, 3493}"
372,1,35,0,0.0629306,"\int \frac{\sec ^7(c+d x)}{(a+i a \tan (c+d x))^{5/2}} \, dx","Int[Sec[c + d*x]^7/(a + I*a*Tan[c + d*x])^(5/2),x]","\frac{2 i a \sec ^7(c+d x)}{7 d (a+i a \tan (c+d x))^{7/2}}","\frac{2 i a \sec ^7(c+d x)}{7 d (a+i a \tan (c+d x))^{7/2}}",1,"(((2*I)/7)*a*Sec[c + d*x]^7)/(d*(a + I*a*Tan[c + d*x])^(7/2))","A",1,1,26,0.03846,1,"{3493}"
373,1,123,0,0.169913,"\int \frac{\sec ^5(c+d x)}{(a+i a \tan (c+d x))^{5/2}} \, dx","Int[Sec[c + d*x]^5/(a + I*a*Tan[c + d*x])^(5/2),x]","-\frac{4 i \sec (c+d x)}{a^2 d \sqrt{a+i a \tan (c+d x)}}+\frac{4 i \sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{a} \sec (c+d x)}{\sqrt{2} \sqrt{a+i a \tan (c+d x)}}\right)}{a^{5/2} d}-\frac{2 i \sec ^3(c+d x)}{3 a d (a+i a \tan (c+d x))^{3/2}}","-\frac{4 i \sec (c+d x)}{a^2 d \sqrt{a+i a \tan (c+d x)}}+\frac{4 i \sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{a} \sec (c+d x)}{\sqrt{2} \sqrt{a+i a \tan (c+d x)}}\right)}{a^{5/2} d}-\frac{2 i \sec ^3(c+d x)}{3 a d (a+i a \tan (c+d x))^{3/2}}",1,"((4*I)*Sqrt[2]*ArcTanh[(Sqrt[a]*Sec[c + d*x])/(Sqrt[2]*Sqrt[a + I*a*Tan[c + d*x]])])/(a^(5/2)*d) - (((2*I)/3)*Sec[c + d*x]^3)/(a*d*(a + I*a*Tan[c + d*x])^(3/2)) - ((4*I)*Sec[c + d*x])/(a^2*d*Sqrt[a + I*a*Tan[c + d*x]])","A",4,3,26,0.1154,1,"{3491, 3489, 206}"
374,1,86,0,0.1438487,"\int \frac{\sec ^3(c+d x)}{(a+i a \tan (c+d x))^{5/2}} \, dx","Int[Sec[c + d*x]^3/(a + I*a*Tan[c + d*x])^(5/2),x]","\frac{i \sec (c+d x)}{a d (a+i a \tan (c+d x))^{3/2}}-\frac{i \tanh ^{-1}\left(\frac{\sqrt{a} \sec (c+d x)}{\sqrt{2} \sqrt{a+i a \tan (c+d x)}}\right)}{\sqrt{2} a^{5/2} d}","\frac{i \sec (c+d x)}{a d (a+i a \tan (c+d x))^{3/2}}-\frac{i \tanh ^{-1}\left(\frac{\sqrt{a} \sec (c+d x)}{\sqrt{2} \sqrt{a+i a \tan (c+d x)}}\right)}{\sqrt{2} a^{5/2} d}",1,"((-I)*ArcTanh[(Sqrt[a]*Sec[c + d*x])/(Sqrt[2]*Sqrt[a + I*a*Tan[c + d*x]])])/(Sqrt[2]*a^(5/2)*d) + (I*Sec[c + d*x])/(a*d*(a + I*a*Tan[c + d*x])^(3/2))","A",4,4,26,0.1538,1,"{3501, 3502, 3489, 206}"
375,1,122,0,0.1154771,"\int \frac{\sec (c+d x)}{(a+i a \tan (c+d x))^{5/2}} \, dx","Int[Sec[c + d*x]/(a + I*a*Tan[c + d*x])^(5/2),x]","\frac{3 i \tanh ^{-1}\left(\frac{\sqrt{a} \sec (c+d x)}{\sqrt{2} \sqrt{a+i a \tan (c+d x)}}\right)}{16 \sqrt{2} a^{5/2} d}+\frac{3 i \sec (c+d x)}{16 a d (a+i a \tan (c+d x))^{3/2}}+\frac{i \sec (c+d x)}{4 d (a+i a \tan (c+d x))^{5/2}}","\frac{3 i \tanh ^{-1}\left(\frac{\sqrt{a} \sec (c+d x)}{\sqrt{2} \sqrt{a+i a \tan (c+d x)}}\right)}{16 \sqrt{2} a^{5/2} d}+\frac{3 i \sec (c+d x)}{16 a d (a+i a \tan (c+d x))^{3/2}}+\frac{i \sec (c+d x)}{4 d (a+i a \tan (c+d x))^{5/2}}",1,"(((3*I)/16)*ArcTanh[(Sqrt[a]*Sec[c + d*x])/(Sqrt[2]*Sqrt[a + I*a*Tan[c + d*x]])])/(Sqrt[2]*a^(5/2)*d) + ((I/4)*Sec[c + d*x])/(d*(a + I*a*Tan[c + d*x])^(5/2)) + (((3*I)/16)*Sec[c + d*x])/(a*d*(a + I*a*Tan[c + d*x])^(3/2))","A",4,3,24,0.1250,1,"{3502, 3489, 206}"
376,1,192,0,0.2585201,"\int \frac{\cos (c+d x)}{(a+i a \tan (c+d x))^{5/2}} \, dx","Int[Cos[c + d*x]/(a + I*a*Tan[c + d*x])^(5/2),x]","-\frac{35 i \cos (c+d x) \sqrt{a+i a \tan (c+d x)}}{128 a^3 d}+\frac{35 i \cos (c+d x)}{192 a^2 d \sqrt{a+i a \tan (c+d x)}}+\frac{35 i \tanh ^{-1}\left(\frac{\sqrt{a} \sec (c+d x)}{\sqrt{2} \sqrt{a+i a \tan (c+d x)}}\right)}{128 \sqrt{2} a^{5/2} d}+\frac{7 i \cos (c+d x)}{48 a d (a+i a \tan (c+d x))^{3/2}}+\frac{i \cos (c+d x)}{6 d (a+i a \tan (c+d x))^{5/2}}","-\frac{35 i \cos (c+d x) \sqrt{a+i a \tan (c+d x)}}{128 a^3 d}+\frac{35 i \cos (c+d x)}{192 a^2 d \sqrt{a+i a \tan (c+d x)}}+\frac{35 i \tanh ^{-1}\left(\frac{\sqrt{a} \sec (c+d x)}{\sqrt{2} \sqrt{a+i a \tan (c+d x)}}\right)}{128 \sqrt{2} a^{5/2} d}+\frac{7 i \cos (c+d x)}{48 a d (a+i a \tan (c+d x))^{3/2}}+\frac{i \cos (c+d x)}{6 d (a+i a \tan (c+d x))^{5/2}}",1,"(((35*I)/128)*ArcTanh[(Sqrt[a]*Sec[c + d*x])/(Sqrt[2]*Sqrt[a + I*a*Tan[c + d*x]])])/(Sqrt[2]*a^(5/2)*d) + ((I/6)*Cos[c + d*x])/(d*(a + I*a*Tan[c + d*x])^(5/2)) + (((7*I)/48)*Cos[c + d*x])/(a*d*(a + I*a*Tan[c + d*x])^(3/2)) + (((35*I)/192)*Cos[c + d*x])/(a^2*d*Sqrt[a + I*a*Tan[c + d*x]]) - (((35*I)/128)*Cos[c + d*x]*Sqrt[a + I*a*Tan[c + d*x]])/(a^3*d)","A",6,4,24,0.1667,1,"{3502, 3490, 3489, 206}"
377,1,270,0,0.4222617,"\int \frac{\cos ^3(c+d x)}{(a+i a \tan (c+d x))^{5/2}} \, dx","Int[Cos[c + d*x]^3/(a + I*a*Tan[c + d*x])^(5/2),x]","-\frac{77 i \cos ^3(c+d x) \sqrt{a+i a \tan (c+d x)}}{512 a^3 d}+\frac{33 i \cos ^3(c+d x)}{256 a^2 d \sqrt{a+i a \tan (c+d x)}}-\frac{1155 i \cos (c+d x) \sqrt{a+i a \tan (c+d x)}}{4096 a^3 d}+\frac{385 i \cos (c+d x)}{2048 a^2 d \sqrt{a+i a \tan (c+d x)}}+\frac{1155 i \tanh ^{-1}\left(\frac{\sqrt{a} \sec (c+d x)}{\sqrt{2} \sqrt{a+i a \tan (c+d x)}}\right)}{4096 \sqrt{2} a^{5/2} d}+\frac{11 i \cos ^3(c+d x)}{96 a d (a+i a \tan (c+d x))^{3/2}}+\frac{i \cos ^3(c+d x)}{8 d (a+i a \tan (c+d x))^{5/2}}","-\frac{77 i \cos ^3(c+d x) \sqrt{a+i a \tan (c+d x)}}{512 a^3 d}+\frac{33 i \cos ^3(c+d x)}{256 a^2 d \sqrt{a+i a \tan (c+d x)}}-\frac{1155 i \cos (c+d x) \sqrt{a+i a \tan (c+d x)}}{4096 a^3 d}+\frac{385 i \cos (c+d x)}{2048 a^2 d \sqrt{a+i a \tan (c+d x)}}+\frac{1155 i \tanh ^{-1}\left(\frac{\sqrt{a} \sec (c+d x)}{\sqrt{2} \sqrt{a+i a \tan (c+d x)}}\right)}{4096 \sqrt{2} a^{5/2} d}+\frac{11 i \cos ^3(c+d x)}{96 a d (a+i a \tan (c+d x))^{3/2}}+\frac{i \cos ^3(c+d x)}{8 d (a+i a \tan (c+d x))^{5/2}}",1,"(((1155*I)/4096)*ArcTanh[(Sqrt[a]*Sec[c + d*x])/(Sqrt[2]*Sqrt[a + I*a*Tan[c + d*x]])])/(Sqrt[2]*a^(5/2)*d) + ((I/8)*Cos[c + d*x]^3)/(d*(a + I*a*Tan[c + d*x])^(5/2)) + (((11*I)/96)*Cos[c + d*x]^3)/(a*d*(a + I*a*Tan[c + d*x])^(3/2)) + (((385*I)/2048)*Cos[c + d*x])/(a^2*d*Sqrt[a + I*a*Tan[c + d*x]]) + (((33*I)/256)*Cos[c + d*x]^3)/(a^2*d*Sqrt[a + I*a*Tan[c + d*x]]) - (((1155*I)/4096)*Cos[c + d*x]*Sqrt[a + I*a*Tan[c + d*x]])/(a^3*d) - (((77*I)/512)*Cos[c + d*x]^3*Sqrt[a + I*a*Tan[c + d*x]])/(a^3*d)","A",8,5,26,0.1923,1,"{3502, 3497, 3490, 3489, 206}"
378,1,146,0,0.0931584,"\int \frac{\sec ^{10}(c+d x)}{(a+i a \tan (c+d x))^{7/2}} \, dx","Int[Sec[c + d*x]^10/(a + I*a*Tan[c + d*x])^(7/2),x]","-\frac{2 i (a+i a \tan (c+d x))^{11/2}}{11 a^9 d}+\frac{16 i (a+i a \tan (c+d x))^{9/2}}{9 a^8 d}-\frac{48 i (a+i a \tan (c+d x))^{7/2}}{7 a^7 d}+\frac{64 i (a+i a \tan (c+d x))^{5/2}}{5 a^6 d}-\frac{32 i (a+i a \tan (c+d x))^{3/2}}{3 a^5 d}","-\frac{2 i (a+i a \tan (c+d x))^{11/2}}{11 a^9 d}+\frac{16 i (a+i a \tan (c+d x))^{9/2}}{9 a^8 d}-\frac{48 i (a+i a \tan (c+d x))^{7/2}}{7 a^7 d}+\frac{64 i (a+i a \tan (c+d x))^{5/2}}{5 a^6 d}-\frac{32 i (a+i a \tan (c+d x))^{3/2}}{3 a^5 d}",1,"(((-32*I)/3)*(a + I*a*Tan[c + d*x])^(3/2))/(a^5*d) + (((64*I)/5)*(a + I*a*Tan[c + d*x])^(5/2))/(a^6*d) - (((48*I)/7)*(a + I*a*Tan[c + d*x])^(7/2))/(a^7*d) + (((16*I)/9)*(a + I*a*Tan[c + d*x])^(9/2))/(a^8*d) - (((2*I)/11)*(a + I*a*Tan[c + d*x])^(11/2))/(a^9*d)","A",3,2,26,0.07692,1,"{3487, 43}"
379,1,113,0,0.0863583,"\int \frac{\sec ^8(c+d x)}{(a+i a \tan (c+d x))^{7/2}} \, dx","Int[Sec[c + d*x]^8/(a + I*a*Tan[c + d*x])^(7/2),x]","\frac{2 i (a+i a \tan (c+d x))^{7/2}}{7 a^7 d}-\frac{12 i (a+i a \tan (c+d x))^{5/2}}{5 a^6 d}+\frac{8 i (a+i a \tan (c+d x))^{3/2}}{a^5 d}-\frac{16 i \sqrt{a+i a \tan (c+d x)}}{a^4 d}","\frac{2 i (a+i a \tan (c+d x))^{7/2}}{7 a^7 d}-\frac{12 i (a+i a \tan (c+d x))^{5/2}}{5 a^6 d}+\frac{8 i (a+i a \tan (c+d x))^{3/2}}{a^5 d}-\frac{16 i \sqrt{a+i a \tan (c+d x)}}{a^4 d}",1,"((-16*I)*Sqrt[a + I*a*Tan[c + d*x]])/(a^4*d) + ((8*I)*(a + I*a*Tan[c + d*x])^(3/2))/(a^5*d) - (((12*I)/5)*(a + I*a*Tan[c + d*x])^(5/2))/(a^6*d) + (((2*I)/7)*(a + I*a*Tan[c + d*x])^(7/2))/(a^7*d)","A",3,2,26,0.07692,1,"{3487, 43}"
380,1,84,0,0.0795285,"\int \frac{\sec ^6(c+d x)}{(a+i a \tan (c+d x))^{7/2}} \, dx","Int[Sec[c + d*x]^6/(a + I*a*Tan[c + d*x])^(7/2),x]","-\frac{2 i (a+i a \tan (c+d x))^{3/2}}{3 a^5 d}+\frac{8 i \sqrt{a+i a \tan (c+d x)}}{a^4 d}+\frac{8 i}{a^3 d \sqrt{a+i a \tan (c+d x)}}","-\frac{2 i (a+i a \tan (c+d x))^{3/2}}{3 a^5 d}+\frac{8 i \sqrt{a+i a \tan (c+d x)}}{a^4 d}+\frac{8 i}{a^3 d \sqrt{a+i a \tan (c+d x)}}",1,"(8*I)/(a^3*d*Sqrt[a + I*a*Tan[c + d*x]]) + ((8*I)*Sqrt[a + I*a*Tan[c + d*x]])/(a^4*d) - (((2*I)/3)*(a + I*a*Tan[c + d*x])^(3/2))/(a^5*d)","A",3,2,26,0.07692,1,"{3487, 43}"
381,1,57,0,0.0736954,"\int \frac{\sec ^4(c+d x)}{(a+i a \tan (c+d x))^{7/2}} \, dx","Int[Sec[c + d*x]^4/(a + I*a*Tan[c + d*x])^(7/2),x]","\frac{4 i}{3 a^2 d (a+i a \tan (c+d x))^{3/2}}-\frac{2 i}{a^3 d \sqrt{a+i a \tan (c+d x)}}","\frac{4 i}{3 a^2 d (a+i a \tan (c+d x))^{3/2}}-\frac{2 i}{a^3 d \sqrt{a+i a \tan (c+d x)}}",1,"((4*I)/3)/(a^2*d*(a + I*a*Tan[c + d*x])^(3/2)) - (2*I)/(a^3*d*Sqrt[a + I*a*Tan[c + d*x]])","A",3,2,26,0.07692,1,"{3487, 43}"
382,1,29,0,0.0641361,"\int \frac{\sec ^2(c+d x)}{(a+i a \tan (c+d x))^{7/2}} \, dx","Int[Sec[c + d*x]^2/(a + I*a*Tan[c + d*x])^(7/2),x]","\frac{2 i}{5 a d (a+i a \tan (c+d x))^{5/2}}","\frac{2 i}{5 a d (a+i a \tan (c+d x))^{5/2}}",1,"((2*I)/5)/(a*d*(a + I*a*Tan[c + d*x])^(5/2))","A",2,2,26,0.07692,1,"{3487, 32}"
383,1,233,0,0.1421917,"\int \frac{\cos ^2(c+d x)}{(a+i a \tan (c+d x))^{7/2}} \, dx","Int[Cos[c + d*x]^2/(a + I*a*Tan[c + d*x])^(7/2),x]","-\frac{i a^2}{2 d (a-i a \tan (c+d x)) (a+i a \tan (c+d x))^{9/2}}+\frac{11 i}{96 a^2 d (a+i a \tan (c+d x))^{3/2}}+\frac{11 i}{64 a^3 d \sqrt{a+i a \tan (c+d x)}}-\frac{11 i \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{64 \sqrt{2} a^{7/2} d}+\frac{11 i a}{36 d (a+i a \tan (c+d x))^{9/2}}+\frac{11 i}{56 d (a+i a \tan (c+d x))^{7/2}}+\frac{11 i}{80 a d (a+i a \tan (c+d x))^{5/2}}","-\frac{i a^2}{2 d (a-i a \tan (c+d x)) (a+i a \tan (c+d x))^{9/2}}+\frac{11 i}{96 a^2 d (a+i a \tan (c+d x))^{3/2}}+\frac{11 i}{64 a^3 d \sqrt{a+i a \tan (c+d x)}}-\frac{11 i \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{64 \sqrt{2} a^{7/2} d}+\frac{11 i a}{36 d (a+i a \tan (c+d x))^{9/2}}+\frac{11 i}{56 d (a+i a \tan (c+d x))^{7/2}}+\frac{11 i}{80 a d (a+i a \tan (c+d x))^{5/2}}",1,"(((-11*I)/64)*ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/(Sqrt[2]*Sqrt[a])])/(Sqrt[2]*a^(7/2)*d) + (((11*I)/36)*a)/(d*(a + I*a*Tan[c + d*x])^(9/2)) - ((I/2)*a^2)/(d*(a - I*a*Tan[c + d*x])*(a + I*a*Tan[c + d*x])^(9/2)) + ((11*I)/56)/(d*(a + I*a*Tan[c + d*x])^(7/2)) + ((11*I)/80)/(a*d*(a + I*a*Tan[c + d*x])^(5/2)) + ((11*I)/96)/(a^2*d*(a + I*a*Tan[c + d*x])^(3/2)) + ((11*I)/64)/(a^3*d*Sqrt[a + I*a*Tan[c + d*x]])","A",9,4,26,0.1538,1,"{3487, 51, 63, 206}"
384,1,306,0,0.1768433,"\int \frac{\cos ^4(c+d x)}{(a+i a \tan (c+d x))^{7/2}} \, dx","Int[Cos[c + d*x]^4/(a + I*a*Tan[c + d*x])^(7/2),x]","-\frac{i a^4}{4 d (a-i a \tan (c+d x))^2 (a+i a \tan (c+d x))^{11/2}}-\frac{15 i a^3}{16 d (a-i a \tan (c+d x)) (a+i a \tan (c+d x))^{11/2}}+\frac{195 i a^2}{352 d (a+i a \tan (c+d x))^{11/2}}+\frac{65 i}{512 a^2 d (a+i a \tan (c+d x))^{3/2}}+\frac{195 i}{1024 a^3 d \sqrt{a+i a \tan (c+d x)}}-\frac{195 i \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{1024 \sqrt{2} a^{7/2} d}+\frac{65 i a}{192 d (a+i a \tan (c+d x))^{9/2}}+\frac{195 i}{896 d (a+i a \tan (c+d x))^{7/2}}+\frac{39 i}{256 a d (a+i a \tan (c+d x))^{5/2}}","-\frac{i a^4}{4 d (a-i a \tan (c+d x))^2 (a+i a \tan (c+d x))^{11/2}}-\frac{15 i a^3}{16 d (a-i a \tan (c+d x)) (a+i a \tan (c+d x))^{11/2}}+\frac{195 i a^2}{352 d (a+i a \tan (c+d x))^{11/2}}+\frac{65 i}{512 a^2 d (a+i a \tan (c+d x))^{3/2}}+\frac{195 i}{1024 a^3 d \sqrt{a+i a \tan (c+d x)}}-\frac{195 i \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{1024 \sqrt{2} a^{7/2} d}+\frac{65 i a}{192 d (a+i a \tan (c+d x))^{9/2}}+\frac{195 i}{896 d (a+i a \tan (c+d x))^{7/2}}+\frac{39 i}{256 a d (a+i a \tan (c+d x))^{5/2}}",1,"(((-195*I)/1024)*ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/(Sqrt[2]*Sqrt[a])])/(Sqrt[2]*a^(7/2)*d) + (((195*I)/352)*a^2)/(d*(a + I*a*Tan[c + d*x])^(11/2)) - ((I/4)*a^4)/(d*(a - I*a*Tan[c + d*x])^2*(a + I*a*Tan[c + d*x])^(11/2)) - (((15*I)/16)*a^3)/(d*(a - I*a*Tan[c + d*x])*(a + I*a*Tan[c + d*x])^(11/2)) + (((65*I)/192)*a)/(d*(a + I*a*Tan[c + d*x])^(9/2)) + ((195*I)/896)/(d*(a + I*a*Tan[c + d*x])^(7/2)) + ((39*I)/256)/(a*d*(a + I*a*Tan[c + d*x])^(5/2)) + ((65*I)/512)/(a^2*d*(a + I*a*Tan[c + d*x])^(3/2)) + ((195*I)/1024)/(a^3*d*Sqrt[a + I*a*Tan[c + d*x]])","A",11,4,26,0.1538,1,"{3487, 51, 63, 206}"
385,1,110,0,0.1944144,"\int \frac{\sec ^{13}(c+d x)}{(a+i a \tan (c+d x))^{7/2}} \, dx","Int[Sec[c + d*x]^13/(a + I*a*Tan[c + d*x])^(7/2),x]","\frac{16 i a^2 \sec ^{13}(c+d x)}{255 d (a+i a \tan (c+d x))^{11/2}}+\frac{64 i a^3 \sec ^{13}(c+d x)}{3315 d (a+i a \tan (c+d x))^{13/2}}+\frac{2 i a \sec ^{13}(c+d x)}{17 d (a+i a \tan (c+d x))^{9/2}}","\frac{16 i a^2 \sec ^{13}(c+d x)}{255 d (a+i a \tan (c+d x))^{11/2}}+\frac{64 i a^3 \sec ^{13}(c+d x)}{3315 d (a+i a \tan (c+d x))^{13/2}}+\frac{2 i a \sec ^{13}(c+d x)}{17 d (a+i a \tan (c+d x))^{9/2}}",1,"(((64*I)/3315)*a^3*Sec[c + d*x]^13)/(d*(a + I*a*Tan[c + d*x])^(13/2)) + (((16*I)/255)*a^2*Sec[c + d*x]^13)/(d*(a + I*a*Tan[c + d*x])^(11/2)) + (((2*I)/17)*a*Sec[c + d*x]^13)/(d*(a + I*a*Tan[c + d*x])^(9/2))","A",3,2,26,0.07692,1,"{3494, 3493}"
386,1,73,0,0.1272922,"\int \frac{\sec ^{11}(c+d x)}{(a+i a \tan (c+d x))^{7/2}} \, dx","Int[Sec[c + d*x]^11/(a + I*a*Tan[c + d*x])^(7/2),x]","\frac{8 i a^2 \sec ^{11}(c+d x)}{143 d (a+i a \tan (c+d x))^{11/2}}+\frac{2 i a \sec ^{11}(c+d x)}{13 d (a+i a \tan (c+d x))^{9/2}}","\frac{8 i a^2 \sec ^{11}(c+d x)}{143 d (a+i a \tan (c+d x))^{11/2}}+\frac{2 i a \sec ^{11}(c+d x)}{13 d (a+i a \tan (c+d x))^{9/2}}",1,"(((8*I)/143)*a^2*Sec[c + d*x]^11)/(d*(a + I*a*Tan[c + d*x])^(11/2)) + (((2*I)/13)*a*Sec[c + d*x]^11)/(d*(a + I*a*Tan[c + d*x])^(9/2))","A",2,2,26,0.07692,1,"{3494, 3493}"
387,1,35,0,0.0621879,"\int \frac{\sec ^9(c+d x)}{(a+i a \tan (c+d x))^{7/2}} \, dx","Int[Sec[c + d*x]^9/(a + I*a*Tan[c + d*x])^(7/2),x]","\frac{2 i a \sec ^9(c+d x)}{9 d (a+i a \tan (c+d x))^{9/2}}","\frac{2 i a \sec ^9(c+d x)}{9 d (a+i a \tan (c+d x))^{9/2}}",1,"(((2*I)/9)*a*Sec[c + d*x]^9)/(d*(a + I*a*Tan[c + d*x])^(9/2))","A",1,1,26,0.03846,1,"{3493}"
388,1,160,0,0.2512629,"\int \frac{\sec ^7(c+d x)}{(a+i a \tan (c+d x))^{7/2}} \, dx","Int[Sec[c + d*x]^7/(a + I*a*Tan[c + d*x])^(7/2),x]","-\frac{4 i \sec ^3(c+d x)}{3 a^2 d (a+i a \tan (c+d x))^{3/2}}-\frac{8 i \sec (c+d x)}{a^3 d \sqrt{a+i a \tan (c+d x)}}+\frac{8 i \sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{a} \sec (c+d x)}{\sqrt{2} \sqrt{a+i a \tan (c+d x)}}\right)}{a^{7/2} d}-\frac{2 i \sec ^5(c+d x)}{5 a d (a+i a \tan (c+d x))^{5/2}}","-\frac{4 i \sec ^3(c+d x)}{3 a^2 d (a+i a \tan (c+d x))^{3/2}}-\frac{8 i \sec (c+d x)}{a^3 d \sqrt{a+i a \tan (c+d x)}}+\frac{8 i \sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{a} \sec (c+d x)}{\sqrt{2} \sqrt{a+i a \tan (c+d x)}}\right)}{a^{7/2} d}-\frac{2 i \sec ^5(c+d x)}{5 a d (a+i a \tan (c+d x))^{5/2}}",1,"((8*I)*Sqrt[2]*ArcTanh[(Sqrt[a]*Sec[c + d*x])/(Sqrt[2]*Sqrt[a + I*a*Tan[c + d*x]])])/(a^(7/2)*d) - (((2*I)/5)*Sec[c + d*x]^5)/(a*d*(a + I*a*Tan[c + d*x])^(5/2)) - (((4*I)/3)*Sec[c + d*x]^3)/(a^2*d*(a + I*a*Tan[c + d*x])^(3/2)) - ((8*I)*Sec[c + d*x])/(a^3*d*Sqrt[a + I*a*Tan[c + d*x]])","A",5,3,26,0.1154,1,"{3491, 3489, 206}"
389,1,121,0,0.2166501,"\int \frac{\sec ^5(c+d x)}{(a+i a \tan (c+d x))^{7/2}} \, dx","Int[Sec[c + d*x]^5/(a + I*a*Tan[c + d*x])^(7/2),x]","\frac{6 i \sec (c+d x)}{a^2 d (a+i a \tan (c+d x))^{3/2}}-\frac{3 i \sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{a} \sec (c+d x)}{\sqrt{2} \sqrt{a+i a \tan (c+d x)}}\right)}{a^{7/2} d}-\frac{2 i \sec ^3(c+d x)}{a d (a+i a \tan (c+d x))^{5/2}}","\frac{6 i \sec (c+d x)}{a^2 d (a+i a \tan (c+d x))^{3/2}}-\frac{3 i \sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{a} \sec (c+d x)}{\sqrt{2} \sqrt{a+i a \tan (c+d x)}}\right)}{a^{7/2} d}-\frac{2 i \sec ^3(c+d x)}{a d (a+i a \tan (c+d x))^{5/2}}",1,"((-3*I)*Sqrt[2]*ArcTanh[(Sqrt[a]*Sec[c + d*x])/(Sqrt[2]*Sqrt[a + I*a*Tan[c + d*x]])])/(a^(7/2)*d) - ((2*I)*Sec[c + d*x]^3)/(a*d*(a + I*a*Tan[c + d*x])^(5/2)) + ((6*I)*Sec[c + d*x])/(a^2*d*(a + I*a*Tan[c + d*x])^(3/2))","A",5,4,26,0.1538,1,"{3501, 3502, 3489, 206}"
390,1,125,0,0.1877836,"\int \frac{\sec ^3(c+d x)}{(a+i a \tan (c+d x))^{7/2}} \, dx","Int[Sec[c + d*x]^3/(a + I*a*Tan[c + d*x])^(7/2),x]","-\frac{i \sec (c+d x)}{8 a^2 d (a+i a \tan (c+d x))^{3/2}}-\frac{i \tanh ^{-1}\left(\frac{\sqrt{a} \sec (c+d x)}{\sqrt{2} \sqrt{a+i a \tan (c+d x)}}\right)}{8 \sqrt{2} a^{7/2} d}+\frac{i \sec (c+d x)}{2 a d (a+i a \tan (c+d x))^{5/2}}","-\frac{i \sec (c+d x)}{8 a^2 d (a+i a \tan (c+d x))^{3/2}}-\frac{i \tanh ^{-1}\left(\frac{\sqrt{a} \sec (c+d x)}{\sqrt{2} \sqrt{a+i a \tan (c+d x)}}\right)}{8 \sqrt{2} a^{7/2} d}+\frac{i \sec (c+d x)}{2 a d (a+i a \tan (c+d x))^{5/2}}",1,"((-I/8)*ArcTanh[(Sqrt[a]*Sec[c + d*x])/(Sqrt[2]*Sqrt[a + I*a*Tan[c + d*x]])])/(Sqrt[2]*a^(7/2)*d) + ((I/2)*Sec[c + d*x])/(a*d*(a + I*a*Tan[c + d*x])^(5/2)) - ((I/8)*Sec[c + d*x])/(a^2*d*(a + I*a*Tan[c + d*x])^(3/2))","A",5,4,26,0.1538,1,"{3501, 3502, 3489, 206}"
391,1,157,0,0.1648062,"\int \frac{\sec (c+d x)}{(a+i a \tan (c+d x))^{7/2}} \, dx","Int[Sec[c + d*x]/(a + I*a*Tan[c + d*x])^(7/2),x]","\frac{5 i \sec (c+d x)}{64 a^2 d (a+i a \tan (c+d x))^{3/2}}+\frac{5 i \tanh ^{-1}\left(\frac{\sqrt{a} \sec (c+d x)}{\sqrt{2} \sqrt{a+i a \tan (c+d x)}}\right)}{64 \sqrt{2} a^{7/2} d}+\frac{5 i \sec (c+d x)}{48 a d (a+i a \tan (c+d x))^{5/2}}+\frac{i \sec (c+d x)}{6 d (a+i a \tan (c+d x))^{7/2}}","\frac{5 i \sec (c+d x)}{64 a^2 d (a+i a \tan (c+d x))^{3/2}}+\frac{5 i \tanh ^{-1}\left(\frac{\sqrt{a} \sec (c+d x)}{\sqrt{2} \sqrt{a+i a \tan (c+d x)}}\right)}{64 \sqrt{2} a^{7/2} d}+\frac{5 i \sec (c+d x)}{48 a d (a+i a \tan (c+d x))^{5/2}}+\frac{i \sec (c+d x)}{6 d (a+i a \tan (c+d x))^{7/2}}",1,"(((5*I)/64)*ArcTanh[(Sqrt[a]*Sec[c + d*x])/(Sqrt[2]*Sqrt[a + I*a*Tan[c + d*x]])])/(Sqrt[2]*a^(7/2)*d) + ((I/6)*Sec[c + d*x])/(d*(a + I*a*Tan[c + d*x])^(7/2)) + (((5*I)/48)*Sec[c + d*x])/(a*d*(a + I*a*Tan[c + d*x])^(5/2)) + (((5*I)/64)*Sec[c + d*x])/(a^2*d*(a + I*a*Tan[c + d*x])^(3/2))","A",5,3,24,0.1250,1,"{3502, 3489, 206}"
392,1,227,0,0.3753534,"\int \frac{\cos (c+d x)}{(a+i a \tan (c+d x))^{7/2}} \, dx","Int[Cos[c + d*x]/(a + I*a*Tan[c + d*x])^(7/2),x]","-\frac{315 i \cos (c+d x) \sqrt{a+i a \tan (c+d x)}}{2048 a^4 d}+\frac{105 i \cos (c+d x)}{1024 a^3 d \sqrt{a+i a \tan (c+d x)}}+\frac{21 i \cos (c+d x)}{256 a^2 d (a+i a \tan (c+d x))^{3/2}}+\frac{315 i \tanh ^{-1}\left(\frac{\sqrt{a} \sec (c+d x)}{\sqrt{2} \sqrt{a+i a \tan (c+d x)}}\right)}{2048 \sqrt{2} a^{7/2} d}+\frac{3 i \cos (c+d x)}{32 a d (a+i a \tan (c+d x))^{5/2}}+\frac{i \cos (c+d x)}{8 d (a+i a \tan (c+d x))^{7/2}}","-\frac{315 i \cos (c+d x) \sqrt{a+i a \tan (c+d x)}}{2048 a^4 d}+\frac{105 i \cos (c+d x)}{1024 a^3 d \sqrt{a+i a \tan (c+d x)}}+\frac{21 i \cos (c+d x)}{256 a^2 d (a+i a \tan (c+d x))^{3/2}}+\frac{315 i \tanh ^{-1}\left(\frac{\sqrt{a} \sec (c+d x)}{\sqrt{2} \sqrt{a+i a \tan (c+d x)}}\right)}{2048 \sqrt{2} a^{7/2} d}+\frac{3 i \cos (c+d x)}{32 a d (a+i a \tan (c+d x))^{5/2}}+\frac{i \cos (c+d x)}{8 d (a+i a \tan (c+d x))^{7/2}}",1,"(((315*I)/2048)*ArcTanh[(Sqrt[a]*Sec[c + d*x])/(Sqrt[2]*Sqrt[a + I*a*Tan[c + d*x]])])/(Sqrt[2]*a^(7/2)*d) + ((I/8)*Cos[c + d*x])/(d*(a + I*a*Tan[c + d*x])^(7/2)) + (((3*I)/32)*Cos[c + d*x])/(a*d*(a + I*a*Tan[c + d*x])^(5/2)) + (((21*I)/256)*Cos[c + d*x])/(a^2*d*(a + I*a*Tan[c + d*x])^(3/2)) + (((105*I)/1024)*Cos[c + d*x])/(a^3*d*Sqrt[a + I*a*Tan[c + d*x]]) - (((315*I)/2048)*Cos[c + d*x]*Sqrt[a + I*a*Tan[c + d*x]])/(a^4*d)","A",7,4,24,0.1667,1,"{3502, 3490, 3489, 206}"
393,1,307,0,0.5201065,"\int \frac{\cos ^3(c+d x)}{(a+i a \tan (c+d x))^{7/2}} \, dx","Int[Cos[c + d*x]^3/(a + I*a*Tan[c + d*x])^(7/2),x]","-\frac{1001 i \cos ^3(c+d x) \sqrt{a+i a \tan (c+d x)}}{10240 a^4 d}+\frac{429 i \cos ^3(c+d x)}{5120 a^3 d \sqrt{a+i a \tan (c+d x)}}+\frac{143 i \cos ^3(c+d x)}{1920 a^2 d (a+i a \tan (c+d x))^{3/2}}-\frac{3003 i \cos (c+d x) \sqrt{a+i a \tan (c+d x)}}{16384 a^4 d}+\frac{1001 i \cos (c+d x)}{8192 a^3 d \sqrt{a+i a \tan (c+d x)}}+\frac{3003 i \tanh ^{-1}\left(\frac{\sqrt{a} \sec (c+d x)}{\sqrt{2} \sqrt{a+i a \tan (c+d x)}}\right)}{16384 \sqrt{2} a^{7/2} d}+\frac{13 i \cos ^3(c+d x)}{160 a d (a+i a \tan (c+d x))^{5/2}}+\frac{i \cos ^3(c+d x)}{10 d (a+i a \tan (c+d x))^{7/2}}","-\frac{1001 i \cos ^3(c+d x) \sqrt{a+i a \tan (c+d x)}}{10240 a^4 d}+\frac{429 i \cos ^3(c+d x)}{5120 a^3 d \sqrt{a+i a \tan (c+d x)}}+\frac{143 i \cos ^3(c+d x)}{1920 a^2 d (a+i a \tan (c+d x))^{3/2}}-\frac{3003 i \cos (c+d x) \sqrt{a+i a \tan (c+d x)}}{16384 a^4 d}+\frac{1001 i \cos (c+d x)}{8192 a^3 d \sqrt{a+i a \tan (c+d x)}}+\frac{3003 i \tanh ^{-1}\left(\frac{\sqrt{a} \sec (c+d x)}{\sqrt{2} \sqrt{a+i a \tan (c+d x)}}\right)}{16384 \sqrt{2} a^{7/2} d}+\frac{13 i \cos ^3(c+d x)}{160 a d (a+i a \tan (c+d x))^{5/2}}+\frac{i \cos ^3(c+d x)}{10 d (a+i a \tan (c+d x))^{7/2}}",1,"(((3003*I)/16384)*ArcTanh[(Sqrt[a]*Sec[c + d*x])/(Sqrt[2]*Sqrt[a + I*a*Tan[c + d*x]])])/(Sqrt[2]*a^(7/2)*d) + ((I/10)*Cos[c + d*x]^3)/(d*(a + I*a*Tan[c + d*x])^(7/2)) + (((13*I)/160)*Cos[c + d*x]^3)/(a*d*(a + I*a*Tan[c + d*x])^(5/2)) + (((143*I)/1920)*Cos[c + d*x]^3)/(a^2*d*(a + I*a*Tan[c + d*x])^(3/2)) + (((1001*I)/8192)*Cos[c + d*x])/(a^3*d*Sqrt[a + I*a*Tan[c + d*x]]) + (((429*I)/5120)*Cos[c + d*x]^3)/(a^3*d*Sqrt[a + I*a*Tan[c + d*x]]) - (((3003*I)/16384)*Cos[c + d*x]*Sqrt[a + I*a*Tan[c + d*x]])/(a^4*d) - (((1001*I)/10240)*Cos[c + d*x]^3*Sqrt[a + I*a*Tan[c + d*x]])/(a^4*d)","A",9,5,26,0.1923,1,"{3502, 3497, 3490, 3489, 206}"
394,1,524,0,0.4453261,"\int (e \sec (c+d x))^{3/2} \sqrt{a+i a \tan (c+d x)} \, dx","Int[(e*Sec[c + d*x])^(3/2)*Sqrt[a + I*a*Tan[c + d*x]],x]","-\frac{i a^{3/2} e^{3/2} \sec (c+d x) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{e} \sqrt{a-i a \tan (c+d x)}}{\sqrt{a} \sqrt{e \sec (c+d x)}}\right)}{\sqrt{2} d \sqrt{a-i a \tan (c+d x)} \sqrt{a+i a \tan (c+d x)}}+\frac{i a^{3/2} e^{3/2} \sec (c+d x) \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt{e} \sqrt{a-i a \tan (c+d x)}}{\sqrt{a} \sqrt{e \sec (c+d x)}}\right)}{\sqrt{2} d \sqrt{a-i a \tan (c+d x)} \sqrt{a+i a \tan (c+d x)}}+\frac{i a^{3/2} e^{3/2} \sec (c+d x) \log \left(-\frac{\sqrt{2} \sqrt{a} \sqrt{e} \sqrt{a-i a \tan (c+d x)}}{\sqrt{e \sec (c+d x)}}+\cos (c+d x) (a-i a \tan (c+d x))+a\right)}{2 \sqrt{2} d \sqrt{a-i a \tan (c+d x)} \sqrt{a+i a \tan (c+d x)}}-\frac{i a^{3/2} e^{3/2} \sec (c+d x) \log \left(\frac{\sqrt{2} \sqrt{a} \sqrt{e} \sqrt{a-i a \tan (c+d x)}}{\sqrt{e \sec (c+d x)}}+\cos (c+d x) (a-i a \tan (c+d x))+a\right)}{2 \sqrt{2} d \sqrt{a-i a \tan (c+d x)} \sqrt{a+i a \tan (c+d x)}}+\frac{i a (e \sec (c+d x))^{3/2}}{d \sqrt{a+i a \tan (c+d x)}}","-\frac{i a^{3/2} e^{3/2} \sec (c+d x) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{e} \sqrt{a-i a \tan (c+d x)}}{\sqrt{a} \sqrt{e \sec (c+d x)}}\right)}{\sqrt{2} d \sqrt{a-i a \tan (c+d x)} \sqrt{a+i a \tan (c+d x)}}+\frac{i a^{3/2} e^{3/2} \sec (c+d x) \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt{e} \sqrt{a-i a \tan (c+d x)}}{\sqrt{a} \sqrt{e \sec (c+d x)}}\right)}{\sqrt{2} d \sqrt{a-i a \tan (c+d x)} \sqrt{a+i a \tan (c+d x)}}+\frac{i a^{3/2} e^{3/2} \sec (c+d x) \log \left(-\frac{\sqrt{2} \sqrt{a} \sqrt{e} \sqrt{a-i a \tan (c+d x)}}{\sqrt{e \sec (c+d x)}}+\cos (c+d x) (a-i a \tan (c+d x))+a\right)}{2 \sqrt{2} d \sqrt{a-i a \tan (c+d x)} \sqrt{a+i a \tan (c+d x)}}-\frac{i a^{3/2} e^{3/2} \sec (c+d x) \log \left(\frac{\sqrt{2} \sqrt{a} \sqrt{e} \sqrt{a-i a \tan (c+d x)}}{\sqrt{e \sec (c+d x)}}+\cos (c+d x) (a-i a \tan (c+d x))+a\right)}{2 \sqrt{2} d \sqrt{a-i a \tan (c+d x)} \sqrt{a+i a \tan (c+d x)}}+\frac{i a (e \sec (c+d x))^{3/2}}{d \sqrt{a+i a \tan (c+d x)}}",1,"(I*a*(e*Sec[c + d*x])^(3/2))/(d*Sqrt[a + I*a*Tan[c + d*x]]) - (I*a^(3/2)*e^(3/2)*ArcTan[1 - (Sqrt[2]*Sqrt[e]*Sqrt[a - I*a*Tan[c + d*x]])/(Sqrt[a]*Sqrt[e*Sec[c + d*x]])]*Sec[c + d*x])/(Sqrt[2]*d*Sqrt[a - I*a*Tan[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]]) + (I*a^(3/2)*e^(3/2)*ArcTan[1 + (Sqrt[2]*Sqrt[e]*Sqrt[a - I*a*Tan[c + d*x]])/(Sqrt[a]*Sqrt[e*Sec[c + d*x]])]*Sec[c + d*x])/(Sqrt[2]*d*Sqrt[a - I*a*Tan[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]]) + ((I/2)*a^(3/2)*e^(3/2)*Log[a - (Sqrt[2]*Sqrt[a]*Sqrt[e]*Sqrt[a - I*a*Tan[c + d*x]])/Sqrt[e*Sec[c + d*x]] + Cos[c + d*x]*(a - I*a*Tan[c + d*x])]*Sec[c + d*x])/(Sqrt[2]*d*Sqrt[a - I*a*Tan[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]]) - ((I/2)*a^(3/2)*e^(3/2)*Log[a + (Sqrt[2]*Sqrt[a]*Sqrt[e]*Sqrt[a - I*a*Tan[c + d*x]])/Sqrt[e*Sec[c + d*x]] + Cos[c + d*x]*(a - I*a*Tan[c + d*x])]*Sec[c + d*x])/(Sqrt[2]*d*Sqrt[a - I*a*Tan[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]])","A",12,9,30,0.3000,1,"{3498, 3499, 3495, 297, 1162, 617, 204, 1165, 628}"
395,1,323,0,0.1907693,"\int \sqrt{e \sec (c+d x)} \sqrt{a+i a \tan (c+d x)} \, dx","Int[Sqrt[e*Sec[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]],x]","\frac{i \sqrt{2} \sqrt{a} \sqrt{e} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{e} \sqrt{a+i a \tan (c+d x)}}{\sqrt{a} \sqrt{e \sec (c+d x)}}\right)}{d}-\frac{i \sqrt{2} \sqrt{a} \sqrt{e} \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt{e} \sqrt{a+i a \tan (c+d x)}}{\sqrt{a} \sqrt{e \sec (c+d x)}}\right)}{d}-\frac{i \sqrt{a} \sqrt{e} \log \left(-\frac{\sqrt{2} \sqrt{a} \sqrt{e} \sqrt{a+i a \tan (c+d x)}}{\sqrt{e \sec (c+d x)}}+\cos (c+d x) (a+i a \tan (c+d x))+a\right)}{\sqrt{2} d}+\frac{i \sqrt{a} \sqrt{e} \log \left(\frac{\sqrt{2} \sqrt{a} \sqrt{e} \sqrt{a+i a \tan (c+d x)}}{\sqrt{e \sec (c+d x)}}+\cos (c+d x) (a+i a \tan (c+d x))+a\right)}{\sqrt{2} d}","\frac{i \sqrt{2} \sqrt{a} \sqrt{e} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{e} \sqrt{a+i a \tan (c+d x)}}{\sqrt{a} \sqrt{e \sec (c+d x)}}\right)}{d}-\frac{i \sqrt{2} \sqrt{a} \sqrt{e} \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt{e} \sqrt{a+i a \tan (c+d x)}}{\sqrt{a} \sqrt{e \sec (c+d x)}}\right)}{d}-\frac{i \sqrt{a} \sqrt{e} \log \left(-\frac{\sqrt{2} \sqrt{a} \sqrt{e} \sqrt{a+i a \tan (c+d x)}}{\sqrt{e \sec (c+d x)}}+\cos (c+d x) (a+i a \tan (c+d x))+a\right)}{\sqrt{2} d}+\frac{i \sqrt{a} \sqrt{e} \log \left(\frac{\sqrt{2} \sqrt{a} \sqrt{e} \sqrt{a+i a \tan (c+d x)}}{\sqrt{e \sec (c+d x)}}+\cos (c+d x) (a+i a \tan (c+d x))+a\right)}{\sqrt{2} d}",1,"(I*Sqrt[2]*Sqrt[a]*Sqrt[e]*ArcTan[1 - (Sqrt[2]*Sqrt[e]*Sqrt[a + I*a*Tan[c + d*x]])/(Sqrt[a]*Sqrt[e*Sec[c + d*x]])])/d - (I*Sqrt[2]*Sqrt[a]*Sqrt[e]*ArcTan[1 + (Sqrt[2]*Sqrt[e]*Sqrt[a + I*a*Tan[c + d*x]])/(Sqrt[a]*Sqrt[e*Sec[c + d*x]])])/d - (I*Sqrt[a]*Sqrt[e]*Log[a - (Sqrt[2]*Sqrt[a]*Sqrt[e]*Sqrt[a + I*a*Tan[c + d*x]])/Sqrt[e*Sec[c + d*x]] + Cos[c + d*x]*(a + I*a*Tan[c + d*x])])/(Sqrt[2]*d) + (I*Sqrt[a]*Sqrt[e]*Log[a + (Sqrt[2]*Sqrt[a]*Sqrt[e]*Sqrt[a + I*a*Tan[c + d*x]])/Sqrt[e*Sec[c + d*x]] + Cos[c + d*x]*(a + I*a*Tan[c + d*x])])/(Sqrt[2]*d)","A",10,7,30,0.2333,1,"{3495, 297, 1162, 617, 204, 1165, 628}"
396,1,36,0,0.0608407,"\int \frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{e \sec (c+d x)}} \, dx","Int[Sqrt[a + I*a*Tan[c + d*x]]/Sqrt[e*Sec[c + d*x]],x]","-\frac{2 i \sqrt{a+i a \tan (c+d x)}}{d \sqrt{e \sec (c+d x)}}","-\frac{2 i \sqrt{a+i a \tan (c+d x)}}{d \sqrt{e \sec (c+d x)}}",1,"((-2*I)*Sqrt[a + I*a*Tan[c + d*x]])/(d*Sqrt[e*Sec[c + d*x]])","A",1,1,30,0.03333,1,"{3488}"
397,1,81,0,0.1321409,"\int \frac{\sqrt{a+i a \tan (c+d x)}}{(e \sec (c+d x))^{3/2}} \, dx","Int[Sqrt[a + I*a*Tan[c + d*x]]/(e*Sec[c + d*x])^(3/2),x]","\frac{4 i a \sqrt{e \sec (c+d x)}}{3 d e^2 \sqrt{a+i a \tan (c+d x)}}-\frac{2 i \sqrt{a+i a \tan (c+d x)}}{3 d (e \sec (c+d x))^{3/2}}","\frac{4 i a \sqrt{e \sec (c+d x)}}{3 d e^2 \sqrt{a+i a \tan (c+d x)}}-\frac{2 i \sqrt{a+i a \tan (c+d x)}}{3 d (e \sec (c+d x))^{3/2}}",1,"(((4*I)/3)*a*Sqrt[e*Sec[c + d*x]])/(d*e^2*Sqrt[a + I*a*Tan[c + d*x]]) - (((2*I)/3)*Sqrt[a + I*a*Tan[c + d*x]])/(d*(e*Sec[c + d*x])^(3/2))","A",2,2,30,0.06667,1,"{3497, 3488}"
398,1,122,0,0.1969727,"\int \frac{\sqrt{a+i a \tan (c+d x)}}{(e \sec (c+d x))^{5/2}} \, dx","Int[Sqrt[a + I*a*Tan[c + d*x]]/(e*Sec[c + d*x])^(5/2),x]","\frac{8 i a}{15 d e^2 \sqrt{a+i a \tan (c+d x)} \sqrt{e \sec (c+d x)}}-\frac{16 i \sqrt{a+i a \tan (c+d x)}}{15 d e^2 \sqrt{e \sec (c+d x)}}-\frac{2 i \sqrt{a+i a \tan (c+d x)}}{5 d (e \sec (c+d x))^{5/2}}","\frac{8 i a}{15 d e^2 \sqrt{a+i a \tan (c+d x)} \sqrt{e \sec (c+d x)}}-\frac{16 i \sqrt{a+i a \tan (c+d x)}}{15 d e^2 \sqrt{e \sec (c+d x)}}-\frac{2 i \sqrt{a+i a \tan (c+d x)}}{5 d (e \sec (c+d x))^{5/2}}",1,"(((8*I)/15)*a)/(d*e^2*Sqrt[e*Sec[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]]) - (((2*I)/5)*Sqrt[a + I*a*Tan[c + d*x]])/(d*(e*Sec[c + d*x])^(5/2)) - (((16*I)/15)*Sqrt[a + I*a*Tan[c + d*x]])/(d*e^2*Sqrt[e*Sec[c + d*x]])","A",3,3,30,0.1000,1,"{3497, 3502, 3488}"
399,1,164,0,0.2825315,"\int \frac{\sqrt{a+i a \tan (c+d x)}}{(e \sec (c+d x))^{7/2}} \, dx","Int[Sqrt[a + I*a*Tan[c + d*x]]/(e*Sec[c + d*x])^(7/2),x]","\frac{32 i a \sqrt{e \sec (c+d x)}}{35 d e^4 \sqrt{a+i a \tan (c+d x)}}+\frac{12 i a}{35 d e^2 \sqrt{a+i a \tan (c+d x)} (e \sec (c+d x))^{3/2}}-\frac{16 i \sqrt{a+i a \tan (c+d x)}}{35 d e^2 (e \sec (c+d x))^{3/2}}-\frac{2 i \sqrt{a+i a \tan (c+d x)}}{7 d (e \sec (c+d x))^{7/2}}","\frac{32 i a \sqrt{e \sec (c+d x)}}{35 d e^4 \sqrt{a+i a \tan (c+d x)}}+\frac{12 i a}{35 d e^2 \sqrt{a+i a \tan (c+d x)} (e \sec (c+d x))^{3/2}}-\frac{16 i \sqrt{a+i a \tan (c+d x)}}{35 d e^2 (e \sec (c+d x))^{3/2}}-\frac{2 i \sqrt{a+i a \tan (c+d x)}}{7 d (e \sec (c+d x))^{7/2}}",1,"(((12*I)/35)*a)/(d*e^2*(e*Sec[c + d*x])^(3/2)*Sqrt[a + I*a*Tan[c + d*x]]) + (((32*I)/35)*a*Sqrt[e*Sec[c + d*x]])/(d*e^4*Sqrt[a + I*a*Tan[c + d*x]]) - (((2*I)/7)*Sqrt[a + I*a*Tan[c + d*x]])/(d*(e*Sec[c + d*x])^(7/2)) - (((16*I)/35)*Sqrt[a + I*a*Tan[c + d*x]])/(d*e^2*(e*Sec[c + d*x])^(3/2))","A",4,3,30,0.1000,1,"{3497, 3502, 3488}"
400,1,453,0,0.5059284,"\int (e \sec (c+d x))^{5/2} (a+i a \tan (c+d x))^{3/2} \, dx","Int[(e*Sec[c + d*x])^(5/2)*(a + I*a*Tan[c + d*x])^(3/2),x]","\frac{7 i a^{3/2} e^{5/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{e} \sqrt{a+i a \tan (c+d x)}}{\sqrt{a} \sqrt{e \sec (c+d x)}}\right)}{8 \sqrt{2} d}-\frac{7 i a^{3/2} e^{5/2} \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt{e} \sqrt{a+i a \tan (c+d x)}}{\sqrt{a} \sqrt{e \sec (c+d x)}}\right)}{8 \sqrt{2} d}-\frac{7 i a^{3/2} e^{5/2} \log \left(-\frac{\sqrt{2} \sqrt{a} \sqrt{e} \sqrt{a+i a \tan (c+d x)}}{\sqrt{e \sec (c+d x)}}+\cos (c+d x) (a+i a \tan (c+d x))+a\right)}{16 \sqrt{2} d}+\frac{7 i a^{3/2} e^{5/2} \log \left(\frac{\sqrt{2} \sqrt{a} \sqrt{e} \sqrt{a+i a \tan (c+d x)}}{\sqrt{e \sec (c+d x)}}+\cos (c+d x) (a+i a \tan (c+d x))+a\right)}{16 \sqrt{2} d}+\frac{7 i a^2 (e \sec (c+d x))^{5/2}}{12 d \sqrt{a+i a \tan (c+d x)}}-\frac{7 i a e^2 \sqrt{a+i a \tan (c+d x)} \sqrt{e \sec (c+d x)}}{8 d}+\frac{i a \sqrt{a+i a \tan (c+d x)} (e \sec (c+d x))^{5/2}}{3 d}","\frac{7 i a^{3/2} e^{5/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{e} \sqrt{a+i a \tan (c+d x)}}{\sqrt{a} \sqrt{e \sec (c+d x)}}\right)}{8 \sqrt{2} d}-\frac{7 i a^{3/2} e^{5/2} \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt{e} \sqrt{a+i a \tan (c+d x)}}{\sqrt{a} \sqrt{e \sec (c+d x)}}\right)}{8 \sqrt{2} d}-\frac{7 i a^{3/2} e^{5/2} \log \left(-\frac{\sqrt{2} \sqrt{a} \sqrt{e} \sqrt{a+i a \tan (c+d x)}}{\sqrt{e \sec (c+d x)}}+\cos (c+d x) (a+i a \tan (c+d x))+a\right)}{16 \sqrt{2} d}+\frac{7 i a^{3/2} e^{5/2} \log \left(\frac{\sqrt{2} \sqrt{a} \sqrt{e} \sqrt{a+i a \tan (c+d x)}}{\sqrt{e \sec (c+d x)}}+\cos (c+d x) (a+i a \tan (c+d x))+a\right)}{16 \sqrt{2} d}+\frac{7 i a^2 (e \sec (c+d x))^{5/2}}{12 d \sqrt{a+i a \tan (c+d x)}}-\frac{7 i a e^2 \sqrt{a+i a \tan (c+d x)} \sqrt{e \sec (c+d x)}}{8 d}+\frac{i a \sqrt{a+i a \tan (c+d x)} (e \sec (c+d x))^{5/2}}{3 d}",1,"(((7*I)/8)*a^(3/2)*e^(5/2)*ArcTan[1 - (Sqrt[2]*Sqrt[e]*Sqrt[a + I*a*Tan[c + d*x]])/(Sqrt[a]*Sqrt[e*Sec[c + d*x]])])/(Sqrt[2]*d) - (((7*I)/8)*a^(3/2)*e^(5/2)*ArcTan[1 + (Sqrt[2]*Sqrt[e]*Sqrt[a + I*a*Tan[c + d*x]])/(Sqrt[a]*Sqrt[e*Sec[c + d*x]])])/(Sqrt[2]*d) - (((7*I)/16)*a^(3/2)*e^(5/2)*Log[a - (Sqrt[2]*Sqrt[a]*Sqrt[e]*Sqrt[a + I*a*Tan[c + d*x]])/Sqrt[e*Sec[c + d*x]] + Cos[c + d*x]*(a + I*a*Tan[c + d*x])])/(Sqrt[2]*d) + (((7*I)/16)*a^(3/2)*e^(5/2)*Log[a + (Sqrt[2]*Sqrt[a]*Sqrt[e]*Sqrt[a + I*a*Tan[c + d*x]])/Sqrt[e*Sec[c + d*x]] + Cos[c + d*x]*(a + I*a*Tan[c + d*x])])/(Sqrt[2]*d) + (((7*I)/12)*a^2*(e*Sec[c + d*x])^(5/2))/(d*Sqrt[a + I*a*Tan[c + d*x]]) - (((7*I)/8)*a*e^2*Sqrt[e*Sec[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]])/d + ((I/3)*a*(e*Sec[c + d*x])^(5/2)*Sqrt[a + I*a*Tan[c + d*x]])/d","A",13,9,30,0.3000,1,"{3498, 3501, 3495, 297, 1162, 617, 204, 1165, 628}"
401,1,571,0,0.5428182,"\int (e \sec (c+d x))^{3/2} (a+i a \tan (c+d x))^{3/2} \, dx","Int[(e*Sec[c + d*x])^(3/2)*(a + I*a*Tan[c + d*x])^(3/2),x]","-\frac{5 i a^{5/2} e^{3/2} \sec (c+d x) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{e} \sqrt{a-i a \tan (c+d x)}}{\sqrt{a} \sqrt{e \sec (c+d x)}}\right)}{4 \sqrt{2} d \sqrt{a-i a \tan (c+d x)} \sqrt{a+i a \tan (c+d x)}}+\frac{5 i a^{5/2} e^{3/2} \sec (c+d x) \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt{e} \sqrt{a-i a \tan (c+d x)}}{\sqrt{a} \sqrt{e \sec (c+d x)}}\right)}{4 \sqrt{2} d \sqrt{a-i a \tan (c+d x)} \sqrt{a+i a \tan (c+d x)}}+\frac{5 i a^{5/2} e^{3/2} \sec (c+d x) \log \left(-\frac{\sqrt{2} \sqrt{a} \sqrt{e} \sqrt{a-i a \tan (c+d x)}}{\sqrt{e \sec (c+d x)}}+\cos (c+d x) (a-i a \tan (c+d x))+a\right)}{8 \sqrt{2} d \sqrt{a-i a \tan (c+d x)} \sqrt{a+i a \tan (c+d x)}}-\frac{5 i a^{5/2} e^{3/2} \sec (c+d x) \log \left(\frac{\sqrt{2} \sqrt{a} \sqrt{e} \sqrt{a-i a \tan (c+d x)}}{\sqrt{e \sec (c+d x)}}+\cos (c+d x) (a-i a \tan (c+d x))+a\right)}{8 \sqrt{2} d \sqrt{a-i a \tan (c+d x)} \sqrt{a+i a \tan (c+d x)}}+\frac{5 i a^2 (e \sec (c+d x))^{3/2}}{4 d \sqrt{a+i a \tan (c+d x)}}+\frac{i a \sqrt{a+i a \tan (c+d x)} (e \sec (c+d x))^{3/2}}{2 d}","-\frac{5 i a^{5/2} e^{3/2} \sec (c+d x) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{e} \sqrt{a-i a \tan (c+d x)}}{\sqrt{a} \sqrt{e \sec (c+d x)}}\right)}{4 \sqrt{2} d \sqrt{a-i a \tan (c+d x)} \sqrt{a+i a \tan (c+d x)}}+\frac{5 i a^{5/2} e^{3/2} \sec (c+d x) \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt{e} \sqrt{a-i a \tan (c+d x)}}{\sqrt{a} \sqrt{e \sec (c+d x)}}\right)}{4 \sqrt{2} d \sqrt{a-i a \tan (c+d x)} \sqrt{a+i a \tan (c+d x)}}+\frac{5 i a^{5/2} e^{3/2} \sec (c+d x) \log \left(-\frac{\sqrt{2} \sqrt{a} \sqrt{e} \sqrt{a-i a \tan (c+d x)}}{\sqrt{e \sec (c+d x)}}+\cos (c+d x) (a-i a \tan (c+d x))+a\right)}{8 \sqrt{2} d \sqrt{a-i a \tan (c+d x)} \sqrt{a+i a \tan (c+d x)}}-\frac{5 i a^{5/2} e^{3/2} \sec (c+d x) \log \left(\frac{\sqrt{2} \sqrt{a} \sqrt{e} \sqrt{a-i a \tan (c+d x)}}{\sqrt{e \sec (c+d x)}}+\cos (c+d x) (a-i a \tan (c+d x))+a\right)}{8 \sqrt{2} d \sqrt{a-i a \tan (c+d x)} \sqrt{a+i a \tan (c+d x)}}+\frac{5 i a^2 (e \sec (c+d x))^{3/2}}{4 d \sqrt{a+i a \tan (c+d x)}}+\frac{i a \sqrt{a+i a \tan (c+d x)} (e \sec (c+d x))^{3/2}}{2 d}",1,"(((5*I)/4)*a^2*(e*Sec[c + d*x])^(3/2))/(d*Sqrt[a + I*a*Tan[c + d*x]]) - (((5*I)/4)*a^(5/2)*e^(3/2)*ArcTan[1 - (Sqrt[2]*Sqrt[e]*Sqrt[a - I*a*Tan[c + d*x]])/(Sqrt[a]*Sqrt[e*Sec[c + d*x]])]*Sec[c + d*x])/(Sqrt[2]*d*Sqrt[a - I*a*Tan[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]]) + (((5*I)/4)*a^(5/2)*e^(3/2)*ArcTan[1 + (Sqrt[2]*Sqrt[e]*Sqrt[a - I*a*Tan[c + d*x]])/(Sqrt[a]*Sqrt[e*Sec[c + d*x]])]*Sec[c + d*x])/(Sqrt[2]*d*Sqrt[a - I*a*Tan[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]]) + (((5*I)/8)*a^(5/2)*e^(3/2)*Log[a - (Sqrt[2]*Sqrt[a]*Sqrt[e]*Sqrt[a - I*a*Tan[c + d*x]])/Sqrt[e*Sec[c + d*x]] + Cos[c + d*x]*(a - I*a*Tan[c + d*x])]*Sec[c + d*x])/(Sqrt[2]*d*Sqrt[a - I*a*Tan[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]]) - (((5*I)/8)*a^(5/2)*e^(3/2)*Log[a + (Sqrt[2]*Sqrt[a]*Sqrt[e]*Sqrt[a - I*a*Tan[c + d*x]])/Sqrt[e*Sec[c + d*x]] + Cos[c + d*x]*(a - I*a*Tan[c + d*x])]*Sec[c + d*x])/(Sqrt[2]*d*Sqrt[a - I*a*Tan[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]]) + ((I/2)*a*(e*Sec[c + d*x])^(3/2)*Sqrt[a + I*a*Tan[c + d*x]])/d","A",13,9,30,0.3000,1,"{3498, 3499, 3495, 297, 1162, 617, 204, 1165, 628}"
402,1,364,0,0.3151205,"\int \sqrt{e \sec (c+d x)} (a+i a \tan (c+d x))^{3/2} \, dx","Int[Sqrt[e*Sec[c + d*x]]*(a + I*a*Tan[c + d*x])^(3/2),x]","\frac{3 i a^{3/2} \sqrt{e} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{e} \sqrt{a+i a \tan (c+d x)}}{\sqrt{a} \sqrt{e \sec (c+d x)}}\right)}{\sqrt{2} d}-\frac{3 i a^{3/2} \sqrt{e} \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt{e} \sqrt{a+i a \tan (c+d x)}}{\sqrt{a} \sqrt{e \sec (c+d x)}}\right)}{\sqrt{2} d}-\frac{3 i a^{3/2} \sqrt{e} \log \left(-\frac{\sqrt{2} \sqrt{a} \sqrt{e} \sqrt{a+i a \tan (c+d x)}}{\sqrt{e \sec (c+d x)}}+\cos (c+d x) (a+i a \tan (c+d x))+a\right)}{2 \sqrt{2} d}+\frac{3 i a^{3/2} \sqrt{e} \log \left(\frac{\sqrt{2} \sqrt{a} \sqrt{e} \sqrt{a+i a \tan (c+d x)}}{\sqrt{e \sec (c+d x)}}+\cos (c+d x) (a+i a \tan (c+d x))+a\right)}{2 \sqrt{2} d}+\frac{i a \sqrt{a+i a \tan (c+d x)} \sqrt{e \sec (c+d x)}}{d}","\frac{3 i a^{3/2} \sqrt{e} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{e} \sqrt{a+i a \tan (c+d x)}}{\sqrt{a} \sqrt{e \sec (c+d x)}}\right)}{\sqrt{2} d}-\frac{3 i a^{3/2} \sqrt{e} \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt{e} \sqrt{a+i a \tan (c+d x)}}{\sqrt{a} \sqrt{e \sec (c+d x)}}\right)}{\sqrt{2} d}-\frac{3 i a^{3/2} \sqrt{e} \log \left(-\frac{\sqrt{2} \sqrt{a} \sqrt{e} \sqrt{a+i a \tan (c+d x)}}{\sqrt{e \sec (c+d x)}}+\cos (c+d x) (a+i a \tan (c+d x))+a\right)}{2 \sqrt{2} d}+\frac{3 i a^{3/2} \sqrt{e} \log \left(\frac{\sqrt{2} \sqrt{a} \sqrt{e} \sqrt{a+i a \tan (c+d x)}}{\sqrt{e \sec (c+d x)}}+\cos (c+d x) (a+i a \tan (c+d x))+a\right)}{2 \sqrt{2} d}+\frac{i a \sqrt{a+i a \tan (c+d x)} \sqrt{e \sec (c+d x)}}{d}",1,"((3*I)*a^(3/2)*Sqrt[e]*ArcTan[1 - (Sqrt[2]*Sqrt[e]*Sqrt[a + I*a*Tan[c + d*x]])/(Sqrt[a]*Sqrt[e*Sec[c + d*x]])])/(Sqrt[2]*d) - ((3*I)*a^(3/2)*Sqrt[e]*ArcTan[1 + (Sqrt[2]*Sqrt[e]*Sqrt[a + I*a*Tan[c + d*x]])/(Sqrt[a]*Sqrt[e*Sec[c + d*x]])])/(Sqrt[2]*d) - (((3*I)/2)*a^(3/2)*Sqrt[e]*Log[a - (Sqrt[2]*Sqrt[a]*Sqrt[e]*Sqrt[a + I*a*Tan[c + d*x]])/Sqrt[e*Sec[c + d*x]] + Cos[c + d*x]*(a + I*a*Tan[c + d*x])])/(Sqrt[2]*d) + (((3*I)/2)*a^(3/2)*Sqrt[e]*Log[a + (Sqrt[2]*Sqrt[a]*Sqrt[e]*Sqrt[a + I*a*Tan[c + d*x]])/Sqrt[e*Sec[c + d*x]] + Cos[c + d*x]*(a + I*a*Tan[c + d*x])])/(Sqrt[2]*d) + (I*a*Sqrt[e*Sec[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]])/d","A",11,8,30,0.2667,1,"{3498, 3495, 297, 1162, 617, 204, 1165, 628}"
403,1,520,0,0.4338013,"\int \frac{(a+i a \tan (c+d x))^{3/2}}{\sqrt{e \sec (c+d x)}} \, dx","Int[(a + I*a*Tan[c + d*x])^(3/2)/Sqrt[e*Sec[c + d*x]],x]","\frac{i \sqrt{2} a^{5/2} \sec (c+d x) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{e} \sqrt{a-i a \tan (c+d x)}}{\sqrt{a} \sqrt{e \sec (c+d x)}}\right)}{d \sqrt{e} \sqrt{a-i a \tan (c+d x)} \sqrt{a+i a \tan (c+d x)}}-\frac{i \sqrt{2} a^{5/2} \sec (c+d x) \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt{e} \sqrt{a-i a \tan (c+d x)}}{\sqrt{a} \sqrt{e \sec (c+d x)}}\right)}{d \sqrt{e} \sqrt{a-i a \tan (c+d x)} \sqrt{a+i a \tan (c+d x)}}-\frac{i a^{5/2} \sec (c+d x) \log \left(-\frac{\sqrt{2} \sqrt{a} \sqrt{e} \sqrt{a-i a \tan (c+d x)}}{\sqrt{e \sec (c+d x)}}+\cos (c+d x) (a-i a \tan (c+d x))+a\right)}{\sqrt{2} d \sqrt{e} \sqrt{a-i a \tan (c+d x)} \sqrt{a+i a \tan (c+d x)}}+\frac{i a^{5/2} \sec (c+d x) \log \left(\frac{\sqrt{2} \sqrt{a} \sqrt{e} \sqrt{a-i a \tan (c+d x)}}{\sqrt{e \sec (c+d x)}}+\cos (c+d x) (a-i a \tan (c+d x))+a\right)}{\sqrt{2} d \sqrt{e} \sqrt{a-i a \tan (c+d x)} \sqrt{a+i a \tan (c+d x)}}-\frac{4 i a \sqrt{a+i a \tan (c+d x)}}{d \sqrt{e \sec (c+d x)}}","\frac{i \sqrt{2} a^{5/2} \sec (c+d x) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{e} \sqrt{a-i a \tan (c+d x)}}{\sqrt{a} \sqrt{e \sec (c+d x)}}\right)}{d \sqrt{e} \sqrt{a-i a \tan (c+d x)} \sqrt{a+i a \tan (c+d x)}}-\frac{i \sqrt{2} a^{5/2} \sec (c+d x) \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt{e} \sqrt{a-i a \tan (c+d x)}}{\sqrt{a} \sqrt{e \sec (c+d x)}}\right)}{d \sqrt{e} \sqrt{a-i a \tan (c+d x)} \sqrt{a+i a \tan (c+d x)}}-\frac{i a^{5/2} \sec (c+d x) \log \left(-\frac{\sqrt{2} \sqrt{a} \sqrt{e} \sqrt{a-i a \tan (c+d x)}}{\sqrt{e \sec (c+d x)}}+\cos (c+d x) (a-i a \tan (c+d x))+a\right)}{\sqrt{2} d \sqrt{e} \sqrt{a-i a \tan (c+d x)} \sqrt{a+i a \tan (c+d x)}}+\frac{i a^{5/2} \sec (c+d x) \log \left(\frac{\sqrt{2} \sqrt{a} \sqrt{e} \sqrt{a-i a \tan (c+d x)}}{\sqrt{e \sec (c+d x)}}+\cos (c+d x) (a-i a \tan (c+d x))+a\right)}{\sqrt{2} d \sqrt{e} \sqrt{a-i a \tan (c+d x)} \sqrt{a+i a \tan (c+d x)}}-\frac{4 i a \sqrt{a+i a \tan (c+d x)}}{d \sqrt{e \sec (c+d x)}}",1,"(I*Sqrt[2]*a^(5/2)*ArcTan[1 - (Sqrt[2]*Sqrt[e]*Sqrt[a - I*a*Tan[c + d*x]])/(Sqrt[a]*Sqrt[e*Sec[c + d*x]])]*Sec[c + d*x])/(d*Sqrt[e]*Sqrt[a - I*a*Tan[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]]) - (I*Sqrt[2]*a^(5/2)*ArcTan[1 + (Sqrt[2]*Sqrt[e]*Sqrt[a - I*a*Tan[c + d*x]])/(Sqrt[a]*Sqrt[e*Sec[c + d*x]])]*Sec[c + d*x])/(d*Sqrt[e]*Sqrt[a - I*a*Tan[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]]) - (I*a^(5/2)*Log[a - (Sqrt[2]*Sqrt[a]*Sqrt[e]*Sqrt[a - I*a*Tan[c + d*x]])/Sqrt[e*Sec[c + d*x]] + Cos[c + d*x]*(a - I*a*Tan[c + d*x])]*Sec[c + d*x])/(Sqrt[2]*d*Sqrt[e]*Sqrt[a - I*a*Tan[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]]) + (I*a^(5/2)*Log[a + (Sqrt[2]*Sqrt[a]*Sqrt[e]*Sqrt[a - I*a*Tan[c + d*x]])/Sqrt[e*Sec[c + d*x]] + Cos[c + d*x]*(a - I*a*Tan[c + d*x])]*Sec[c + d*x])/(Sqrt[2]*d*Sqrt[e]*Sqrt[a - I*a*Tan[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]]) - ((4*I)*a*Sqrt[a + I*a*Tan[c + d*x]])/(d*Sqrt[e*Sec[c + d*x]])","A",12,9,30,0.3000,1,"{3496, 3499, 3495, 297, 1162, 617, 204, 1165, 628}"
404,1,38,0,0.0914253,"\int \frac{(a+i a \tan (c+d x))^{3/2}}{(e \sec (c+d x))^{3/2}} \, dx","Int[(a + I*a*Tan[c + d*x])^(3/2)/(e*Sec[c + d*x])^(3/2),x]","-\frac{2 i (a+i a \tan (c+d x))^{3/2}}{3 d (e \sec (c+d x))^{3/2}}","-\frac{2 i (a+i a \tan (c+d x))^{3/2}}{3 d (e \sec (c+d x))^{3/2}}",1,"(((-2*I)/3)*(a + I*a*Tan[c + d*x])^(3/2))/(d*(e*Sec[c + d*x])^(3/2))","A",1,1,30,0.03333,1,"{3488}"
405,1,81,0,0.1580462,"\int \frac{(a+i a \tan (c+d x))^{3/2}}{(e \sec (c+d x))^{5/2}} \, dx","Int[(a + I*a*Tan[c + d*x])^(3/2)/(e*Sec[c + d*x])^(5/2),x]","-\frac{4 i a \sqrt{a+i a \tan (c+d x)}}{5 d e^2 \sqrt{e \sec (c+d x)}}-\frac{2 i (a+i a \tan (c+d x))^{3/2}}{5 d (e \sec (c+d x))^{5/2}}","-\frac{4 i a \sqrt{a+i a \tan (c+d x)}}{5 d e^2 \sqrt{e \sec (c+d x)}}-\frac{2 i (a+i a \tan (c+d x))^{3/2}}{5 d (e \sec (c+d x))^{5/2}}",1,"(((-4*I)/5)*a*Sqrt[a + I*a*Tan[c + d*x]])/(d*e^2*Sqrt[e*Sec[c + d*x]]) - (((2*I)/5)*(a + I*a*Tan[c + d*x])^(3/2))/(d*(e*Sec[c + d*x])^(5/2))","A",2,2,30,0.06667,1,"{3497, 3488}"
406,1,125,0,0.2296689,"\int \frac{(a+i a \tan (c+d x))^{3/2}}{(e \sec (c+d x))^{7/2}} \, dx","Int[(a + I*a*Tan[c + d*x])^(3/2)/(e*Sec[c + d*x])^(7/2),x]","\frac{16 i a^2 \sqrt{e \sec (c+d x)}}{21 d e^4 \sqrt{a+i a \tan (c+d x)}}-\frac{8 i a \sqrt{a+i a \tan (c+d x)}}{21 d e^2 (e \sec (c+d x))^{3/2}}-\frac{2 i (a+i a \tan (c+d x))^{3/2}}{7 d (e \sec (c+d x))^{7/2}}","\frac{16 i a^2 \sqrt{e \sec (c+d x)}}{21 d e^4 \sqrt{a+i a \tan (c+d x)}}-\frac{8 i a \sqrt{a+i a \tan (c+d x)}}{21 d e^2 (e \sec (c+d x))^{3/2}}-\frac{2 i (a+i a \tan (c+d x))^{3/2}}{7 d (e \sec (c+d x))^{7/2}}",1,"(((16*I)/21)*a^2*Sqrt[e*Sec[c + d*x]])/(d*e^4*Sqrt[a + I*a*Tan[c + d*x]]) - (((8*I)/21)*a*Sqrt[a + I*a*Tan[c + d*x]])/(d*e^2*(e*Sec[c + d*x])^(3/2)) - (((2*I)/7)*(a + I*a*Tan[c + d*x])^(3/2))/(d*(e*Sec[c + d*x])^(7/2))","A",3,2,30,0.06667,1,"{3497, 3488}"
407,1,167,0,0.2855463,"\int \frac{(a+i a \tan (c+d x))^{3/2}}{(e \sec (c+d x))^{9/2}} \, dx","Int[(a + I*a*Tan[c + d*x])^(3/2)/(e*Sec[c + d*x])^(9/2),x]","\frac{16 i a^2}{45 d e^4 \sqrt{a+i a \tan (c+d x)} \sqrt{e \sec (c+d x)}}-\frac{32 i a \sqrt{a+i a \tan (c+d x)}}{45 d e^4 \sqrt{e \sec (c+d x)}}-\frac{4 i a \sqrt{a+i a \tan (c+d x)}}{15 d e^2 (e \sec (c+d x))^{5/2}}-\frac{2 i (a+i a \tan (c+d x))^{3/2}}{9 d (e \sec (c+d x))^{9/2}}","\frac{16 i a^2}{45 d e^4 \sqrt{a+i a \tan (c+d x)} \sqrt{e \sec (c+d x)}}-\frac{32 i a \sqrt{a+i a \tan (c+d x)}}{45 d e^4 \sqrt{e \sec (c+d x)}}-\frac{4 i a \sqrt{a+i a \tan (c+d x)}}{15 d e^2 (e \sec (c+d x))^{5/2}}-\frac{2 i (a+i a \tan (c+d x))^{3/2}}{9 d (e \sec (c+d x))^{9/2}}",1,"(((16*I)/45)*a^2)/(d*e^4*Sqrt[e*Sec[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]]) - (((4*I)/15)*a*Sqrt[a + I*a*Tan[c + d*x]])/(d*e^2*(e*Sec[c + d*x])^(5/2)) - (((32*I)/45)*a*Sqrt[a + I*a*Tan[c + d*x]])/(d*e^4*Sqrt[e*Sec[c + d*x]]) - (((2*I)/9)*(a + I*a*Tan[c + d*x])^(3/2))/(d*(e*Sec[c + d*x])^(9/2))","A",4,3,30,0.1000,1,"{3497, 3502, 3488}"
408,1,612,0,0.6897866,"\int (e \sec (c+d x))^{3/2} (a+i a \tan (c+d x))^{5/2} \, dx","Int[(e*Sec[c + d*x])^(3/2)*(a + I*a*Tan[c + d*x])^(5/2),x]","-\frac{15 i a^{7/2} e^{3/2} \sec (c+d x) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{e} \sqrt{a-i a \tan (c+d x)}}{\sqrt{a} \sqrt{e \sec (c+d x)}}\right)}{8 \sqrt{2} d \sqrt{a-i a \tan (c+d x)} \sqrt{a+i a \tan (c+d x)}}+\frac{15 i a^{7/2} e^{3/2} \sec (c+d x) \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt{e} \sqrt{a-i a \tan (c+d x)}}{\sqrt{a} \sqrt{e \sec (c+d x)}}\right)}{8 \sqrt{2} d \sqrt{a-i a \tan (c+d x)} \sqrt{a+i a \tan (c+d x)}}+\frac{15 i a^{7/2} e^{3/2} \sec (c+d x) \log \left(-\frac{\sqrt{2} \sqrt{a} \sqrt{e} \sqrt{a-i a \tan (c+d x)}}{\sqrt{e \sec (c+d x)}}+\cos (c+d x) (a-i a \tan (c+d x))+a\right)}{16 \sqrt{2} d \sqrt{a-i a \tan (c+d x)} \sqrt{a+i a \tan (c+d x)}}-\frac{15 i a^{7/2} e^{3/2} \sec (c+d x) \log \left(\frac{\sqrt{2} \sqrt{a} \sqrt{e} \sqrt{a-i a \tan (c+d x)}}{\sqrt{e \sec (c+d x)}}+\cos (c+d x) (a-i a \tan (c+d x))+a\right)}{16 \sqrt{2} d \sqrt{a-i a \tan (c+d x)} \sqrt{a+i a \tan (c+d x)}}+\frac{15 i a^3 (e \sec (c+d x))^{3/2}}{8 d \sqrt{a+i a \tan (c+d x)}}+\frac{3 i a^2 \sqrt{a+i a \tan (c+d x)} (e \sec (c+d x))^{3/2}}{4 d}+\frac{i a (a+i a \tan (c+d x))^{3/2} (e \sec (c+d x))^{3/2}}{3 d}","-\frac{15 i a^{7/2} e^{3/2} \sec (c+d x) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{e} \sqrt{a-i a \tan (c+d x)}}{\sqrt{a} \sqrt{e \sec (c+d x)}}\right)}{8 \sqrt{2} d \sqrt{a-i a \tan (c+d x)} \sqrt{a+i a \tan (c+d x)}}+\frac{15 i a^{7/2} e^{3/2} \sec (c+d x) \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt{e} \sqrt{a-i a \tan (c+d x)}}{\sqrt{a} \sqrt{e \sec (c+d x)}}\right)}{8 \sqrt{2} d \sqrt{a-i a \tan (c+d x)} \sqrt{a+i a \tan (c+d x)}}+\frac{15 i a^{7/2} e^{3/2} \sec (c+d x) \log \left(-\frac{\sqrt{2} \sqrt{a} \sqrt{e} \sqrt{a-i a \tan (c+d x)}}{\sqrt{e \sec (c+d x)}}+\cos (c+d x) (a-i a \tan (c+d x))+a\right)}{16 \sqrt{2} d \sqrt{a-i a \tan (c+d x)} \sqrt{a+i a \tan (c+d x)}}-\frac{15 i a^{7/2} e^{3/2} \sec (c+d x) \log \left(\frac{\sqrt{2} \sqrt{a} \sqrt{e} \sqrt{a-i a \tan (c+d x)}}{\sqrt{e \sec (c+d x)}}+\cos (c+d x) (a-i a \tan (c+d x))+a\right)}{16 \sqrt{2} d \sqrt{a-i a \tan (c+d x)} \sqrt{a+i a \tan (c+d x)}}+\frac{15 i a^3 (e \sec (c+d x))^{3/2}}{8 d \sqrt{a+i a \tan (c+d x)}}+\frac{3 i a^2 \sqrt{a+i a \tan (c+d x)} (e \sec (c+d x))^{3/2}}{4 d}+\frac{i a (a+i a \tan (c+d x))^{3/2} (e \sec (c+d x))^{3/2}}{3 d}",1,"(((15*I)/8)*a^3*(e*Sec[c + d*x])^(3/2))/(d*Sqrt[a + I*a*Tan[c + d*x]]) - (((15*I)/8)*a^(7/2)*e^(3/2)*ArcTan[1 - (Sqrt[2]*Sqrt[e]*Sqrt[a - I*a*Tan[c + d*x]])/(Sqrt[a]*Sqrt[e*Sec[c + d*x]])]*Sec[c + d*x])/(Sqrt[2]*d*Sqrt[a - I*a*Tan[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]]) + (((15*I)/8)*a^(7/2)*e^(3/2)*ArcTan[1 + (Sqrt[2]*Sqrt[e]*Sqrt[a - I*a*Tan[c + d*x]])/(Sqrt[a]*Sqrt[e*Sec[c + d*x]])]*Sec[c + d*x])/(Sqrt[2]*d*Sqrt[a - I*a*Tan[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]]) + (((15*I)/16)*a^(7/2)*e^(3/2)*Log[a - (Sqrt[2]*Sqrt[a]*Sqrt[e]*Sqrt[a - I*a*Tan[c + d*x]])/Sqrt[e*Sec[c + d*x]] + Cos[c + d*x]*(a - I*a*Tan[c + d*x])]*Sec[c + d*x])/(Sqrt[2]*d*Sqrt[a - I*a*Tan[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]]) - (((15*I)/16)*a^(7/2)*e^(3/2)*Log[a + (Sqrt[2]*Sqrt[a]*Sqrt[e]*Sqrt[a - I*a*Tan[c + d*x]])/Sqrt[e*Sec[c + d*x]] + Cos[c + d*x]*(a - I*a*Tan[c + d*x])]*Sec[c + d*x])/(Sqrt[2]*d*Sqrt[a - I*a*Tan[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]]) + (((3*I)/4)*a^2*(e*Sec[c + d*x])^(3/2)*Sqrt[a + I*a*Tan[c + d*x]])/d + ((I/3)*a*(e*Sec[c + d*x])^(3/2)*(a + I*a*Tan[c + d*x])^(3/2))/d","A",14,9,30,0.3000,1,"{3498, 3499, 3495, 297, 1162, 617, 204, 1165, 628}"
409,1,411,0,0.4532385,"\int \sqrt{e \sec (c+d x)} (a+i a \tan (c+d x))^{5/2} \, dx","Int[Sqrt[e*Sec[c + d*x]]*(a + I*a*Tan[c + d*x])^(5/2),x]","\frac{21 i a^{5/2} \sqrt{e} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{e} \sqrt{a+i a \tan (c+d x)}}{\sqrt{a} \sqrt{e \sec (c+d x)}}\right)}{4 \sqrt{2} d}-\frac{21 i a^{5/2} \sqrt{e} \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt{e} \sqrt{a+i a \tan (c+d x)}}{\sqrt{a} \sqrt{e \sec (c+d x)}}\right)}{4 \sqrt{2} d}+\frac{7 i a^2 \sqrt{a+i a \tan (c+d x)} \sqrt{e \sec (c+d x)}}{4 d}-\frac{21 i a^{5/2} \sqrt{e} \log \left(-\frac{\sqrt{2} \sqrt{a} \sqrt{e} \sqrt{a+i a \tan (c+d x)}}{\sqrt{e \sec (c+d x)}}+\cos (c+d x) (a+i a \tan (c+d x))+a\right)}{8 \sqrt{2} d}+\frac{21 i a^{5/2} \sqrt{e} \log \left(\frac{\sqrt{2} \sqrt{a} \sqrt{e} \sqrt{a+i a \tan (c+d x)}}{\sqrt{e \sec (c+d x)}}+\cos (c+d x) (a+i a \tan (c+d x))+a\right)}{8 \sqrt{2} d}+\frac{i a (a+i a \tan (c+d x))^{3/2} \sqrt{e \sec (c+d x)}}{2 d}","\frac{21 i a^{5/2} \sqrt{e} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{e} \sqrt{a+i a \tan (c+d x)}}{\sqrt{a} \sqrt{e \sec (c+d x)}}\right)}{4 \sqrt{2} d}-\frac{21 i a^{5/2} \sqrt{e} \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt{e} \sqrt{a+i a \tan (c+d x)}}{\sqrt{a} \sqrt{e \sec (c+d x)}}\right)}{4 \sqrt{2} d}+\frac{7 i a^2 \sqrt{a+i a \tan (c+d x)} \sqrt{e \sec (c+d x)}}{4 d}-\frac{21 i a^{5/2} \sqrt{e} \log \left(-\frac{\sqrt{2} \sqrt{a} \sqrt{e} \sqrt{a+i a \tan (c+d x)}}{\sqrt{e \sec (c+d x)}}+\cos (c+d x) (a+i a \tan (c+d x))+a\right)}{8 \sqrt{2} d}+\frac{21 i a^{5/2} \sqrt{e} \log \left(\frac{\sqrt{2} \sqrt{a} \sqrt{e} \sqrt{a+i a \tan (c+d x)}}{\sqrt{e \sec (c+d x)}}+\cos (c+d x) (a+i a \tan (c+d x))+a\right)}{8 \sqrt{2} d}+\frac{i a (a+i a \tan (c+d x))^{3/2} \sqrt{e \sec (c+d x)}}{2 d}",1,"(((21*I)/4)*a^(5/2)*Sqrt[e]*ArcTan[1 - (Sqrt[2]*Sqrt[e]*Sqrt[a + I*a*Tan[c + d*x]])/(Sqrt[a]*Sqrt[e*Sec[c + d*x]])])/(Sqrt[2]*d) - (((21*I)/4)*a^(5/2)*Sqrt[e]*ArcTan[1 + (Sqrt[2]*Sqrt[e]*Sqrt[a + I*a*Tan[c + d*x]])/(Sqrt[a]*Sqrt[e*Sec[c + d*x]])])/(Sqrt[2]*d) - (((21*I)/8)*a^(5/2)*Sqrt[e]*Log[a - (Sqrt[2]*Sqrt[a]*Sqrt[e]*Sqrt[a + I*a*Tan[c + d*x]])/Sqrt[e*Sec[c + d*x]] + Cos[c + d*x]*(a + I*a*Tan[c + d*x])])/(Sqrt[2]*d) + (((21*I)/8)*a^(5/2)*Sqrt[e]*Log[a + (Sqrt[2]*Sqrt[a]*Sqrt[e]*Sqrt[a + I*a*Tan[c + d*x]])/Sqrt[e*Sec[c + d*x]] + Cos[c + d*x]*(a + I*a*Tan[c + d*x])])/(Sqrt[2]*d) + (((7*I)/4)*a^2*Sqrt[e*Sec[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]])/d + ((I/2)*a*Sqrt[e*Sec[c + d*x]]*(a + I*a*Tan[c + d*x])^(3/2))/d","A",12,8,30,0.2667,1,"{3498, 3495, 297, 1162, 617, 204, 1165, 628}"
410,1,563,0,0.5750086,"\int \frac{(a+i a \tan (c+d x))^{5/2}}{\sqrt{e \sec (c+d x)}} \, dx","Int[(a + I*a*Tan[c + d*x])^(5/2)/Sqrt[e*Sec[c + d*x]],x]","\frac{5 i a^{7/2} \sec (c+d x) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{e} \sqrt{a-i a \tan (c+d x)}}{\sqrt{a} \sqrt{e \sec (c+d x)}}\right)}{\sqrt{2} d \sqrt{e} \sqrt{a-i a \tan (c+d x)} \sqrt{a+i a \tan (c+d x)}}-\frac{5 i a^{7/2} \sec (c+d x) \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt{e} \sqrt{a-i a \tan (c+d x)}}{\sqrt{a} \sqrt{e \sec (c+d x)}}\right)}{\sqrt{2} d \sqrt{e} \sqrt{a-i a \tan (c+d x)} \sqrt{a+i a \tan (c+d x)}}-\frac{10 i a^2 \sqrt{a+i a \tan (c+d x)}}{d \sqrt{e \sec (c+d x)}}-\frac{5 i a^{7/2} \sec (c+d x) \log \left(-\frac{\sqrt{2} \sqrt{a} \sqrt{e} \sqrt{a-i a \tan (c+d x)}}{\sqrt{e \sec (c+d x)}}+\cos (c+d x) (a-i a \tan (c+d x))+a\right)}{2 \sqrt{2} d \sqrt{e} \sqrt{a-i a \tan (c+d x)} \sqrt{a+i a \tan (c+d x)}}+\frac{5 i a^{7/2} \sec (c+d x) \log \left(\frac{\sqrt{2} \sqrt{a} \sqrt{e} \sqrt{a-i a \tan (c+d x)}}{\sqrt{e \sec (c+d x)}}+\cos (c+d x) (a-i a \tan (c+d x))+a\right)}{2 \sqrt{2} d \sqrt{e} \sqrt{a-i a \tan (c+d x)} \sqrt{a+i a \tan (c+d x)}}+\frac{i a (a+i a \tan (c+d x))^{3/2}}{d \sqrt{e \sec (c+d x)}}","\frac{5 i a^{7/2} \sec (c+d x) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{e} \sqrt{a-i a \tan (c+d x)}}{\sqrt{a} \sqrt{e \sec (c+d x)}}\right)}{\sqrt{2} d \sqrt{e} \sqrt{a-i a \tan (c+d x)} \sqrt{a+i a \tan (c+d x)}}-\frac{5 i a^{7/2} \sec (c+d x) \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt{e} \sqrt{a-i a \tan (c+d x)}}{\sqrt{a} \sqrt{e \sec (c+d x)}}\right)}{\sqrt{2} d \sqrt{e} \sqrt{a-i a \tan (c+d x)} \sqrt{a+i a \tan (c+d x)}}-\frac{10 i a^2 \sqrt{a+i a \tan (c+d x)}}{d \sqrt{e \sec (c+d x)}}-\frac{5 i a^{7/2} \sec (c+d x) \log \left(-\frac{\sqrt{2} \sqrt{a} \sqrt{e} \sqrt{a-i a \tan (c+d x)}}{\sqrt{e \sec (c+d x)}}+\cos (c+d x) (a-i a \tan (c+d x))+a\right)}{2 \sqrt{2} d \sqrt{e} \sqrt{a-i a \tan (c+d x)} \sqrt{a+i a \tan (c+d x)}}+\frac{5 i a^{7/2} \sec (c+d x) \log \left(\frac{\sqrt{2} \sqrt{a} \sqrt{e} \sqrt{a-i a \tan (c+d x)}}{\sqrt{e \sec (c+d x)}}+\cos (c+d x) (a-i a \tan (c+d x))+a\right)}{2 \sqrt{2} d \sqrt{e} \sqrt{a-i a \tan (c+d x)} \sqrt{a+i a \tan (c+d x)}}+\frac{i a (a+i a \tan (c+d x))^{3/2}}{d \sqrt{e \sec (c+d x)}}",1,"((5*I)*a^(7/2)*ArcTan[1 - (Sqrt[2]*Sqrt[e]*Sqrt[a - I*a*Tan[c + d*x]])/(Sqrt[a]*Sqrt[e*Sec[c + d*x]])]*Sec[c + d*x])/(Sqrt[2]*d*Sqrt[e]*Sqrt[a - I*a*Tan[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]]) - ((5*I)*a^(7/2)*ArcTan[1 + (Sqrt[2]*Sqrt[e]*Sqrt[a - I*a*Tan[c + d*x]])/(Sqrt[a]*Sqrt[e*Sec[c + d*x]])]*Sec[c + d*x])/(Sqrt[2]*d*Sqrt[e]*Sqrt[a - I*a*Tan[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]]) - (((5*I)/2)*a^(7/2)*Log[a - (Sqrt[2]*Sqrt[a]*Sqrt[e]*Sqrt[a - I*a*Tan[c + d*x]])/Sqrt[e*Sec[c + d*x]] + Cos[c + d*x]*(a - I*a*Tan[c + d*x])]*Sec[c + d*x])/(Sqrt[2]*d*Sqrt[e]*Sqrt[a - I*a*Tan[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]]) + (((5*I)/2)*a^(7/2)*Log[a + (Sqrt[2]*Sqrt[a]*Sqrt[e]*Sqrt[a - I*a*Tan[c + d*x]])/Sqrt[e*Sec[c + d*x]] + Cos[c + d*x]*(a - I*a*Tan[c + d*x])]*Sec[c + d*x])/(Sqrt[2]*d*Sqrt[e]*Sqrt[a - I*a*Tan[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]]) - ((10*I)*a^2*Sqrt[a + I*a*Tan[c + d*x]])/(d*Sqrt[e*Sec[c + d*x]]) + (I*a*(a + I*a*Tan[c + d*x])^(3/2))/(d*Sqrt[e*Sec[c + d*x]])","A",13,10,30,0.3333,1,"{3498, 3496, 3499, 3495, 297, 1162, 617, 204, 1165, 628}"
411,1,362,0,0.3298074,"\int \frac{(a+i a \tan (c+d x))^{5/2}}{(e \sec (c+d x))^{3/2}} \, dx","Int[(a + I*a*Tan[c + d*x])^(5/2)/(e*Sec[c + d*x])^(3/2),x]","-\frac{i \sqrt{2} a^{5/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{e} \sqrt{a+i a \tan (c+d x)}}{\sqrt{a} \sqrt{e \sec (c+d x)}}\right)}{d e^{3/2}}+\frac{i \sqrt{2} a^{5/2} \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt{e} \sqrt{a+i a \tan (c+d x)}}{\sqrt{a} \sqrt{e \sec (c+d x)}}\right)}{d e^{3/2}}+\frac{i a^{5/2} \log \left(-\frac{\sqrt{2} \sqrt{a} \sqrt{e} \sqrt{a+i a \tan (c+d x)}}{\sqrt{e \sec (c+d x)}}+\cos (c+d x) (a+i a \tan (c+d x))+a\right)}{\sqrt{2} d e^{3/2}}-\frac{i a^{5/2} \log \left(\frac{\sqrt{2} \sqrt{a} \sqrt{e} \sqrt{a+i a \tan (c+d x)}}{\sqrt{e \sec (c+d x)}}+\cos (c+d x) (a+i a \tan (c+d x))+a\right)}{\sqrt{2} d e^{3/2}}-\frac{4 i a (a+i a \tan (c+d x))^{3/2}}{3 d (e \sec (c+d x))^{3/2}}","-\frac{i \sqrt{2} a^{5/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{e} \sqrt{a+i a \tan (c+d x)}}{\sqrt{a} \sqrt{e \sec (c+d x)}}\right)}{d e^{3/2}}+\frac{i \sqrt{2} a^{5/2} \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt{e} \sqrt{a+i a \tan (c+d x)}}{\sqrt{a} \sqrt{e \sec (c+d x)}}\right)}{d e^{3/2}}+\frac{i a^{5/2} \log \left(-\frac{\sqrt{2} \sqrt{a} \sqrt{e} \sqrt{a+i a \tan (c+d x)}}{\sqrt{e \sec (c+d x)}}+\cos (c+d x) (a+i a \tan (c+d x))+a\right)}{\sqrt{2} d e^{3/2}}-\frac{i a^{5/2} \log \left(\frac{\sqrt{2} \sqrt{a} \sqrt{e} \sqrt{a+i a \tan (c+d x)}}{\sqrt{e \sec (c+d x)}}+\cos (c+d x) (a+i a \tan (c+d x))+a\right)}{\sqrt{2} d e^{3/2}}-\frac{4 i a (a+i a \tan (c+d x))^{3/2}}{3 d (e \sec (c+d x))^{3/2}}",1,"((-I)*Sqrt[2]*a^(5/2)*ArcTan[1 - (Sqrt[2]*Sqrt[e]*Sqrt[a + I*a*Tan[c + d*x]])/(Sqrt[a]*Sqrt[e*Sec[c + d*x]])])/(d*e^(3/2)) + (I*Sqrt[2]*a^(5/2)*ArcTan[1 + (Sqrt[2]*Sqrt[e]*Sqrt[a + I*a*Tan[c + d*x]])/(Sqrt[a]*Sqrt[e*Sec[c + d*x]])])/(d*e^(3/2)) + (I*a^(5/2)*Log[a - (Sqrt[2]*Sqrt[a]*Sqrt[e]*Sqrt[a + I*a*Tan[c + d*x]])/Sqrt[e*Sec[c + d*x]] + Cos[c + d*x]*(a + I*a*Tan[c + d*x])])/(Sqrt[2]*d*e^(3/2)) - (I*a^(5/2)*Log[a + (Sqrt[2]*Sqrt[a]*Sqrt[e]*Sqrt[a + I*a*Tan[c + d*x]])/Sqrt[e*Sec[c + d*x]] + Cos[c + d*x]*(a + I*a*Tan[c + d*x])])/(Sqrt[2]*d*e^(3/2)) - (((4*I)/3)*a*(a + I*a*Tan[c + d*x])^(3/2))/(d*(e*Sec[c + d*x])^(3/2))","A",11,8,30,0.2667,1,"{3496, 3495, 297, 1162, 617, 204, 1165, 628}"
412,1,38,0,0.0747706,"\int \frac{(a+i a \tan (c+d x))^{5/2}}{(e \sec (c+d x))^{5/2}} \, dx","Int[(a + I*a*Tan[c + d*x])^(5/2)/(e*Sec[c + d*x])^(5/2),x]","-\frac{2 i (a+i a \tan (c+d x))^{5/2}}{5 d (e \sec (c+d x))^{5/2}}","-\frac{2 i (a+i a \tan (c+d x))^{5/2}}{5 d (e \sec (c+d x))^{5/2}}",1,"(((-2*I)/5)*(a + I*a*Tan[c + d*x])^(5/2))/(d*(e*Sec[c + d*x])^(5/2))","A",1,1,30,0.03333,1,"{3488}"
413,1,81,0,0.1537572,"\int \frac{(a+i a \tan (c+d x))^{5/2}}{(e \sec (c+d x))^{7/2}} \, dx","Int[(a + I*a*Tan[c + d*x])^(5/2)/(e*Sec[c + d*x])^(7/2),x]","-\frac{4 i a (a+i a \tan (c+d x))^{3/2}}{21 d e^2 (e \sec (c+d x))^{3/2}}-\frac{2 i (a+i a \tan (c+d x))^{5/2}}{7 d (e \sec (c+d x))^{7/2}}","-\frac{4 i a (a+i a \tan (c+d x))^{3/2}}{21 d e^2 (e \sec (c+d x))^{3/2}}-\frac{2 i (a+i a \tan (c+d x))^{5/2}}{7 d (e \sec (c+d x))^{7/2}}",1,"(((-4*I)/21)*a*(a + I*a*Tan[c + d*x])^(3/2))/(d*e^2*(e*Sec[c + d*x])^(3/2)) - (((2*I)/7)*(a + I*a*Tan[c + d*x])^(5/2))/(d*(e*Sec[c + d*x])^(7/2))","A",2,2,30,0.06667,1,"{3497, 3488}"
414,1,125,0,0.2215434,"\int \frac{(a+i a \tan (c+d x))^{5/2}}{(e \sec (c+d x))^{9/2}} \, dx","Int[(a + I*a*Tan[c + d*x])^(5/2)/(e*Sec[c + d*x])^(9/2),x]","-\frac{16 i a^2 \sqrt{a+i a \tan (c+d x)}}{45 d e^4 \sqrt{e \sec (c+d x)}}-\frac{8 i a (a+i a \tan (c+d x))^{3/2}}{45 d e^2 (e \sec (c+d x))^{5/2}}-\frac{2 i (a+i a \tan (c+d x))^{5/2}}{9 d (e \sec (c+d x))^{9/2}}","-\frac{16 i a^2 \sqrt{a+i a \tan (c+d x)}}{45 d e^4 \sqrt{e \sec (c+d x)}}-\frac{8 i a (a+i a \tan (c+d x))^{3/2}}{45 d e^2 (e \sec (c+d x))^{5/2}}-\frac{2 i (a+i a \tan (c+d x))^{5/2}}{9 d (e \sec (c+d x))^{9/2}}",1,"(((-16*I)/45)*a^2*Sqrt[a + I*a*Tan[c + d*x]])/(d*e^4*Sqrt[e*Sec[c + d*x]]) - (((8*I)/45)*a*(a + I*a*Tan[c + d*x])^(3/2))/(d*e^2*(e*Sec[c + d*x])^(5/2)) - (((2*I)/9)*(a + I*a*Tan[c + d*x])^(5/2))/(d*(e*Sec[c + d*x])^(9/2))","A",3,2,30,0.06667,1,"{3497, 3488}"
415,1,169,0,0.311941,"\int \frac{(a+i a \tan (c+d x))^{5/2}}{(e \sec (c+d x))^{11/2}} \, dx","Int[(a + I*a*Tan[c + d*x])^(5/2)/(e*Sec[c + d*x])^(11/2),x]","\frac{32 i a^3 \sqrt{e \sec (c+d x)}}{77 d e^6 \sqrt{a+i a \tan (c+d x)}}-\frac{16 i a^2 \sqrt{a+i a \tan (c+d x)}}{77 d e^4 (e \sec (c+d x))^{3/2}}-\frac{12 i a (a+i a \tan (c+d x))^{3/2}}{77 d e^2 (e \sec (c+d x))^{7/2}}-\frac{2 i (a+i a \tan (c+d x))^{5/2}}{11 d (e \sec (c+d x))^{11/2}}","\frac{32 i a^3 \sqrt{e \sec (c+d x)}}{77 d e^6 \sqrt{a+i a \tan (c+d x)}}-\frac{16 i a^2 \sqrt{a+i a \tan (c+d x)}}{77 d e^4 (e \sec (c+d x))^{3/2}}-\frac{12 i a (a+i a \tan (c+d x))^{3/2}}{77 d e^2 (e \sec (c+d x))^{7/2}}-\frac{2 i (a+i a \tan (c+d x))^{5/2}}{11 d (e \sec (c+d x))^{11/2}}",1,"(((32*I)/77)*a^3*Sqrt[e*Sec[c + d*x]])/(d*e^6*Sqrt[a + I*a*Tan[c + d*x]]) - (((16*I)/77)*a^2*Sqrt[a + I*a*Tan[c + d*x]])/(d*e^4*(e*Sec[c + d*x])^(3/2)) - (((12*I)/77)*a*(a + I*a*Tan[c + d*x])^(3/2))/(d*e^2*(e*Sec[c + d*x])^(7/2)) - (((2*I)/11)*(a + I*a*Tan[c + d*x])^(5/2))/(d*(e*Sec[c + d*x])^(11/2))","A",4,2,30,0.06667,1,"{3497, 3488}"
416,1,369,0,0.3076874,"\int \frac{(e \sec (c+d x))^{5/2}}{\sqrt{a+i a \tan (c+d x)}} \, dx","Int[(e*Sec[c + d*x])^(5/2)/Sqrt[a + I*a*Tan[c + d*x]],x]","\frac{i e^{5/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{e} \sqrt{a+i a \tan (c+d x)}}{\sqrt{a} \sqrt{e \sec (c+d x)}}\right)}{\sqrt{2} \sqrt{a} d}-\frac{i e^{5/2} \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt{e} \sqrt{a+i a \tan (c+d x)}}{\sqrt{a} \sqrt{e \sec (c+d x)}}\right)}{\sqrt{2} \sqrt{a} d}-\frac{i e^2 \sqrt{a+i a \tan (c+d x)} \sqrt{e \sec (c+d x)}}{a d}-\frac{i e^{5/2} \log \left(-\frac{\sqrt{2} \sqrt{a} \sqrt{e} \sqrt{a+i a \tan (c+d x)}}{\sqrt{e \sec (c+d x)}}+\cos (c+d x) (a+i a \tan (c+d x))+a\right)}{2 \sqrt{2} \sqrt{a} d}+\frac{i e^{5/2} \log \left(\frac{\sqrt{2} \sqrt{a} \sqrt{e} \sqrt{a+i a \tan (c+d x)}}{\sqrt{e \sec (c+d x)}}+\cos (c+d x) (a+i a \tan (c+d x))+a\right)}{2 \sqrt{2} \sqrt{a} d}","\frac{i e^{5/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{e} \sqrt{a+i a \tan (c+d x)}}{\sqrt{a} \sqrt{e \sec (c+d x)}}\right)}{\sqrt{2} \sqrt{a} d}-\frac{i e^{5/2} \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt{e} \sqrt{a+i a \tan (c+d x)}}{\sqrt{a} \sqrt{e \sec (c+d x)}}\right)}{\sqrt{2} \sqrt{a} d}-\frac{i e^2 \sqrt{a+i a \tan (c+d x)} \sqrt{e \sec (c+d x)}}{a d}-\frac{i e^{5/2} \log \left(-\frac{\sqrt{2} \sqrt{a} \sqrt{e} \sqrt{a+i a \tan (c+d x)}}{\sqrt{e \sec (c+d x)}}+\cos (c+d x) (a+i a \tan (c+d x))+a\right)}{2 \sqrt{2} \sqrt{a} d}+\frac{i e^{5/2} \log \left(\frac{\sqrt{2} \sqrt{a} \sqrt{e} \sqrt{a+i a \tan (c+d x)}}{\sqrt{e \sec (c+d x)}}+\cos (c+d x) (a+i a \tan (c+d x))+a\right)}{2 \sqrt{2} \sqrt{a} d}",1,"(I*e^(5/2)*ArcTan[1 - (Sqrt[2]*Sqrt[e]*Sqrt[a + I*a*Tan[c + d*x]])/(Sqrt[a]*Sqrt[e*Sec[c + d*x]])])/(Sqrt[2]*Sqrt[a]*d) - (I*e^(5/2)*ArcTan[1 + (Sqrt[2]*Sqrt[e]*Sqrt[a + I*a*Tan[c + d*x]])/(Sqrt[a]*Sqrt[e*Sec[c + d*x]])])/(Sqrt[2]*Sqrt[a]*d) - ((I/2)*e^(5/2)*Log[a - (Sqrt[2]*Sqrt[a]*Sqrt[e]*Sqrt[a + I*a*Tan[c + d*x]])/Sqrt[e*Sec[c + d*x]] + Cos[c + d*x]*(a + I*a*Tan[c + d*x])])/(Sqrt[2]*Sqrt[a]*d) + ((I/2)*e^(5/2)*Log[a + (Sqrt[2]*Sqrt[a]*Sqrt[e]*Sqrt[a + I*a*Tan[c + d*x]])/Sqrt[e*Sec[c + d*x]] + Cos[c + d*x]*(a + I*a*Tan[c + d*x])])/(Sqrt[2]*Sqrt[a]*d) - (I*e^2*Sqrt[e*Sec[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]])/(a*d)","A",11,8,30,0.2667,1,"{3501, 3495, 297, 1162, 617, 204, 1165, 628}"
417,1,483,0,0.3527193,"\int \frac{(e \sec (c+d x))^{3/2}}{\sqrt{a+i a \tan (c+d x)}} \, dx","Int[(e*Sec[c + d*x])^(3/2)/Sqrt[a + I*a*Tan[c + d*x]],x]","-\frac{i \sqrt{2} \sqrt{a} e^{3/2} \sec (c+d x) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{e} \sqrt{a-i a \tan (c+d x)}}{\sqrt{a} \sqrt{e \sec (c+d x)}}\right)}{d \sqrt{a-i a \tan (c+d x)} \sqrt{a+i a \tan (c+d x)}}+\frac{i \sqrt{2} \sqrt{a} e^{3/2} \sec (c+d x) \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt{e} \sqrt{a-i a \tan (c+d x)}}{\sqrt{a} \sqrt{e \sec (c+d x)}}\right)}{d \sqrt{a-i a \tan (c+d x)} \sqrt{a+i a \tan (c+d x)}}+\frac{i \sqrt{a} e^{3/2} \sec (c+d x) \log \left(-\frac{\sqrt{2} \sqrt{a} \sqrt{e} \sqrt{a-i a \tan (c+d x)}}{\sqrt{e \sec (c+d x)}}+\cos (c+d x) (a-i a \tan (c+d x))+a\right)}{\sqrt{2} d \sqrt{a-i a \tan (c+d x)} \sqrt{a+i a \tan (c+d x)}}-\frac{i \sqrt{a} e^{3/2} \sec (c+d x) \log \left(\frac{\sqrt{2} \sqrt{a} \sqrt{e} \sqrt{a-i a \tan (c+d x)}}{\sqrt{e \sec (c+d x)}}+\cos (c+d x) (a-i a \tan (c+d x))+a\right)}{\sqrt{2} d \sqrt{a-i a \tan (c+d x)} \sqrt{a+i a \tan (c+d x)}}","-\frac{i \sqrt{2} \sqrt{a} e^{3/2} \sec (c+d x) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{e} \sqrt{a-i a \tan (c+d x)}}{\sqrt{a} \sqrt{e \sec (c+d x)}}\right)}{d \sqrt{a-i a \tan (c+d x)} \sqrt{a+i a \tan (c+d x)}}+\frac{i \sqrt{2} \sqrt{a} e^{3/2} \sec (c+d x) \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt{e} \sqrt{a-i a \tan (c+d x)}}{\sqrt{a} \sqrt{e \sec (c+d x)}}\right)}{d \sqrt{a-i a \tan (c+d x)} \sqrt{a+i a \tan (c+d x)}}+\frac{i \sqrt{a} e^{3/2} \sec (c+d x) \log \left(-\frac{\sqrt{2} \sqrt{a} \sqrt{e} \sqrt{a-i a \tan (c+d x)}}{\sqrt{e \sec (c+d x)}}+\cos (c+d x) (a-i a \tan (c+d x))+a\right)}{\sqrt{2} d \sqrt{a-i a \tan (c+d x)} \sqrt{a+i a \tan (c+d x)}}-\frac{i \sqrt{a} e^{3/2} \sec (c+d x) \log \left(\frac{\sqrt{2} \sqrt{a} \sqrt{e} \sqrt{a-i a \tan (c+d x)}}{\sqrt{e \sec (c+d x)}}+\cos (c+d x) (a-i a \tan (c+d x))+a\right)}{\sqrt{2} d \sqrt{a-i a \tan (c+d x)} \sqrt{a+i a \tan (c+d x)}}",1,"((-I)*Sqrt[2]*Sqrt[a]*e^(3/2)*ArcTan[1 - (Sqrt[2]*Sqrt[e]*Sqrt[a - I*a*Tan[c + d*x]])/(Sqrt[a]*Sqrt[e*Sec[c + d*x]])]*Sec[c + d*x])/(d*Sqrt[a - I*a*Tan[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]]) + (I*Sqrt[2]*Sqrt[a]*e^(3/2)*ArcTan[1 + (Sqrt[2]*Sqrt[e]*Sqrt[a - I*a*Tan[c + d*x]])/(Sqrt[a]*Sqrt[e*Sec[c + d*x]])]*Sec[c + d*x])/(d*Sqrt[a - I*a*Tan[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]]) + (I*Sqrt[a]*e^(3/2)*Log[a - (Sqrt[2]*Sqrt[a]*Sqrt[e]*Sqrt[a - I*a*Tan[c + d*x]])/Sqrt[e*Sec[c + d*x]] + Cos[c + d*x]*(a - I*a*Tan[c + d*x])]*Sec[c + d*x])/(Sqrt[2]*d*Sqrt[a - I*a*Tan[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]]) - (I*Sqrt[a]*e^(3/2)*Log[a + (Sqrt[2]*Sqrt[a]*Sqrt[e]*Sqrt[a - I*a*Tan[c + d*x]])/Sqrt[e*Sec[c + d*x]] + Cos[c + d*x]*(a - I*a*Tan[c + d*x])]*Sec[c + d*x])/(Sqrt[2]*d*Sqrt[a - I*a*Tan[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]])","A",11,8,30,0.2667,1,"{3499, 3495, 297, 1162, 617, 204, 1165, 628}"
418,1,36,0,0.068347,"\int \frac{\sqrt{e \sec (c+d x)}}{\sqrt{a+i a \tan (c+d x)}} \, dx","Int[Sqrt[e*Sec[c + d*x]]/Sqrt[a + I*a*Tan[c + d*x]],x]","\frac{2 i \sqrt{e \sec (c+d x)}}{d \sqrt{a+i a \tan (c+d x)}}","\frac{2 i \sqrt{e \sec (c+d x)}}{d \sqrt{a+i a \tan (c+d x)}}",1,"((2*I)*Sqrt[e*Sec[c + d*x]])/(d*Sqrt[a + I*a*Tan[c + d*x]])","A",1,1,30,0.03333,1,"{3488}"
419,1,80,0,0.1383184,"\int \frac{1}{\sqrt{e \sec (c+d x)} \sqrt{a+i a \tan (c+d x)}} \, dx","Int[1/(Sqrt[e*Sec[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]]),x]","\frac{2 i}{3 d \sqrt{a+i a \tan (c+d x)} \sqrt{e \sec (c+d x)}}-\frac{4 i \sqrt{a+i a \tan (c+d x)}}{3 a d \sqrt{e \sec (c+d x)}}","\frac{2 i}{3 d \sqrt{a+i a \tan (c+d x)} \sqrt{e \sec (c+d x)}}-\frac{4 i \sqrt{a+i a \tan (c+d x)}}{3 a d \sqrt{e \sec (c+d x)}}",1,"((2*I)/3)/(d*Sqrt[e*Sec[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]]) - (((4*I)/3)*Sqrt[a + I*a*Tan[c + d*x]])/(a*d*Sqrt[e*Sec[c + d*x]])","A",2,2,30,0.06667,1,"{3502, 3488}"
420,1,121,0,0.220198,"\int \frac{1}{(e \sec (c+d x))^{3/2} \sqrt{a+i a \tan (c+d x)}} \, dx","Int[1/((e*Sec[c + d*x])^(3/2)*Sqrt[a + I*a*Tan[c + d*x]]),x]","\frac{16 i \sqrt{e \sec (c+d x)}}{15 d e^2 \sqrt{a+i a \tan (c+d x)}}-\frac{8 i \sqrt{a+i a \tan (c+d x)}}{15 a d (e \sec (c+d x))^{3/2}}+\frac{2 i}{5 d \sqrt{a+i a \tan (c+d x)} (e \sec (c+d x))^{3/2}}","\frac{16 i \sqrt{e \sec (c+d x)}}{15 d e^2 \sqrt{a+i a \tan (c+d x)}}-\frac{8 i \sqrt{a+i a \tan (c+d x)}}{15 a d (e \sec (c+d x))^{3/2}}+\frac{2 i}{5 d \sqrt{a+i a \tan (c+d x)} (e \sec (c+d x))^{3/2}}",1,"((2*I)/5)/(d*(e*Sec[c + d*x])^(3/2)*Sqrt[a + I*a*Tan[c + d*x]]) + (((16*I)/15)*Sqrt[e*Sec[c + d*x]])/(d*e^2*Sqrt[a + I*a*Tan[c + d*x]]) - (((8*I)/15)*Sqrt[a + I*a*Tan[c + d*x]])/(a*d*(e*Sec[c + d*x])^(3/2))","A",3,3,30,0.1000,1,"{3502, 3497, 3488}"
421,1,165,0,0.2906966,"\int \frac{1}{(e \sec (c+d x))^{5/2} \sqrt{a+i a \tan (c+d x)}} \, dx","Int[1/((e*Sec[c + d*x])^(5/2)*Sqrt[a + I*a*Tan[c + d*x]]),x]","-\frac{32 i \sqrt{a+i a \tan (c+d x)}}{35 a d e^2 \sqrt{e \sec (c+d x)}}+\frac{16 i}{35 d e^2 \sqrt{a+i a \tan (c+d x)} \sqrt{e \sec (c+d x)}}-\frac{12 i \sqrt{a+i a \tan (c+d x)}}{35 a d (e \sec (c+d x))^{5/2}}+\frac{2 i}{7 d \sqrt{a+i a \tan (c+d x)} (e \sec (c+d x))^{5/2}}","-\frac{32 i \sqrt{a+i a \tan (c+d x)}}{35 a d e^2 \sqrt{e \sec (c+d x)}}+\frac{16 i}{35 d e^2 \sqrt{a+i a \tan (c+d x)} \sqrt{e \sec (c+d x)}}-\frac{12 i \sqrt{a+i a \tan (c+d x)}}{35 a d (e \sec (c+d x))^{5/2}}+\frac{2 i}{7 d \sqrt{a+i a \tan (c+d x)} (e \sec (c+d x))^{5/2}}",1,"((2*I)/7)/(d*(e*Sec[c + d*x])^(5/2)*Sqrt[a + I*a*Tan[c + d*x]]) + ((16*I)/35)/(d*e^2*Sqrt[e*Sec[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]]) - (((12*I)/35)*Sqrt[a + I*a*Tan[c + d*x]])/(a*d*(e*Sec[c + d*x])^(5/2)) - (((32*I)/35)*Sqrt[a + I*a*Tan[c + d*x]])/(a*d*e^2*Sqrt[e*Sec[c + d*x]])","A",4,3,30,0.1000,1,"{3502, 3497, 3488}"
422,1,206,0,0.3870391,"\int \frac{1}{(e \sec (c+d x))^{7/2} \sqrt{a+i a \tan (c+d x)}} \, dx","Int[1/((e*Sec[c + d*x])^(7/2)*Sqrt[a + I*a*Tan[c + d*x]]),x]","\frac{256 i \sqrt{e \sec (c+d x)}}{315 d e^4 \sqrt{a+i a \tan (c+d x)}}-\frac{128 i \sqrt{a+i a \tan (c+d x)}}{315 a d e^2 (e \sec (c+d x))^{3/2}}+\frac{32 i}{105 d e^2 \sqrt{a+i a \tan (c+d x)} (e \sec (c+d x))^{3/2}}-\frac{16 i \sqrt{a+i a \tan (c+d x)}}{63 a d (e \sec (c+d x))^{7/2}}+\frac{2 i}{9 d \sqrt{a+i a \tan (c+d x)} (e \sec (c+d x))^{7/2}}","\frac{256 i \sqrt{e \sec (c+d x)}}{315 d e^4 \sqrt{a+i a \tan (c+d x)}}-\frac{128 i \sqrt{a+i a \tan (c+d x)}}{315 a d e^2 (e \sec (c+d x))^{3/2}}+\frac{32 i}{105 d e^2 \sqrt{a+i a \tan (c+d x)} (e \sec (c+d x))^{3/2}}-\frac{16 i \sqrt{a+i a \tan (c+d x)}}{63 a d (e \sec (c+d x))^{7/2}}+\frac{2 i}{9 d \sqrt{a+i a \tan (c+d x)} (e \sec (c+d x))^{7/2}}",1,"((2*I)/9)/(d*(e*Sec[c + d*x])^(7/2)*Sqrt[a + I*a*Tan[c + d*x]]) + ((32*I)/105)/(d*e^2*(e*Sec[c + d*x])^(3/2)*Sqrt[a + I*a*Tan[c + d*x]]) + (((256*I)/315)*Sqrt[e*Sec[c + d*x]])/(d*e^4*Sqrt[a + I*a*Tan[c + d*x]]) - (((16*I)/63)*Sqrt[a + I*a*Tan[c + d*x]])/(a*d*(e*Sec[c + d*x])^(7/2)) - (((128*I)/315)*Sqrt[a + I*a*Tan[c + d*x]])/(a*d*e^2*(e*Sec[c + d*x])^(3/2))","A",5,3,30,0.1000,1,"{3502, 3497, 3488}"
423,1,529,0,0.5673202,"\int \frac{(e \sec (c+d x))^{7/2}}{(a+i a \tan (c+d x))^{3/2}} \, dx","Int[(e*Sec[c + d*x])^(7/2)/(a + I*a*Tan[c + d*x])^(3/2),x]","-\frac{3 i e^{7/2} \sec (c+d x) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{e} \sqrt{a-i a \tan (c+d x)}}{\sqrt{a} \sqrt{e \sec (c+d x)}}\right)}{\sqrt{2} \sqrt{a} d \sqrt{a-i a \tan (c+d x)} \sqrt{a+i a \tan (c+d x)}}+\frac{3 i e^{7/2} \sec (c+d x) \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt{e} \sqrt{a-i a \tan (c+d x)}}{\sqrt{a} \sqrt{e \sec (c+d x)}}\right)}{\sqrt{2} \sqrt{a} d \sqrt{a-i a \tan (c+d x)} \sqrt{a+i a \tan (c+d x)}}-\frac{i e^2 (e \sec (c+d x))^{3/2}}{a d \sqrt{a+i a \tan (c+d x)}}+\frac{3 i e^{7/2} \sec (c+d x) \log \left(-\frac{\sqrt{2} \sqrt{a} \sqrt{e} \sqrt{a-i a \tan (c+d x)}}{\sqrt{e \sec (c+d x)}}+\cos (c+d x) (a-i a \tan (c+d x))+a\right)}{2 \sqrt{2} \sqrt{a} d \sqrt{a-i a \tan (c+d x)} \sqrt{a+i a \tan (c+d x)}}-\frac{3 i e^{7/2} \sec (c+d x) \log \left(\frac{\sqrt{2} \sqrt{a} \sqrt{e} \sqrt{a-i a \tan (c+d x)}}{\sqrt{e \sec (c+d x)}}+\cos (c+d x) (a-i a \tan (c+d x))+a\right)}{2 \sqrt{2} \sqrt{a} d \sqrt{a-i a \tan (c+d x)} \sqrt{a+i a \tan (c+d x)}}","-\frac{3 i e^{7/2} \sec (c+d x) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{e} \sqrt{a-i a \tan (c+d x)}}{\sqrt{a} \sqrt{e \sec (c+d x)}}\right)}{\sqrt{2} \sqrt{a} d \sqrt{a-i a \tan (c+d x)} \sqrt{a+i a \tan (c+d x)}}+\frac{3 i e^{7/2} \sec (c+d x) \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt{e} \sqrt{a-i a \tan (c+d x)}}{\sqrt{a} \sqrt{e \sec (c+d x)}}\right)}{\sqrt{2} \sqrt{a} d \sqrt{a-i a \tan (c+d x)} \sqrt{a+i a \tan (c+d x)}}-\frac{i e^2 (e \sec (c+d x))^{3/2}}{a d \sqrt{a+i a \tan (c+d x)}}+\frac{3 i e^{7/2} \sec (c+d x) \log \left(-\frac{\sqrt{2} \sqrt{a} \sqrt{e} \sqrt{a-i a \tan (c+d x)}}{\sqrt{e \sec (c+d x)}}+\cos (c+d x) (a-i a \tan (c+d x))+a\right)}{2 \sqrt{2} \sqrt{a} d \sqrt{a-i a \tan (c+d x)} \sqrt{a+i a \tan (c+d x)}}-\frac{3 i e^{7/2} \sec (c+d x) \log \left(\frac{\sqrt{2} \sqrt{a} \sqrt{e} \sqrt{a-i a \tan (c+d x)}}{\sqrt{e \sec (c+d x)}}+\cos (c+d x) (a-i a \tan (c+d x))+a\right)}{2 \sqrt{2} \sqrt{a} d \sqrt{a-i a \tan (c+d x)} \sqrt{a+i a \tan (c+d x)}}",1,"((-I)*e^2*(e*Sec[c + d*x])^(3/2))/(a*d*Sqrt[a + I*a*Tan[c + d*x]]) - ((3*I)*e^(7/2)*ArcTan[1 - (Sqrt[2]*Sqrt[e]*Sqrt[a - I*a*Tan[c + d*x]])/(Sqrt[a]*Sqrt[e*Sec[c + d*x]])]*Sec[c + d*x])/(Sqrt[2]*Sqrt[a]*d*Sqrt[a - I*a*Tan[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]]) + ((3*I)*e^(7/2)*ArcTan[1 + (Sqrt[2]*Sqrt[e]*Sqrt[a - I*a*Tan[c + d*x]])/(Sqrt[a]*Sqrt[e*Sec[c + d*x]])]*Sec[c + d*x])/(Sqrt[2]*Sqrt[a]*d*Sqrt[a - I*a*Tan[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]]) + (((3*I)/2)*e^(7/2)*Log[a - (Sqrt[2]*Sqrt[a]*Sqrt[e]*Sqrt[a - I*a*Tan[c + d*x]])/Sqrt[e*Sec[c + d*x]] + Cos[c + d*x]*(a - I*a*Tan[c + d*x])]*Sec[c + d*x])/(Sqrt[2]*Sqrt[a]*d*Sqrt[a - I*a*Tan[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]]) - (((3*I)/2)*e^(7/2)*Log[a + (Sqrt[2]*Sqrt[a]*Sqrt[e]*Sqrt[a - I*a*Tan[c + d*x]])/Sqrt[e*Sec[c + d*x]] + Cos[c + d*x]*(a - I*a*Tan[c + d*x])]*Sec[c + d*x])/(Sqrt[2]*Sqrt[a]*d*Sqrt[a - I*a*Tan[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]])","A",13,10,30,0.3333,1,"{3500, 3498, 3499, 3495, 297, 1162, 617, 204, 1165, 628}"
424,1,365,0,0.3158778,"\int \frac{(e \sec (c+d x))^{5/2}}{(a+i a \tan (c+d x))^{3/2}} \, dx","Int[(e*Sec[c + d*x])^(5/2)/(a + I*a*Tan[c + d*x])^(3/2),x]","-\frac{i \sqrt{2} e^{5/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{e} \sqrt{a+i a \tan (c+d x)}}{\sqrt{a} \sqrt{e \sec (c+d x)}}\right)}{a^{3/2} d}+\frac{i \sqrt{2} e^{5/2} \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt{e} \sqrt{a+i a \tan (c+d x)}}{\sqrt{a} \sqrt{e \sec (c+d x)}}\right)}{a^{3/2} d}+\frac{i e^{5/2} \log \left(-\frac{\sqrt{2} \sqrt{a} \sqrt{e} \sqrt{a+i a \tan (c+d x)}}{\sqrt{e \sec (c+d x)}}+\cos (c+d x) (a+i a \tan (c+d x))+a\right)}{\sqrt{2} a^{3/2} d}-\frac{i e^{5/2} \log \left(\frac{\sqrt{2} \sqrt{a} \sqrt{e} \sqrt{a+i a \tan (c+d x)}}{\sqrt{e \sec (c+d x)}}+\cos (c+d x) (a+i a \tan (c+d x))+a\right)}{\sqrt{2} a^{3/2} d}+\frac{4 i e^2 \sqrt{e \sec (c+d x)}}{a d \sqrt{a+i a \tan (c+d x)}}","-\frac{i \sqrt{2} e^{5/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{e} \sqrt{a+i a \tan (c+d x)}}{\sqrt{a} \sqrt{e \sec (c+d x)}}\right)}{a^{3/2} d}+\frac{i \sqrt{2} e^{5/2} \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt{e} \sqrt{a+i a \tan (c+d x)}}{\sqrt{a} \sqrt{e \sec (c+d x)}}\right)}{a^{3/2} d}+\frac{i e^{5/2} \log \left(-\frac{\sqrt{2} \sqrt{a} \sqrt{e} \sqrt{a+i a \tan (c+d x)}}{\sqrt{e \sec (c+d x)}}+\cos (c+d x) (a+i a \tan (c+d x))+a\right)}{\sqrt{2} a^{3/2} d}-\frac{i e^{5/2} \log \left(\frac{\sqrt{2} \sqrt{a} \sqrt{e} \sqrt{a+i a \tan (c+d x)}}{\sqrt{e \sec (c+d x)}}+\cos (c+d x) (a+i a \tan (c+d x))+a\right)}{\sqrt{2} a^{3/2} d}+\frac{4 i e^2 \sqrt{e \sec (c+d x)}}{a d \sqrt{a+i a \tan (c+d x)}}",1,"((-I)*Sqrt[2]*e^(5/2)*ArcTan[1 - (Sqrt[2]*Sqrt[e]*Sqrt[a + I*a*Tan[c + d*x]])/(Sqrt[a]*Sqrt[e*Sec[c + d*x]])])/(a^(3/2)*d) + (I*Sqrt[2]*e^(5/2)*ArcTan[1 + (Sqrt[2]*Sqrt[e]*Sqrt[a + I*a*Tan[c + d*x]])/(Sqrt[a]*Sqrt[e*Sec[c + d*x]])])/(a^(3/2)*d) + (I*e^(5/2)*Log[a - (Sqrt[2]*Sqrt[a]*Sqrt[e]*Sqrt[a + I*a*Tan[c + d*x]])/Sqrt[e*Sec[c + d*x]] + Cos[c + d*x]*(a + I*a*Tan[c + d*x])])/(Sqrt[2]*a^(3/2)*d) - (I*e^(5/2)*Log[a + (Sqrt[2]*Sqrt[a]*Sqrt[e]*Sqrt[a + I*a*Tan[c + d*x]])/Sqrt[e*Sec[c + d*x]] + Cos[c + d*x]*(a + I*a*Tan[c + d*x])])/(Sqrt[2]*a^(3/2)*d) + ((4*I)*e^2*Sqrt[e*Sec[c + d*x]])/(a*d*Sqrt[a + I*a*Tan[c + d*x]])","A",11,8,30,0.2667,1,"{3500, 3495, 297, 1162, 617, 204, 1165, 628}"
425,1,38,0,0.0758921,"\int \frac{(e \sec (c+d x))^{3/2}}{(a+i a \tan (c+d x))^{3/2}} \, dx","Int[(e*Sec[c + d*x])^(3/2)/(a + I*a*Tan[c + d*x])^(3/2),x]","\frac{2 i (e \sec (c+d x))^{3/2}}{3 d (a+i a \tan (c+d x))^{3/2}}","\frac{2 i (e \sec (c+d x))^{3/2}}{3 d (a+i a \tan (c+d x))^{3/2}}",1,"(((2*I)/3)*(e*Sec[c + d*x])^(3/2))/(d*(a + I*a*Tan[c + d*x])^(3/2))","A",1,1,30,0.03333,1,"{3488}"
426,1,80,0,0.1449433,"\int \frac{\sqrt{e \sec (c+d x)}}{(a+i a \tan (c+d x))^{3/2}} \, dx","Int[Sqrt[e*Sec[c + d*x]]/(a + I*a*Tan[c + d*x])^(3/2),x]","\frac{4 i \sqrt{e \sec (c+d x)}}{5 a d \sqrt{a+i a \tan (c+d x)}}+\frac{2 i \sqrt{e \sec (c+d x)}}{5 d (a+i a \tan (c+d x))^{3/2}}","\frac{4 i \sqrt{e \sec (c+d x)}}{5 a d \sqrt{a+i a \tan (c+d x)}}+\frac{2 i \sqrt{e \sec (c+d x)}}{5 d (a+i a \tan (c+d x))^{3/2}}",1,"(((2*I)/5)*Sqrt[e*Sec[c + d*x]])/(d*(a + I*a*Tan[c + d*x])^(3/2)) + (((4*I)/5)*Sqrt[e*Sec[c + d*x]])/(a*d*Sqrt[a + I*a*Tan[c + d*x]])","A",2,2,30,0.06667,1,"{3502, 3488}"
427,1,121,0,0.2092315,"\int \frac{1}{\sqrt{e \sec (c+d x)} (a+i a \tan (c+d x))^{3/2}} \, dx","Int[1/(Sqrt[e*Sec[c + d*x]]*(a + I*a*Tan[c + d*x])^(3/2)),x]","-\frac{16 i \sqrt{a+i a \tan (c+d x)}}{21 a^2 d \sqrt{e \sec (c+d x)}}+\frac{8 i}{21 a d \sqrt{a+i a \tan (c+d x)} \sqrt{e \sec (c+d x)}}+\frac{2 i}{7 d (a+i a \tan (c+d x))^{3/2} \sqrt{e \sec (c+d x)}}","-\frac{16 i \sqrt{a+i a \tan (c+d x)}}{21 a^2 d \sqrt{e \sec (c+d x)}}+\frac{8 i}{21 a d \sqrt{a+i a \tan (c+d x)} \sqrt{e \sec (c+d x)}}+\frac{2 i}{7 d (a+i a \tan (c+d x))^{3/2} \sqrt{e \sec (c+d x)}}",1,"((2*I)/7)/(d*Sqrt[e*Sec[c + d*x]]*(a + I*a*Tan[c + d*x])^(3/2)) + ((8*I)/21)/(a*d*Sqrt[e*Sec[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]]) - (((16*I)/21)*Sqrt[a + I*a*Tan[c + d*x]])/(a^2*d*Sqrt[e*Sec[c + d*x]])","A",3,2,30,0.06667,1,"{3502, 3488}"
428,1,165,0,0.3057623,"\int \frac{1}{(e \sec (c+d x))^{3/2} (a+i a \tan (c+d x))^{3/2}} \, dx","Int[1/((e*Sec[c + d*x])^(3/2)*(a + I*a*Tan[c + d*x])^(3/2)),x]","-\frac{16 i \sqrt{a+i a \tan (c+d x)}}{45 a^2 d (e \sec (c+d x))^{3/2}}+\frac{32 i \sqrt{e \sec (c+d x)}}{45 a d e^2 \sqrt{a+i a \tan (c+d x)}}+\frac{4 i}{15 a d \sqrt{a+i a \tan (c+d x)} (e \sec (c+d x))^{3/2}}+\frac{2 i}{9 d (a+i a \tan (c+d x))^{3/2} (e \sec (c+d x))^{3/2}}","-\frac{16 i \sqrt{a+i a \tan (c+d x)}}{45 a^2 d (e \sec (c+d x))^{3/2}}+\frac{32 i \sqrt{e \sec (c+d x)}}{45 a d e^2 \sqrt{a+i a \tan (c+d x)}}+\frac{4 i}{15 a d \sqrt{a+i a \tan (c+d x)} (e \sec (c+d x))^{3/2}}+\frac{2 i}{9 d (a+i a \tan (c+d x))^{3/2} (e \sec (c+d x))^{3/2}}",1,"((2*I)/9)/(d*(e*Sec[c + d*x])^(3/2)*(a + I*a*Tan[c + d*x])^(3/2)) + ((4*I)/15)/(a*d*(e*Sec[c + d*x])^(3/2)*Sqrt[a + I*a*Tan[c + d*x]]) + (((32*I)/45)*Sqrt[e*Sec[c + d*x]])/(a*d*e^2*Sqrt[a + I*a*Tan[c + d*x]]) - (((16*I)/45)*Sqrt[a + I*a*Tan[c + d*x]])/(a^2*d*(e*Sec[c + d*x])^(3/2))","A",4,3,30,0.1000,1,"{3502, 3497, 3488}"
429,1,209,0,0.3925676,"\int \frac{1}{(e \sec (c+d x))^{5/2} (a+i a \tan (c+d x))^{3/2}} \, dx","Int[1/((e*Sec[c + d*x])^(5/2)*(a + I*a*Tan[c + d*x])^(3/2)),x]","-\frac{256 i \sqrt{a+i a \tan (c+d x)}}{385 a^2 d e^2 \sqrt{e \sec (c+d x)}}-\frac{96 i \sqrt{a+i a \tan (c+d x)}}{385 a^2 d (e \sec (c+d x))^{5/2}}+\frac{128 i}{385 a d e^2 \sqrt{a+i a \tan (c+d x)} \sqrt{e \sec (c+d x)}}+\frac{16 i}{77 a d \sqrt{a+i a \tan (c+d x)} (e \sec (c+d x))^{5/2}}+\frac{2 i}{11 d (a+i a \tan (c+d x))^{3/2} (e \sec (c+d x))^{5/2}}","-\frac{256 i \sqrt{a+i a \tan (c+d x)}}{385 a^2 d e^2 \sqrt{e \sec (c+d x)}}-\frac{96 i \sqrt{a+i a \tan (c+d x)}}{385 a^2 d (e \sec (c+d x))^{5/2}}+\frac{128 i}{385 a d e^2 \sqrt{a+i a \tan (c+d x)} \sqrt{e \sec (c+d x)}}+\frac{16 i}{77 a d \sqrt{a+i a \tan (c+d x)} (e \sec (c+d x))^{5/2}}+\frac{2 i}{11 d (a+i a \tan (c+d x))^{3/2} (e \sec (c+d x))^{5/2}}",1,"((2*I)/11)/(d*(e*Sec[c + d*x])^(5/2)*(a + I*a*Tan[c + d*x])^(3/2)) + ((16*I)/77)/(a*d*(e*Sec[c + d*x])^(5/2)*Sqrt[a + I*a*Tan[c + d*x]]) + ((128*I)/385)/(a*d*e^2*Sqrt[e*Sec[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]]) - (((96*I)/385)*Sqrt[a + I*a*Tan[c + d*x]])/(a^2*d*(e*Sec[c + d*x])^(5/2)) - (((256*I)/385)*Sqrt[a + I*a*Tan[c + d*x]])/(a^2*d*e^2*Sqrt[e*Sec[c + d*x]])","A",5,3,30,0.1000,1,"{3502, 3497, 3488}"
430,1,411,0,0.433811,"\int \frac{(e \sec (c+d x))^{9/2}}{(a+i a \tan (c+d x))^{5/2}} \, dx","Int[(e*Sec[c + d*x])^(9/2)/(a + I*a*Tan[c + d*x])^(5/2),x]","-\frac{5 i e^{9/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{e} \sqrt{a+i a \tan (c+d x)}}{\sqrt{a} \sqrt{e \sec (c+d x)}}\right)}{\sqrt{2} a^{5/2} d}+\frac{5 i e^{9/2} \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt{e} \sqrt{a+i a \tan (c+d x)}}{\sqrt{a} \sqrt{e \sec (c+d x)}}\right)}{\sqrt{2} a^{5/2} d}+\frac{5 i e^4 \sqrt{a+i a \tan (c+d x)} \sqrt{e \sec (c+d x)}}{a^3 d}+\frac{5 i e^{9/2} \log \left(-\frac{\sqrt{2} \sqrt{a} \sqrt{e} \sqrt{a+i a \tan (c+d x)}}{\sqrt{e \sec (c+d x)}}+\cos (c+d x) (a+i a \tan (c+d x))+a\right)}{2 \sqrt{2} a^{5/2} d}-\frac{5 i e^{9/2} \log \left(\frac{\sqrt{2} \sqrt{a} \sqrt{e} \sqrt{a+i a \tan (c+d x)}}{\sqrt{e \sec (c+d x)}}+\cos (c+d x) (a+i a \tan (c+d x))+a\right)}{2 \sqrt{2} a^{5/2} d}+\frac{4 i e^2 (e \sec (c+d x))^{5/2}}{a d (a+i a \tan (c+d x))^{3/2}}","-\frac{5 i e^{9/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{e} \sqrt{a+i a \tan (c+d x)}}{\sqrt{a} \sqrt{e \sec (c+d x)}}\right)}{\sqrt{2} a^{5/2} d}+\frac{5 i e^{9/2} \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt{e} \sqrt{a+i a \tan (c+d x)}}{\sqrt{a} \sqrt{e \sec (c+d x)}}\right)}{\sqrt{2} a^{5/2} d}+\frac{5 i e^4 \sqrt{a+i a \tan (c+d x)} \sqrt{e \sec (c+d x)}}{a^3 d}+\frac{5 i e^{9/2} \log \left(-\frac{\sqrt{2} \sqrt{a} \sqrt{e} \sqrt{a+i a \tan (c+d x)}}{\sqrt{e \sec (c+d x)}}+\cos (c+d x) (a+i a \tan (c+d x))+a\right)}{2 \sqrt{2} a^{5/2} d}-\frac{5 i e^{9/2} \log \left(\frac{\sqrt{2} \sqrt{a} \sqrt{e} \sqrt{a+i a \tan (c+d x)}}{\sqrt{e \sec (c+d x)}}+\cos (c+d x) (a+i a \tan (c+d x))+a\right)}{2 \sqrt{2} a^{5/2} d}+\frac{4 i e^2 (e \sec (c+d x))^{5/2}}{a d (a+i a \tan (c+d x))^{3/2}}",1,"((-5*I)*e^(9/2)*ArcTan[1 - (Sqrt[2]*Sqrt[e]*Sqrt[a + I*a*Tan[c + d*x]])/(Sqrt[a]*Sqrt[e*Sec[c + d*x]])])/(Sqrt[2]*a^(5/2)*d) + ((5*I)*e^(9/2)*ArcTan[1 + (Sqrt[2]*Sqrt[e]*Sqrt[a + I*a*Tan[c + d*x]])/(Sqrt[a]*Sqrt[e*Sec[c + d*x]])])/(Sqrt[2]*a^(5/2)*d) + (((5*I)/2)*e^(9/2)*Log[a - (Sqrt[2]*Sqrt[a]*Sqrt[e]*Sqrt[a + I*a*Tan[c + d*x]])/Sqrt[e*Sec[c + d*x]] + Cos[c + d*x]*(a + I*a*Tan[c + d*x])])/(Sqrt[2]*a^(5/2)*d) - (((5*I)/2)*e^(9/2)*Log[a + (Sqrt[2]*Sqrt[a]*Sqrt[e]*Sqrt[a + I*a*Tan[c + d*x]])/Sqrt[e*Sec[c + d*x]] + Cos[c + d*x]*(a + I*a*Tan[c + d*x])])/(Sqrt[2]*a^(5/2)*d) + ((4*I)*e^2*(e*Sec[c + d*x])^(5/2))/(a*d*(a + I*a*Tan[c + d*x])^(3/2)) + ((5*I)*e^4*Sqrt[e*Sec[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]])/(a^3*d)","A",12,9,30,0.3000,1,"{3500, 3501, 3495, 297, 1162, 617, 204, 1165, 628}"
431,1,527,0,0.4535704,"\int \frac{(e \sec (c+d x))^{7/2}}{(a+i a \tan (c+d x))^{5/2}} \, dx","Int[(e*Sec[c + d*x])^(7/2)/(a + I*a*Tan[c + d*x])^(5/2),x]","\frac{i \sqrt{2} e^{7/2} \sec (c+d x) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{e} \sqrt{a-i a \tan (c+d x)}}{\sqrt{a} \sqrt{e \sec (c+d x)}}\right)}{a^{3/2} d \sqrt{a-i a \tan (c+d x)} \sqrt{a+i a \tan (c+d x)}}-\frac{i \sqrt{2} e^{7/2} \sec (c+d x) \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt{e} \sqrt{a-i a \tan (c+d x)}}{\sqrt{a} \sqrt{e \sec (c+d x)}}\right)}{a^{3/2} d \sqrt{a-i a \tan (c+d x)} \sqrt{a+i a \tan (c+d x)}}-\frac{i e^{7/2} \sec (c+d x) \log \left(-\frac{\sqrt{2} \sqrt{a} \sqrt{e} \sqrt{a-i a \tan (c+d x)}}{\sqrt{e \sec (c+d x)}}+\cos (c+d x) (a-i a \tan (c+d x))+a\right)}{\sqrt{2} a^{3/2} d \sqrt{a-i a \tan (c+d x)} \sqrt{a+i a \tan (c+d x)}}+\frac{i e^{7/2} \sec (c+d x) \log \left(\frac{\sqrt{2} \sqrt{a} \sqrt{e} \sqrt{a-i a \tan (c+d x)}}{\sqrt{e \sec (c+d x)}}+\cos (c+d x) (a-i a \tan (c+d x))+a\right)}{\sqrt{2} a^{3/2} d \sqrt{a-i a \tan (c+d x)} \sqrt{a+i a \tan (c+d x)}}+\frac{4 i e^2 (e \sec (c+d x))^{3/2}}{3 a d (a+i a \tan (c+d x))^{3/2}}","\frac{i \sqrt{2} e^{7/2} \sec (c+d x) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{e} \sqrt{a-i a \tan (c+d x)}}{\sqrt{a} \sqrt{e \sec (c+d x)}}\right)}{a^{3/2} d \sqrt{a-i a \tan (c+d x)} \sqrt{a+i a \tan (c+d x)}}-\frac{i \sqrt{2} e^{7/2} \sec (c+d x) \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt{e} \sqrt{a-i a \tan (c+d x)}}{\sqrt{a} \sqrt{e \sec (c+d x)}}\right)}{a^{3/2} d \sqrt{a-i a \tan (c+d x)} \sqrt{a+i a \tan (c+d x)}}-\frac{i e^{7/2} \sec (c+d x) \log \left(-\frac{\sqrt{2} \sqrt{a} \sqrt{e} \sqrt{a-i a \tan (c+d x)}}{\sqrt{e \sec (c+d x)}}+\cos (c+d x) (a-i a \tan (c+d x))+a\right)}{\sqrt{2} a^{3/2} d \sqrt{a-i a \tan (c+d x)} \sqrt{a+i a \tan (c+d x)}}+\frac{i e^{7/2} \sec (c+d x) \log \left(\frac{\sqrt{2} \sqrt{a} \sqrt{e} \sqrt{a-i a \tan (c+d x)}}{\sqrt{e \sec (c+d x)}}+\cos (c+d x) (a-i a \tan (c+d x))+a\right)}{\sqrt{2} a^{3/2} d \sqrt{a-i a \tan (c+d x)} \sqrt{a+i a \tan (c+d x)}}+\frac{4 i e^2 (e \sec (c+d x))^{3/2}}{3 a d (a+i a \tan (c+d x))^{3/2}}",1,"(((4*I)/3)*e^2*(e*Sec[c + d*x])^(3/2))/(a*d*(a + I*a*Tan[c + d*x])^(3/2)) + (I*Sqrt[2]*e^(7/2)*ArcTan[1 - (Sqrt[2]*Sqrt[e]*Sqrt[a - I*a*Tan[c + d*x]])/(Sqrt[a]*Sqrt[e*Sec[c + d*x]])]*Sec[c + d*x])/(a^(3/2)*d*Sqrt[a - I*a*Tan[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]]) - (I*Sqrt[2]*e^(7/2)*ArcTan[1 + (Sqrt[2]*Sqrt[e]*Sqrt[a - I*a*Tan[c + d*x]])/(Sqrt[a]*Sqrt[e*Sec[c + d*x]])]*Sec[c + d*x])/(a^(3/2)*d*Sqrt[a - I*a*Tan[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]]) - (I*e^(7/2)*Log[a - (Sqrt[2]*Sqrt[a]*Sqrt[e]*Sqrt[a - I*a*Tan[c + d*x]])/Sqrt[e*Sec[c + d*x]] + Cos[c + d*x]*(a - I*a*Tan[c + d*x])]*Sec[c + d*x])/(Sqrt[2]*a^(3/2)*d*Sqrt[a - I*a*Tan[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]]) + (I*e^(7/2)*Log[a + (Sqrt[2]*Sqrt[a]*Sqrt[e]*Sqrt[a - I*a*Tan[c + d*x]])/Sqrt[e*Sec[c + d*x]] + Cos[c + d*x]*(a - I*a*Tan[c + d*x])]*Sec[c + d*x])/(Sqrt[2]*a^(3/2)*d*Sqrt[a - I*a*Tan[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]])","A",12,9,30,0.3000,1,"{3500, 3499, 3495, 297, 1162, 617, 204, 1165, 628}"
432,1,38,0,0.0783137,"\int \frac{(e \sec (c+d x))^{5/2}}{(a+i a \tan (c+d x))^{5/2}} \, dx","Int[(e*Sec[c + d*x])^(5/2)/(a + I*a*Tan[c + d*x])^(5/2),x]","\frac{2 i (e \sec (c+d x))^{5/2}}{5 d (a+i a \tan (c+d x))^{5/2}}","\frac{2 i (e \sec (c+d x))^{5/2}}{5 d (a+i a \tan (c+d x))^{5/2}}",1,"(((2*I)/5)*(e*Sec[c + d*x])^(5/2))/(d*(a + I*a*Tan[c + d*x])^(5/2))","A",1,1,30,0.03333,1,"{3488}"
433,1,80,0,0.1659891,"\int \frac{(e \sec (c+d x))^{3/2}}{(a+i a \tan (c+d x))^{5/2}} \, dx","Int[(e*Sec[c + d*x])^(3/2)/(a + I*a*Tan[c + d*x])^(5/2),x]","\frac{4 i (e \sec (c+d x))^{3/2}}{21 a d (a+i a \tan (c+d x))^{3/2}}+\frac{2 i (e \sec (c+d x))^{3/2}}{7 d (a+i a \tan (c+d x))^{5/2}}","\frac{4 i (e \sec (c+d x))^{3/2}}{21 a d (a+i a \tan (c+d x))^{3/2}}+\frac{2 i (e \sec (c+d x))^{3/2}}{7 d (a+i a \tan (c+d x))^{5/2}}",1,"(((2*I)/7)*(e*Sec[c + d*x])^(3/2))/(d*(a + I*a*Tan[c + d*x])^(5/2)) + (((4*I)/21)*(e*Sec[c + d*x])^(3/2))/(a*d*(a + I*a*Tan[c + d*x])^(3/2))","A",2,2,30,0.06667,1,"{3502, 3488}"
434,1,121,0,0.2197564,"\int \frac{\sqrt{e \sec (c+d x)}}{(a+i a \tan (c+d x))^{5/2}} \, dx","Int[Sqrt[e*Sec[c + d*x]]/(a + I*a*Tan[c + d*x])^(5/2),x]","\frac{16 i \sqrt{e \sec (c+d x)}}{45 a^2 d \sqrt{a+i a \tan (c+d x)}}+\frac{8 i \sqrt{e \sec (c+d x)}}{45 a d (a+i a \tan (c+d x))^{3/2}}+\frac{2 i \sqrt{e \sec (c+d x)}}{9 d (a+i a \tan (c+d x))^{5/2}}","\frac{16 i \sqrt{e \sec (c+d x)}}{45 a^2 d \sqrt{a+i a \tan (c+d x)}}+\frac{8 i \sqrt{e \sec (c+d x)}}{45 a d (a+i a \tan (c+d x))^{3/2}}+\frac{2 i \sqrt{e \sec (c+d x)}}{9 d (a+i a \tan (c+d x))^{5/2}}",1,"(((2*I)/9)*Sqrt[e*Sec[c + d*x]])/(d*(a + I*a*Tan[c + d*x])^(5/2)) + (((8*I)/45)*Sqrt[e*Sec[c + d*x]])/(a*d*(a + I*a*Tan[c + d*x])^(3/2)) + (((16*I)/45)*Sqrt[e*Sec[c + d*x]])/(a^2*d*Sqrt[a + I*a*Tan[c + d*x]])","A",3,2,30,0.06667,1,"{3502, 3488}"
435,1,162,0,0.3010085,"\int \frac{1}{\sqrt{e \sec (c+d x)} (a+i a \tan (c+d x))^{5/2}} \, dx","Int[1/(Sqrt[e*Sec[c + d*x]]*(a + I*a*Tan[c + d*x])^(5/2)),x]","-\frac{32 i \sqrt{a+i a \tan (c+d x)}}{77 a^3 d \sqrt{e \sec (c+d x)}}+\frac{16 i}{77 a^2 d \sqrt{a+i a \tan (c+d x)} \sqrt{e \sec (c+d x)}}+\frac{12 i}{77 a d (a+i a \tan (c+d x))^{3/2} \sqrt{e \sec (c+d x)}}+\frac{2 i}{11 d (a+i a \tan (c+d x))^{5/2} \sqrt{e \sec (c+d x)}}","-\frac{32 i \sqrt{a+i a \tan (c+d x)}}{77 a^3 d \sqrt{e \sec (c+d x)}}+\frac{16 i}{77 a^2 d \sqrt{a+i a \tan (c+d x)} \sqrt{e \sec (c+d x)}}+\frac{12 i}{77 a d (a+i a \tan (c+d x))^{3/2} \sqrt{e \sec (c+d x)}}+\frac{2 i}{11 d (a+i a \tan (c+d x))^{5/2} \sqrt{e \sec (c+d x)}}",1,"((2*I)/11)/(d*Sqrt[e*Sec[c + d*x]]*(a + I*a*Tan[c + d*x])^(5/2)) + ((12*I)/77)/(a*d*Sqrt[e*Sec[c + d*x]]*(a + I*a*Tan[c + d*x])^(3/2)) + ((16*I)/77)/(a^2*d*Sqrt[e*Sec[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]]) - (((32*I)/77)*Sqrt[a + I*a*Tan[c + d*x]])/(a^3*d*Sqrt[e*Sec[c + d*x]])","A",4,2,30,0.06667,1,"{3502, 3488}"
436,1,206,0,0.3989622,"\int \frac{1}{(e \sec (c+d x))^{3/2} (a+i a \tan (c+d x))^{5/2}} \, dx","Int[1/((e*Sec[c + d*x])^(3/2)*(a + I*a*Tan[c + d*x])^(5/2)),x]","\frac{256 i \sqrt{e \sec (c+d x)}}{585 a^2 d e^2 \sqrt{a+i a \tan (c+d x)}}-\frac{128 i \sqrt{a+i a \tan (c+d x)}}{585 a^3 d (e \sec (c+d x))^{3/2}}+\frac{32 i}{195 a^2 d \sqrt{a+i a \tan (c+d x)} (e \sec (c+d x))^{3/2}}+\frac{16 i}{117 a d (a+i a \tan (c+d x))^{3/2} (e \sec (c+d x))^{3/2}}+\frac{2 i}{13 d (a+i a \tan (c+d x))^{5/2} (e \sec (c+d x))^{3/2}}","\frac{256 i \sqrt{e \sec (c+d x)}}{585 a^2 d e^2 \sqrt{a+i a \tan (c+d x)}}-\frac{128 i \sqrt{a+i a \tan (c+d x)}}{585 a^3 d (e \sec (c+d x))^{3/2}}+\frac{32 i}{195 a^2 d \sqrt{a+i a \tan (c+d x)} (e \sec (c+d x))^{3/2}}+\frac{16 i}{117 a d (a+i a \tan (c+d x))^{3/2} (e \sec (c+d x))^{3/2}}+\frac{2 i}{13 d (a+i a \tan (c+d x))^{5/2} (e \sec (c+d x))^{3/2}}",1,"((2*I)/13)/(d*(e*Sec[c + d*x])^(3/2)*(a + I*a*Tan[c + d*x])^(5/2)) + ((16*I)/117)/(a*d*(e*Sec[c + d*x])^(3/2)*(a + I*a*Tan[c + d*x])^(3/2)) + ((32*I)/195)/(a^2*d*(e*Sec[c + d*x])^(3/2)*Sqrt[a + I*a*Tan[c + d*x]]) + (((256*I)/585)*Sqrt[e*Sec[c + d*x]])/(a^2*d*e^2*Sqrt[a + I*a*Tan[c + d*x]]) - (((128*I)/585)*Sqrt[a + I*a*Tan[c + d*x]])/(a^3*d*(e*Sec[c + d*x])^(3/2))","A",5,3,30,0.1000,1,"{3502, 3497, 3488}"
437,1,86,0,0.2109341,"\int \frac{(e \sec (c+d x))^{7/3}}{\sqrt{a+i a \tan (c+d x)}} \, dx","Int[(e*Sec[c + d*x])^(7/3)/Sqrt[a + I*a*Tan[c + d*x]],x]","\frac{3 i 2^{2/3} a \sqrt[3]{1+i \tan (c+d x)} (e \sec (c+d x))^{7/3} \text{Hypergeometric2F1}\left(\frac{1}{3},\frac{7}{6},\frac{13}{6},\frac{1}{2} (1-i \tan (c+d x))\right)}{7 d (a+i a \tan (c+d x))^{3/2}}","\frac{3 i 2^{2/3} a \sqrt[3]{1+i \tan (c+d x)} (e \sec (c+d x))^{7/3} \text{Hypergeometric2F1}\left(\frac{1}{3},\frac{7}{6},\frac{13}{6},\frac{1}{2} (1-i \tan (c+d x))\right)}{7 d (a+i a \tan (c+d x))^{3/2}}",1,"(((3*I)/7)*2^(2/3)*a*Hypergeometric2F1[1/3, 7/6, 13/6, (1 - I*Tan[c + d*x])/2]*(e*Sec[c + d*x])^(7/3)*(1 + I*Tan[c + d*x])^(1/3))/(d*(a + I*a*Tan[c + d*x])^(3/2))","A",4,4,30,0.1333,1,"{3505, 3523, 70, 69}"
438,1,86,0,0.198889,"\int \frac{(e \sec (c+d x))^{5/3}}{\sqrt{a+i a \tan (c+d x)}} \, dx","Int[(e*Sec[c + d*x])^(5/3)/Sqrt[a + I*a*Tan[c + d*x]],x]","\frac{3 i \sqrt[3]{2} a (1+i \tan (c+d x))^{2/3} (e \sec (c+d x))^{5/3} \text{Hypergeometric2F1}\left(\frac{2}{3},\frac{5}{6},\frac{11}{6},\frac{1}{2} (1-i \tan (c+d x))\right)}{5 d (a+i a \tan (c+d x))^{3/2}}","\frac{3 i \sqrt[3]{2} a (1+i \tan (c+d x))^{2/3} (e \sec (c+d x))^{5/3} \text{Hypergeometric2F1}\left(\frac{2}{3},\frac{5}{6},\frac{11}{6},\frac{1}{2} (1-i \tan (c+d x))\right)}{5 d (a+i a \tan (c+d x))^{3/2}}",1,"(((3*I)/5)*2^(1/3)*a*Hypergeometric2F1[2/3, 5/6, 11/6, (1 - I*Tan[c + d*x])/2]*(e*Sec[c + d*x])^(5/3)*(1 + I*Tan[c + d*x])^(2/3))/(d*(a + I*a*Tan[c + d*x])^(3/2))","A",4,4,30,0.1333,1,"{3505, 3523, 70, 69}"
439,1,85,0,0.1903866,"\int \frac{(e \sec (c+d x))^{2/3}}{\sqrt{a+i a \tan (c+d x)}} \, dx","Int[(e*Sec[c + d*x])^(2/3)/Sqrt[a + I*a*Tan[c + d*x]],x]","\frac{3 i \sqrt[6]{1+i \tan (c+d x)} (e \sec (c+d x))^{2/3} \text{Hypergeometric2F1}\left(\frac{1}{3},\frac{7}{6},\frac{4}{3},\frac{1}{2} (1-i \tan (c+d x))\right)}{2 \sqrt[6]{2} d \sqrt{a+i a \tan (c+d x)}}","\frac{3 i \sqrt[6]{1+i \tan (c+d x)} (e \sec (c+d x))^{2/3} \text{Hypergeometric2F1}\left(\frac{1}{3},\frac{7}{6},\frac{4}{3},\frac{1}{2} (1-i \tan (c+d x))\right)}{2 \sqrt[6]{2} d \sqrt{a+i a \tan (c+d x)}}",1,"(((3*I)/2)*Hypergeometric2F1[1/3, 7/6, 4/3, (1 - I*Tan[c + d*x])/2]*(e*Sec[c + d*x])^(2/3)*(1 + I*Tan[c + d*x])^(1/6))/(2^(1/6)*d*Sqrt[a + I*a*Tan[c + d*x]])","A",4,4,30,0.1333,1,"{3505, 3523, 70, 69}"
440,1,83,0,0.1821156,"\int \frac{\sqrt[3]{e \sec (c+d x)}}{\sqrt{a+i a \tan (c+d x)}} \, dx","Int[(e*Sec[c + d*x])^(1/3)/Sqrt[a + I*a*Tan[c + d*x]],x]","\frac{3 i \sqrt[3]{1+i \tan (c+d x)} \sqrt[3]{e \sec (c+d x)} \text{Hypergeometric2F1}\left(\frac{1}{6},\frac{4}{3},\frac{7}{6},\frac{1}{2} (1-i \tan (c+d x))\right)}{\sqrt[3]{2} d \sqrt{a+i a \tan (c+d x)}}","\frac{3 i \sqrt[3]{1+i \tan (c+d x)} \sqrt[3]{e \sec (c+d x)} \text{Hypergeometric2F1}\left(\frac{1}{6},\frac{4}{3},\frac{7}{6},\frac{1}{2} (1-i \tan (c+d x))\right)}{\sqrt[3]{2} d \sqrt{a+i a \tan (c+d x)}}",1,"((3*I)*Hypergeometric2F1[1/6, 4/3, 7/6, (1 - I*Tan[c + d*x])/2]*(e*Sec[c + d*x])^(1/3)*(1 + I*Tan[c + d*x])^(1/3))/(2^(1/3)*d*Sqrt[a + I*a*Tan[c + d*x]])","A",4,4,30,0.1333,1,"{3505, 3523, 70, 69}"
441,1,83,0,0.1963085,"\int \frac{1}{\sqrt[3]{e \sec (c+d x)} \sqrt{a+i a \tan (c+d x)}} \, dx","Int[1/((e*Sec[c + d*x])^(1/3)*Sqrt[a + I*a*Tan[c + d*x]]),x]","-\frac{3 i (1+i \tan (c+d x))^{2/3} \text{Hypergeometric2F1}\left(-\frac{1}{6},\frac{5}{3},\frac{5}{6},\frac{1}{2} (1-i \tan (c+d x))\right)}{2^{2/3} d \sqrt{a+i a \tan (c+d x)} \sqrt[3]{e \sec (c+d x)}}","-\frac{3 i (1+i \tan (c+d x))^{2/3} \text{Hypergeometric2F1}\left(-\frac{1}{6},\frac{5}{3},\frac{5}{6},\frac{1}{2} (1-i \tan (c+d x))\right)}{2^{2/3} d \sqrt{a+i a \tan (c+d x)} \sqrt[3]{e \sec (c+d x)}}",1,"((-3*I)*Hypergeometric2F1[-1/6, 5/3, 5/6, (1 - I*Tan[c + d*x])/2]*(1 + I*Tan[c + d*x])^(2/3))/(2^(2/3)*d*(e*Sec[c + d*x])^(1/3)*Sqrt[a + I*a*Tan[c + d*x]])","A",4,4,30,0.1333,1,"{3505, 3523, 70, 69}"
442,1,88,0,0.2098785,"\int \frac{1}{(e \sec (c+d x))^{4/3} \sqrt{a+i a \tan (c+d x)}} \, dx","Int[1/((e*Sec[c + d*x])^(4/3)*Sqrt[a + I*a*Tan[c + d*x]]),x]","-\frac{3 i \sqrt[6]{1+i \tan (c+d x)} \sqrt{a+i a \tan (c+d x)} \text{Hypergeometric2F1}\left(-\frac{2}{3},\frac{13}{6},\frac{1}{3},\frac{1}{2} (1-i \tan (c+d x))\right)}{8 \sqrt[6]{2} a d (e \sec (c+d x))^{4/3}}","-\frac{3 i \sqrt[6]{1+i \tan (c+d x)} \sqrt{a+i a \tan (c+d x)} \text{Hypergeometric2F1}\left(-\frac{2}{3},\frac{13}{6},\frac{1}{3},\frac{1}{2} (1-i \tan (c+d x))\right)}{8 \sqrt[6]{2} a d (e \sec (c+d x))^{4/3}}",1,"(((-3*I)/8)*Hypergeometric2F1[-2/3, 13/6, 1/3, (1 - I*Tan[c + d*x])/2]*(1 + I*Tan[c + d*x])^(1/6)*Sqrt[a + I*a*Tan[c + d*x]])/(2^(1/6)*a*d*(e*Sec[c + d*x])^(4/3))","A",4,4,30,0.1333,1,"{3505, 3523, 70, 69}"
443,1,437,0,0.3979683,"\int \frac{(d \sec (e+f x))^{2/3}}{(a+i a \tan (e+f x))^{7/3}} \, dx","Int[(d*Sec[e + f*x])^(2/3)/(a + I*a*Tan[e + f*x])^(7/3),x]","\frac{5 i \tan ^{-1}\left(\frac{\sqrt[3]{a}+2^{2/3} \sqrt[3]{a-i a \tan (e+f x)}}{\sqrt{3} \sqrt[3]{a}}\right) (d \sec (e+f x))^{2/3}}{12\ 2^{2/3} \sqrt{3} a^{5/3} f \sqrt[3]{a-i a \tan (e+f x)} \sqrt[3]{a+i a \tan (e+f x)}}-\frac{5 x (d \sec (e+f x))^{2/3}}{72\ 2^{2/3} a^{5/3} \sqrt[3]{a-i a \tan (e+f x)} \sqrt[3]{a+i a \tan (e+f x)}}+\frac{5 i (d \sec (e+f x))^{2/3}}{24 f \sqrt[3]{a+i a \tan (e+f x)} \left(a^2+i a^2 \tan (e+f x)\right)}-\frac{5 i (d \sec (e+f x))^{2/3} \log \left(\sqrt[3]{2} \sqrt[3]{a}-\sqrt[3]{a-i a \tan (e+f x)}\right)}{24\ 2^{2/3} a^{5/3} f \sqrt[3]{a-i a \tan (e+f x)} \sqrt[3]{a+i a \tan (e+f x)}}-\frac{5 i (d \sec (e+f x))^{2/3} \log (\cos (e+f x))}{72\ 2^{2/3} a^{5/3} f \sqrt[3]{a-i a \tan (e+f x)} \sqrt[3]{a+i a \tan (e+f x)}}+\frac{i (d \sec (e+f x))^{2/3}}{4 f (a+i a \tan (e+f x))^{7/3}}","\frac{5 i \tan ^{-1}\left(\frac{\sqrt[3]{a}+2^{2/3} \sqrt[3]{a-i a \tan (e+f x)}}{\sqrt{3} \sqrt[3]{a}}\right) (d \sec (e+f x))^{2/3}}{12\ 2^{2/3} \sqrt{3} a^{5/3} f \sqrt[3]{a-i a \tan (e+f x)} \sqrt[3]{a+i a \tan (e+f x)}}-\frac{5 x (d \sec (e+f x))^{2/3}}{72\ 2^{2/3} a^{5/3} \sqrt[3]{a-i a \tan (e+f x)} \sqrt[3]{a+i a \tan (e+f x)}}+\frac{5 i (d \sec (e+f x))^{2/3}}{24 f \sqrt[3]{a+i a \tan (e+f x)} \left(a^2+i a^2 \tan (e+f x)\right)}-\frac{5 i (d \sec (e+f x))^{2/3} \log \left(\sqrt[3]{2} \sqrt[3]{a}-\sqrt[3]{a-i a \tan (e+f x)}\right)}{24\ 2^{2/3} a^{5/3} f \sqrt[3]{a-i a \tan (e+f x)} \sqrt[3]{a+i a \tan (e+f x)}}-\frac{5 i (d \sec (e+f x))^{2/3} \log (\cos (e+f x))}{72\ 2^{2/3} a^{5/3} f \sqrt[3]{a-i a \tan (e+f x)} \sqrt[3]{a+i a \tan (e+f x)}}+\frac{i (d \sec (e+f x))^{2/3}}{4 f (a+i a \tan (e+f x))^{7/3}}",1,"((I/4)*(d*Sec[e + f*x])^(2/3))/(f*(a + I*a*Tan[e + f*x])^(7/3)) - (5*x*(d*Sec[e + f*x])^(2/3))/(72*2^(2/3)*a^(5/3)*(a - I*a*Tan[e + f*x])^(1/3)*(a + I*a*Tan[e + f*x])^(1/3)) + (((5*I)/12)*ArcTan[(a^(1/3) + 2^(2/3)*(a - I*a*Tan[e + f*x])^(1/3))/(Sqrt[3]*a^(1/3))]*(d*Sec[e + f*x])^(2/3))/(2^(2/3)*Sqrt[3]*a^(5/3)*f*(a - I*a*Tan[e + f*x])^(1/3)*(a + I*a*Tan[e + f*x])^(1/3)) - (((5*I)/72)*Log[Cos[e + f*x]]*(d*Sec[e + f*x])^(2/3))/(2^(2/3)*a^(5/3)*f*(a - I*a*Tan[e + f*x])^(1/3)*(a + I*a*Tan[e + f*x])^(1/3)) - (((5*I)/24)*Log[2^(1/3)*a^(1/3) - (a - I*a*Tan[e + f*x])^(1/3)]*(d*Sec[e + f*x])^(2/3))/(2^(2/3)*a^(5/3)*f*(a - I*a*Tan[e + f*x])^(1/3)*(a + I*a*Tan[e + f*x])^(1/3)) + (((5*I)/24)*(d*Sec[e + f*x])^(2/3))/(f*(a + I*a*Tan[e + f*x])^(1/3)*(a^2 + I*a^2*Tan[e + f*x]))","A",9,8,30,0.2667,1,"{3505, 3522, 3487, 51, 57, 617, 204, 31}"
444,1,378,0,0.3426368,"\int \frac{(d \sec (e+f x))^{2/3}}{(a+i a \tan (e+f x))^{4/3}} \, dx","Int[(d*Sec[e + f*x])^(2/3)/(a + I*a*Tan[e + f*x])^(4/3),x]","\frac{i \tan ^{-1}\left(\frac{\sqrt[3]{a}+2^{2/3} \sqrt[3]{a-i a \tan (e+f x)}}{\sqrt{3} \sqrt[3]{a}}\right) (d \sec (e+f x))^{2/3}}{2^{2/3} \sqrt{3} a^{2/3} f \sqrt[3]{a-i a \tan (e+f x)} \sqrt[3]{a+i a \tan (e+f x)}}-\frac{x (d \sec (e+f x))^{2/3}}{6\ 2^{2/3} a^{2/3} \sqrt[3]{a-i a \tan (e+f x)} \sqrt[3]{a+i a \tan (e+f x)}}-\frac{i (d \sec (e+f x))^{2/3} \log \left(\sqrt[3]{2} \sqrt[3]{a}-\sqrt[3]{a-i a \tan (e+f x)}\right)}{2\ 2^{2/3} a^{2/3} f \sqrt[3]{a-i a \tan (e+f x)} \sqrt[3]{a+i a \tan (e+f x)}}-\frac{i (d \sec (e+f x))^{2/3} \log (\cos (e+f x))}{6\ 2^{2/3} a^{2/3} f \sqrt[3]{a-i a \tan (e+f x)} \sqrt[3]{a+i a \tan (e+f x)}}+\frac{i (d \sec (e+f x))^{2/3}}{2 f (a+i a \tan (e+f x))^{4/3}}","\frac{i \tan ^{-1}\left(\frac{\sqrt[3]{a}+2^{2/3} \sqrt[3]{a-i a \tan (e+f x)}}{\sqrt{3} \sqrt[3]{a}}\right) (d \sec (e+f x))^{2/3}}{2^{2/3} \sqrt{3} a^{2/3} f \sqrt[3]{a-i a \tan (e+f x)} \sqrt[3]{a+i a \tan (e+f x)}}-\frac{x (d \sec (e+f x))^{2/3}}{6\ 2^{2/3} a^{2/3} \sqrt[3]{a-i a \tan (e+f x)} \sqrt[3]{a+i a \tan (e+f x)}}-\frac{i (d \sec (e+f x))^{2/3} \log \left(\sqrt[3]{2} \sqrt[3]{a}-\sqrt[3]{a-i a \tan (e+f x)}\right)}{2\ 2^{2/3} a^{2/3} f \sqrt[3]{a-i a \tan (e+f x)} \sqrt[3]{a+i a \tan (e+f x)}}-\frac{i (d \sec (e+f x))^{2/3} \log (\cos (e+f x))}{6\ 2^{2/3} a^{2/3} f \sqrt[3]{a-i a \tan (e+f x)} \sqrt[3]{a+i a \tan (e+f x)}}+\frac{i (d \sec (e+f x))^{2/3}}{2 f (a+i a \tan (e+f x))^{4/3}}",1,"((I/2)*(d*Sec[e + f*x])^(2/3))/(f*(a + I*a*Tan[e + f*x])^(4/3)) - (x*(d*Sec[e + f*x])^(2/3))/(6*2^(2/3)*a^(2/3)*(a - I*a*Tan[e + f*x])^(1/3)*(a + I*a*Tan[e + f*x])^(1/3)) + (I*ArcTan[(a^(1/3) + 2^(2/3)*(a - I*a*Tan[e + f*x])^(1/3))/(Sqrt[3]*a^(1/3))]*(d*Sec[e + f*x])^(2/3))/(2^(2/3)*Sqrt[3]*a^(2/3)*f*(a - I*a*Tan[e + f*x])^(1/3)*(a + I*a*Tan[e + f*x])^(1/3)) - ((I/6)*Log[Cos[e + f*x]]*(d*Sec[e + f*x])^(2/3))/(2^(2/3)*a^(2/3)*f*(a - I*a*Tan[e + f*x])^(1/3)*(a + I*a*Tan[e + f*x])^(1/3)) - ((I/2)*Log[2^(1/3)*a^(1/3) - (a - I*a*Tan[e + f*x])^(1/3)]*(d*Sec[e + f*x])^(2/3))/(2^(2/3)*a^(2/3)*f*(a - I*a*Tan[e + f*x])^(1/3)*(a + I*a*Tan[e + f*x])^(1/3))","A",8,8,30,0.2667,1,"{3505, 3522, 3487, 51, 57, 617, 204, 31}"
445,1,340,0,0.1712687,"\int \frac{(d \sec (e+f x))^{2/3}}{\sqrt[3]{a+i a \tan (e+f x)}} \, dx","Int[(d*Sec[e + f*x])^(2/3)/(a + I*a*Tan[e + f*x])^(1/3),x]","\frac{i \sqrt{3} \sqrt[3]{a} \tan ^{-1}\left(\frac{\sqrt[3]{a}+2^{2/3} \sqrt[3]{a-i a \tan (e+f x)}}{\sqrt{3} \sqrt[3]{a}}\right) (d \sec (e+f x))^{2/3}}{2^{2/3} f \sqrt[3]{a-i a \tan (e+f x)} \sqrt[3]{a+i a \tan (e+f x)}}-\frac{\sqrt[3]{a} x (d \sec (e+f x))^{2/3}}{2\ 2^{2/3} \sqrt[3]{a-i a \tan (e+f x)} \sqrt[3]{a+i a \tan (e+f x)}}-\frac{3 i \sqrt[3]{a} (d \sec (e+f x))^{2/3} \log \left(\sqrt[3]{2} \sqrt[3]{a}-\sqrt[3]{a-i a \tan (e+f x)}\right)}{2\ 2^{2/3} f \sqrt[3]{a-i a \tan (e+f x)} \sqrt[3]{a+i a \tan (e+f x)}}-\frac{i \sqrt[3]{a} (d \sec (e+f x))^{2/3} \log (\cos (e+f x))}{2\ 2^{2/3} f \sqrt[3]{a-i a \tan (e+f x)} \sqrt[3]{a+i a \tan (e+f x)}}","\frac{i \sqrt{3} \sqrt[3]{a} \tan ^{-1}\left(\frac{\sqrt[3]{a}+2^{2/3} \sqrt[3]{a-i a \tan (e+f x)}}{\sqrt{3} \sqrt[3]{a}}\right) (d \sec (e+f x))^{2/3}}{2^{2/3} f \sqrt[3]{a-i a \tan (e+f x)} \sqrt[3]{a+i a \tan (e+f x)}}-\frac{\sqrt[3]{a} x (d \sec (e+f x))^{2/3}}{2\ 2^{2/3} \sqrt[3]{a-i a \tan (e+f x)} \sqrt[3]{a+i a \tan (e+f x)}}-\frac{3 i \sqrt[3]{a} (d \sec (e+f x))^{2/3} \log \left(\sqrt[3]{2} \sqrt[3]{a}-\sqrt[3]{a-i a \tan (e+f x)}\right)}{2\ 2^{2/3} f \sqrt[3]{a-i a \tan (e+f x)} \sqrt[3]{a+i a \tan (e+f x)}}-\frac{i \sqrt[3]{a} (d \sec (e+f x))^{2/3} \log (\cos (e+f x))}{2\ 2^{2/3} f \sqrt[3]{a-i a \tan (e+f x)} \sqrt[3]{a+i a \tan (e+f x)}}",1,"-(a^(1/3)*x*(d*Sec[e + f*x])^(2/3))/(2*2^(2/3)*(a - I*a*Tan[e + f*x])^(1/3)*(a + I*a*Tan[e + f*x])^(1/3)) + (I*Sqrt[3]*a^(1/3)*ArcTan[(a^(1/3) + 2^(2/3)*(a - I*a*Tan[e + f*x])^(1/3))/(Sqrt[3]*a^(1/3))]*(d*Sec[e + f*x])^(2/3))/(2^(2/3)*f*(a - I*a*Tan[e + f*x])^(1/3)*(a + I*a*Tan[e + f*x])^(1/3)) - ((I/2)*a^(1/3)*Log[Cos[e + f*x]]*(d*Sec[e + f*x])^(2/3))/(2^(2/3)*f*(a - I*a*Tan[e + f*x])^(1/3)*(a + I*a*Tan[e + f*x])^(1/3)) - (((3*I)/2)*a^(1/3)*Log[2^(1/3)*a^(1/3) - (a - I*a*Tan[e + f*x])^(1/3)]*(d*Sec[e + f*x])^(2/3))/(2^(2/3)*f*(a - I*a*Tan[e + f*x])^(1/3)*(a + I*a*Tan[e + f*x])^(1/3))","A",6,6,30,0.2000,1,"{3492, 3481, 57, 617, 204, 31}"
446,1,37,0,0.0772428,"\int (d \sec (e+f x))^{2/3} (a+i a \tan (e+f x))^{2/3} \, dx","Int[(d*Sec[e + f*x])^(2/3)*(a + I*a*Tan[e + f*x])^(2/3),x]","\frac{3 i a (d \sec (e+f x))^{2/3}}{f \sqrt[3]{a+i a \tan (e+f x)}}","\frac{3 i a (d \sec (e+f x))^{2/3}}{f \sqrt[3]{a+i a \tan (e+f x)}}",1,"((3*I)*a*(d*Sec[e + f*x])^(2/3))/(f*(a + I*a*Tan[e + f*x])^(1/3))","A",1,1,30,0.03333,1,"{3493}"
447,1,81,0,0.1543537,"\int (d \sec (e+f x))^{2/3} (a+i a \tan (e+f x))^{5/3} \, dx","Int[(d*Sec[e + f*x])^(2/3)*(a + I*a*Tan[e + f*x])^(5/3),x]","\frac{9 i a^2 (d \sec (e+f x))^{2/3}}{2 f \sqrt[3]{a+i a \tan (e+f x)}}+\frac{3 i a (a+i a \tan (e+f x))^{2/3} (d \sec (e+f x))^{2/3}}{4 f}","\frac{9 i a^2 (d \sec (e+f x))^{2/3}}{2 f \sqrt[3]{a+i a \tan (e+f x)}}+\frac{3 i a (a+i a \tan (e+f x))^{2/3} (d \sec (e+f x))^{2/3}}{4 f}",1,"(((9*I)/2)*a^2*(d*Sec[e + f*x])^(2/3))/(f*(a + I*a*Tan[e + f*x])^(1/3)) + (((3*I)/4)*a*(d*Sec[e + f*x])^(2/3)*(a + I*a*Tan[e + f*x])^(2/3))/f","A",2,2,30,0.06667,1,"{3494, 3493}"
448,1,122,0,0.2350404,"\int (d \sec (e+f x))^{2/3} (a+i a \tan (e+f x))^{8/3} \, dx","Int[(d*Sec[e + f*x])^(2/3)*(a + I*a*Tan[e + f*x])^(8/3),x]","\frac{54 i a^3 (d \sec (e+f x))^{2/3}}{7 f \sqrt[3]{a+i a \tan (e+f x)}}+\frac{9 i a^2 (a+i a \tan (e+f x))^{2/3} (d \sec (e+f x))^{2/3}}{7 f}+\frac{3 i a (a+i a \tan (e+f x))^{5/3} (d \sec (e+f x))^{2/3}}{7 f}","\frac{54 i a^3 (d \sec (e+f x))^{2/3}}{7 f \sqrt[3]{a+i a \tan (e+f x)}}+\frac{9 i a^2 (a+i a \tan (e+f x))^{2/3} (d \sec (e+f x))^{2/3}}{7 f}+\frac{3 i a (a+i a \tan (e+f x))^{5/3} (d \sec (e+f x))^{2/3}}{7 f}",1,"(((54*I)/7)*a^3*(d*Sec[e + f*x])^(2/3))/(f*(a + I*a*Tan[e + f*x])^(1/3)) + (((9*I)/7)*a^2*(d*Sec[e + f*x])^(2/3)*(a + I*a*Tan[e + f*x])^(2/3))/f + (((3*I)/7)*a*(d*Sec[e + f*x])^(2/3)*(a + I*a*Tan[e + f*x])^(5/3))/f","A",3,2,30,0.06667,1,"{3494, 3493}"
449,1,163,0,0.3207437,"\int (d \sec (e+f x))^{2/3} (a+i a \tan (e+f x))^{11/3} \, dx","Int[(d*Sec[e + f*x])^(2/3)*(a + I*a*Tan[e + f*x])^(11/3),x]","\frac{486 i a^4 (d \sec (e+f x))^{2/3}}{35 f \sqrt[3]{a+i a \tan (e+f x)}}+\frac{81 i a^3 (a+i a \tan (e+f x))^{2/3} (d \sec (e+f x))^{2/3}}{35 f}+\frac{27 i a^2 (a+i a \tan (e+f x))^{5/3} (d \sec (e+f x))^{2/3}}{35 f}+\frac{3 i a (a+i a \tan (e+f x))^{8/3} (d \sec (e+f x))^{2/3}}{10 f}","\frac{486 i a^4 (d \sec (e+f x))^{2/3}}{35 f \sqrt[3]{a+i a \tan (e+f x)}}+\frac{81 i a^3 (a+i a \tan (e+f x))^{2/3} (d \sec (e+f x))^{2/3}}{35 f}+\frac{27 i a^2 (a+i a \tan (e+f x))^{5/3} (d \sec (e+f x))^{2/3}}{35 f}+\frac{3 i a (a+i a \tan (e+f x))^{8/3} (d \sec (e+f x))^{2/3}}{10 f}",1,"(((486*I)/35)*a^4*(d*Sec[e + f*x])^(2/3))/(f*(a + I*a*Tan[e + f*x])^(1/3)) + (((81*I)/35)*a^3*(d*Sec[e + f*x])^(2/3)*(a + I*a*Tan[e + f*x])^(2/3))/f + (((27*I)/35)*a^2*(d*Sec[e + f*x])^(2/3)*(a + I*a*Tan[e + f*x])^(5/3))/f + (((3*I)/10)*a*(d*Sec[e + f*x])^(2/3)*(a + I*a*Tan[e + f*x])^(8/3))/f","A",4,2,30,0.06667,1,"{3494, 3493}"
450,1,86,0,0.1490665,"\int (e \sec (c+d x))^m (a+i a \tan (c+d x))^5 \, dx","Int[(e*Sec[c + d*x])^m*(a + I*a*Tan[c + d*x])^5,x]","\frac{i a^5 2^{\frac{m}{2}+5} (1+i \tan (c+d x))^{-m/2} (e \sec (c+d x))^m \text{Hypergeometric2F1}\left(-\frac{m}{2}-4,\frac{m}{2},\frac{m+2}{2},\frac{1}{2} (1-i \tan (c+d x))\right)}{d m}","\frac{i a^5 2^{\frac{m}{2}+5} (1+i \tan (c+d x))^{-m/2} (e \sec (c+d x))^m \text{Hypergeometric2F1}\left(-\frac{m}{2}-4,\frac{m}{2},\frac{m+2}{2},\frac{1}{2} (1-i \tan (c+d x))\right)}{d m}",1,"(I*2^(5 + m/2)*a^5*Hypergeometric2F1[-4 - m/2, m/2, (2 + m)/2, (1 - I*Tan[c + d*x])/2]*(e*Sec[c + d*x])^m)/(d*m*(1 + I*Tan[c + d*x])^(m/2))","A",4,4,26,0.1538,1,"{3505, 3523, 70, 69}"
451,1,86,0,0.1476167,"\int (e \sec (c+d x))^m (a+i a \tan (c+d x))^3 \, dx","Int[(e*Sec[c + d*x])^m*(a + I*a*Tan[c + d*x])^3,x]","\frac{i a^3 2^{\frac{m}{2}+3} (1+i \tan (c+d x))^{-m/2} (e \sec (c+d x))^m \text{Hypergeometric2F1}\left(-\frac{m}{2}-2,\frac{m}{2},\frac{m+2}{2},\frac{1}{2} (1-i \tan (c+d x))\right)}{d m}","\frac{i a^3 2^{\frac{m}{2}+3} (1+i \tan (c+d x))^{-m/2} (e \sec (c+d x))^m \text{Hypergeometric2F1}\left(-\frac{m}{2}-2,\frac{m}{2},\frac{m+2}{2},\frac{1}{2} (1-i \tan (c+d x))\right)}{d m}",1,"(I*2^(3 + m/2)*a^3*Hypergeometric2F1[-2 - m/2, m/2, (2 + m)/2, (1 - I*Tan[c + d*x])/2]*(e*Sec[c + d*x])^m)/(d*m*(1 + I*Tan[c + d*x])^(m/2))","A",4,4,26,0.1538,1,"{3505, 3523, 70, 69}"
452,1,86,0,0.1497194,"\int (e \sec (c+d x))^m (a+i a \tan (c+d x))^2 \, dx","Int[(e*Sec[c + d*x])^m*(a + I*a*Tan[c + d*x])^2,x]","\frac{i a^2 2^{\frac{m}{2}+2} (1+i \tan (c+d x))^{-m/2} (e \sec (c+d x))^m \text{Hypergeometric2F1}\left(-\frac{m}{2}-1,\frac{m}{2},\frac{m+2}{2},\frac{1}{2} (1-i \tan (c+d x))\right)}{d m}","\frac{i a^2 2^{\frac{m}{2}+2} (1+i \tan (c+d x))^{-m/2} (e \sec (c+d x))^m \text{Hypergeometric2F1}\left(-\frac{m}{2}-1,\frac{m}{2},\frac{m+2}{2},\frac{1}{2} (1-i \tan (c+d x))\right)}{d m}",1,"(I*2^(2 + m/2)*a^2*Hypergeometric2F1[-1 - m/2, m/2, (2 + m)/2, (1 - I*Tan[c + d*x])/2]*(e*Sec[c + d*x])^m)/(d*m*(1 + I*Tan[c + d*x])^(m/2))","A",4,4,26,0.1538,1,"{3505, 3523, 70, 69}"
453,1,82,0,0.1258376,"\int (e \sec (c+d x))^m (a+i a \tan (c+d x)) \, dx","Int[(e*Sec[c + d*x])^m*(a + I*a*Tan[c + d*x]),x]","\frac{i a 2^{\frac{m}{2}+1} (1+i \tan (c+d x))^{-m/2} (e \sec (c+d x))^m \text{Hypergeometric2F1}\left(-\frac{m}{2},\frac{m}{2},\frac{m+2}{2},\frac{1}{2} (1-i \tan (c+d x))\right)}{d m}","\frac{i a 2^{\frac{m}{2}+1} (1+i \tan (c+d x))^{-m/2} (e \sec (c+d x))^m \text{Hypergeometric2F1}\left(-\frac{m}{2},\frac{m}{2},\frac{m+2}{2},\frac{1}{2} (1-i \tan (c+d x))\right)}{d m}",1,"(I*2^(1 + m/2)*a*Hypergeometric2F1[-m/2, m/2, (2 + m)/2, (1 - I*Tan[c + d*x])/2]*(e*Sec[c + d*x])^m)/(d*m*(1 + I*Tan[c + d*x])^(m/2))","A",4,4,24,0.1667,1,"{3505, 3523, 70, 69}"
454,1,86,0,0.153605,"\int \frac{(e \sec (c+d x))^m}{a+i a \tan (c+d x)} \, dx","Int[(e*Sec[c + d*x])^m/(a + I*a*Tan[c + d*x]),x]","\frac{i 2^{\frac{m}{2}-1} (1+i \tan (c+d x))^{-m/2} (e \sec (c+d x))^m \text{Hypergeometric2F1}\left(2-\frac{m}{2},\frac{m}{2},\frac{m+2}{2},\frac{1}{2} (1-i \tan (c+d x))\right)}{a d m}","\frac{i 2^{\frac{m}{2}-1} (1+i \tan (c+d x))^{-m/2} (e \sec (c+d x))^m \text{Hypergeometric2F1}\left(2-\frac{m}{2},\frac{m}{2},\frac{m+2}{2},\frac{1}{2} (1-i \tan (c+d x))\right)}{a d m}",1,"(I*2^(-1 + m/2)*Hypergeometric2F1[2 - m/2, m/2, (2 + m)/2, (1 - I*Tan[c + d*x])/2]*(e*Sec[c + d*x])^m)/(a*d*m*(1 + I*Tan[c + d*x])^(m/2))","A",4,4,26,0.1538,1,"{3505, 3523, 70, 69}"
455,1,86,0,0.1585333,"\int \frac{(e \sec (c+d x))^m}{(a+i a \tan (c+d x))^2} \, dx","Int[(e*Sec[c + d*x])^m/(a + I*a*Tan[c + d*x])^2,x]","\frac{i 2^{\frac{m}{2}-2} (1+i \tan (c+d x))^{-m/2} (e \sec (c+d x))^m \text{Hypergeometric2F1}\left(3-\frac{m}{2},\frac{m}{2},\frac{m+2}{2},\frac{1}{2} (1-i \tan (c+d x))\right)}{a^2 d m}","\frac{i 2^{\frac{m}{2}-2} (1+i \tan (c+d x))^{-m/2} (e \sec (c+d x))^m \text{Hypergeometric2F1}\left(3-\frac{m}{2},\frac{m}{2},\frac{m+2}{2},\frac{1}{2} (1-i \tan (c+d x))\right)}{a^2 d m}",1,"(I*2^(-2 + m/2)*Hypergeometric2F1[3 - m/2, m/2, (2 + m)/2, (1 - I*Tan[c + d*x])/2]*(e*Sec[c + d*x])^m)/(a^2*d*m*(1 + I*Tan[c + d*x])^(m/2))","A",4,4,26,0.1538,1,"{3505, 3523, 70, 69}"
456,1,86,0,0.1575046,"\int \frac{(e \sec (c+d x))^m}{(a+i a \tan (c+d x))^3} \, dx","Int[(e*Sec[c + d*x])^m/(a + I*a*Tan[c + d*x])^3,x]","\frac{i 2^{\frac{m}{2}-3} (1+i \tan (c+d x))^{-m/2} (e \sec (c+d x))^m \text{Hypergeometric2F1}\left(4-\frac{m}{2},\frac{m}{2},\frac{m+2}{2},\frac{1}{2} (1-i \tan (c+d x))\right)}{a^3 d m}","\frac{i 2^{\frac{m}{2}-3} (1+i \tan (c+d x))^{-m/2} (e \sec (c+d x))^m \text{Hypergeometric2F1}\left(4-\frac{m}{2},\frac{m}{2},\frac{m+2}{2},\frac{1}{2} (1-i \tan (c+d x))\right)}{a^3 d m}",1,"(I*2^(-3 + m/2)*Hypergeometric2F1[4 - m/2, m/2, (2 + m)/2, (1 - I*Tan[c + d*x])/2]*(e*Sec[c + d*x])^m)/(a^3*d*m*(1 + I*Tan[c + d*x])^(m/2))","A",4,4,26,0.1538,1,"{3505, 3523, 70, 69}"
457,1,109,0,0.206088,"\int (e \sec (c+d x))^m (a+i a \tan (c+d x))^{7/2} \, dx","Int[(e*Sec[c + d*x])^m*(a + I*a*Tan[c + d*x])^(7/2),x]","\frac{i a^3 2^{\frac{m+7}{2}} \sqrt{a+i a \tan (c+d x)} (1+i \tan (c+d x))^{\frac{1}{2} (-m-1)} (e \sec (c+d x))^m \text{Hypergeometric2F1}\left(\frac{1}{2} (-m-5),\frac{m}{2},\frac{m+2}{2},\frac{1}{2} (1-i \tan (c+d x))\right)}{d m}","\frac{i a^3 2^{\frac{m+7}{2}} \sqrt{a+i a \tan (c+d x)} (1+i \tan (c+d x))^{\frac{1}{2} (-m-1)} (e \sec (c+d x))^m \text{Hypergeometric2F1}\left(\frac{1}{2} (-m-5),\frac{m}{2},\frac{m+2}{2},\frac{1}{2} (1-i \tan (c+d x))\right)}{d m}",1,"(I*2^((7 + m)/2)*a^3*Hypergeometric2F1[(-5 - m)/2, m/2, (2 + m)/2, (1 - I*Tan[c + d*x])/2]*(e*Sec[c + d*x])^m*(1 + I*Tan[c + d*x])^((-1 - m)/2)*Sqrt[a + I*a*Tan[c + d*x]])/(d*m)","A",4,4,28,0.1429,1,"{3505, 3523, 70, 69}"
458,1,109,0,0.1982877,"\int (e \sec (c+d x))^m (a+i a \tan (c+d x))^{5/2} \, dx","Int[(e*Sec[c + d*x])^m*(a + I*a*Tan[c + d*x])^(5/2),x]","\frac{i a^2 2^{\frac{m+5}{2}} \sqrt{a+i a \tan (c+d x)} (1+i \tan (c+d x))^{\frac{1}{2} (-m-1)} (e \sec (c+d x))^m \text{Hypergeometric2F1}\left(\frac{1}{2} (-m-3),\frac{m}{2},\frac{m+2}{2},\frac{1}{2} (1-i \tan (c+d x))\right)}{d m}","\frac{i a^2 2^{\frac{m+5}{2}} \sqrt{a+i a \tan (c+d x)} (1+i \tan (c+d x))^{\frac{1}{2} (-m-1)} (e \sec (c+d x))^m \text{Hypergeometric2F1}\left(\frac{1}{2} (-m-3),\frac{m}{2},\frac{m+2}{2},\frac{1}{2} (1-i \tan (c+d x))\right)}{d m}",1,"(I*2^((5 + m)/2)*a^2*Hypergeometric2F1[(-3 - m)/2, m/2, (2 + m)/2, (1 - I*Tan[c + d*x])/2]*(e*Sec[c + d*x])^m*(1 + I*Tan[c + d*x])^((-1 - m)/2)*Sqrt[a + I*a*Tan[c + d*x]])/(d*m)","A",4,4,28,0.1429,1,"{3505, 3523, 70, 69}"
459,1,107,0,0.1962411,"\int (e \sec (c+d x))^m (a+i a \tan (c+d x))^{3/2} \, dx","Int[(e*Sec[c + d*x])^m*(a + I*a*Tan[c + d*x])^(3/2),x]","\frac{i a 2^{\frac{m+3}{2}} \sqrt{a+i a \tan (c+d x)} (1+i \tan (c+d x))^{\frac{1}{2} (-m-1)} (e \sec (c+d x))^m \text{Hypergeometric2F1}\left(\frac{1}{2} (-m-1),\frac{m}{2},\frac{m+2}{2},\frac{1}{2} (1-i \tan (c+d x))\right)}{d m}","\frac{i a 2^{\frac{m+3}{2}} \sqrt{a+i a \tan (c+d x)} (1+i \tan (c+d x))^{\frac{1}{2} (-m-1)} (e \sec (c+d x))^m \text{Hypergeometric2F1}\left(\frac{1}{2} (-m-1),\frac{m}{2},\frac{m+2}{2},\frac{1}{2} (1-i \tan (c+d x))\right)}{d m}",1,"(I*2^((3 + m)/2)*a*Hypergeometric2F1[(-1 - m)/2, m/2, (2 + m)/2, (1 - I*Tan[c + d*x])/2]*(e*Sec[c + d*x])^m*(1 + I*Tan[c + d*x])^((-1 - m)/2)*Sqrt[a + I*a*Tan[c + d*x]])/(d*m)","A",4,4,28,0.1429,1,"{3505, 3523, 70, 69}"
460,1,107,0,0.1787563,"\int (e \sec (c+d x))^m \sqrt{a+i a \tan (c+d x)} \, dx","Int[(e*Sec[c + d*x])^m*Sqrt[a + I*a*Tan[c + d*x]],x]","\frac{i a 2^{\frac{m+1}{2}} (1+i \tan (c+d x))^{\frac{1-m}{2}} (e \sec (c+d x))^m \text{Hypergeometric2F1}\left(\frac{1-m}{2},\frac{m}{2},\frac{m+2}{2},\frac{1}{2} (1-i \tan (c+d x))\right)}{d m \sqrt{a+i a \tan (c+d x)}}","\frac{i a 2^{\frac{m+1}{2}} (1+i \tan (c+d x))^{\frac{1-m}{2}} (e \sec (c+d x))^m \text{Hypergeometric2F1}\left(\frac{1-m}{2},\frac{m}{2},\frac{m+2}{2},\frac{1}{2} (1-i \tan (c+d x))\right)}{d m \sqrt{a+i a \tan (c+d x)}}",1,"(I*2^((1 + m)/2)*a*Hypergeometric2F1[(1 - m)/2, m/2, (2 + m)/2, (1 - I*Tan[c + d*x])/2]*(e*Sec[c + d*x])^m*(1 + I*Tan[c + d*x])^((1 - m)/2))/(d*m*Sqrt[a + I*a*Tan[c + d*x]])","A",4,4,28,0.1429,1,"{3505, 3523, 70, 69}"
461,1,106,0,0.1935424,"\int \frac{(e \sec (c+d x))^m}{\sqrt{a+i a \tan (c+d x)}} \, dx","Int[(e*Sec[c + d*x])^m/Sqrt[a + I*a*Tan[c + d*x]],x]","\frac{i 2^{\frac{m-1}{2}} (1+i \tan (c+d x))^{\frac{1-m}{2}} (e \sec (c+d x))^m \text{Hypergeometric2F1}\left(\frac{3-m}{2},\frac{m}{2},\frac{m+2}{2},\frac{1}{2} (1-i \tan (c+d x))\right)}{d m \sqrt{a+i a \tan (c+d x)}}","\frac{i 2^{\frac{m-1}{2}} (1+i \tan (c+d x))^{\frac{1-m}{2}} (e \sec (c+d x))^m \text{Hypergeometric2F1}\left(\frac{3-m}{2},\frac{m}{2},\frac{m+2}{2},\frac{1}{2} (1-i \tan (c+d x))\right)}{d m \sqrt{a+i a \tan (c+d x)}}",1,"(I*2^((-1 + m)/2)*Hypergeometric2F1[(3 - m)/2, m/2, (2 + m)/2, (1 - I*Tan[c + d*x])/2]*(e*Sec[c + d*x])^m*(1 + I*Tan[c + d*x])^((1 - m)/2))/(d*m*Sqrt[a + I*a*Tan[c + d*x]])","A",4,4,28,0.1429,1,"{3505, 3523, 70, 69}"
462,1,109,0,0.2087192,"\int \frac{(e \sec (c+d x))^m}{(a+i a \tan (c+d x))^{3/2}} \, dx","Int[(e*Sec[c + d*x])^m/(a + I*a*Tan[c + d*x])^(3/2),x]","\frac{i 2^{\frac{m-3}{2}} (1+i \tan (c+d x))^{\frac{1-m}{2}} (e \sec (c+d x))^m \text{Hypergeometric2F1}\left(\frac{5-m}{2},\frac{m}{2},\frac{m+2}{2},\frac{1}{2} (1-i \tan (c+d x))\right)}{a d m \sqrt{a+i a \tan (c+d x)}}","\frac{i 2^{\frac{m-3}{2}} (1+i \tan (c+d x))^{\frac{1-m}{2}} (e \sec (c+d x))^m \text{Hypergeometric2F1}\left(\frac{5-m}{2},\frac{m}{2},\frac{m+2}{2},\frac{1}{2} (1-i \tan (c+d x))\right)}{a d m \sqrt{a+i a \tan (c+d x)}}",1,"(I*2^((-3 + m)/2)*Hypergeometric2F1[(5 - m)/2, m/2, (2 + m)/2, (1 - I*Tan[c + d*x])/2]*(e*Sec[c + d*x])^m*(1 + I*Tan[c + d*x])^((1 - m)/2))/(a*d*m*Sqrt[a + I*a*Tan[c + d*x]])","A",4,4,28,0.1429,1,"{3505, 3523, 70, 69}"
463,1,109,0,0.2104445,"\int \frac{(e \sec (c+d x))^m}{(a+i a \tan (c+d x))^{5/2}} \, dx","Int[(e*Sec[c + d*x])^m/(a + I*a*Tan[c + d*x])^(5/2),x]","\frac{i 2^{\frac{m-5}{2}} (1+i \tan (c+d x))^{\frac{1-m}{2}} (e \sec (c+d x))^m \text{Hypergeometric2F1}\left(\frac{7-m}{2},\frac{m}{2},\frac{m+2}{2},\frac{1}{2} (1-i \tan (c+d x))\right)}{a^2 d m \sqrt{a+i a \tan (c+d x)}}","\frac{i 2^{\frac{m-5}{2}} (1+i \tan (c+d x))^{\frac{1-m}{2}} (e \sec (c+d x))^m \text{Hypergeometric2F1}\left(\frac{7-m}{2},\frac{m}{2},\frac{m+2}{2},\frac{1}{2} (1-i \tan (c+d x))\right)}{a^2 d m \sqrt{a+i a \tan (c+d x)}}",1,"(I*2^((-5 + m)/2)*Hypergeometric2F1[(7 - m)/2, m/2, (2 + m)/2, (1 - I*Tan[c + d*x])/2]*(e*Sec[c + d*x])^m*(1 + I*Tan[c + d*x])^((1 - m)/2))/(a^2*d*m*Sqrt[a + I*a*Tan[c + d*x]])","A",4,4,28,0.1429,1,"{3505, 3523, 70, 69}"
464,1,105,0,0.1457324,"\int (e \sec (c+d x))^m (a+i a \tan (c+d x))^n \, dx","Int[(e*Sec[c + d*x])^m*(a + I*a*Tan[c + d*x])^n,x]","\frac{i 2^{\frac{m}{2}+n} (a+i a \tan (c+d x))^n (e \sec (c+d x))^m (1+i \tan (c+d x))^{-\frac{m}{2}-n} \text{Hypergeometric2F1}\left(\frac{m}{2},-\frac{m}{2}-n+1,\frac{m+2}{2},\frac{1}{2} (1-i \tan (c+d x))\right)}{d m}","\frac{i 2^{\frac{m}{2}+n} (a+i a \tan (c+d x))^n (e \sec (c+d x))^m (1+i \tan (c+d x))^{-\frac{m}{2}-n} \text{Hypergeometric2F1}\left(\frac{m}{2},-\frac{m}{2}-n+1,\frac{m+2}{2},\frac{1}{2} (1-i \tan (c+d x))\right)}{d m}",1,"(I*2^(m/2 + n)*Hypergeometric2F1[m/2, 1 - m/2 - n, (2 + m)/2, (1 - I*Tan[c + d*x])/2]*(e*Sec[c + d*x])^m*(1 + I*Tan[c + d*x])^(-m/2 - n)*(a + I*a*Tan[c + d*x])^n)/(d*m)","A",4,4,26,0.1538,1,"{3505, 3523, 70, 69}"
465,1,97,0,0.0696611,"\int \sec ^6(c+d x) (a+i a \tan (c+d x))^n \, dx","Int[Sec[c + d*x]^6*(a + I*a*Tan[c + d*x])^n,x]","-\frac{4 i (a+i a \tan (c+d x))^{n+3}}{a^3 d (n+3)}+\frac{4 i (a+i a \tan (c+d x))^{n+4}}{a^4 d (n+4)}-\frac{i (a+i a \tan (c+d x))^{n+5}}{a^5 d (n+5)}","-\frac{4 i (a+i a \tan (c+d x))^{n+3}}{a^3 d (n+3)}+\frac{4 i (a+i a \tan (c+d x))^{n+4}}{a^4 d (n+4)}-\frac{i (a+i a \tan (c+d x))^{n+5}}{a^5 d (n+5)}",1,"((-4*I)*(a + I*a*Tan[c + d*x])^(3 + n))/(a^3*d*(3 + n)) + ((4*I)*(a + I*a*Tan[c + d*x])^(4 + n))/(a^4*d*(4 + n)) - (I*(a + I*a*Tan[c + d*x])^(5 + n))/(a^5*d*(5 + n))","A",3,2,24,0.08333,1,"{3487, 43}"
466,1,65,0,0.0555908,"\int \sec ^4(c+d x) (a+i a \tan (c+d x))^n \, dx","Int[Sec[c + d*x]^4*(a + I*a*Tan[c + d*x])^n,x]","\frac{i (a+i a \tan (c+d x))^{n+3}}{a^3 d (n+3)}-\frac{2 i (a+i a \tan (c+d x))^{n+2}}{a^2 d (n+2)}","\frac{i (a+i a \tan (c+d x))^{n+3}}{a^3 d (n+3)}-\frac{2 i (a+i a \tan (c+d x))^{n+2}}{a^2 d (n+2)}",1,"((-2*I)*(a + I*a*Tan[c + d*x])^(2 + n))/(a^2*d*(2 + n)) + (I*(a + I*a*Tan[c + d*x])^(3 + n))/(a^3*d*(3 + n))","A",3,2,24,0.08333,1,"{3487, 43}"
467,1,32,0,0.0462205,"\int \sec ^2(c+d x) (a+i a \tan (c+d x))^n \, dx","Int[Sec[c + d*x]^2*(a + I*a*Tan[c + d*x])^n,x]","-\frac{i (a+i a \tan (c+d x))^{n+1}}{a d (n+1)}","-\frac{i (a+i a \tan (c+d x))^{n+1}}{a d (n+1)}",1,"((-I)*(a + I*a*Tan[c + d*x])^(1 + n))/(a*d*(1 + n))","A",2,2,24,0.08333,1,"{3487, 32}"
468,1,56,0,0.0572094,"\int \cos ^2(c+d x) (a+i a \tan (c+d x))^n \, dx","Int[Cos[c + d*x]^2*(a + I*a*Tan[c + d*x])^n,x]","\frac{i a (a+i a \tan (c+d x))^{n-1} \text{Hypergeometric2F1}\left(2,n-1,n,\frac{1}{2} (1+i \tan (c+d x))\right)}{4 d (1-n)}","\frac{i a (a+i a \tan (c+d x))^{n-1} \text{Hypergeometric2F1}\left(2,n-1,n,\frac{1}{2} (1+i \tan (c+d x))\right)}{4 d (1-n)}",1,"((I/4)*a*Hypergeometric2F1[2, -1 + n, n, (1 + I*Tan[c + d*x])/2]*(a + I*a*Tan[c + d*x])^(-1 + n))/(d*(1 - n))","A",2,2,24,0.08333,1,"{3487, 68}"
469,1,60,0,0.0550382,"\int \cos ^4(c+d x) (a+i a \tan (c+d x))^n \, dx","Int[Cos[c + d*x]^4*(a + I*a*Tan[c + d*x])^n,x]","\frac{i a^2 (a+i a \tan (c+d x))^{n-2} \text{Hypergeometric2F1}\left(3,n-2,n-1,\frac{1}{2} (1+i \tan (c+d x))\right)}{8 d (2-n)}","\frac{i a^2 (a+i a \tan (c+d x))^{n-2} \text{Hypergeometric2F1}\left(3,n-2,n-1,\frac{1}{2} (1+i \tan (c+d x))\right)}{8 d (2-n)}",1,"((I/8)*a^2*Hypergeometric2F1[3, -2 + n, -1 + n, (1 + I*Tan[c + d*x])/2]*(a + I*a*Tan[c + d*x])^(-2 + n))/(d*(2 - n))","A",2,2,24,0.08333,1,"{3487, 68}"
470,1,60,0,0.0539792,"\int \cos ^6(c+d x) (a+i a \tan (c+d x))^n \, dx","Int[Cos[c + d*x]^6*(a + I*a*Tan[c + d*x])^n,x]","\frac{i a^3 (a+i a \tan (c+d x))^{n-3} \text{Hypergeometric2F1}\left(4,n-3,n-2,\frac{1}{2} (1+i \tan (c+d x))\right)}{16 d (3-n)}","\frac{i a^3 (a+i a \tan (c+d x))^{n-3} \text{Hypergeometric2F1}\left(4,n-3,n-2,\frac{1}{2} (1+i \tan (c+d x))\right)}{16 d (3-n)}",1,"((I/16)*a^3*Hypergeometric2F1[4, -3 + n, -2 + n, (1 + I*Tan[c + d*x])/2]*(a + I*a*Tan[c + d*x])^(-3 + n))/(d*(3 - n))","A",2,2,24,0.08333,1,"{3487, 68}"
471,1,94,0,0.1873761,"\int \sec ^5(c+d x) (a+i a \tan (c+d x))^n \, dx","Int[Sec[c + d*x]^5*(a + I*a*Tan[c + d*x])^n,x]","\frac{i a^2 2^{n+\frac{5}{2}} \sec ^5(c+d x) (1+i \tan (c+d x))^{-n-\frac{1}{2}} (a+i a \tan (c+d x))^{n-2} \text{Hypergeometric2F1}\left(\frac{5}{2},-n-\frac{3}{2},\frac{7}{2},\frac{1}{2} (1-i \tan (c+d x))\right)}{5 d}","\frac{i a^2 2^{n+\frac{5}{2}} \sec ^5(c+d x) (1+i \tan (c+d x))^{-n-\frac{1}{2}} (a+i a \tan (c+d x))^{n-2} \text{Hypergeometric2F1}\left(\frac{5}{2},-n-\frac{3}{2},\frac{7}{2},\frac{1}{2} (1-i \tan (c+d x))\right)}{5 d}",1,"((I/5)*2^(5/2 + n)*a^2*Hypergeometric2F1[5/2, -3/2 - n, 7/2, (1 - I*Tan[c + d*x])/2]*Sec[c + d*x]^5*(1 + I*Tan[c + d*x])^(-1/2 - n)*(a + I*a*Tan[c + d*x])^(-2 + n))/d","A",4,4,24,0.1667,1,"{3505, 3523, 70, 69}"
472,1,92,0,0.1820357,"\int \sec ^3(c+d x) (a+i a \tan (c+d x))^n \, dx","Int[Sec[c + d*x]^3*(a + I*a*Tan[c + d*x])^n,x]","\frac{i a 2^{n+\frac{3}{2}} \sec ^3(c+d x) (1+i \tan (c+d x))^{-n-\frac{1}{2}} (a+i a \tan (c+d x))^{n-1} \text{Hypergeometric2F1}\left(\frac{3}{2},-n-\frac{1}{2},\frac{5}{2},\frac{1}{2} (1-i \tan (c+d x))\right)}{3 d}","\frac{i a 2^{n+\frac{3}{2}} \sec ^3(c+d x) (1+i \tan (c+d x))^{-n-\frac{1}{2}} (a+i a \tan (c+d x))^{n-1} \text{Hypergeometric2F1}\left(\frac{3}{2},-n-\frac{1}{2},\frac{5}{2},\frac{1}{2} (1-i \tan (c+d x))\right)}{3 d}",1,"((I/3)*2^(3/2 + n)*a*Hypergeometric2F1[3/2, -1/2 - n, 5/2, (1 - I*Tan[c + d*x])/2]*Sec[c + d*x]^3*(1 + I*Tan[c + d*x])^(-1/2 - n)*(a + I*a*Tan[c + d*x])^(-1 + n))/d","A",4,4,24,0.1667,1,"{3505, 3523, 70, 69}"
473,1,88,0,0.1492616,"\int \sec (c+d x) (a+i a \tan (c+d x))^n \, dx","Int[Sec[c + d*x]*(a + I*a*Tan[c + d*x])^n,x]","\frac{i a 2^{n+\frac{1}{2}} \sec (c+d x) (1+i \tan (c+d x))^{\frac{1}{2}-n} (a+i a \tan (c+d x))^{n-1} \text{Hypergeometric2F1}\left(\frac{1}{2},\frac{1}{2}-n,\frac{3}{2},\frac{1}{2} (1-i \tan (c+d x))\right)}{d}","\frac{i a 2^{n+\frac{1}{2}} \sec (c+d x) (1+i \tan (c+d x))^{\frac{1}{2}-n} (a+i a \tan (c+d x))^{n-1} \text{Hypergeometric2F1}\left(\frac{1}{2},\frac{1}{2}-n,\frac{3}{2},\frac{1}{2} (1-i \tan (c+d x))\right)}{d}",1,"(I*2^(1/2 + n)*a*Hypergeometric2F1[1/2, 1/2 - n, 3/2, (1 - I*Tan[c + d*x])/2]*Sec[c + d*x]*(1 + I*Tan[c + d*x])^(1/2 - n)*(a + I*a*Tan[c + d*x])^(-1 + n))/d","A",4,4,22,0.1818,1,"{3505, 3523, 70, 69}"
474,1,85,0,0.1663542,"\int \cos (c+d x) (a+i a \tan (c+d x))^n \, dx","Int[Cos[c + d*x]*(a + I*a*Tan[c + d*x])^n,x]","-\frac{i 2^{n-\frac{1}{2}} \cos (c+d x) (1+i \tan (c+d x))^{\frac{1}{2}-n} (a+i a \tan (c+d x))^n \text{Hypergeometric2F1}\left(-\frac{1}{2},\frac{3}{2}-n,\frac{1}{2},\frac{1}{2} (1-i \tan (c+d x))\right)}{d}","-\frac{i 2^{n-\frac{1}{2}} \cos (c+d x) (1+i \tan (c+d x))^{\frac{1}{2}-n} (a+i a \tan (c+d x))^n \text{Hypergeometric2F1}\left(-\frac{1}{2},\frac{3}{2}-n,\frac{1}{2},\frac{1}{2} (1-i \tan (c+d x))\right)}{d}",1,"((-I)*2^(-1/2 + n)*Cos[c + d*x]*Hypergeometric2F1[-1/2, 3/2 - n, 1/2, (1 - I*Tan[c + d*x])/2]*(1 + I*Tan[c + d*x])^(1/2 - n)*(a + I*a*Tan[c + d*x])^n)/d","A",4,4,22,0.1818,1,"{3505, 3523, 70, 69}"
475,1,94,0,0.1892608,"\int \cos ^3(c+d x) (a+i a \tan (c+d x))^n \, dx","Int[Cos[c + d*x]^3*(a + I*a*Tan[c + d*x])^n,x]","-\frac{i 2^{n-\frac{3}{2}} \cos ^3(c+d x) (1+i \tan (c+d x))^{\frac{1}{2}-n} (a+i a \tan (c+d x))^{n+1} \text{Hypergeometric2F1}\left(-\frac{3}{2},\frac{5}{2}-n,-\frac{1}{2},\frac{1}{2} (1-i \tan (c+d x))\right)}{3 a d}","-\frac{i 2^{n-\frac{3}{2}} \cos ^3(c+d x) (1+i \tan (c+d x))^{\frac{1}{2}-n} (a+i a \tan (c+d x))^{n+1} \text{Hypergeometric2F1}\left(-\frac{3}{2},\frac{5}{2}-n,-\frac{1}{2},\frac{1}{2} (1-i \tan (c+d x))\right)}{3 a d}",1,"((-I/3)*2^(-3/2 + n)*Cos[c + d*x]^3*Hypergeometric2F1[-3/2, 5/2 - n, -1/2, (1 - I*Tan[c + d*x])/2]*(1 + I*Tan[c + d*x])^(1/2 - n)*(a + I*a*Tan[c + d*x])^(1 + n))/(a*d)","A",4,4,24,0.1667,1,"{3505, 3523, 70, 69}"
476,1,94,0,0.1934905,"\int \cos ^5(c+d x) (a+i a \tan (c+d x))^n \, dx","Int[Cos[c + d*x]^5*(a + I*a*Tan[c + d*x])^n,x]","-\frac{i 2^{n-\frac{5}{2}} \cos ^5(c+d x) (1+i \tan (c+d x))^{\frac{1}{2}-n} (a+i a \tan (c+d x))^{n+2} \text{Hypergeometric2F1}\left(-\frac{5}{2},\frac{7}{2}-n,-\frac{3}{2},\frac{1}{2} (1-i \tan (c+d x))\right)}{5 a^2 d}","-\frac{i 2^{n-\frac{5}{2}} \cos ^5(c+d x) (1+i \tan (c+d x))^{\frac{1}{2}-n} (a+i a \tan (c+d x))^{n+2} \text{Hypergeometric2F1}\left(-\frac{5}{2},\frac{7}{2}-n,-\frac{3}{2},\frac{1}{2} (1-i \tan (c+d x))\right)}{5 a^2 d}",1,"((-I/5)*2^(-5/2 + n)*Cos[c + d*x]^5*Hypergeometric2F1[-5/2, 7/2 - n, -3/2, (1 - I*Tan[c + d*x])/2]*(1 + I*Tan[c + d*x])^(1/2 - n)*(a + I*a*Tan[c + d*x])^(2 + n))/(a^2*d)","A",4,4,24,0.1667,1,"{3505, 3523, 70, 69}"
477,1,96,0,0.2016243,"\int (e \sec (c+d x))^{5/2} (a+i a \tan (c+d x))^n \, dx","Int[(e*Sec[c + d*x])^(5/2)*(a + I*a*Tan[c + d*x])^n,x]","\frac{i a 2^{n+\frac{9}{4}} (e \sec (c+d x))^{5/2} (1+i \tan (c+d x))^{-n-\frac{1}{4}} (a+i a \tan (c+d x))^{n-1} \text{Hypergeometric2F1}\left(\frac{5}{4},-n-\frac{1}{4},\frac{9}{4},\frac{1}{2} (1-i \tan (c+d x))\right)}{5 d}","\frac{i a 2^{n+\frac{9}{4}} (e \sec (c+d x))^{5/2} (1+i \tan (c+d x))^{-n-\frac{1}{4}} (a+i a \tan (c+d x))^{n-1} \text{Hypergeometric2F1}\left(\frac{5}{4},-n-\frac{1}{4},\frac{9}{4},\frac{1}{2} (1-i \tan (c+d x))\right)}{5 d}",1,"((I/5)*2^(9/4 + n)*a*Hypergeometric2F1[5/4, -1/4 - n, 9/4, (1 - I*Tan[c + d*x])/2]*(e*Sec[c + d*x])^(5/2)*(1 + I*Tan[c + d*x])^(-1/4 - n)*(a + I*a*Tan[c + d*x])^(-1 + n))/d","A",4,4,28,0.1429,1,"{3505, 3523, 70, 69}"
478,1,96,0,0.1985031,"\int (e \sec (c+d x))^{3/2} (a+i a \tan (c+d x))^n \, dx","Int[(e*Sec[c + d*x])^(3/2)*(a + I*a*Tan[c + d*x])^n,x]","\frac{i a 2^{n+\frac{7}{4}} (e \sec (c+d x))^{3/2} (1+i \tan (c+d x))^{\frac{1}{4}-n} (a+i a \tan (c+d x))^{n-1} \text{Hypergeometric2F1}\left(\frac{3}{4},\frac{1}{4}-n,\frac{7}{4},\frac{1}{2} (1-i \tan (c+d x))\right)}{3 d}","\frac{i a 2^{n+\frac{7}{4}} (e \sec (c+d x))^{3/2} (1+i \tan (c+d x))^{\frac{1}{4}-n} (a+i a \tan (c+d x))^{n-1} \text{Hypergeometric2F1}\left(\frac{3}{4},\frac{1}{4}-n,\frac{7}{4},\frac{1}{2} (1-i \tan (c+d x))\right)}{3 d}",1,"((I/3)*2^(7/4 + n)*a*Hypergeometric2F1[3/4, 1/4 - n, 7/4, (1 - I*Tan[c + d*x])/2]*(e*Sec[c + d*x])^(3/2)*(1 + I*Tan[c + d*x])^(1/4 - n)*(a + I*a*Tan[c + d*x])^(-1 + n))/d","A",4,4,28,0.1429,1,"{3505, 3523, 70, 69}"
479,1,94,0,0.174919,"\int \sqrt{e \sec (c+d x)} (a+i a \tan (c+d x))^n \, dx","Int[Sqrt[e*Sec[c + d*x]]*(a + I*a*Tan[c + d*x])^n,x]","\frac{i a 2^{n+\frac{5}{4}} \sqrt{e \sec (c+d x)} (1+i \tan (c+d x))^{\frac{3}{4}-n} (a+i a \tan (c+d x))^{n-1} \text{Hypergeometric2F1}\left(\frac{1}{4},\frac{3}{4}-n,\frac{5}{4},\frac{1}{2} (1-i \tan (c+d x))\right)}{d}","\frac{i a 2^{n+\frac{5}{4}} \sqrt{e \sec (c+d x)} (1+i \tan (c+d x))^{\frac{3}{4}-n} (a+i a \tan (c+d x))^{n-1} \text{Hypergeometric2F1}\left(\frac{1}{4},\frac{3}{4}-n,\frac{5}{4},\frac{1}{2} (1-i \tan (c+d x))\right)}{d}",1,"(I*2^(5/4 + n)*a*Hypergeometric2F1[1/4, 3/4 - n, 5/4, (1 - I*Tan[c + d*x])/2]*Sqrt[e*Sec[c + d*x]]*(1 + I*Tan[c + d*x])^(3/4 - n)*(a + I*a*Tan[c + d*x])^(-1 + n))/d","A",4,4,28,0.1429,1,"{3505, 3523, 70, 69}"
480,1,91,0,0.1781574,"\int \frac{(a+i a \tan (c+d x))^n}{\sqrt{e \sec (c+d x)}} \, dx","Int[(a + I*a*Tan[c + d*x])^n/Sqrt[e*Sec[c + d*x]],x]","-\frac{i 2^{n+\frac{3}{4}} (1+i \tan (c+d x))^{\frac{1}{4}-n} (a+i a \tan (c+d x))^n \text{Hypergeometric2F1}\left(-\frac{1}{4},\frac{5}{4}-n,\frac{3}{4},\frac{1}{2} (1-i \tan (c+d x))\right)}{d \sqrt{e \sec (c+d x)}}","-\frac{i 2^{n+\frac{3}{4}} (1+i \tan (c+d x))^{\frac{1}{4}-n} (a+i a \tan (c+d x))^n \text{Hypergeometric2F1}\left(-\frac{1}{4},\frac{5}{4}-n,\frac{3}{4},\frac{1}{2} (1-i \tan (c+d x))\right)}{d \sqrt{e \sec (c+d x)}}",1,"((-I)*2^(3/4 + n)*Hypergeometric2F1[-1/4, 5/4 - n, 3/4, (1 - I*Tan[c + d*x])/2]*(1 + I*Tan[c + d*x])^(1/4 - n)*(a + I*a*Tan[c + d*x])^n)/(d*Sqrt[e*Sec[c + d*x]])","A",4,4,28,0.1429,1,"{3505, 3523, 70, 69}"
481,1,93,0,0.2083436,"\int \frac{(a+i a \tan (c+d x))^n}{(e \sec (c+d x))^{3/2}} \, dx","Int[(a + I*a*Tan[c + d*x])^n/(e*Sec[c + d*x])^(3/2),x]","-\frac{i 2^{n+\frac{1}{4}} (1+i \tan (c+d x))^{\frac{3}{4}-n} (a+i a \tan (c+d x))^n \text{Hypergeometric2F1}\left(-\frac{3}{4},\frac{7}{4}-n,\frac{1}{4},\frac{1}{2} (1-i \tan (c+d x))\right)}{3 d (e \sec (c+d x))^{3/2}}","-\frac{i 2^{n+\frac{1}{4}} (1+i \tan (c+d x))^{\frac{3}{4}-n} (a+i a \tan (c+d x))^n \text{Hypergeometric2F1}\left(-\frac{3}{4},\frac{7}{4}-n,\frac{1}{4},\frac{1}{2} (1-i \tan (c+d x))\right)}{3 d (e \sec (c+d x))^{3/2}}",1,"((-I/3)*2^(1/4 + n)*Hypergeometric2F1[-3/4, 7/4 - n, 1/4, (1 - I*Tan[c + d*x])/2]*(1 + I*Tan[c + d*x])^(3/4 - n)*(a + I*a*Tan[c + d*x])^n)/(d*(e*Sec[c + d*x])^(3/2))","A",4,4,28,0.1429,1,"{3505, 3523, 70, 69}"
482,1,98,0,0.2101637,"\int \frac{(a+i a \tan (c+d x))^n}{(e \sec (c+d x))^{5/2}} \, dx","Int[(a + I*a*Tan[c + d*x])^n/(e*Sec[c + d*x])^(5/2),x]","-\frac{i 2^{n-\frac{1}{4}} (1+i \tan (c+d x))^{\frac{1}{4}-n} (a+i a \tan (c+d x))^{n+1} \text{Hypergeometric2F1}\left(-\frac{5}{4},\frac{9}{4}-n,-\frac{1}{4},\frac{1}{2} (1-i \tan (c+d x))\right)}{5 a d (e \sec (c+d x))^{5/2}}","-\frac{i 2^{n-\frac{1}{4}} (1+i \tan (c+d x))^{\frac{1}{4}-n} (a+i a \tan (c+d x))^{n+1} \text{Hypergeometric2F1}\left(-\frac{5}{4},\frac{9}{4}-n,-\frac{1}{4},\frac{1}{2} (1-i \tan (c+d x))\right)}{5 a d (e \sec (c+d x))^{5/2}}",1,"((-I/5)*2^(-1/4 + n)*Hypergeometric2F1[-5/4, 9/4 - n, -1/4, (1 - I*Tan[c + d*x])/2]*(1 + I*Tan[c + d*x])^(1/4 - n)*(a + I*a*Tan[c + d*x])^(1 + n))/(a*d*(e*Sec[c + d*x])^(5/2))","A",4,4,28,0.1429,1,"{3505, 3523, 70, 69}"
483,1,269,0,0.4061691,"\int (e \sec (c+d x))^{-4-n} (a+i a \tan (c+d x))^n \, dx","Int[(e*Sec[c + d*x])^(-4 - n)*(a + I*a*Tan[c + d*x])^n,x]","\frac{24 i (a+i a \tan (c+d x))^{n+3} (e \sec (c+d x))^{-n-4}}{a^3 d (4-n) n \left(4-n^2\right)}-\frac{24 i (a+i a \tan (c+d x))^{n+4} (e \sec (c+d x))^{-n-4}}{a^4 d n \left(n^4-20 n^2+64\right)}-\frac{12 i (a+i a \tan (c+d x))^{n+2} (e \sec (c+d x))^{-n-4}}{a^2 d (2-n) (4-n) n}+\frac{4 i (a+i a \tan (c+d x))^{n+1} (e \sec (c+d x))^{-n-4}}{a d \left(n^2-6 n+8\right)}+\frac{i (a+i a \tan (c+d x))^n (e \sec (c+d x))^{-n-4}}{d (4-n)}","\frac{24 i (a+i a \tan (c+d x))^{n+3} (e \sec (c+d x))^{-n-4}}{a^3 d (4-n) n \left(4-n^2\right)}-\frac{24 i (a+i a \tan (c+d x))^{n+4} (e \sec (c+d x))^{-n-4}}{a^4 d n \left(n^4-20 n^2+64\right)}-\frac{12 i (a+i a \tan (c+d x))^{n+2} (e \sec (c+d x))^{-n-4}}{a^2 d (2-n) (4-n) n}+\frac{4 i (a+i a \tan (c+d x))^{n+1} (e \sec (c+d x))^{-n-4}}{a d \left(n^2-6 n+8\right)}+\frac{i (a+i a \tan (c+d x))^n (e \sec (c+d x))^{-n-4}}{d (4-n)}",1,"(I*(e*Sec[c + d*x])^(-4 - n)*(a + I*a*Tan[c + d*x])^n)/(d*(4 - n)) + ((4*I)*(e*Sec[c + d*x])^(-4 - n)*(a + I*a*Tan[c + d*x])^(1 + n))/(a*d*(8 - 6*n + n^2)) - ((12*I)*(e*Sec[c + d*x])^(-4 - n)*(a + I*a*Tan[c + d*x])^(2 + n))/(a^2*d*(2 - n)*(4 - n)*n) + ((24*I)*(e*Sec[c + d*x])^(-4 - n)*(a + I*a*Tan[c + d*x])^(3 + n))/(a^3*d*(4 - n)*n*(4 - n^2)) - ((24*I)*(e*Sec[c + d*x])^(-4 - n)*(a + I*a*Tan[c + d*x])^(4 + n))/(a^4*d*n*(64 - 20*n^2 + n^4))","A",5,2,30,0.06667,1,"{3504, 3488}"
484,1,205,0,0.3045663,"\int (e \sec (c+d x))^{-3-n} (a+i a \tan (c+d x))^n \, dx","Int[(e*Sec[c + d*x])^(-3 - n)*(a + I*a*Tan[c + d*x])^n,x]","-\frac{6 i (a+i a \tan (c+d x))^{n+2} (e \sec (c+d x))^{-n-3}}{a^2 d (3-n) \left(1-n^2\right)}+\frac{6 i (a+i a \tan (c+d x))^{n+3} (e \sec (c+d x))^{-n-3}}{a^3 d \left(n^4-10 n^2+9\right)}+\frac{3 i (a+i a \tan (c+d x))^{n+1} (e \sec (c+d x))^{-n-3}}{a d \left(n^2-4 n+3\right)}+\frac{i (a+i a \tan (c+d x))^n (e \sec (c+d x))^{-n-3}}{d (3-n)}","-\frac{6 i (a+i a \tan (c+d x))^{n+2} (e \sec (c+d x))^{-n-3}}{a^2 d (3-n) \left(1-n^2\right)}+\frac{6 i (a+i a \tan (c+d x))^{n+3} (e \sec (c+d x))^{-n-3}}{a^3 d \left(n^4-10 n^2+9\right)}+\frac{3 i (a+i a \tan (c+d x))^{n+1} (e \sec (c+d x))^{-n-3}}{a d \left(n^2-4 n+3\right)}+\frac{i (a+i a \tan (c+d x))^n (e \sec (c+d x))^{-n-3}}{d (3-n)}",1,"(I*(e*Sec[c + d*x])^(-3 - n)*(a + I*a*Tan[c + d*x])^n)/(d*(3 - n)) + ((3*I)*(e*Sec[c + d*x])^(-3 - n)*(a + I*a*Tan[c + d*x])^(1 + n))/(a*d*(3 - 4*n + n^2)) - ((6*I)*(e*Sec[c + d*x])^(-3 - n)*(a + I*a*Tan[c + d*x])^(2 + n))/(a^2*d*(3 - n)*(1 - n^2)) + ((6*I)*(e*Sec[c + d*x])^(-3 - n)*(a + I*a*Tan[c + d*x])^(3 + n))/(a^3*d*(9 - 10*n^2 + n^4))","A",4,2,30,0.06667,1,"{3504, 3488}"
485,1,148,0,0.1979281,"\int (e \sec (c+d x))^{-2-n} (a+i a \tan (c+d x))^n \, dx","Int[(e*Sec[c + d*x])^(-2 - n)*(a + I*a*Tan[c + d*x])^n,x]","\frac{2 i (a+i a \tan (c+d x))^{n+2} (e \sec (c+d x))^{-n-2}}{a^2 d n \left(4-n^2\right)}+\frac{i (a+i a \tan (c+d x))^n (e \sec (c+d x))^{-n-2}}{d (2-n)}-\frac{2 i (a+i a \tan (c+d x))^{n+1} (e \sec (c+d x))^{-n-2}}{a d (2-n) n}","\frac{2 i (a+i a \tan (c+d x))^{n+2} (e \sec (c+d x))^{-n-2}}{a^2 d n \left(4-n^2\right)}+\frac{i (a+i a \tan (c+d x))^n (e \sec (c+d x))^{-n-2}}{d (2-n)}-\frac{2 i (a+i a \tan (c+d x))^{n+1} (e \sec (c+d x))^{-n-2}}{a d (2-n) n}",1,"(I*(e*Sec[c + d*x])^(-2 - n)*(a + I*a*Tan[c + d*x])^n)/(d*(2 - n)) - ((2*I)*(e*Sec[c + d*x])^(-2 - n)*(a + I*a*Tan[c + d*x])^(1 + n))/(a*d*(2 - n)*n) + ((2*I)*(e*Sec[c + d*x])^(-2 - n)*(a + I*a*Tan[c + d*x])^(2 + n))/(a^2*d*n*(4 - n^2))","A",3,2,30,0.06667,1,"{3504, 3488}"
486,1,94,0,0.1163566,"\int (e \sec (c+d x))^{-1-n} (a+i a \tan (c+d x))^n \, dx","Int[(e*Sec[c + d*x])^(-1 - n)*(a + I*a*Tan[c + d*x])^n,x]","\frac{i (a+i a \tan (c+d x))^n (e \sec (c+d x))^{-n-1}}{d (1-n)}-\frac{i (a+i a \tan (c+d x))^{n+1} (e \sec (c+d x))^{-n-1}}{a d \left(1-n^2\right)}","\frac{i (a+i a \tan (c+d x))^n (e \sec (c+d x))^{-n-1}}{d (1-n)}-\frac{i (a+i a \tan (c+d x))^{n+1} (e \sec (c+d x))^{-n-1}}{a d \left(1-n^2\right)}",1,"(I*(e*Sec[c + d*x])^(-1 - n)*(a + I*a*Tan[c + d*x])^n)/(d*(1 - n)) - (I*(e*Sec[c + d*x])^(-1 - n)*(a + I*a*Tan[c + d*x])^(1 + n))/(a*d*(1 - n^2))","A",2,2,30,0.06667,1,"{3504, 3488}"
487,1,37,0,0.0477303,"\int (e \sec (c+d x))^{-n} (a+i a \tan (c+d x))^n \, dx","Int[(a + I*a*Tan[c + d*x])^n/(e*Sec[c + d*x])^n,x]","-\frac{i (a+i a \tan (c+d x))^n (e \sec (c+d x))^{-n}}{d n}","-\frac{i (a+i a \tan (c+d x))^n (e \sec (c+d x))^{-n}}{d n}",1,"((-I)*(a + I*a*Tan[c + d*x])^n)/(d*n*(e*Sec[c + d*x])^n)","A",1,1,28,0.03571,1,"{3488}"
488,1,118,0,0.217809,"\int (e \sec (c+d x))^{1-n} (a+i a \tan (c+d x))^n \, dx","Int[(e*Sec[c + d*x])^(1 - n)*(a + I*a*Tan[c + d*x])^n,x]","\frac{i 2^{\frac{n+1}{2}} (1+i \tan (c+d x))^{\frac{1}{2} (-n-1)} (a+i a \tan (c+d x))^n (e \sec (c+d x))^{1-n} \text{Hypergeometric2F1}\left(\frac{1-n}{2},\frac{1-n}{2},\frac{3-n}{2},\frac{1}{2} (1-i \tan (c+d x))\right)}{d (1-n)}","\frac{i 2^{\frac{n+1}{2}} (1+i \tan (c+d x))^{\frac{1}{2} (-n-1)} (a+i a \tan (c+d x))^n (e \sec (c+d x))^{1-n} \text{Hypergeometric2F1}\left(\frac{1-n}{2},\frac{1-n}{2},\frac{3-n}{2},\frac{1}{2} (1-i \tan (c+d x))\right)}{d (1-n)}",1,"(I*2^((1 + n)/2)*Hypergeometric2F1[(1 - n)/2, (1 - n)/2, (3 - n)/2, (1 - I*Tan[c + d*x])/2]*(e*Sec[c + d*x])^(1 - n)*(1 + I*Tan[c + d*x])^((-1 - n)/2)*(a + I*a*Tan[c + d*x])^n)/(d*(1 - n))","A",4,4,30,0.1333,1,"{3505, 3523, 70, 69}"
489,1,113,0,0.1832014,"\int (e \sec (c+d x))^{2-n} (a+i a \tan (c+d x))^n \, dx","Int[(e*Sec[c + d*x])^(2 - n)*(a + I*a*Tan[c + d*x])^n,x]","\frac{i a 2^{\frac{n}{2}+1} (1+i \tan (c+d x))^{-n/2} (a+i a \tan (c+d x))^{n-1} (e \sec (c+d x))^{2-n} \text{Hypergeometric2F1}\left(\frac{2-n}{2},-\frac{n}{2},\frac{4-n}{2},\frac{1}{2} (1-i \tan (c+d x))\right)}{d (2-n)}","\frac{i a 2^{\frac{n}{2}+1} (1+i \tan (c+d x))^{-n/2} (a+i a \tan (c+d x))^{n-1} (e \sec (c+d x))^{2-n} \text{Hypergeometric2F1}\left(\frac{2-n}{2},-\frac{n}{2},\frac{4-n}{2},\frac{1}{2} (1-i \tan (c+d x))\right)}{d (2-n)}",1,"(I*2^(1 + n/2)*a*Hypergeometric2F1[(2 - n)/2, -n/2, (4 - n)/2, (1 - I*Tan[c + d*x])/2]*(e*Sec[c + d*x])^(2 - n)*(a + I*a*Tan[c + d*x])^(-1 + n))/(d*(2 - n)*(1 + I*Tan[c + d*x])^(n/2))","A",4,4,30,0.1333,1,"{3505, 3523, 70, 69}"
490,1,121,0,0.2354458,"\int (e \sec (c+d x))^{3-n} (a+i a \tan (c+d x))^n \, dx","Int[(e*Sec[c + d*x])^(3 - n)*(a + I*a*Tan[c + d*x])^n,x]","\frac{i a 2^{\frac{n+3}{2}} (1+i \tan (c+d x))^{\frac{1}{2} (-n-1)} (a+i a \tan (c+d x))^{n-1} (e \sec (c+d x))^{3-n} \text{Hypergeometric2F1}\left(\frac{1}{2} (-n-1),\frac{3-n}{2},\frac{5-n}{2},\frac{1}{2} (1-i \tan (c+d x))\right)}{d (3-n)}","\frac{i a 2^{\frac{n+3}{2}} (1+i \tan (c+d x))^{\frac{1}{2} (-n-1)} (a+i a \tan (c+d x))^{n-1} (e \sec (c+d x))^{3-n} \text{Hypergeometric2F1}\left(\frac{1}{2} (-n-1),\frac{3-n}{2},\frac{5-n}{2},\frac{1}{2} (1-i \tan (c+d x))\right)}{d (3-n)}",1,"(I*2^((3 + n)/2)*a*Hypergeometric2F1[(-1 - n)/2, (3 - n)/2, (5 - n)/2, (1 - I*Tan[c + d*x])/2]*(e*Sec[c + d*x])^(3 - n)*(1 + I*Tan[c + d*x])^((-1 - n)/2)*(a + I*a*Tan[c + d*x])^(-1 + n))/(d*(3 - n))","A",4,4,30,0.1333,1,"{3505, 3523, 70, 69}"
491,1,156,0,0.225592,"\int (e \sec (c+d x))^{6-2 n} (a+i a \tan (c+d x))^n \, dx","Int[(e*Sec[c + d*x])^(6 - 2*n)*(a + I*a*Tan[c + d*x])^n,x]","\frac{8 i a^3 (a+i a \tan (c+d x))^{n-3} (e \sec (c+d x))^{6-2 n}}{d (5-n) \left(n^2-7 n+12\right)}+\frac{4 i a^2 (a+i a \tan (c+d x))^{n-2} (e \sec (c+d x))^{6-2 n}}{d \left(n^2-9 n+20\right)}+\frac{i a (a+i a \tan (c+d x))^{n-1} (e \sec (c+d x))^{6-2 n}}{d (5-n)}","\frac{8 i a^3 (a+i a \tan (c+d x))^{n-3} (e \sec (c+d x))^{6-2 n}}{d (5-n) \left(n^2-7 n+12\right)}+\frac{4 i a^2 (a+i a \tan (c+d x))^{n-2} (e \sec (c+d x))^{6-2 n}}{d \left(n^2-9 n+20\right)}+\frac{i a (a+i a \tan (c+d x))^{n-1} (e \sec (c+d x))^{6-2 n}}{d (5-n)}",1,"((8*I)*a^3*(e*Sec[c + d*x])^(6 - 2*n)*(a + I*a*Tan[c + d*x])^(-3 + n))/(d*(5 - n)*(12 - 7*n + n^2)) + ((4*I)*a^2*(e*Sec[c + d*x])^(6 - 2*n)*(a + I*a*Tan[c + d*x])^(-2 + n))/(d*(20 - 9*n + n^2)) + (I*a*(e*Sec[c + d*x])^(6 - 2*n)*(a + I*a*Tan[c + d*x])^(-1 + n))/(d*(5 - n))","A",3,2,30,0.06667,1,"{3494, 3493}"
492,1,97,0,0.2084119,"\int (e \sec (c+d x))^{5-2 n} (a+i a \tan (c+d x))^n \, dx","Int[(e*Sec[c + d*x])^(5 - 2*n)*(a + I*a*Tan[c + d*x])^n,x]","-\frac{i 2^{\frac{5}{2}-n} (1-i \tan (c+d x))^{n-\frac{5}{2}} (a+i a \tan (c+d x))^n (e \sec (c+d x))^{5-2 n} \text{Hypergeometric2F1}\left(\frac{5}{2},\frac{1}{2} (2 n-3),\frac{7}{2},\frac{1}{2} (1+i \tan (c+d x))\right)}{5 d}","-\frac{i 2^{\frac{5}{2}-n} (1-i \tan (c+d x))^{n-\frac{5}{2}} (a+i a \tan (c+d x))^n (e \sec (c+d x))^{5-2 n} \text{Hypergeometric2F1}\left(\frac{5}{2},\frac{1}{2} (2 n-3),\frac{7}{2},\frac{1}{2} (1+i \tan (c+d x))\right)}{5 d}",1,"((-I/5)*2^(5/2 - n)*Hypergeometric2F1[5/2, (-3 + 2*n)/2, 7/2, (1 + I*Tan[c + d*x])/2]*(e*Sec[c + d*x])^(5 - 2*n)*(1 - I*Tan[c + d*x])^(-5/2 + n)*(a + I*a*Tan[c + d*x])^n)/d","A",5,5,30,0.1667,1,"{3505, 3523, 7, 70, 69}"
493,1,98,0,0.1318306,"\int (e \sec (c+d x))^{4-2 n} (a+i a \tan (c+d x))^n \, dx","Int[(e*Sec[c + d*x])^(4 - 2*n)*(a + I*a*Tan[c + d*x])^n,x]","\frac{2 i a^2 (a+i a \tan (c+d x))^{n-2} (e \sec (c+d x))^{4-2 n}}{d \left(n^2-5 n+6\right)}+\frac{i a (a+i a \tan (c+d x))^{n-1} (e \sec (c+d x))^{4-2 n}}{d (3-n)}","\frac{2 i a^2 (a+i a \tan (c+d x))^{n-2} (e \sec (c+d x))^{4-2 n}}{d \left(n^2-5 n+6\right)}+\frac{i a (a+i a \tan (c+d x))^{n-1} (e \sec (c+d x))^{4-2 n}}{d (3-n)}",1,"((2*I)*a^2*(e*Sec[c + d*x])^(4 - 2*n)*(a + I*a*Tan[c + d*x])^(-2 + n))/(d*(6 - 5*n + n^2)) + (I*a*(e*Sec[c + d*x])^(4 - 2*n)*(a + I*a*Tan[c + d*x])^(-1 + n))/(d*(3 - n))","A",2,2,30,0.06667,1,"{3494, 3493}"
494,1,97,0,0.2080144,"\int (e \sec (c+d x))^{3-2 n} (a+i a \tan (c+d x))^n \, dx","Int[(e*Sec[c + d*x])^(3 - 2*n)*(a + I*a*Tan[c + d*x])^n,x]","-\frac{i 2^{\frac{3}{2}-n} (1-i \tan (c+d x))^{n-\frac{3}{2}} (a+i a \tan (c+d x))^n (e \sec (c+d x))^{3-2 n} \text{Hypergeometric2F1}\left(\frac{3}{2},\frac{1}{2} (2 n-1),\frac{5}{2},\frac{1}{2} (1+i \tan (c+d x))\right)}{3 d}","-\frac{i 2^{\frac{3}{2}-n} (1-i \tan (c+d x))^{n-\frac{3}{2}} (a+i a \tan (c+d x))^n (e \sec (c+d x))^{3-2 n} \text{Hypergeometric2F1}\left(\frac{3}{2},\frac{1}{2} (2 n-1),\frac{5}{2},\frac{1}{2} (1+i \tan (c+d x))\right)}{3 d}",1,"((-I/3)*2^(3/2 - n)*Hypergeometric2F1[3/2, (-1 + 2*n)/2, 5/2, (1 + I*Tan[c + d*x])/2]*(e*Sec[c + d*x])^(3 - 2*n)*(1 - I*Tan[c + d*x])^(-3/2 + n)*(a + I*a*Tan[c + d*x])^n)/d","A",5,5,30,0.1667,1,"{3505, 3523, 7, 70, 69}"
495,1,46,0,0.0563509,"\int (e \sec (c+d x))^{2-2 n} (a+i a \tan (c+d x))^n \, dx","Int[(e*Sec[c + d*x])^(2 - 2*n)*(a + I*a*Tan[c + d*x])^n,x]","\frac{i a (a+i a \tan (c+d x))^{n-1} (e \sec (c+d x))^{2-2 n}}{d (1-n)}","\frac{i a (a+i a \tan (c+d x))^{n-1} (e \sec (c+d x))^{2-2 n}}{d (1-n)}",1,"(I*a*(e*Sec[c + d*x])^(2 - 2*n)*(a + I*a*Tan[c + d*x])^(-1 + n))/(d*(1 - n))","A",1,1,30,0.03333,1,"{3493}"
496,1,95,0,0.1849634,"\int (e \sec (c+d x))^{1-2 n} (a+i a \tan (c+d x))^n \, dx","Int[(e*Sec[c + d*x])^(1 - 2*n)*(a + I*a*Tan[c + d*x])^n,x]","-\frac{i 2^{\frac{1}{2}-n} (1-i \tan (c+d x))^{n-\frac{1}{2}} (a+i a \tan (c+d x))^n (e \sec (c+d x))^{1-2 n} \text{Hypergeometric2F1}\left(\frac{1}{2},\frac{1}{2} (2 n+1),\frac{3}{2},\frac{1}{2} (1+i \tan (c+d x))\right)}{d}","-\frac{i 2^{\frac{1}{2}-n} (1-i \tan (c+d x))^{n-\frac{1}{2}} (a+i a \tan (c+d x))^n (e \sec (c+d x))^{1-2 n} \text{Hypergeometric2F1}\left(\frac{1}{2},\frac{1}{2} (2 n+1),\frac{3}{2},\frac{1}{2} (1+i \tan (c+d x))\right)}{d}",1,"((-I)*2^(1/2 - n)*Hypergeometric2F1[1/2, (1 + 2*n)/2, 3/2, (1 + I*Tan[c + d*x])/2]*(e*Sec[c + d*x])^(1 - 2*n)*(1 - I*Tan[c + d*x])^(-1/2 + n)*(a + I*a*Tan[c + d*x])^n)/d","A",5,5,30,0.1667,1,"{3505, 3523, 7, 70, 69}"
497,1,65,0,0.0781432,"\int (e \sec (c+d x))^{-2 n} (a+i a \tan (c+d x))^n \, dx","Int[(a + I*a*Tan[c + d*x])^n/(e*Sec[c + d*x])^(2*n),x]","-\frac{i (a+i a \tan (c+d x))^n (e \sec (c+d x))^{-2 n} \text{Hypergeometric2F1}\left(1,-n,1-n,\frac{1}{2} (1-i \tan (c+d x))\right)}{2 d n}","-\frac{i (a+i a \tan (c+d x))^n (e \sec (c+d x))^{-2 n} \text{Hypergeometric2F1}\left(1,-n,1-n,\frac{1}{2} (1-i \tan (c+d x))\right)}{2 d n}",1,"((-I/2)*Hypergeometric2F1[1, -n, 1 - n, (1 - I*Tan[c + d*x])/2]*(a + I*a*Tan[c + d*x])^n)/(d*n*(e*Sec[c + d*x])^(2*n))","A",3,3,28,0.1071,1,"{3492, 3481, 68}"
498,1,95,0,0.1918696,"\int (e \sec (c+d x))^{-1-2 n} (a+i a \tan (c+d x))^n \, dx","Int[(e*Sec[c + d*x])^(-1 - 2*n)*(a + I*a*Tan[c + d*x])^n,x]","\frac{i 2^{-n-\frac{1}{2}} (1-i \tan (c+d x))^{n+\frac{1}{2}} (a+i a \tan (c+d x))^n (e \sec (c+d x))^{-2 n-1} \text{Hypergeometric2F1}\left(-\frac{1}{2},\frac{1}{2} (2 n+3),\frac{1}{2},\frac{1}{2} (1+i \tan (c+d x))\right)}{d}","\frac{i 2^{-n-\frac{1}{2}} (1-i \tan (c+d x))^{n+\frac{1}{2}} (a+i a \tan (c+d x))^n (e \sec (c+d x))^{-2 n-1} \text{Hypergeometric2F1}\left(-\frac{1}{2},\frac{1}{2} (2 n+3),\frac{1}{2},\frac{1}{2} (1+i \tan (c+d x))\right)}{d}",1,"(I*2^(-1/2 - n)*Hypergeometric2F1[-1/2, (3 + 2*n)/2, 1/2, (1 + I*Tan[c + d*x])/2]*(e*Sec[c + d*x])^(-1 - 2*n)*(1 - I*Tan[c + d*x])^(1/2 + n)*(a + I*a*Tan[c + d*x])^n)/d","A",5,5,30,0.1667,1,"{3505, 3523, 7, 70, 69}"
499,1,74,0,0.1489414,"\int (e \sec (c+d x))^{-2-2 n} (a+i a \tan (c+d x))^n \, dx","Int[(e*Sec[c + d*x])^(-2 - 2*n)*(a + I*a*Tan[c + d*x])^n,x]","-\frac{i (a+i a \tan (c+d x))^{n+1} (e \sec (c+d x))^{-2 (n+1)} \text{Hypergeometric2F1}\left(2,-n-1,-n,\frac{1}{2} (1-i \tan (c+d x))\right)}{4 a d (n+1)}","-\frac{i (a+i a \tan (c+d x))^{n+1} (e \sec (c+d x))^{-2 (n+1)} \text{Hypergeometric2F1}\left(2,-n-1,-n,\frac{1}{2} (1-i \tan (c+d x))\right)}{4 a d (n+1)}",1,"((-I/4)*Hypergeometric2F1[2, -1 - n, -n, (1 - I*Tan[c + d*x])/2]*(a + I*a*Tan[c + d*x])^(1 + n))/(a*d*(1 + n)*(e*Sec[c + d*x])^(2*(1 + n)))","A",4,4,30,0.1333,1,"{3505, 3523, 7, 68}"
500,1,97,0,0.2142566,"\int (e \sec (c+d x))^{-3-2 n} (a+i a \tan (c+d x))^n \, dx","Int[(e*Sec[c + d*x])^(-3 - 2*n)*(a + I*a*Tan[c + d*x])^n,x]","\frac{i 2^{-n-\frac{3}{2}} (1-i \tan (c+d x))^{n+\frac{3}{2}} (a+i a \tan (c+d x))^n (e \sec (c+d x))^{-2 n-3} \text{Hypergeometric2F1}\left(-\frac{3}{2},\frac{1}{2} (2 n+5),-\frac{1}{2},\frac{1}{2} (1+i \tan (c+d x))\right)}{3 d}","\frac{i 2^{-n-\frac{3}{2}} (1-i \tan (c+d x))^{n+\frac{3}{2}} (a+i a \tan (c+d x))^n (e \sec (c+d x))^{-2 n-3} \text{Hypergeometric2F1}\left(-\frac{3}{2},\frac{1}{2} (2 n+5),-\frac{1}{2},\frac{1}{2} (1+i \tan (c+d x))\right)}{3 d}",1,"((I/3)*2^(-3/2 - n)*Hypergeometric2F1[-3/2, (5 + 2*n)/2, -1/2, (1 + I*Tan[c + d*x])/2]*(e*Sec[c + d*x])^(-3 - 2*n)*(1 - I*Tan[c + d*x])^(3/2 + n)*(a + I*a*Tan[c + d*x])^n)/d","A",5,5,30,0.1667,1,"{3505, 3523, 7, 70, 69}"
501,1,66,0,0.1890045,"\int (d \sec (e+f x))^{2 n} (a+i a \tan (e+f x))^{-2-n} \, dx","Int[(d*Sec[e + f*x])^(2*n)*(a + I*a*Tan[e + f*x])^(-2 - n),x]","\frac{i (a+i a \tan (e+f x))^{-n} (d \sec (e+f x))^{2 n} \text{Hypergeometric2F1}\left(3,n,n+1,\frac{1}{2} (1-i \tan (e+f x))\right)}{8 a^2 f n}","\frac{i (a+i a \tan (e+f x))^{-n} (d \sec (e+f x))^{2 n} \text{Hypergeometric2F1}\left(3,n,n+1,\frac{1}{2} (1-i \tan (e+f x))\right)}{8 a^2 f n}",1,"((I/8)*Hypergeometric2F1[3, n, 1 + n, (1 - I*Tan[e + f*x])/2]*(d*Sec[e + f*x])^(2*n))/(a^2*f*n*(a + I*a*Tan[e + f*x])^n)","A",4,4,32,0.1250,1,"{3505, 3522, 3487, 68}"
502,1,66,0,0.1825863,"\int (d \sec (e+f x))^{2 n} (a+i a \tan (e+f x))^{-1-n} \, dx","Int[(d*Sec[e + f*x])^(2*n)*(a + I*a*Tan[e + f*x])^(-1 - n),x]","\frac{i (a+i a \tan (e+f x))^{-n} (d \sec (e+f x))^{2 n} \text{Hypergeometric2F1}\left(2,n,n+1,\frac{1}{2} (1-i \tan (e+f x))\right)}{4 a f n}","\frac{i (a+i a \tan (e+f x))^{-n} (d \sec (e+f x))^{2 n} \text{Hypergeometric2F1}\left(2,n,n+1,\frac{1}{2} (1-i \tan (e+f x))\right)}{4 a f n}",1,"((I/4)*Hypergeometric2F1[2, n, 1 + n, (1 - I*Tan[e + f*x])/2]*(d*Sec[e + f*x])^(2*n))/(a*f*n*(a + I*a*Tan[e + f*x])^n)","A",4,4,32,0.1250,1,"{3505, 3522, 3487, 68}"
503,1,63,0,0.0744578,"\int (d \sec (e+f x))^{2 n} (a+i a \tan (e+f x))^{-n} \, dx","Int[(d*Sec[e + f*x])^(2*n)/(a + I*a*Tan[e + f*x])^n,x]","\frac{i (a+i a \tan (e+f x))^{-n} (d \sec (e+f x))^{2 n} \text{Hypergeometric2F1}\left(1,n,n+1,\frac{1}{2} (1-i \tan (e+f x))\right)}{2 f n}","\frac{i (a+i a \tan (e+f x))^{-n} (d \sec (e+f x))^{2 n} \text{Hypergeometric2F1}\left(1,n,n+1,\frac{1}{2} (1-i \tan (e+f x))\right)}{2 f n}",1,"((I/2)*Hypergeometric2F1[1, n, 1 + n, (1 - I*Tan[e + f*x])/2]*(d*Sec[e + f*x])^(2*n))/(f*n*(a + I*a*Tan[e + f*x])^n)","A",3,3,30,0.1000,1,"{3492, 3481, 68}"
504,1,40,0,0.0574708,"\int (d \sec (e+f x))^{2 n} (a+i a \tan (e+f x))^{1-n} \, dx","Int[(d*Sec[e + f*x])^(2*n)*(a + I*a*Tan[e + f*x])^(1 - n),x]","\frac{i a (a+i a \tan (e+f x))^{-n} (d \sec (e+f x))^{2 n}}{f n}","\frac{i a (a+i a \tan (e+f x))^{-n} (d \sec (e+f x))^{2 n}}{f n}",1,"(I*a*(d*Sec[e + f*x])^(2*n))/(f*n*(a + I*a*Tan[e + f*x])^n)","A",1,1,32,0.03125,1,"{3493}"
505,1,92,0,0.127938,"\int (d \sec (e+f x))^{2 n} (a+i a \tan (e+f x))^{2-n} \, dx","Int[(d*Sec[e + f*x])^(2*n)*(a + I*a*Tan[e + f*x])^(2 - n),x]","\frac{2 i a^2 (a+i a \tan (e+f x))^{-n} (d \sec (e+f x))^{2 n}}{f n (n+1)}+\frac{i a (a+i a \tan (e+f x))^{1-n} (d \sec (e+f x))^{2 n}}{f (n+1)}","\frac{2 i a^2 (a+i a \tan (e+f x))^{-n} (d \sec (e+f x))^{2 n}}{f n (n+1)}+\frac{i a (a+i a \tan (e+f x))^{1-n} (d \sec (e+f x))^{2 n}}{f (n+1)}",1,"(I*a*(d*Sec[e + f*x])^(2*n)*(a + I*a*Tan[e + f*x])^(1 - n))/(f*(1 + n)) + ((2*I)*a^2*(d*Sec[e + f*x])^(2*n))/(f*n*(1 + n)*(a + I*a*Tan[e + f*x])^n)","A",2,2,32,0.06250,1,"{3494, 3493}"
506,1,148,0,0.2110182,"\int (d \sec (e+f x))^{2 n} (a+i a \tan (e+f x))^{3-n} \, dx","Int[(d*Sec[e + f*x])^(2*n)*(a + I*a*Tan[e + f*x])^(3 - n),x]","\frac{4 i a^2 (a+i a \tan (e+f x))^{1-n} (d \sec (e+f x))^{2 n}}{f \left(n^2+3 n+2\right)}+\frac{8 i a^3 (a+i a \tan (e+f x))^{-n} (d \sec (e+f x))^{2 n}}{f n \left(n^2+3 n+2\right)}+\frac{i a (a+i a \tan (e+f x))^{2-n} (d \sec (e+f x))^{2 n}}{f (n+2)}","\frac{4 i a^2 (a+i a \tan (e+f x))^{1-n} (d \sec (e+f x))^{2 n}}{f \left(n^2+3 n+2\right)}+\frac{8 i a^3 (a+i a \tan (e+f x))^{-n} (d \sec (e+f x))^{2 n}}{f n \left(n^2+3 n+2\right)}+\frac{i a (a+i a \tan (e+f x))^{2-n} (d \sec (e+f x))^{2 n}}{f (n+2)}",1,"((4*I)*a^2*(d*Sec[e + f*x])^(2*n)*(a + I*a*Tan[e + f*x])^(1 - n))/(f*(2 + 3*n + n^2)) + (I*a*(d*Sec[e + f*x])^(2*n)*(a + I*a*Tan[e + f*x])^(2 - n))/(f*(2 + n)) + ((8*I)*a^3*(d*Sec[e + f*x])^(2*n))/(f*n*(2 + 3*n + n^2)*(a + I*a*Tan[e + f*x])^n)","A",3,2,32,0.06250,1,"{3494, 3493}"
507,1,60,0,0.0369258,"\int \sec ^6(c+d x) (a+b \tan (c+d x)) \, dx","Int[Sec[c + d*x]^6*(a + b*Tan[c + d*x]),x]","\frac{a \tan ^5(c+d x)}{5 d}+\frac{2 a \tan ^3(c+d x)}{3 d}+\frac{a \tan (c+d x)}{d}+\frac{b \sec ^6(c+d x)}{6 d}","\frac{a \tan ^5(c+d x)}{5 d}+\frac{2 a \tan ^3(c+d x)}{3 d}+\frac{a \tan (c+d x)}{d}+\frac{b \sec ^6(c+d x)}{6 d}",1,"(b*Sec[c + d*x]^6)/(6*d) + (a*Tan[c + d*x])/d + (2*a*Tan[c + d*x]^3)/(3*d) + (a*Tan[c + d*x]^5)/(5*d)","A",3,2,19,0.1053,1,"{3486, 3767}"
508,1,74,0,0.0464041,"\int \sec ^5(c+d x) (a+b \tan (c+d x)) \, dx","Int[Sec[c + d*x]^5*(a + b*Tan[c + d*x]),x]","\frac{3 a \tanh ^{-1}(\sin (c+d x))}{8 d}+\frac{a \tan (c+d x) \sec ^3(c+d x)}{4 d}+\frac{3 a \tan (c+d x) \sec (c+d x)}{8 d}+\frac{b \sec ^5(c+d x)}{5 d}","\frac{3 a \tanh ^{-1}(\sin (c+d x))}{8 d}+\frac{a \tan (c+d x) \sec ^3(c+d x)}{4 d}+\frac{3 a \tan (c+d x) \sec (c+d x)}{8 d}+\frac{b \sec ^5(c+d x)}{5 d}",1,"(3*a*ArcTanh[Sin[c + d*x]])/(8*d) + (b*Sec[c + d*x]^5)/(5*d) + (3*a*Sec[c + d*x]*Tan[c + d*x])/(8*d) + (a*Sec[c + d*x]^3*Tan[c + d*x])/(4*d)","A",4,3,19,0.1579,1,"{3486, 3768, 3770}"
509,1,44,0,0.0318142,"\int \sec ^4(c+d x) (a+b \tan (c+d x)) \, dx","Int[Sec[c + d*x]^4*(a + b*Tan[c + d*x]),x]","\frac{a \tan ^3(c+d x)}{3 d}+\frac{a \tan (c+d x)}{d}+\frac{b \sec ^4(c+d x)}{4 d}","\frac{a \tan ^3(c+d x)}{3 d}+\frac{a \tan (c+d x)}{d}+\frac{b \sec ^4(c+d x)}{4 d}",1,"(b*Sec[c + d*x]^4)/(4*d) + (a*Tan[c + d*x])/d + (a*Tan[c + d*x]^3)/(3*d)","A",3,2,19,0.1053,1,"{3486, 3767}"
510,1,52,0,0.0347972,"\int \sec ^3(c+d x) (a+b \tan (c+d x)) \, dx","Int[Sec[c + d*x]^3*(a + b*Tan[c + d*x]),x]","\frac{a \tanh ^{-1}(\sin (c+d x))}{2 d}+\frac{a \tan (c+d x) \sec (c+d x)}{2 d}+\frac{b \sec ^3(c+d x)}{3 d}","\frac{a \tanh ^{-1}(\sin (c+d x))}{2 d}+\frac{a \tan (c+d x) \sec (c+d x)}{2 d}+\frac{b \sec ^3(c+d x)}{3 d}",1,"(a*ArcTanh[Sin[c + d*x]])/(2*d) + (b*Sec[c + d*x]^3)/(3*d) + (a*Sec[c + d*x]*Tan[c + d*x])/(2*d)","A",3,3,19,0.1579,1,"{3486, 3768, 3770}"
511,1,28,0,0.0284686,"\int \sec ^2(c+d x) (a+b \tan (c+d x)) \, dx","Int[Sec[c + d*x]^2*(a + b*Tan[c + d*x]),x]","\frac{a \tan (c+d x)}{d}+\frac{b \sec ^2(c+d x)}{2 d}","\frac{a \tan (c+d x)}{d}+\frac{b \sec ^2(c+d x)}{2 d}",1,"(b*Sec[c + d*x]^2)/(2*d) + (a*Tan[c + d*x])/d","A",3,3,19,0.1579,1,"{3486, 3767, 8}"
512,1,24,0,0.0151662,"\int \sec (c+d x) (a+b \tan (c+d x)) \, dx","Int[Sec[c + d*x]*(a + b*Tan[c + d*x]),x]","\frac{a \tanh ^{-1}(\sin (c+d x))}{d}+\frac{b \sec (c+d x)}{d}","\frac{a \tanh ^{-1}(\sin (c+d x))}{d}+\frac{b \sec (c+d x)}{d}",1,"(a*ArcTanh[Sin[c + d*x]])/d + (b*Sec[c + d*x])/d","A",2,2,17,0.1176,1,"{3486, 3770}"
513,1,24,0,0.0196113,"\int \cos (c+d x) (a+b \tan (c+d x)) \, dx","Int[Cos[c + d*x]*(a + b*Tan[c + d*x]),x]","\frac{a \sin (c+d x)}{d}-\frac{b \cos (c+d x)}{d}","\frac{a \sin (c+d x)}{d}-\frac{b \cos (c+d x)}{d}",1,"-((b*Cos[c + d*x])/d) + (a*Sin[c + d*x])/d","A",2,2,17,0.1176,1,"{3486, 2637}"
514,1,43,0,0.0281819,"\int \cos ^2(c+d x) (a+b \tan (c+d x)) \, dx","Int[Cos[c + d*x]^2*(a + b*Tan[c + d*x]),x]","\frac{a \sin (c+d x) \cos (c+d x)}{2 d}+\frac{a x}{2}-\frac{b \cos ^2(c+d x)}{2 d}","\frac{a \sin (c+d x) \cos (c+d x)}{2 d}+\frac{a x}{2}-\frac{b \cos ^2(c+d x)}{2 d}",1,"(a*x)/2 - (b*Cos[c + d*x]^2)/(2*d) + (a*Cos[c + d*x]*Sin[c + d*x])/(2*d)","A",3,3,19,0.1579,1,"{3486, 2635, 8}"
515,1,44,0,0.0315729,"\int \cos ^3(c+d x) (a+b \tan (c+d x)) \, dx","Int[Cos[c + d*x]^3*(a + b*Tan[c + d*x]),x]","-\frac{a \sin ^3(c+d x)}{3 d}+\frac{a \sin (c+d x)}{d}-\frac{b \cos ^3(c+d x)}{3 d}","-\frac{a \sin ^3(c+d x)}{3 d}+\frac{a \sin (c+d x)}{d}-\frac{b \cos ^3(c+d x)}{3 d}",1,"-(b*Cos[c + d*x]^3)/(3*d) + (a*Sin[c + d*x])/d - (a*Sin[c + d*x]^3)/(3*d)","A",3,2,19,0.1053,1,"{3486, 2633}"
516,1,65,0,0.040945,"\int \cos ^4(c+d x) (a+b \tan (c+d x)) \, dx","Int[Cos[c + d*x]^4*(a + b*Tan[c + d*x]),x]","\frac{a \sin (c+d x) \cos ^3(c+d x)}{4 d}+\frac{3 a \sin (c+d x) \cos (c+d x)}{8 d}+\frac{3 a x}{8}-\frac{b \cos ^4(c+d x)}{4 d}","\frac{a \sin (c+d x) \cos ^3(c+d x)}{4 d}+\frac{3 a \sin (c+d x) \cos (c+d x)}{8 d}+\frac{3 a x}{8}-\frac{b \cos ^4(c+d x)}{4 d}",1,"(3*a*x)/8 - (b*Cos[c + d*x]^4)/(4*d) + (3*a*Cos[c + d*x]*Sin[c + d*x])/(8*d) + (a*Cos[c + d*x]^3*Sin[c + d*x])/(4*d)","A",4,3,19,0.1579,1,"{3486, 2635, 8}"
517,1,119,0,0.1065584,"\int \sec ^8(c+d x) (a+b \tan (c+d x))^2 \, dx","Int[Sec[c + d*x]^8*(a + b*Tan[c + d*x])^2,x]","\frac{\left(a^2+3 b^2\right) \tan ^7(c+d x)}{7 d}+\frac{3 \left(a^2+b^2\right) \tan ^5(c+d x)}{5 d}+\frac{\left(3 a^2+b^2\right) \tan ^3(c+d x)}{3 d}+\frac{a^2 \tan (c+d x)}{d}+\frac{a b \sec ^8(c+d x)}{4 d}+\frac{b^2 \tan ^9(c+d x)}{9 d}","\frac{\left(a^2+3 b^2\right) \tan ^7(c+d x)}{7 d}+\frac{3 \left(a^2+b^2\right) \tan ^5(c+d x)}{5 d}+\frac{\left(3 a^2+b^2\right) \tan ^3(c+d x)}{3 d}+\frac{a^2 \tan (c+d x)}{d}+\frac{a b \sec ^8(c+d x)}{4 d}+\frac{b^2 \tan ^9(c+d x)}{9 d}",1,"(a*b*Sec[c + d*x]^8)/(4*d) + (a^2*Tan[c + d*x])/d + ((3*a^2 + b^2)*Tan[c + d*x]^3)/(3*d) + (3*(a^2 + b^2)*Tan[c + d*x]^5)/(5*d) + ((a^2 + 3*b^2)*Tan[c + d*x]^7)/(7*d) + (b^2*Tan[c + d*x]^9)/(9*d)","A",4,3,21,0.1429,1,"{3506, 696, 1810}"
518,1,97,0,0.0825734,"\int \sec ^6(c+d x) (a+b \tan (c+d x))^2 \, dx","Int[Sec[c + d*x]^6*(a + b*Tan[c + d*x])^2,x]","\frac{\left(a^2+2 b^2\right) \tan ^5(c+d x)}{5 d}+\frac{\left(2 a^2+b^2\right) \tan ^3(c+d x)}{3 d}+\frac{a^2 \tan (c+d x)}{d}+\frac{a b \sec ^6(c+d x)}{3 d}+\frac{b^2 \tan ^7(c+d x)}{7 d}","\frac{\left(a^2+2 b^2\right) \tan ^5(c+d x)}{5 d}+\frac{\left(2 a^2+b^2\right) \tan ^3(c+d x)}{3 d}+\frac{a^2 \tan (c+d x)}{d}+\frac{a b \sec ^6(c+d x)}{3 d}+\frac{b^2 \tan ^7(c+d x)}{7 d}",1,"(a*b*Sec[c + d*x]^6)/(3*d) + (a^2*Tan[c + d*x])/d + ((2*a^2 + b^2)*Tan[c + d*x]^3)/(3*d) + ((a^2 + 2*b^2)*Tan[c + d*x]^5)/(5*d) + (b^2*Tan[c + d*x]^7)/(7*d)","A",4,3,21,0.1429,1,"{3506, 696, 1810}"
519,1,75,0,0.0659744,"\int \sec ^4(c+d x) (a+b \tan (c+d x))^2 \, dx","Int[Sec[c + d*x]^4*(a + b*Tan[c + d*x])^2,x]","\frac{\left(a^2+b^2\right) (a+b \tan (c+d x))^3}{3 b^3 d}+\frac{(a+b \tan (c+d x))^5}{5 b^3 d}-\frac{a (a+b \tan (c+d x))^4}{2 b^3 d}","\frac{\left(a^2+b^2\right) (a+b \tan (c+d x))^3}{3 b^3 d}+\frac{(a+b \tan (c+d x))^5}{5 b^3 d}-\frac{a (a+b \tan (c+d x))^4}{2 b^3 d}",1,"((a^2 + b^2)*(a + b*Tan[c + d*x])^3)/(3*b^3*d) - (a*(a + b*Tan[c + d*x])^4)/(2*b^3*d) + (a + b*Tan[c + d*x])^5/(5*b^3*d)","A",3,2,21,0.09524,1,"{3506, 697}"
520,1,22,0,0.0365484,"\int \sec ^2(c+d x) (a+b \tan (c+d x))^2 \, dx","Int[Sec[c + d*x]^2*(a + b*Tan[c + d*x])^2,x]","\frac{(a+b \tan (c+d x))^3}{3 b d}","\frac{(a+b \tan (c+d x))^3}{3 b d}",1,"(a + b*Tan[c + d*x])^3/(3*b*d)","A",2,2,21,0.09524,1,"{3506, 32}"
521,1,49,0,0.0528003,"\int \cos ^2(c+d x) (a+b \tan (c+d x))^2 \, dx","Int[Cos[c + d*x]^2*(a + b*Tan[c + d*x])^2,x]","\frac{1}{2} x \left(a^2+b^2\right)-\frac{\cos ^2(c+d x) (b-a \tan (c+d x)) (a+b \tan (c+d x))}{2 d}","\frac{1}{2} x \left(a^2+b^2\right)-\frac{\cos ^2(c+d x) (b-a \tan (c+d x)) (a+b \tan (c+d x))}{2 d}",1,"((a^2 + b^2)*x)/2 - (Cos[c + d*x]^2*(b - a*Tan[c + d*x])*(a + b*Tan[c + d*x]))/(2*d)","A",3,3,21,0.1429,1,"{3506, 723, 203}"
522,1,88,0,0.0783186,"\int \cos ^4(c+d x) (a+b \tan (c+d x))^2 \, dx","Int[Cos[c + d*x]^4*(a + b*Tan[c + d*x])^2,x]","-\frac{\cos ^2(c+d x) \left(2 a b-\left(3 a^2+b^2\right) \tan (c+d x)\right)}{8 d}+\frac{1}{8} x \left(3 a^2+b^2\right)-\frac{\cos ^4(c+d x) (b-a \tan (c+d x)) (a+b \tan (c+d x))}{4 d}","-\frac{\cos ^2(c+d x) \left(2 a b-\left(3 a^2+b^2\right) \tan (c+d x)\right)}{8 d}+\frac{1}{8} x \left(3 a^2+b^2\right)-\frac{\cos ^4(c+d x) (b-a \tan (c+d x)) (a+b \tan (c+d x))}{4 d}",1,"((3*a^2 + b^2)*x)/8 - (Cos[c + d*x]^4*(b - a*Tan[c + d*x])*(a + b*Tan[c + d*x]))/(4*d) - (Cos[c + d*x]^2*(2*a*b - (3*a^2 + b^2)*Tan[c + d*x]))/(8*d)","A",4,4,21,0.1905,1,"{3506, 739, 639, 203}"
523,1,163,0,0.1317231,"\int \sec ^7(c+d x) (a+b \tan (c+d x))^2 \, dx","Int[Sec[c + d*x]^7*(a + b*Tan[c + d*x])^2,x]","\frac{5 \left(8 a^2-b^2\right) \tanh ^{-1}(\sin (c+d x))}{128 d}+\frac{\left(8 a^2-b^2\right) \tan (c+d x) \sec ^5(c+d x)}{48 d}+\frac{5 \left(8 a^2-b^2\right) \tan (c+d x) \sec ^3(c+d x)}{192 d}+\frac{5 \left(8 a^2-b^2\right) \tan (c+d x) \sec (c+d x)}{128 d}+\frac{9 a b \sec ^7(c+d x)}{56 d}+\frac{b \sec ^7(c+d x) (a+b \tan (c+d x))}{8 d}","\frac{5 \left(8 a^2-b^2\right) \tanh ^{-1}(\sin (c+d x))}{128 d}+\frac{\left(8 a^2-b^2\right) \tan (c+d x) \sec ^5(c+d x)}{48 d}+\frac{5 \left(8 a^2-b^2\right) \tan (c+d x) \sec ^3(c+d x)}{192 d}+\frac{5 \left(8 a^2-b^2\right) \tan (c+d x) \sec (c+d x)}{128 d}+\frac{9 a b \sec ^7(c+d x)}{56 d}+\frac{b \sec ^7(c+d x) (a+b \tan (c+d x))}{8 d}",1,"(5*(8*a^2 - b^2)*ArcTanh[Sin[c + d*x]])/(128*d) + (9*a*b*Sec[c + d*x]^7)/(56*d) + (5*(8*a^2 - b^2)*Sec[c + d*x]*Tan[c + d*x])/(128*d) + (5*(8*a^2 - b^2)*Sec[c + d*x]^3*Tan[c + d*x])/(192*d) + ((8*a^2 - b^2)*Sec[c + d*x]^5*Tan[c + d*x])/(48*d) + (b*Sec[c + d*x]^7*(a + b*Tan[c + d*x]))/(8*d)","A",6,4,21,0.1905,1,"{3508, 3486, 3768, 3770}"
524,1,131,0,0.1151881,"\int \sec ^5(c+d x) (a+b \tan (c+d x))^2 \, dx","Int[Sec[c + d*x]^5*(a + b*Tan[c + d*x])^2,x]","\frac{\left(6 a^2-b^2\right) \tanh ^{-1}(\sin (c+d x))}{16 d}+\frac{\left(6 a^2-b^2\right) \tan (c+d x) \sec ^3(c+d x)}{24 d}+\frac{\left(6 a^2-b^2\right) \tan (c+d x) \sec (c+d x)}{16 d}+\frac{7 a b \sec ^5(c+d x)}{30 d}+\frac{b \sec ^5(c+d x) (a+b \tan (c+d x))}{6 d}","\frac{\left(6 a^2-b^2\right) \tanh ^{-1}(\sin (c+d x))}{16 d}+\frac{\left(6 a^2-b^2\right) \tan (c+d x) \sec ^3(c+d x)}{24 d}+\frac{\left(6 a^2-b^2\right) \tan (c+d x) \sec (c+d x)}{16 d}+\frac{7 a b \sec ^5(c+d x)}{30 d}+\frac{b \sec ^5(c+d x) (a+b \tan (c+d x))}{6 d}",1,"((6*a^2 - b^2)*ArcTanh[Sin[c + d*x]])/(16*d) + (7*a*b*Sec[c + d*x]^5)/(30*d) + ((6*a^2 - b^2)*Sec[c + d*x]*Tan[c + d*x])/(16*d) + ((6*a^2 - b^2)*Sec[c + d*x]^3*Tan[c + d*x])/(24*d) + (b*Sec[c + d*x]^5*(a + b*Tan[c + d*x]))/(6*d)","A",5,4,21,0.1905,1,"{3508, 3486, 3768, 3770}"
525,1,99,0,0.0988038,"\int \sec ^3(c+d x) (a+b \tan (c+d x))^2 \, dx","Int[Sec[c + d*x]^3*(a + b*Tan[c + d*x])^2,x]","\frac{\left(4 a^2-b^2\right) \tanh ^{-1}(\sin (c+d x))}{8 d}+\frac{\left(4 a^2-b^2\right) \tan (c+d x) \sec (c+d x)}{8 d}+\frac{5 a b \sec ^3(c+d x)}{12 d}+\frac{b \sec ^3(c+d x) (a+b \tan (c+d x))}{4 d}","\frac{\left(4 a^2-b^2\right) \tanh ^{-1}(\sin (c+d x))}{8 d}+\frac{\left(4 a^2-b^2\right) \tan (c+d x) \sec (c+d x)}{8 d}+\frac{5 a b \sec ^3(c+d x)}{12 d}+\frac{b \sec ^3(c+d x) (a+b \tan (c+d x))}{4 d}",1,"((4*a^2 - b^2)*ArcTanh[Sin[c + d*x]])/(8*d) + (5*a*b*Sec[c + d*x]^3)/(12*d) + ((4*a^2 - b^2)*Sec[c + d*x]*Tan[c + d*x])/(8*d) + (b*Sec[c + d*x]^3*(a + b*Tan[c + d*x]))/(4*d)","A",4,4,21,0.1905,1,"{3508, 3486, 3768, 3770}"
526,1,65,0,0.051964,"\int \sec (c+d x) (a+b \tan (c+d x))^2 \, dx","Int[Sec[c + d*x]*(a + b*Tan[c + d*x])^2,x]","\frac{\left(2 a^2-b^2\right) \tanh ^{-1}(\sin (c+d x))}{2 d}+\frac{3 a b \sec (c+d x)}{2 d}+\frac{b \sec (c+d x) (a+b \tan (c+d x))}{2 d}","\frac{\left(2 a^2-b^2\right) \tanh ^{-1}(\sin (c+d x))}{2 d}+\frac{3 a b \sec (c+d x)}{2 d}+\frac{b \sec (c+d x) (a+b \tan (c+d x))}{2 d}",1,"((2*a^2 - b^2)*ArcTanh[Sin[c + d*x]])/(2*d) + (3*a*b*Sec[c + d*x])/(2*d) + (b*Sec[c + d*x]*(a + b*Tan[c + d*x]))/(2*d)","A",3,3,19,0.1579,1,"{3508, 3486, 3770}"
527,1,47,0,0.0332454,"\int \cos (c+d x) (a+b \tan (c+d x))^2 \, dx","Int[Cos[c + d*x]*(a + b*Tan[c + d*x])^2,x]","\frac{\left(a^2-b^2\right) \sin (c+d x)}{d}-\frac{2 a b \cos (c+d x)}{d}+\frac{b^2 \tanh ^{-1}(\sin (c+d x))}{d}","\frac{\left(a^2-b^2\right) \sin (c+d x)}{d}-\frac{2 a b \cos (c+d x)}{d}+\frac{b^2 \tanh ^{-1}(\sin (c+d x))}{d}",1,"(b^2*ArcTanh[Sin[c + d*x]])/d - (2*a*b*Cos[c + d*x])/d + ((a^2 - b^2)*Sin[c + d*x])/d","A",1,1,19,0.05263,1,"{3507}"
528,1,90,0,0.0945082,"\int \cos ^3(c+d x) (a+b \tan (c+d x))^2 \, dx","Int[Cos[c + d*x]^3*(a + b*Tan[c + d*x])^2,x]","-\frac{\left(2 a^2+b^2\right) \sin ^3(c+d x)}{6 d}+\frac{\left(2 a^2+b^2\right) \sin (c+d x)}{2 d}-\frac{a b \cos ^3(c+d x)}{6 d}-\frac{b \cos ^3(c+d x) (a+b \tan (c+d x))}{2 d}","-\frac{\left(2 a^2+b^2\right) \sin ^3(c+d x)}{6 d}+\frac{\left(2 a^2+b^2\right) \sin (c+d x)}{2 d}-\frac{a b \cos ^3(c+d x)}{6 d}-\frac{b \cos ^3(c+d x) (a+b \tan (c+d x))}{2 d}",1,"-(a*b*Cos[c + d*x]^3)/(6*d) + ((2*a^2 + b^2)*Sin[c + d*x])/(2*d) - ((2*a^2 + b^2)*Sin[c + d*x]^3)/(6*d) - (b*Cos[c + d*x]^3*(a + b*Tan[c + d*x]))/(2*d)","A",4,3,21,0.1429,1,"{3508, 3486, 2633}"
529,1,114,0,0.1023166,"\int \cos ^5(c+d x) (a+b \tan (c+d x))^2 \, dx","Int[Cos[c + d*x]^5*(a + b*Tan[c + d*x])^2,x]","\frac{\left(4 a^2+b^2\right) \sin ^5(c+d x)}{20 d}-\frac{\left(4 a^2+b^2\right) \sin ^3(c+d x)}{6 d}+\frac{\left(4 a^2+b^2\right) \sin (c+d x)}{4 d}-\frac{3 a b \cos ^5(c+d x)}{20 d}-\frac{b \cos ^5(c+d x) (a+b \tan (c+d x))}{4 d}","\frac{\left(4 a^2+b^2\right) \sin ^5(c+d x)}{20 d}-\frac{\left(4 a^2+b^2\right) \sin ^3(c+d x)}{6 d}+\frac{\left(4 a^2+b^2\right) \sin (c+d x)}{4 d}-\frac{3 a b \cos ^5(c+d x)}{20 d}-\frac{b \cos ^5(c+d x) (a+b \tan (c+d x))}{4 d}",1,"(-3*a*b*Cos[c + d*x]^5)/(20*d) + ((4*a^2 + b^2)*Sin[c + d*x])/(4*d) - ((4*a^2 + b^2)*Sin[c + d*x]^3)/(6*d) + ((4*a^2 + b^2)*Sin[c + d*x]^5)/(20*d) - (b*Cos[c + d*x]^5*(a + b*Tan[c + d*x]))/(4*d)","A",4,3,21,0.1429,1,"{3508, 3486, 2633}"
530,1,138,0,0.1073959,"\int \cos ^7(c+d x) (a+b \tan (c+d x))^2 \, dx","Int[Cos[c + d*x]^7*(a + b*Tan[c + d*x])^2,x]","-\frac{\left(6 a^2+b^2\right) \sin ^7(c+d x)}{42 d}+\frac{\left(6 a^2+b^2\right) \sin ^5(c+d x)}{10 d}-\frac{\left(6 a^2+b^2\right) \sin ^3(c+d x)}{6 d}+\frac{\left(6 a^2+b^2\right) \sin (c+d x)}{6 d}-\frac{5 a b \cos ^7(c+d x)}{42 d}-\frac{b \cos ^7(c+d x) (a+b \tan (c+d x))}{6 d}","-\frac{\left(6 a^2+b^2\right) \sin ^7(c+d x)}{42 d}+\frac{\left(6 a^2+b^2\right) \sin ^5(c+d x)}{10 d}-\frac{\left(6 a^2+b^2\right) \sin ^3(c+d x)}{6 d}+\frac{\left(6 a^2+b^2\right) \sin (c+d x)}{6 d}-\frac{5 a b \cos ^7(c+d x)}{42 d}-\frac{b \cos ^7(c+d x) (a+b \tan (c+d x))}{6 d}",1,"(-5*a*b*Cos[c + d*x]^7)/(42*d) + ((6*a^2 + b^2)*Sin[c + d*x])/(6*d) - ((6*a^2 + b^2)*Sin[c + d*x]^3)/(6*d) + ((6*a^2 + b^2)*Sin[c + d*x]^5)/(10*d) - ((6*a^2 + b^2)*Sin[c + d*x]^7)/(42*d) - (b*Cos[c + d*x]^7*(a + b*Tan[c + d*x]))/(6*d)","A",4,3,21,0.1429,1,"{3508, 3486, 2633}"
531,1,194,0,0.1470275,"\int \sec ^8(c+d x) (a+b \tan (c+d x))^3 \, dx","Int[Sec[c + d*x]^8*(a + b*Tan[c + d*x])^3,x]","\frac{a \left(a^2+9 b^2\right) \tan ^7(c+d x)}{7 d}+\frac{3 a \left(a^2+3 b^2\right) \tan ^5(c+d x)}{5 d}+\frac{a \left(a^2+b^2\right) \tan ^3(c+d x)}{d}+\frac{3 a^2 b \sec ^8(c+d x)}{8 d}+\frac{a^3 \tan (c+d x)}{d}+\frac{a b^2 \tan ^9(c+d x)}{3 d}+\frac{b^3 \tan ^{10}(c+d x)}{10 d}+\frac{3 b^3 \tan ^8(c+d x)}{8 d}+\frac{b^3 \tan ^6(c+d x)}{2 d}+\frac{b^3 \tan ^4(c+d x)}{4 d}","\frac{a \left(a^2+9 b^2\right) \tan ^7(c+d x)}{7 d}+\frac{3 a \left(a^2+3 b^2\right) \tan ^5(c+d x)}{5 d}+\frac{a \left(a^2+b^2\right) \tan ^3(c+d x)}{d}+\frac{3 a^2 b \sec ^8(c+d x)}{8 d}+\frac{a^3 \tan (c+d x)}{d}+\frac{a b^2 \tan ^9(c+d x)}{3 d}+\frac{b^3 \tan ^{10}(c+d x)}{10 d}+\frac{3 b^3 \tan ^8(c+d x)}{8 d}+\frac{b^3 \tan ^6(c+d x)}{2 d}+\frac{b^3 \tan ^4(c+d x)}{4 d}",1,"(3*a^2*b*Sec[c + d*x]^8)/(8*d) + (a^3*Tan[c + d*x])/d + (a*(a^2 + b^2)*Tan[c + d*x]^3)/d + (b^3*Tan[c + d*x]^4)/(4*d) + (3*a*(a^2 + 3*b^2)*Tan[c + d*x]^5)/(5*d) + (b^3*Tan[c + d*x]^6)/(2*d) + (a*(a^2 + 9*b^2)*Tan[c + d*x]^7)/(7*d) + (3*b^3*Tan[c + d*x]^8)/(8*d) + (a*b^2*Tan[c + d*x]^9)/(3*d) + (b^3*Tan[c + d*x]^10)/(10*d)","A",4,3,21,0.1429,1,"{3506, 696, 1810}"
532,1,138,0,0.125019,"\int \sec ^6(c+d x) (a+b \tan (c+d x))^3 \, dx","Int[Sec[c + d*x]^6*(a + b*Tan[c + d*x])^3,x]","\frac{\left(3 a^2+b^2\right) (a+b \tan (c+d x))^6}{3 b^5 d}-\frac{4 a \left(a^2+b^2\right) (a+b \tan (c+d x))^5}{5 b^5 d}+\frac{\left(a^2+b^2\right)^2 (a+b \tan (c+d x))^4}{4 b^5 d}+\frac{(a+b \tan (c+d x))^8}{8 b^5 d}-\frac{4 a (a+b \tan (c+d x))^7}{7 b^5 d}","\frac{\left(3 a^2+b^2\right) (a+b \tan (c+d x))^6}{3 b^5 d}-\frac{4 a \left(a^2+b^2\right) (a+b \tan (c+d x))^5}{5 b^5 d}+\frac{\left(a^2+b^2\right)^2 (a+b \tan (c+d x))^4}{4 b^5 d}+\frac{(a+b \tan (c+d x))^8}{8 b^5 d}-\frac{4 a (a+b \tan (c+d x))^7}{7 b^5 d}",1,"((a^2 + b^2)^2*(a + b*Tan[c + d*x])^4)/(4*b^5*d) - (4*a*(a^2 + b^2)*(a + b*Tan[c + d*x])^5)/(5*b^5*d) + ((3*a^2 + b^2)*(a + b*Tan[c + d*x])^6)/(3*b^5*d) - (4*a*(a + b*Tan[c + d*x])^7)/(7*b^5*d) + (a + b*Tan[c + d*x])^8/(8*b^5*d)","A",3,2,21,0.09524,1,"{3506, 697}"
533,1,75,0,0.0708607,"\int \sec ^4(c+d x) (a+b \tan (c+d x))^3 \, dx","Int[Sec[c + d*x]^4*(a + b*Tan[c + d*x])^3,x]","\frac{\left(a^2+b^2\right) (a+b \tan (c+d x))^4}{4 b^3 d}+\frac{(a+b \tan (c+d x))^6}{6 b^3 d}-\frac{2 a (a+b \tan (c+d x))^5}{5 b^3 d}","\frac{\left(a^2+b^2\right) (a+b \tan (c+d x))^4}{4 b^3 d}+\frac{(a+b \tan (c+d x))^6}{6 b^3 d}-\frac{2 a (a+b \tan (c+d x))^5}{5 b^3 d}",1,"((a^2 + b^2)*(a + b*Tan[c + d*x])^4)/(4*b^3*d) - (2*a*(a + b*Tan[c + d*x])^5)/(5*b^3*d) + (a + b*Tan[c + d*x])^6/(6*b^3*d)","A",3,2,21,0.09524,1,"{3506, 697}"
534,1,22,0,0.0363167,"\int \sec ^2(c+d x) (a+b \tan (c+d x))^3 \, dx","Int[Sec[c + d*x]^2*(a + b*Tan[c + d*x])^3,x]","\frac{(a+b \tan (c+d x))^4}{4 b d}","\frac{(a+b \tan (c+d x))^4}{4 b d}",1,"(a + b*Tan[c + d*x])^4/(4*b*d)","A",2,2,21,0.09524,1,"{3506, 32}"
535,1,86,0,0.0932581,"\int \cos ^2(c+d x) (a+b \tan (c+d x))^3 \, dx","Int[Cos[c + d*x]^2*(a + b*Tan[c + d*x])^3,x]","\frac{1}{2} a x \left(a^2+3 b^2\right)-\frac{a b^2 \tan (c+d x)}{2 d}-\frac{\cos ^2(c+d x) (b-a \tan (c+d x)) (a+b \tan (c+d x))^2}{2 d}-\frac{b^3 \log (\cos (c+d x))}{d}","\frac{1}{2} a x \left(a^2+3 b^2\right)-\frac{a b^2 \tan (c+d x)}{2 d}-\frac{\cos ^2(c+d x) (b-a \tan (c+d x)) (a+b \tan (c+d x))^2}{2 d}-\frac{b^3 \log (\cos (c+d x))}{d}",1,"(a*(a^2 + 3*b^2)*x)/2 - (b^3*Log[Cos[c + d*x]])/d - (a*b^2*Tan[c + d*x])/(2*d) - (Cos[c + d*x]^2*(b - a*Tan[c + d*x])*(a + b*Tan[c + d*x])^2)/(2*d)","A",6,6,21,0.2857,1,"{3506, 739, 774, 635, 203, 260}"
536,1,84,0,0.0685598,"\int \cos ^4(c+d x) (a+b \tan (c+d x))^3 \, dx","Int[Cos[c + d*x]^4*(a + b*Tan[c + d*x])^3,x]","\frac{3}{8} a x \left(a^2+b^2\right)-\frac{3 a \cos ^2(c+d x) (b-a \tan (c+d x)) (a+b \tan (c+d x))}{8 d}+\frac{\sin (c+d x) \cos ^3(c+d x) (a+b \tan (c+d x))^3}{4 d}","\frac{3}{8} a x \left(a^2+b^2\right)-\frac{3 a \cos ^2(c+d x) (b-a \tan (c+d x)) (a+b \tan (c+d x))}{8 d}+\frac{\sin (c+d x) \cos ^3(c+d x) (a+b \tan (c+d x))^3}{4 d}",1,"(3*a*(a^2 + b^2)*x)/8 - (3*a*Cos[c + d*x]^2*(b - a*Tan[c + d*x])*(a + b*Tan[c + d*x]))/(8*d) + (Cos[c + d*x]^3*Sin[c + d*x]*(a + b*Tan[c + d*x])^3)/(4*d)","A",4,4,21,0.1905,1,"{3506, 729, 723, 203}"
537,1,177,0,0.1445099,"\int \sec ^5(c+d x) (a+b \tan (c+d x))^3 \, dx","Int[Sec[c + d*x]^5*(a + b*Tan[c + d*x])^3,x]","\frac{b \sec ^5(c+d x) \left(4 \left(8 a^2-b^2\right)+15 a b \tan (c+d x)\right)}{70 d}+\frac{a \left(2 a^2-b^2\right) \tan (c+d x) \sec ^3(c+d x)}{8 d}+\frac{3 a \left(2 a^2-b^2\right) \tan (c+d x) \sec (c+d x)}{16 d}+\frac{3 a \left(2 a^2-b^2\right) \sec (c+d x) \sinh ^{-1}(\tan (c+d x))}{16 d \sqrt{\sec ^2(c+d x)}}+\frac{b \sec ^5(c+d x) (a+b \tan (c+d x))^2}{7 d}","\frac{3 a \left(2 a^2-b^2\right) \tanh ^{-1}(\sin (c+d x))}{16 d}+\frac{b \sec ^5(c+d x) \left(4 \left(8 a^2-b^2\right)+15 a b \tan (c+d x)\right)}{70 d}+\frac{a \left(2 a^2-b^2\right) \tan (c+d x) \sec ^3(c+d x)}{8 d}+\frac{3 a \left(2 a^2-b^2\right) \tan (c+d x) \sec (c+d x)}{16 d}+\frac{b \sec ^5(c+d x) (a+b \tan (c+d x))^2}{7 d}",1,"(3*a*(2*a^2 - b^2)*ArcSinh[Tan[c + d*x]]*Sec[c + d*x])/(16*d*Sqrt[Sec[c + d*x]^2]) + (3*a*(2*a^2 - b^2)*Sec[c + d*x]*Tan[c + d*x])/(16*d) + (a*(2*a^2 - b^2)*Sec[c + d*x]^3*Tan[c + d*x])/(8*d) + (b*Sec[c + d*x]^5*(a + b*Tan[c + d*x])^2)/(7*d) + (b*Sec[c + d*x]^5*(4*(8*a^2 - b^2) + 15*a*b*Tan[c + d*x]))/(70*d)","A",6,5,21,0.2381,1,"{3512, 743, 780, 195, 215}"
538,1,144,0,0.1300117,"\int \sec ^3(c+d x) (a+b \tan (c+d x))^3 \, dx","Int[Sec[c + d*x]^3*(a + b*Tan[c + d*x])^3,x]","\frac{b \sec ^3(c+d x) \left(8 \left(6 a^2-b^2\right)+21 a b \tan (c+d x)\right)}{60 d}+\frac{a \left(4 a^2-3 b^2\right) \tan (c+d x) \sec (c+d x)}{8 d}+\frac{a \left(4 a^2-3 b^2\right) \sec (c+d x) \sinh ^{-1}(\tan (c+d x))}{8 d \sqrt{\sec ^2(c+d x)}}+\frac{b \sec ^3(c+d x) (a+b \tan (c+d x))^2}{5 d}","\frac{a \left(4 a^2-3 b^2\right) \tanh ^{-1}(\sin (c+d x))}{8 d}+\frac{b \sec ^3(c+d x) \left(8 \left(6 a^2-b^2\right)+21 a b \tan (c+d x)\right)}{60 d}+\frac{a \left(4 a^2-3 b^2\right) \tan (c+d x) \sec (c+d x)}{8 d}+\frac{b \sec ^3(c+d x) (a+b \tan (c+d x))^2}{5 d}",1,"(a*(4*a^2 - 3*b^2)*ArcSinh[Tan[c + d*x]]*Sec[c + d*x])/(8*d*Sqrt[Sec[c + d*x]^2]) + (a*(4*a^2 - 3*b^2)*Sec[c + d*x]*Tan[c + d*x])/(8*d) + (b*Sec[c + d*x]^3*(a + b*Tan[c + d*x])^2)/(5*d) + (b*Sec[c + d*x]^3*(8*(6*a^2 - b^2) + 21*a*b*Tan[c + d*x]))/(60*d)","A",5,5,21,0.2381,1,"{3512, 743, 780, 195, 215}"
539,1,109,0,0.0851151,"\int \sec (c+d x) (a+b \tan (c+d x))^3 \, dx","Int[Sec[c + d*x]*(a + b*Tan[c + d*x])^3,x]","\frac{b \sec (c+d x) \left(4 \left(4 a^2-b^2\right)+5 a b \tan (c+d x)\right)}{6 d}+\frac{a \left(2 a^2-3 b^2\right) \sec (c+d x) \sinh ^{-1}(\tan (c+d x))}{2 d \sqrt{\sec ^2(c+d x)}}+\frac{b \sec (c+d x) (a+b \tan (c+d x))^2}{3 d}","\frac{a \left(2 a^2-3 b^2\right) \tanh ^{-1}(\sin (c+d x))}{2 d}+\frac{b \sec (c+d x) \left(4 \left(4 a^2-b^2\right)+5 a b \tan (c+d x)\right)}{6 d}+\frac{b \sec (c+d x) (a+b \tan (c+d x))^2}{3 d}",1,"(a*(2*a^2 - 3*b^2)*ArcSinh[Tan[c + d*x]]*Sec[c + d*x])/(2*d*Sqrt[Sec[c + d*x]^2]) + (b*Sec[c + d*x]*(a + b*Tan[c + d*x])^2)/(3*d) + (b*Sec[c + d*x]*(4*(4*a^2 - b^2) + 5*a*b*Tan[c + d*x]))/(6*d)","A",4,4,19,0.2105,1,"{3512, 743, 780, 215}"
540,1,102,0,0.0801492,"\int \cos (c+d x) (a+b \tan (c+d x))^3 \, dx","Int[Cos[c + d*x]*(a + b*Tan[c + d*x])^3,x]","-\frac{b \sec (c+d x) \left(2 \left(a^2-b^2\right)+a b \tan (c+d x)\right)}{d}+\frac{3 a b^2 \cos (c+d x) \sqrt{\sec ^2(c+d x)} \sinh ^{-1}(\tan (c+d x))}{d}-\frac{\cos (c+d x) (b-a \tan (c+d x)) (a+b \tan (c+d x))^2}{d}","-\frac{b \sec (c+d x) \left(2 \left(a^2-b^2\right)+a b \tan (c+d x)\right)}{d}+\frac{3 a b^2 \tanh ^{-1}(\sin (c+d x))}{d}-\frac{\cos (c+d x) (b-a \tan (c+d x)) (a+b \tan (c+d x))^2}{d}",1,"(3*a*b^2*ArcSinh[Tan[c + d*x]]*Cos[c + d*x]*Sqrt[Sec[c + d*x]^2])/d - (Cos[c + d*x]*(b - a*Tan[c + d*x])*(a + b*Tan[c + d*x])^2)/d - (b*Sec[c + d*x]*(2*(a^2 - b^2) + a*b*Tan[c + d*x]))/d","A",4,4,19,0.2105,1,"{3512, 739, 780, 215}"
541,1,70,0,0.0687944,"\int \cos ^3(c+d x) (a+b \tan (c+d x))^3 \, dx","Int[Cos[c + d*x]^3*(a + b*Tan[c + d*x])^3,x]","-\frac{2 \left(a^2+b^2\right) \cos (c+d x) (b-a \tan (c+d x))}{3 d}-\frac{\cos ^3(c+d x) (b-a \tan (c+d x)) (a+b \tan (c+d x))^2}{3 d}","-\frac{2 \left(a^2+b^2\right) \cos (c+d x) (b-a \tan (c+d x))}{3 d}-\frac{\cos ^3(c+d x) (b-a \tan (c+d x)) (a+b \tan (c+d x))^2}{3 d}",1,"(-2*(a^2 + b^2)*Cos[c + d*x]*(b - a*Tan[c + d*x]))/(3*d) - (Cos[c + d*x]^3*(b - a*Tan[c + d*x])*(a + b*Tan[c + d*x])^2)/(3*d)","A",3,3,21,0.1429,1,"{3512, 723, 637}"
542,1,105,0,0.0946877,"\int \cos ^5(c+d x) (a+b \tan (c+d x))^3 \, dx","Int[Cos[c + d*x]^5*(a + b*Tan[c + d*x])^3,x]","-\frac{2 \left(4 a^2+b^2\right) \cos (c+d x) (b-a \tan (c+d x))}{15 d}-\frac{\cos ^3(c+d x) (b-4 a \tan (c+d x)) (a+b \tan (c+d x))^2}{15 d}+\frac{\sin (c+d x) \cos ^4(c+d x) (a+b \tan (c+d x))^3}{5 d}","-\frac{2 \left(4 a^2+b^2\right) \cos (c+d x) (b-a \tan (c+d x))}{15 d}-\frac{\cos ^3(c+d x) (b-4 a \tan (c+d x)) (a+b \tan (c+d x))^2}{15 d}+\frac{\sin (c+d x) \cos ^4(c+d x) (a+b \tan (c+d x))^3}{5 d}",1,"(-2*(4*a^2 + b^2)*Cos[c + d*x]*(b - a*Tan[c + d*x]))/(15*d) - (Cos[c + d*x]^3*(b - 4*a*Tan[c + d*x])*(a + b*Tan[c + d*x])^2)/(15*d) + (Cos[c + d*x]^4*Sin[c + d*x]*(a + b*Tan[c + d*x])^3)/(5*d)","A",4,4,21,0.1905,1,"{3512, 737, 805, 637}"
543,1,142,0,0.1519757,"\int \cos ^7(c+d x) (a+b \tan (c+d x))^3 \, dx","Int[Cos[c + d*x]^7*(a + b*Tan[c + d*x])^3,x]","\frac{8 a \left(2 a^2+b^2\right) \sin (c+d x)}{35 d}-\frac{2 \cos ^3(c+d x) \left(b \left(6 a^2+b^2\right)-a \left(4 a^2-b^2\right) \tan (c+d x)\right)}{35 d}-\frac{3 \cos ^5(c+d x) (b-2 a \tan (c+d x)) (a+b \tan (c+d x))^2}{35 d}+\frac{\sin (c+d x) \cos ^6(c+d x) (a+b \tan (c+d x))^3}{7 d}","\frac{8 a \left(2 a^2+b^2\right) \sin (c+d x)}{35 d}-\frac{2 \cos ^3(c+d x) \left(b \left(6 a^2+b^2\right)-a \left(4 a^2-b^2\right) \tan (c+d x)\right)}{35 d}-\frac{3 \cos ^5(c+d x) (b-2 a \tan (c+d x)) (a+b \tan (c+d x))^2}{35 d}+\frac{\sin (c+d x) \cos ^6(c+d x) (a+b \tan (c+d x))^3}{7 d}",1,"(8*a*(2*a^2 + b^2)*Sin[c + d*x])/(35*d) - (3*Cos[c + d*x]^5*(b - 2*a*Tan[c + d*x])*(a + b*Tan[c + d*x])^2)/(35*d) + (Cos[c + d*x]^6*Sin[c + d*x]*(a + b*Tan[c + d*x])^3)/(7*d) - (2*Cos[c + d*x]^3*(b*(6*a^2 + b^2) - a*(4*a^2 - b^2)*Tan[c + d*x]))/(35*d)","A",5,5,21,0.2381,1,"{3512, 737, 821, 778, 191}"
544,1,116,0,0.1018349,"\int \frac{\sec ^6(c+d x)}{a+b \tan (c+d x)} \, dx","Int[Sec[c + d*x]^6/(a + b*Tan[c + d*x]),x]","\frac{\left(a^2+2 b^2\right) \tan ^2(c+d x)}{2 b^3 d}-\frac{a \left(a^2+2 b^2\right) \tan (c+d x)}{b^4 d}+\frac{\left(a^2+b^2\right)^2 \log (a+b \tan (c+d x))}{b^5 d}-\frac{a \tan ^3(c+d x)}{3 b^2 d}+\frac{\tan ^4(c+d x)}{4 b d}","\frac{\left(a^2+2 b^2\right) \tan ^2(c+d x)}{2 b^3 d}-\frac{a \left(a^2+2 b^2\right) \tan (c+d x)}{b^4 d}+\frac{\left(a^2+b^2\right)^2 \log (a+b \tan (c+d x))}{b^5 d}-\frac{a \tan ^3(c+d x)}{3 b^2 d}+\frac{\tan ^4(c+d x)}{4 b d}",1,"((a^2 + b^2)^2*Log[a + b*Tan[c + d*x]])/(b^5*d) - (a*(a^2 + 2*b^2)*Tan[c + d*x])/(b^4*d) + ((a^2 + 2*b^2)*Tan[c + d*x]^2)/(2*b^3*d) - (a*Tan[c + d*x]^3)/(3*b^2*d) + Tan[c + d*x]^4/(4*b*d)","A",3,2,21,0.09524,1,"{3506, 697}"
545,1,59,0,0.0645737,"\int \frac{\sec ^4(c+d x)}{a+b \tan (c+d x)} \, dx","Int[Sec[c + d*x]^4/(a + b*Tan[c + d*x]),x]","\frac{\left(a^2+b^2\right) \log (a+b \tan (c+d x))}{b^3 d}-\frac{a \tan (c+d x)}{b^2 d}+\frac{\tan ^2(c+d x)}{2 b d}","\frac{\left(a^2+b^2\right) \log (a+b \tan (c+d x))}{b^3 d}-\frac{a \tan (c+d x)}{b^2 d}+\frac{\tan ^2(c+d x)}{2 b d}",1,"((a^2 + b^2)*Log[a + b*Tan[c + d*x]])/(b^3*d) - (a*Tan[c + d*x])/(b^2*d) + Tan[c + d*x]^2/(2*b*d)","A",3,2,21,0.09524,1,"{3506, 697}"
546,1,18,0,0.0417421,"\int \frac{\sec ^2(c+d x)}{a+b \tan (c+d x)} \, dx","Int[Sec[c + d*x]^2/(a + b*Tan[c + d*x]),x]","\frac{\log (a+b \tan (c+d x))}{b d}","\frac{\log (a+b \tan (c+d x))}{b d}",1,"Log[a + b*Tan[c + d*x]]/(b*d)","A",2,2,21,0.09524,1,"{3506, 31}"
547,1,93,0,0.1360524,"\int \frac{\cos ^2(c+d x)}{a+b \tan (c+d x)} \, dx","Int[Cos[c + d*x]^2/(a + b*Tan[c + d*x]),x]","\frac{\cos ^2(c+d x) (a \tan (c+d x)+b)}{2 d \left(a^2+b^2\right)}+\frac{b^3 \log (a \cos (c+d x)+b \sin (c+d x))}{d \left(a^2+b^2\right)^2}+\frac{a x \left(a^2+3 b^2\right)}{2 \left(a^2+b^2\right)^2}","\frac{\cos ^2(c+d x) (a \tan (c+d x)+b)}{2 d \left(a^2+b^2\right)}+\frac{b^3 \log (a \cos (c+d x)+b \sin (c+d x))}{d \left(a^2+b^2\right)^2}+\frac{a x \left(a^2+3 b^2\right)}{2 \left(a^2+b^2\right)^2}",1,"(a*(a^2 + 3*b^2)*x)/(2*(a^2 + b^2)^2) + (b^3*Log[a*Cos[c + d*x] + b*Sin[c + d*x]])/((a^2 + b^2)^2*d) + (Cos[c + d*x]^2*(b + a*Tan[c + d*x]))/(2*(a^2 + b^2)*d)","A",7,6,21,0.2857,1,"{3506, 741, 801, 635, 203, 260}"
548,1,152,0,0.1971139,"\int \frac{\cos ^4(c+d x)}{a+b \tan (c+d x)} \, dx","Int[Cos[c + d*x]^4/(a + b*Tan[c + d*x]),x]","\frac{\cos ^4(c+d x) (a \tan (c+d x)+b)}{4 d \left(a^2+b^2\right)}+\frac{\cos ^2(c+d x) \left(a \left(3 a^2+7 b^2\right) \tan (c+d x)+4 b^3\right)}{8 d \left(a^2+b^2\right)^2}+\frac{b^5 \log (a \cos (c+d x)+b \sin (c+d x))}{d \left(a^2+b^2\right)^3}+\frac{a x \left(10 a^2 b^2+3 a^4+15 b^4\right)}{8 \left(a^2+b^2\right)^3}","\frac{\cos ^4(c+d x) (a \tan (c+d x)+b)}{4 d \left(a^2+b^2\right)}+\frac{\cos ^2(c+d x) \left(a \left(3 a^2+7 b^2\right) \tan (c+d x)+4 b^3\right)}{8 d \left(a^2+b^2\right)^2}+\frac{b^5 \log (a \cos (c+d x)+b \sin (c+d x))}{d \left(a^2+b^2\right)^3}+\frac{a x \left(10 a^2 b^2+3 a^4+15 b^4\right)}{8 \left(a^2+b^2\right)^3}",1,"(a*(3*a^4 + 10*a^2*b^2 + 15*b^4)*x)/(8*(a^2 + b^2)^3) + (b^5*Log[a*Cos[c + d*x] + b*Sin[c + d*x]])/((a^2 + b^2)^3*d) + (Cos[c + d*x]^4*(b + a*Tan[c + d*x]))/(4*(a^2 + b^2)*d) + (Cos[c + d*x]^2*(4*b^3 + a*(3*a^2 + 7*b^2)*Tan[c + d*x]))/(8*(a^2 + b^2)^2*d)","A",8,7,21,0.3333,1,"{3506, 741, 823, 801, 635, 203, 260}"
549,1,152,0,0.1980177,"\int \frac{\sec ^5(c+d x)}{a+b \tan (c+d x)} \, dx","Int[Sec[c + d*x]^5/(a + b*Tan[c + d*x]),x]","\frac{\left(a^2+b^2\right) \sec (c+d x)}{b^3 d}-\frac{a \left(a^2+b^2\right) \tanh ^{-1}(\sin (c+d x))}{b^4 d}-\frac{\left(a^2+b^2\right)^{3/2} \tanh ^{-1}\left(\frac{\cos (c+d x) (b-a \tan (c+d x))}{\sqrt{a^2+b^2}}\right)}{b^4 d}-\frac{a \tanh ^{-1}(\sin (c+d x))}{2 b^2 d}-\frac{a \tan (c+d x) \sec (c+d x)}{2 b^2 d}+\frac{\sec ^3(c+d x)}{3 b d}","\frac{\left(a^2+b^2\right) \sec (c+d x)}{b^3 d}-\frac{a \left(2 a^2+3 b^2\right) \tanh ^{-1}(\sin (c+d x))}{2 b^4 d}-\frac{\left(a^2+b^2\right)^{3/2} \tanh ^{-1}\left(\frac{\cos (c+d x) (b-a \tan (c+d x))}{\sqrt{a^2+b^2}}\right)}{b^4 d}-\frac{a \tan (c+d x) \sec (c+d x)}{2 b^2 d}+\frac{\sec ^3(c+d x)}{3 b d}",1,"-(a*ArcTanh[Sin[c + d*x]])/(2*b^2*d) - (a*(a^2 + b^2)*ArcTanh[Sin[c + d*x]])/(b^4*d) - ((a^2 + b^2)^(3/2)*ArcTanh[(Cos[c + d*x]*(b - a*Tan[c + d*x]))/Sqrt[a^2 + b^2]])/(b^4*d) + ((a^2 + b^2)*Sec[c + d*x])/(b^3*d) + Sec[c + d*x]^3/(3*b*d) - (a*Sec[c + d*x]*Tan[c + d*x])/(2*b^2*d)","A",9,6,21,0.2857,1,"{3510, 3486, 3768, 3770, 3509, 206}"
550,1,79,0,0.0944538,"\int \frac{\sec ^3(c+d x)}{a+b \tan (c+d x)} \, dx","Int[Sec[c + d*x]^3/(a + b*Tan[c + d*x]),x]","-\frac{\sqrt{a^2+b^2} \tanh ^{-1}\left(\frac{\cos (c+d x) (b-a \tan (c+d x))}{\sqrt{a^2+b^2}}\right)}{b^2 d}-\frac{a \tanh ^{-1}(\sin (c+d x))}{b^2 d}+\frac{\sec (c+d x)}{b d}","-\frac{\sqrt{a^2+b^2} \tanh ^{-1}\left(\frac{\cos (c+d x) (b-a \tan (c+d x))}{\sqrt{a^2+b^2}}\right)}{b^2 d}-\frac{a \tanh ^{-1}(\sin (c+d x))}{b^2 d}+\frac{\sec (c+d x)}{b d}",1,"-((a*ArcTanh[Sin[c + d*x]])/(b^2*d)) - (Sqrt[a^2 + b^2]*ArcTanh[(Cos[c + d*x]*(b - a*Tan[c + d*x]))/Sqrt[a^2 + b^2]])/(b^2*d) + Sec[c + d*x]/(b*d)","A",5,5,21,0.2381,1,"{3510, 3486, 3770, 3509, 206}"
551,1,46,0,0.0307225,"\int \frac{\sec (c+d x)}{a+b \tan (c+d x)} \, dx","Int[Sec[c + d*x]/(a + b*Tan[c + d*x]),x]","-\frac{\tanh ^{-1}\left(\frac{\cos (c+d x) (b-a \tan (c+d x))}{\sqrt{a^2+b^2}}\right)}{d \sqrt{a^2+b^2}}","-\frac{\tanh ^{-1}\left(\frac{\cos (c+d x) (b-a \tan (c+d x))}{\sqrt{a^2+b^2}}\right)}{d \sqrt{a^2+b^2}}",1,"-(ArcTanh[(Cos[c + d*x]*(b - a*Tan[c + d*x]))/Sqrt[a^2 + b^2]]/(Sqrt[a^2 + b^2]*d))","A",2,2,19,0.1053,1,"{3509, 206}"
552,1,90,0,0.1005332,"\int \frac{\cos (c+d x)}{a+b \tan (c+d x)} \, dx","Int[Cos[c + d*x]/(a + b*Tan[c + d*x]),x]","\frac{a \sin (c+d x)}{d \left(a^2+b^2\right)}+\frac{b \cos (c+d x)}{d \left(a^2+b^2\right)}-\frac{b^2 \tanh ^{-1}\left(\frac{\cos (c+d x) (b-a \tan (c+d x))}{\sqrt{a^2+b^2}}\right)}{d \left(a^2+b^2\right)^{3/2}}","\frac{a \sin (c+d x)}{d \left(a^2+b^2\right)}+\frac{b \cos (c+d x)}{d \left(a^2+b^2\right)}-\frac{b^2 \tanh ^{-1}\left(\frac{\cos (c+d x) (b-a \tan (c+d x))}{\sqrt{a^2+b^2}}\right)}{d \left(a^2+b^2\right)^{3/2}}",1,"-((b^2*ArcTanh[(Cos[c + d*x]*(b - a*Tan[c + d*x]))/Sqrt[a^2 + b^2]])/((a^2 + b^2)^(3/2)*d)) + (b*Cos[c + d*x])/((a^2 + b^2)*d) + (a*Sin[c + d*x])/((a^2 + b^2)*d)","A",5,5,19,0.2632,1,"{3511, 3486, 2637, 3509, 206}"
553,1,165,0,0.1944226,"\int \frac{\cos ^3(c+d x)}{a+b \tan (c+d x)} \, dx","Int[Cos[c + d*x]^3/(a + b*Tan[c + d*x]),x]","-\frac{a \sin ^3(c+d x)}{3 d \left(a^2+b^2\right)}+\frac{a b^2 \sin (c+d x)}{d \left(a^2+b^2\right)^2}+\frac{a \sin (c+d x)}{d \left(a^2+b^2\right)}+\frac{b \cos ^3(c+d x)}{3 d \left(a^2+b^2\right)}+\frac{b^3 \cos (c+d x)}{d \left(a^2+b^2\right)^2}-\frac{b^4 \tanh ^{-1}\left(\frac{\cos (c+d x) (b-a \tan (c+d x))}{\sqrt{a^2+b^2}}\right)}{d \left(a^2+b^2\right)^{5/2}}","-\frac{a \sin ^3(c+d x)}{3 d \left(a^2+b^2\right)}+\frac{a b^2 \sin (c+d x)}{d \left(a^2+b^2\right)^2}+\frac{a \sin (c+d x)}{d \left(a^2+b^2\right)}+\frac{b \cos ^3(c+d x)}{3 d \left(a^2+b^2\right)}+\frac{b^3 \cos (c+d x)}{d \left(a^2+b^2\right)^2}-\frac{b^4 \tanh ^{-1}\left(\frac{\cos (c+d x) (b-a \tan (c+d x))}{\sqrt{a^2+b^2}}\right)}{d \left(a^2+b^2\right)^{5/2}}",1,"-((b^4*ArcTanh[(Cos[c + d*x]*(b - a*Tan[c + d*x]))/Sqrt[a^2 + b^2]])/((a^2 + b^2)^(5/2)*d)) + (b^3*Cos[c + d*x])/((a^2 + b^2)^2*d) + (b*Cos[c + d*x]^3)/(3*(a^2 + b^2)*d) + (a*b^2*Sin[c + d*x])/((a^2 + b^2)^2*d) + (a*Sin[c + d*x])/((a^2 + b^2)*d) - (a*Sin[c + d*x]^3)/(3*(a^2 + b^2)*d)","A",9,6,21,0.2857,1,"{3511, 3486, 2633, 2637, 3509, 206}"
554,1,178,0,0.1518076,"\int \frac{\sec ^8(c+d x)}{(a+b \tan (c+d x))^2} \, dx","Int[Sec[c + d*x]^8/(a + b*Tan[c + d*x])^2,x]","\frac{\left(a^2+b^2\right) \tan ^3(c+d x)}{b^4 d}-\frac{a \left(2 a^2+3 b^2\right) \tan ^2(c+d x)}{b^5 d}+\frac{\left(9 a^2 b^2+5 a^4+3 b^4\right) \tan (c+d x)}{b^6 d}-\frac{\left(a^2+b^2\right)^3}{b^7 d (a+b \tan (c+d x))}-\frac{6 a \left(a^2+b^2\right)^2 \log (a+b \tan (c+d x))}{b^7 d}-\frac{a \tan ^4(c+d x)}{2 b^3 d}+\frac{\tan ^5(c+d x)}{5 b^2 d}","\frac{\left(a^2+b^2\right) \tan ^3(c+d x)}{b^4 d}-\frac{a \left(2 a^2+3 b^2\right) \tan ^2(c+d x)}{b^5 d}+\frac{\left(9 a^2 b^2+5 a^4+3 b^4\right) \tan (c+d x)}{b^6 d}-\frac{\left(a^2+b^2\right)^3}{b^7 d (a+b \tan (c+d x))}-\frac{6 a \left(a^2+b^2\right)^2 \log (a+b \tan (c+d x))}{b^7 d}-\frac{a \tan ^4(c+d x)}{2 b^3 d}+\frac{\tan ^5(c+d x)}{5 b^2 d}",1,"(-6*a*(a^2 + b^2)^2*Log[a + b*Tan[c + d*x]])/(b^7*d) + ((5*a^4 + 9*a^2*b^2 + 3*b^4)*Tan[c + d*x])/(b^6*d) - (a*(2*a^2 + 3*b^2)*Tan[c + d*x]^2)/(b^5*d) + ((a^2 + b^2)*Tan[c + d*x]^3)/(b^4*d) - (a*Tan[c + d*x]^4)/(2*b^3*d) + Tan[c + d*x]^5/(5*b^2*d) - (a^2 + b^2)^3/(b^7*d*(a + b*Tan[c + d*x]))","A",3,2,21,0.09524,1,"{3506, 697}"
555,1,116,0,0.0968805,"\int \frac{\sec ^6(c+d x)}{(a+b \tan (c+d x))^2} \, dx","Int[Sec[c + d*x]^6/(a + b*Tan[c + d*x])^2,x]","\frac{\left(3 a^2+2 b^2\right) \tan (c+d x)}{b^4 d}-\frac{\left(a^2+b^2\right)^2}{b^5 d (a+b \tan (c+d x))}-\frac{4 a \left(a^2+b^2\right) \log (a+b \tan (c+d x))}{b^5 d}-\frac{a \tan ^2(c+d x)}{b^3 d}+\frac{\tan ^3(c+d x)}{3 b^2 d}","\frac{\left(3 a^2+2 b^2\right) \tan (c+d x)}{b^4 d}-\frac{\left(a^2+b^2\right)^2}{b^5 d (a+b \tan (c+d x))}-\frac{4 a \left(a^2+b^2\right) \log (a+b \tan (c+d x))}{b^5 d}-\frac{a \tan ^2(c+d x)}{b^3 d}+\frac{\tan ^3(c+d x)}{3 b^2 d}",1,"(-4*a*(a^2 + b^2)*Log[a + b*Tan[c + d*x]])/(b^5*d) + ((3*a^2 + 2*b^2)*Tan[c + d*x])/(b^4*d) - (a*Tan[c + d*x]^2)/(b^3*d) + Tan[c + d*x]^3/(3*b^2*d) - (a^2 + b^2)^2/(b^5*d*(a + b*Tan[c + d*x]))","A",3,2,21,0.09524,1,"{3506, 697}"
556,1,61,0,0.0660522,"\int \frac{\sec ^4(c+d x)}{(a+b \tan (c+d x))^2} \, dx","Int[Sec[c + d*x]^4/(a + b*Tan[c + d*x])^2,x]","-\frac{a^2+b^2}{b^3 d (a+b \tan (c+d x))}-\frac{2 a \log (a+b \tan (c+d x))}{b^3 d}+\frac{\tan (c+d x)}{b^2 d}","-\frac{a^2+b^2}{b^3 d (a+b \tan (c+d x))}-\frac{2 a \log (a+b \tan (c+d x))}{b^3 d}+\frac{\tan (c+d x)}{b^2 d}",1,"(-2*a*Log[a + b*Tan[c + d*x]])/(b^3*d) + Tan[c + d*x]/(b^2*d) - (a^2 + b^2)/(b^3*d*(a + b*Tan[c + d*x]))","A",3,2,21,0.09524,1,"{3506, 697}"
557,1,20,0,0.0391909,"\int \frac{\sec ^2(c+d x)}{(a+b \tan (c+d x))^2} \, dx","Int[Sec[c + d*x]^2/(a + b*Tan[c + d*x])^2,x]","-\frac{1}{b d (a+b \tan (c+d x))}","-\frac{1}{b d (a+b \tan (c+d x))}",1,"-(1/(b*d*(a + b*Tan[c + d*x])))","A",2,2,21,0.09524,1,"{3506, 32}"
558,1,152,0,0.162816,"\int \frac{\cos ^2(c+d x)}{(a+b \tan (c+d x))^2} \, dx","Int[Cos[c + d*x]^2/(a + b*Tan[c + d*x])^2,x]","\frac{b \left(a^2-3 b^2\right)}{2 d \left(a^2+b^2\right)^2 (a+b \tan (c+d x))}+\frac{\cos ^2(c+d x) (a \tan (c+d x)+b)}{2 d \left(a^2+b^2\right) (a+b \tan (c+d x))}+\frac{4 a b^3 \log (a \cos (c+d x)+b \sin (c+d x))}{d \left(a^2+b^2\right)^3}+\frac{x \left(6 a^2 b^2+a^4-3 b^4\right)}{2 \left(a^2+b^2\right)^3}","\frac{b \left(a^2-3 b^2\right)}{2 d \left(a^2+b^2\right)^2 (a+b \tan (c+d x))}+\frac{\cos ^2(c+d x) (a \tan (c+d x)+b)}{2 d \left(a^2+b^2\right) (a+b \tan (c+d x))}+\frac{4 a b^3 \log (a \cos (c+d x)+b \sin (c+d x))}{d \left(a^2+b^2\right)^3}+\frac{x \left(6 a^2 b^2+a^4-3 b^4\right)}{2 \left(a^2+b^2\right)^3}",1,"((a^4 + 6*a^2*b^2 - 3*b^4)*x)/(2*(a^2 + b^2)^3) + (4*a*b^3*Log[a*Cos[c + d*x] + b*Sin[c + d*x]])/((a^2 + b^2)^3*d) + (b*(a^2 - 3*b^2))/(2*(a^2 + b^2)^2*d*(a + b*Tan[c + d*x])) + (Cos[c + d*x]^2*(b + a*Tan[c + d*x]))/(2*(a^2 + b^2)*d*(a + b*Tan[c + d*x]))","A",7,6,21,0.2857,1,"{3506, 741, 801, 635, 203, 260}"
559,1,235,0,0.2656652,"\int \frac{\cos ^4(c+d x)}{(a+b \tan (c+d x))^2} \, dx","Int[Cos[c + d*x]^4/(a + b*Tan[c + d*x])^2,x]","\frac{3 b \left(a^2-b^2\right) \left(a^2+5 b^2\right)}{8 d \left(a^2+b^2\right)^3 (a+b \tan (c+d x))}-\frac{\cos ^2(c+d x) \left(b \left(a^2-5 b^2\right)-3 a \left(a^2+3 b^2\right) \tan (c+d x)\right)}{8 d \left(a^2+b^2\right)^2 (a+b \tan (c+d x))}+\frac{\cos ^4(c+d x) (a \tan (c+d x)+b)}{4 d \left(a^2+b^2\right) (a+b \tan (c+d x))}+\frac{6 a b^5 \log (a \cos (c+d x)+b \sin (c+d x))}{d \left(a^2+b^2\right)^4}+\frac{3 x \left(5 a^4 b^2+15 a^2 b^4+a^6-5 b^6\right)}{8 \left(a^2+b^2\right)^4}","\frac{3 b \left(a^2-b^2\right) \left(a^2+5 b^2\right)}{8 d \left(a^2+b^2\right)^3 (a+b \tan (c+d x))}-\frac{\cos ^2(c+d x) \left(b \left(a^2-5 b^2\right)-3 a \left(a^2+3 b^2\right) \tan (c+d x)\right)}{8 d \left(a^2+b^2\right)^2 (a+b \tan (c+d x))}+\frac{\cos ^4(c+d x) (a \tan (c+d x)+b)}{4 d \left(a^2+b^2\right) (a+b \tan (c+d x))}+\frac{6 a b^5 \log (a \cos (c+d x)+b \sin (c+d x))}{d \left(a^2+b^2\right)^4}+\frac{3 x \left(5 a^4 b^2+15 a^2 b^4+a^6-5 b^6\right)}{8 \left(a^2+b^2\right)^4}",1,"(3*(a^6 + 5*a^4*b^2 + 15*a^2*b^4 - 5*b^6)*x)/(8*(a^2 + b^2)^4) + (6*a*b^5*Log[a*Cos[c + d*x] + b*Sin[c + d*x]])/((a^2 + b^2)^4*d) + (3*b*(a^2 - b^2)*(a^2 + 5*b^2))/(8*(a^2 + b^2)^3*d*(a + b*Tan[c + d*x])) + (Cos[c + d*x]^4*(b + a*Tan[c + d*x]))/(4*(a^2 + b^2)*d*(a + b*Tan[c + d*x])) - (Cos[c + d*x]^2*(b*(a^2 - 5*b^2) - 3*a*(a^2 + 3*b^2)*Tan[c + d*x]))/(8*(a^2 + b^2)^2*d*(a + b*Tan[c + d*x]))","A",8,7,21,0.3333,1,"{3506, 741, 823, 801, 635, 203, 260}"
560,1,235,0,0.2681368,"\int \frac{\sec ^7(c+d x)}{(a+b \tan (c+d x))^2} \, dx","Int[Sec[c + d*x]^7/(a + b*Tan[c + d*x])^2,x]","-\frac{5 \sec (c+d x) \left(8 a \left(a^2+b^2\right)-b \left(4 a^2+3 b^2\right) \tan (c+d x)\right)}{8 b^5 d}+\frac{5 a \left(a^2+b^2\right)^{3/2} \sec (c+d x) \tanh ^{-1}\left(\frac{b-a \tan (c+d x)}{\sqrt{a^2+b^2} \sqrt{\sec ^2(c+d x)}}\right)}{b^6 d \sqrt{\sec ^2(c+d x)}}+\frac{5 \left(12 a^2 b^2+8 a^4+3 b^4\right) \sec (c+d x) \sinh ^{-1}(\tan (c+d x))}{8 b^6 d \sqrt{\sec ^2(c+d x)}}-\frac{5 \sec ^3(c+d x) (4 a-3 b \tan (c+d x))}{12 b^3 d}-\frac{\sec ^5(c+d x)}{b d (a+b \tan (c+d x))}","-\frac{5 \sec (c+d x) \left(8 a \left(a^2+b^2\right)-b \left(4 a^2+3 b^2\right) \tan (c+d x)\right)}{8 b^5 d}+\frac{5 a \left(a^2+b^2\right)^{3/2} \sec (c+d x) \tanh ^{-1}\left(\frac{b-a \tan (c+d x)}{\sqrt{a^2+b^2} \sqrt{\sec ^2(c+d x)}}\right)}{b^6 d \sqrt{\sec ^2(c+d x)}}+\frac{5 \left(12 a^2 b^2+8 a^4+3 b^4\right) \sec (c+d x) \sinh ^{-1}(\tan (c+d x))}{8 b^6 d \sqrt{\sec ^2(c+d x)}}-\frac{5 \sec ^3(c+d x) (4 a-3 b \tan (c+d x))}{12 b^3 d}-\frac{\sec ^5(c+d x)}{b d (a+b \tan (c+d x))}",1,"(5*(8*a^4 + 12*a^2*b^2 + 3*b^4)*ArcSinh[Tan[c + d*x]]*Sec[c + d*x])/(8*b^6*d*Sqrt[Sec[c + d*x]^2]) + (5*a*(a^2 + b^2)^(3/2)*ArcTanh[(b - a*Tan[c + d*x])/(Sqrt[a^2 + b^2]*Sqrt[Sec[c + d*x]^2])]*Sec[c + d*x])/(b^6*d*Sqrt[Sec[c + d*x]^2]) - (5*Sec[c + d*x]^3*(4*a - 3*b*Tan[c + d*x]))/(12*b^3*d) - Sec[c + d*x]^5/(b*d*(a + b*Tan[c + d*x])) - (5*Sec[c + d*x]*(8*a*(a^2 + b^2) - b*(4*a^2 + 3*b^2)*Tan[c + d*x]))/(8*b^5*d)","A",8,7,21,0.3333,1,"{3512, 733, 815, 844, 215, 725, 206}"
561,1,176,0,0.1678835,"\int \frac{\sec ^5(c+d x)}{(a+b \tan (c+d x))^2} \, dx","Int[Sec[c + d*x]^5/(a + b*Tan[c + d*x])^2,x]","\frac{3 a \sqrt{a^2+b^2} \sec (c+d x) \tanh ^{-1}\left(\frac{b-a \tan (c+d x)}{\sqrt{a^2+b^2} \sqrt{\sec ^2(c+d x)}}\right)}{b^4 d \sqrt{\sec ^2(c+d x)}}+\frac{3 \left(2 a^2+b^2\right) \sec (c+d x) \sinh ^{-1}(\tan (c+d x))}{2 b^4 d \sqrt{\sec ^2(c+d x)}}-\frac{3 \sec (c+d x) (2 a-b \tan (c+d x))}{2 b^3 d}-\frac{\sec ^3(c+d x)}{b d (a+b \tan (c+d x))}","\frac{3 a \sqrt{a^2+b^2} \sec (c+d x) \tanh ^{-1}\left(\frac{b-a \tan (c+d x)}{\sqrt{a^2+b^2} \sqrt{\sec ^2(c+d x)}}\right)}{b^4 d \sqrt{\sec ^2(c+d x)}}+\frac{3 \left(2 a^2+b^2\right) \sec (c+d x) \sinh ^{-1}(\tan (c+d x))}{2 b^4 d \sqrt{\sec ^2(c+d x)}}-\frac{3 \sec (c+d x) (2 a-b \tan (c+d x))}{2 b^3 d}-\frac{\sec ^3(c+d x)}{b d (a+b \tan (c+d x))}",1,"(3*(2*a^2 + b^2)*ArcSinh[Tan[c + d*x]]*Sec[c + d*x])/(2*b^4*d*Sqrt[Sec[c + d*x]^2]) + (3*a*Sqrt[a^2 + b^2]*ArcTanh[(b - a*Tan[c + d*x])/(Sqrt[a^2 + b^2]*Sqrt[Sec[c + d*x]^2])]*Sec[c + d*x])/(b^4*d*Sqrt[Sec[c + d*x]^2]) - (3*Sec[c + d*x]*(2*a - b*Tan[c + d*x]))/(2*b^3*d) - Sec[c + d*x]^3/(b*d*(a + b*Tan[c + d*x]))","A",7,7,21,0.3333,1,"{3512, 733, 815, 844, 215, 725, 206}"
562,1,132,0,0.1071033,"\int \frac{\sec ^3(c+d x)}{(a+b \tan (c+d x))^2} \, dx","Int[Sec[c + d*x]^3/(a + b*Tan[c + d*x])^2,x]","\frac{a \sec (c+d x) \tanh ^{-1}\left(\frac{b-a \tan (c+d x)}{\sqrt{a^2+b^2} \sqrt{\sec ^2(c+d x)}}\right)}{b^2 d \sqrt{a^2+b^2} \sqrt{\sec ^2(c+d x)}}-\frac{\sec (c+d x)}{b d (a+b \tan (c+d x))}+\frac{\sec (c+d x) \sinh ^{-1}(\tan (c+d x))}{b^2 d \sqrt{\sec ^2(c+d x)}}","\frac{a \tanh ^{-1}\left(\frac{b \cos (c+d x)-a \sin (c+d x)}{\sqrt{a^2+b^2}}\right)}{b^2 d \sqrt{a^2+b^2}}-\frac{\sec (c+d x)}{b d (a+b \tan (c+d x))}+\frac{\tanh ^{-1}(\sin (c+d x))}{b^2 d}",1,"(ArcSinh[Tan[c + d*x]]*Sec[c + d*x])/(b^2*d*Sqrt[Sec[c + d*x]^2]) + (a*ArcTanh[(b - a*Tan[c + d*x])/(Sqrt[a^2 + b^2]*Sqrt[Sec[c + d*x]^2])]*Sec[c + d*x])/(b^2*Sqrt[a^2 + b^2]*d*Sqrt[Sec[c + d*x]^2]) - Sec[c + d*x]/(b*d*(a + b*Tan[c + d*x]))","A",6,6,21,0.2857,1,"{3512, 733, 844, 215, 725, 206}"
563,1,105,0,0.0733768,"\int \frac{\sec (c+d x)}{(a+b \tan (c+d x))^2} \, dx","Int[Sec[c + d*x]/(a + b*Tan[c + d*x])^2,x]","-\frac{b \sec (c+d x)}{d \left(a^2+b^2\right) (a+b \tan (c+d x))}-\frac{a \sec (c+d x) \tanh ^{-1}\left(\frac{b-a \tan (c+d x)}{\sqrt{a^2+b^2} \sqrt{\sec ^2(c+d x)}}\right)}{d \left(a^2+b^2\right)^{3/2} \sqrt{\sec ^2(c+d x)}}","-\frac{b \sec (c+d x)}{d \left(a^2+b^2\right) (a+b \tan (c+d x))}-\frac{a \tanh ^{-1}\left(\frac{b \cos (c+d x)-a \sin (c+d x)}{\sqrt{a^2+b^2}}\right)}{d \left(a^2+b^2\right)^{3/2}}",1,"-((a*ArcTanh[(b - a*Tan[c + d*x])/(Sqrt[a^2 + b^2]*Sqrt[Sec[c + d*x]^2])]*Sec[c + d*x])/((a^2 + b^2)^(3/2)*d*Sqrt[Sec[c + d*x]^2])) - (b*Sec[c + d*x])/((a^2 + b^2)*d*(a + b*Tan[c + d*x]))","A",4,4,19,0.2105,1,"{3512, 731, 725, 206}"
564,1,157,0,0.1269854,"\int \frac{\cos (c+d x)}{(a+b \tan (c+d x))^2} \, dx","Int[Cos[c + d*x]/(a + b*Tan[c + d*x])^2,x]","\frac{\cos (c+d x) (a \tan (c+d x)+b)}{d \left(a^2+b^2\right) (a+b \tan (c+d x))}+\frac{b \left(a^2-2 b^2\right) \sec (c+d x)}{d \left(a^2+b^2\right)^2 (a+b \tan (c+d x))}-\frac{3 a b^2 \cos (c+d x) \sqrt{\sec ^2(c+d x)} \tanh ^{-1}\left(\frac{b-a \tan (c+d x)}{\sqrt{a^2+b^2} \sqrt{\sec ^2(c+d x)}}\right)}{d \left(a^2+b^2\right)^{5/2}}","\frac{\cos (c+d x) (a \tan (c+d x)+b)}{d \left(a^2+b^2\right) (a+b \tan (c+d x))}+\frac{b \left(a^2-2 b^2\right) \sec (c+d x)}{d \left(a^2+b^2\right)^2 (a+b \tan (c+d x))}-\frac{3 a b^2 \cos (c+d x) \sqrt{\sec ^2(c+d x)} \tanh ^{-1}\left(\frac{b-a \tan (c+d x)}{\sqrt{a^2+b^2} \sqrt{\sec ^2(c+d x)}}\right)}{d \left(a^2+b^2\right)^{5/2}}",1,"(-3*a*b^2*ArcTanh[(b - a*Tan[c + d*x])/(Sqrt[a^2 + b^2]*Sqrt[Sec[c + d*x]^2])]*Cos[c + d*x]*Sqrt[Sec[c + d*x]^2])/((a^2 + b^2)^(5/2)*d) + (b*(a^2 - 2*b^2)*Sec[c + d*x])/((a^2 + b^2)^2*d*(a + b*Tan[c + d*x])) + (Cos[c + d*x]*(b + a*Tan[c + d*x]))/((a^2 + b^2)*d*(a + b*Tan[c + d*x]))","A",5,5,19,0.2632,1,"{3512, 741, 807, 725, 206}"
565,1,241,0,0.2576871,"\int \frac{\cos ^3(c+d x)}{(a+b \tan (c+d x))^2} \, dx","Int[Cos[c + d*x]^3/(a + b*Tan[c + d*x])^2,x]","\frac{\cos ^3(c+d x) (a \tan (c+d x)+b)}{3 d \left(a^2+b^2\right) (a+b \tan (c+d x))}-\frac{\cos (c+d x) \left(b \left(a^2-4 b^2\right)-a \left(2 a^2+7 b^2\right) \tan (c+d x)\right)}{3 d \left(a^2+b^2\right)^2 (a+b \tan (c+d x))}+\frac{b \left(9 a^2 b^2+2 a^4-8 b^4\right) \sec (c+d x)}{3 d \left(a^2+b^2\right)^3 (a+b \tan (c+d x))}-\frac{5 a b^4 \cos (c+d x) \sqrt{\sec ^2(c+d x)} \tanh ^{-1}\left(\frac{b-a \tan (c+d x)}{\sqrt{a^2+b^2} \sqrt{\sec ^2(c+d x)}}\right)}{d \left(a^2+b^2\right)^{7/2}}","\frac{\cos ^3(c+d x) (a \tan (c+d x)+b)}{3 d \left(a^2+b^2\right) (a+b \tan (c+d x))}-\frac{\cos (c+d x) \left(b \left(a^2-4 b^2\right)-a \left(2 a^2+7 b^2\right) \tan (c+d x)\right)}{3 d \left(a^2+b^2\right)^2 (a+b \tan (c+d x))}+\frac{b \left(9 a^2 b^2+2 a^4-8 b^4\right) \sec (c+d x)}{3 d \left(a^2+b^2\right)^3 (a+b \tan (c+d x))}-\frac{5 a b^4 \cos (c+d x) \sqrt{\sec ^2(c+d x)} \tanh ^{-1}\left(\frac{b-a \tan (c+d x)}{\sqrt{a^2+b^2} \sqrt{\sec ^2(c+d x)}}\right)}{d \left(a^2+b^2\right)^{7/2}}",1,"(-5*a*b^4*ArcTanh[(b - a*Tan[c + d*x])/(Sqrt[a^2 + b^2]*Sqrt[Sec[c + d*x]^2])]*Cos[c + d*x]*Sqrt[Sec[c + d*x]^2])/((a^2 + b^2)^(7/2)*d) + (b*(2*a^4 + 9*a^2*b^2 - 8*b^4)*Sec[c + d*x])/(3*(a^2 + b^2)^3*d*(a + b*Tan[c + d*x])) + (Cos[c + d*x]^3*(b + a*Tan[c + d*x]))/(3*(a^2 + b^2)*d*(a + b*Tan[c + d*x])) - (Cos[c + d*x]*(b*(a^2 - 4*b^2) - a*(2*a^2 + 7*b^2)*Tan[c + d*x]))/(3*(a^2 + b^2)^2*d*(a + b*Tan[c + d*x]))","A",6,6,21,0.2857,1,"{3512, 741, 823, 807, 725, 206}"
566,1,185,0,0.1559355,"\int \frac{\sec ^8(c+d x)}{(a+b \tan (c+d x))^3} \, dx","Int[Sec[c + d*x]^8/(a + b*Tan[c + d*x])^3,x]","\frac{3 \left(2 a^2+b^2\right) \tan ^2(c+d x)}{2 b^5 d}-\frac{a \left(10 a^2+9 b^2\right) \tan (c+d x)}{b^6 d}+\frac{6 a \left(a^2+b^2\right)^2}{b^7 d (a+b \tan (c+d x))}-\frac{\left(a^2+b^2\right)^3}{2 b^7 d (a+b \tan (c+d x))^2}+\frac{3 \left(a^2+b^2\right) \left(5 a^2+b^2\right) \log (a+b \tan (c+d x))}{b^7 d}-\frac{a \tan ^3(c+d x)}{b^4 d}+\frac{\tan ^4(c+d x)}{4 b^3 d}","\frac{3 \left(2 a^2+b^2\right) \tan ^2(c+d x)}{2 b^5 d}-\frac{a \left(10 a^2+9 b^2\right) \tan (c+d x)}{b^6 d}+\frac{6 a \left(a^2+b^2\right)^2}{b^7 d (a+b \tan (c+d x))}-\frac{\left(a^2+b^2\right)^3}{2 b^7 d (a+b \tan (c+d x))^2}+\frac{3 \left(a^2+b^2\right) \left(5 a^2+b^2\right) \log (a+b \tan (c+d x))}{b^7 d}-\frac{a \tan ^3(c+d x)}{b^4 d}+\frac{\tan ^4(c+d x)}{4 b^3 d}",1,"(3*(a^2 + b^2)*(5*a^2 + b^2)*Log[a + b*Tan[c + d*x]])/(b^7*d) - (a*(10*a^2 + 9*b^2)*Tan[c + d*x])/(b^6*d) + (3*(2*a^2 + b^2)*Tan[c + d*x]^2)/(2*b^5*d) - (a*Tan[c + d*x]^3)/(b^4*d) + Tan[c + d*x]^4/(4*b^3*d) - (a^2 + b^2)^3/(2*b^7*d*(a + b*Tan[c + d*x])^2) + (6*a*(a^2 + b^2)^2)/(b^7*d*(a + b*Tan[c + d*x]))","A",3,2,21,0.09524,1,"{3506, 697}"
567,1,121,0,0.1019348,"\int \frac{\sec ^6(c+d x)}{(a+b \tan (c+d x))^3} \, dx","Int[Sec[c + d*x]^6/(a + b*Tan[c + d*x])^3,x]","-\frac{\left(a^2+b^2\right)^2}{2 b^5 d (a+b \tan (c+d x))^2}+\frac{4 a \left(a^2+b^2\right)}{b^5 d (a+b \tan (c+d x))}+\frac{2 \left(3 a^2+b^2\right) \log (a+b \tan (c+d x))}{b^5 d}-\frac{3 a \tan (c+d x)}{b^4 d}+\frac{\tan ^2(c+d x)}{2 b^3 d}","-\frac{\left(a^2+b^2\right)^2}{2 b^5 d (a+b \tan (c+d x))^2}+\frac{4 a \left(a^2+b^2\right)}{b^5 d (a+b \tan (c+d x))}+\frac{2 \left(3 a^2+b^2\right) \log (a+b \tan (c+d x))}{b^5 d}-\frac{3 a \tan (c+d x)}{b^4 d}+\frac{\tan ^2(c+d x)}{2 b^3 d}",1,"(2*(3*a^2 + b^2)*Log[a + b*Tan[c + d*x]])/(b^5*d) - (3*a*Tan[c + d*x])/(b^4*d) + Tan[c + d*x]^2/(2*b^3*d) - (a^2 + b^2)^2/(2*b^5*d*(a + b*Tan[c + d*x])^2) + (4*a*(a^2 + b^2))/(b^5*d*(a + b*Tan[c + d*x]))","A",3,2,21,0.09524,1,"{3506, 697}"
568,1,69,0,0.0727754,"\int \frac{\sec ^4(c+d x)}{(a+b \tan (c+d x))^3} \, dx","Int[Sec[c + d*x]^4/(a + b*Tan[c + d*x])^3,x]","-\frac{a^2+b^2}{2 b^3 d (a+b \tan (c+d x))^2}+\frac{2 a}{b^3 d (a+b \tan (c+d x))}+\frac{\log (a+b \tan (c+d x))}{b^3 d}","-\frac{a^2+b^2}{2 b^3 d (a+b \tan (c+d x))^2}+\frac{2 a}{b^3 d (a+b \tan (c+d x))}+\frac{\log (a+b \tan (c+d x))}{b^3 d}",1,"Log[a + b*Tan[c + d*x]]/(b^3*d) - (a^2 + b^2)/(2*b^3*d*(a + b*Tan[c + d*x])^2) + (2*a)/(b^3*d*(a + b*Tan[c + d*x]))","A",3,2,21,0.09524,1,"{3506, 697}"
569,1,22,0,0.0429776,"\int \frac{\sec ^2(c+d x)}{(a+b \tan (c+d x))^3} \, dx","Int[Sec[c + d*x]^2/(a + b*Tan[c + d*x])^3,x]","-\frac{1}{2 b d (a+b \tan (c+d x))^2}","-\frac{1}{2 b d (a+b \tan (c+d x))^2}",1,"-1/(2*b*d*(a + b*Tan[c + d*x])^2)","A",2,2,21,0.09524,1,"{3506, 32}"
570,1,202,0,0.2330422,"\int \frac{\cos ^2(c+d x)}{(a+b \tan (c+d x))^3} \, dx","Int[Cos[c + d*x]^2/(a + b*Tan[c + d*x])^3,x]","\frac{a b \left(a^2-11 b^2\right)}{2 d \left(a^2+b^2\right)^3 (a+b \tan (c+d x))}+\frac{b \left(a^2-2 b^2\right)}{2 d \left(a^2+b^2\right)^2 (a+b \tan (c+d x))^2}+\frac{\cos ^2(c+d x) (a \tan (c+d x)+b)}{2 d \left(a^2+b^2\right) (a+b \tan (c+d x))^2}+\frac{2 b^3 \left(5 a^2-b^2\right) \log (a \cos (c+d x)+b \sin (c+d x))}{d \left(a^2+b^2\right)^4}+\frac{a x \left(10 a^2 b^2+a^4-15 b^4\right)}{2 \left(a^2+b^2\right)^4}","\frac{a b \left(a^2-11 b^2\right)}{2 d \left(a^2+b^2\right)^3 (a+b \tan (c+d x))}+\frac{b \left(a^2-2 b^2\right)}{2 d \left(a^2+b^2\right)^2 (a+b \tan (c+d x))^2}+\frac{\cos ^2(c+d x) (a \tan (c+d x)+b)}{2 d \left(a^2+b^2\right) (a+b \tan (c+d x))^2}+\frac{2 b^3 \left(5 a^2-b^2\right) \log (a \cos (c+d x)+b \sin (c+d x))}{d \left(a^2+b^2\right)^4}+\frac{a x \left(10 a^2 b^2+a^4-15 b^4\right)}{2 \left(a^2+b^2\right)^4}",1,"(a*(a^4 + 10*a^2*b^2 - 15*b^4)*x)/(2*(a^2 + b^2)^4) + (2*b^3*(5*a^2 - b^2)*Log[a*Cos[c + d*x] + b*Sin[c + d*x]])/((a^2 + b^2)^4*d) + (b*(a^2 - 2*b^2))/(2*(a^2 + b^2)^2*d*(a + b*Tan[c + d*x])^2) + (Cos[c + d*x]^2*(b + a*Tan[c + d*x]))/(2*(a^2 + b^2)*d*(a + b*Tan[c + d*x])^2) + (a*b*(a^2 - 11*b^2))/(2*(a^2 + b^2)^3*d*(a + b*Tan[c + d*x]))","A",7,6,21,0.2857,1,"{3506, 741, 801, 635, 203, 260}"
571,1,295,0,0.3493388,"\int \frac{\cos ^4(c+d x)}{(a+b \tan (c+d x))^3} \, dx","Int[Cos[c + d*x]^4/(a + b*Tan[c + d*x])^3,x]","\frac{3 a b \left(6 a^2 b^2+a^4-27 b^4\right)}{8 d \left(a^2+b^2\right)^4 (a+b \tan (c+d x))}+\frac{3 b \left(5 a^2 b^2+a^4-4 b^4\right)}{8 d \left(a^2+b^2\right)^3 (a+b \tan (c+d x))^2}-\frac{\cos ^2(c+d x) \left(2 b \left(a^2-3 b^2\right)-a \left(3 a^2+11 b^2\right) \tan (c+d x)\right)}{8 d \left(a^2+b^2\right)^2 (a+b \tan (c+d x))^2}+\frac{\cos ^4(c+d x) (a \tan (c+d x)+b)}{4 d \left(a^2+b^2\right) (a+b \tan (c+d x))^2}+\frac{3 b^5 \left(7 a^2-b^2\right) \log (a \cos (c+d x)+b \sin (c+d x))}{d \left(a^2+b^2\right)^5}+\frac{3 a x \left(7 a^4 b^2+35 a^2 b^4+a^6-35 b^6\right)}{8 \left(a^2+b^2\right)^5}","\frac{3 a b \left(6 a^2 b^2+a^4-27 b^4\right)}{8 d \left(a^2+b^2\right)^4 (a+b \tan (c+d x))}+\frac{3 b \left(5 a^2 b^2+a^4-4 b^4\right)}{8 d \left(a^2+b^2\right)^3 (a+b \tan (c+d x))^2}-\frac{\cos ^2(c+d x) \left(2 b \left(a^2-3 b^2\right)-a \left(3 a^2+11 b^2\right) \tan (c+d x)\right)}{8 d \left(a^2+b^2\right)^2 (a+b \tan (c+d x))^2}+\frac{\cos ^4(c+d x) (a \tan (c+d x)+b)}{4 d \left(a^2+b^2\right) (a+b \tan (c+d x))^2}+\frac{3 b^5 \left(7 a^2-b^2\right) \log (a \cos (c+d x)+b \sin (c+d x))}{d \left(a^2+b^2\right)^5}+\frac{3 a x \left(7 a^4 b^2+35 a^2 b^4+a^6-35 b^6\right)}{8 \left(a^2+b^2\right)^5}",1,"(3*a*(a^6 + 7*a^4*b^2 + 35*a^2*b^4 - 35*b^6)*x)/(8*(a^2 + b^2)^5) + (3*b^5*(7*a^2 - b^2)*Log[a*Cos[c + d*x] + b*Sin[c + d*x]])/((a^2 + b^2)^5*d) + (3*b*(a^4 + 5*a^2*b^2 - 4*b^4))/(8*(a^2 + b^2)^3*d*(a + b*Tan[c + d*x])^2) + (Cos[c + d*x]^4*(b + a*Tan[c + d*x]))/(4*(a^2 + b^2)*d*(a + b*Tan[c + d*x])^2) + (3*a*b*(a^4 + 6*a^2*b^2 - 27*b^4))/(8*(a^2 + b^2)^4*d*(a + b*Tan[c + d*x])) - (Cos[c + d*x]^2*(2*b*(a^2 - 3*b^2) - a*(3*a^2 + 11*b^2)*Tan[c + d*x]))/(8*(a^2 + b^2)^2*d*(a + b*Tan[c + d*x])^2)","A",8,7,21,0.3333,1,"{3506, 741, 823, 801, 635, 203, 260}"
572,1,239,0,0.2432908,"\int \frac{\sec ^7(c+d x)}{(a+b \tan (c+d x))^3} \, dx","Int[Sec[c + d*x]^7/(a + b*Tan[c + d*x])^3,x]","\frac{5 \sec (c+d x) \left(4 a^2-2 a b \tan (c+d x)+b^2\right)}{2 b^5 d}-\frac{5 \sqrt{a^2+b^2} \left(4 a^2+b^2\right) \sec (c+d x) \tanh ^{-1}\left(\frac{b-a \tan (c+d x)}{\sqrt{a^2+b^2} \sqrt{\sec ^2(c+d x)}}\right)}{2 b^6 d \sqrt{\sec ^2(c+d x)}}-\frac{5 a \left(4 a^2+3 b^2\right) \sec (c+d x) \sinh ^{-1}(\tan (c+d x))}{2 b^6 d \sqrt{\sec ^2(c+d x)}}+\frac{5 \sec ^3(c+d x) (4 a+b \tan (c+d x))}{6 b^3 d (a+b \tan (c+d x))}-\frac{\sec ^5(c+d x)}{2 b d (a+b \tan (c+d x))^2}","\frac{5 \sec (c+d x) \left(4 a^2-2 a b \tan (c+d x)+b^2\right)}{2 b^5 d}-\frac{5 \sqrt{a^2+b^2} \left(4 a^2+b^2\right) \sec (c+d x) \tanh ^{-1}\left(\frac{b-a \tan (c+d x)}{\sqrt{a^2+b^2} \sqrt{\sec ^2(c+d x)}}\right)}{2 b^6 d \sqrt{\sec ^2(c+d x)}}-\frac{5 a \left(4 a^2+3 b^2\right) \sec (c+d x) \sinh ^{-1}(\tan (c+d x))}{2 b^6 d \sqrt{\sec ^2(c+d x)}}+\frac{5 \sec ^3(c+d x) (4 a+b \tan (c+d x))}{6 b^3 d (a+b \tan (c+d x))}-\frac{\sec ^5(c+d x)}{2 b d (a+b \tan (c+d x))^2}",1,"(-5*a*(4*a^2 + 3*b^2)*ArcSinh[Tan[c + d*x]]*Sec[c + d*x])/(2*b^6*d*Sqrt[Sec[c + d*x]^2]) - (5*Sqrt[a^2 + b^2]*(4*a^2 + b^2)*ArcTanh[(b - a*Tan[c + d*x])/(Sqrt[a^2 + b^2]*Sqrt[Sec[c + d*x]^2])]*Sec[c + d*x])/(2*b^6*d*Sqrt[Sec[c + d*x]^2]) - Sec[c + d*x]^5/(2*b*d*(a + b*Tan[c + d*x])^2) + (5*Sec[c + d*x]^3*(4*a + b*Tan[c + d*x]))/(6*b^3*d*(a + b*Tan[c + d*x])) + (5*Sec[c + d*x]*(4*a^2 + b^2 - 2*a*b*Tan[c + d*x]))/(2*b^5*d)","A",8,8,21,0.3810,1,"{3512, 733, 813, 815, 844, 215, 725, 206}"
573,1,189,0,0.1602455,"\int \frac{\sec ^5(c+d x)}{(a+b \tan (c+d x))^3} \, dx","Int[Sec[c + d*x]^5/(a + b*Tan[c + d*x])^3,x]","-\frac{3 \left(2 a^2+b^2\right) \sec (c+d x) \tanh ^{-1}\left(\frac{b-a \tan (c+d x)}{\sqrt{a^2+b^2} \sqrt{\sec ^2(c+d x)}}\right)}{2 b^4 d \sqrt{a^2+b^2} \sqrt{\sec ^2(c+d x)}}+\frac{3 \sec (c+d x) (2 a+b \tan (c+d x))}{2 b^3 d (a+b \tan (c+d x))}-\frac{3 a \sec (c+d x) \sinh ^{-1}(\tan (c+d x))}{b^4 d \sqrt{\sec ^2(c+d x)}}-\frac{\sec ^3(c+d x)}{2 b d (a+b \tan (c+d x))^2}","-\frac{3 \left(2 a^2+b^2\right) \tanh ^{-1}\left(\frac{b \cos (c+d x)-a \sin (c+d x)}{\sqrt{a^2+b^2}}\right)}{2 b^4 d \sqrt{a^2+b^2}}-\frac{3 a \tanh ^{-1}(\sin (c+d x))}{b^4 d}+\frac{3 \sec (c+d x) (2 a+b \tan (c+d x))}{2 b^3 d (a+b \tan (c+d x))}-\frac{\sec ^3(c+d x)}{2 b d (a+b \tan (c+d x))^2}",1,"(-3*a*ArcSinh[Tan[c + d*x]]*Sec[c + d*x])/(b^4*d*Sqrt[Sec[c + d*x]^2]) - (3*(2*a^2 + b^2)*ArcTanh[(b - a*Tan[c + d*x])/(Sqrt[a^2 + b^2]*Sqrt[Sec[c + d*x]^2])]*Sec[c + d*x])/(2*b^4*Sqrt[a^2 + b^2]*d*Sqrt[Sec[c + d*x]^2]) - Sec[c + d*x]^3/(2*b*d*(a + b*Tan[c + d*x])^2) + (3*Sec[c + d*x]*(2*a + b*Tan[c + d*x]))/(2*b^3*d*(a + b*Tan[c + d*x]))","A",7,7,21,0.3333,1,"{3512, 733, 813, 844, 215, 725, 206}"
574,1,118,0,0.0916806,"\int \frac{\sec ^3(c+d x)}{(a+b \tan (c+d x))^3} \, dx","Int[Sec[c + d*x]^3/(a + b*Tan[c + d*x])^3,x]","-\frac{\sec (c+d x) (b-a \tan (c+d x))}{2 d \left(a^2+b^2\right) (a+b \tan (c+d x))^2}-\frac{\sec (c+d x) \tanh ^{-1}\left(\frac{b-a \tan (c+d x)}{\sqrt{a^2+b^2} \sqrt{\sec ^2(c+d x)}}\right)}{2 d \left(a^2+b^2\right)^{3/2} \sqrt{\sec ^2(c+d x)}}","-\frac{\sec (c+d x) (b-a \tan (c+d x))}{2 d \left(a^2+b^2\right) (a+b \tan (c+d x))^2}-\frac{\tanh ^{-1}\left(\frac{b \cos (c+d x)-a \sin (c+d x)}{\sqrt{a^2+b^2}}\right)}{2 d \left(a^2+b^2\right)^{3/2}}",1,"-(ArcTanh[(b - a*Tan[c + d*x])/(Sqrt[a^2 + b^2]*Sqrt[Sec[c + d*x]^2])]*Sec[c + d*x])/(2*(a^2 + b^2)^(3/2)*d*Sqrt[Sec[c + d*x]^2]) - (Sec[c + d*x]*(b - a*Tan[c + d*x]))/(2*(a^2 + b^2)*d*(a + b*Tan[c + d*x])^2)","A",4,4,21,0.1905,1,"{3512, 721, 725, 206}"
575,1,155,0,0.1142417,"\int \frac{\sec (c+d x)}{(a+b \tan (c+d x))^3} \, dx","Int[Sec[c + d*x]/(a + b*Tan[c + d*x])^3,x]","-\frac{3 a b \sec (c+d x)}{2 d \left(a^2+b^2\right)^2 (a+b \tan (c+d x))}-\frac{b \sec (c+d x)}{2 d \left(a^2+b^2\right) (a+b \tan (c+d x))^2}-\frac{\left(2 a^2-b^2\right) \sec (c+d x) \tanh ^{-1}\left(\frac{b-a \tan (c+d x)}{\sqrt{a^2+b^2} \sqrt{\sec ^2(c+d x)}}\right)}{2 d \left(a^2+b^2\right)^{5/2} \sqrt{\sec ^2(c+d x)}}","-\frac{3 a b \sec (c+d x)}{2 d \left(a^2+b^2\right)^2 (a+b \tan (c+d x))}-\frac{b \sec (c+d x)}{2 d \left(a^2+b^2\right) (a+b \tan (c+d x))^2}-\frac{\left(2 a^2-b^2\right) \sec (c+d x) \tanh ^{-1}\left(\frac{b-a \tan (c+d x)}{\sqrt{a^2+b^2} \sqrt{\sec ^2(c+d x)}}\right)}{2 d \left(a^2+b^2\right)^{5/2} \sqrt{\sec ^2(c+d x)}}",1,"-((2*a^2 - b^2)*ArcTanh[(b - a*Tan[c + d*x])/(Sqrt[a^2 + b^2]*Sqrt[Sec[c + d*x]^2])]*Sec[c + d*x])/(2*(a^2 + b^2)^(5/2)*d*Sqrt[Sec[c + d*x]^2]) - (b*Sec[c + d*x])/(2*(a^2 + b^2)*d*(a + b*Tan[c + d*x])^2) - (3*a*b*Sec[c + d*x])/(2*(a^2 + b^2)^2*d*(a + b*Tan[c + d*x]))","A",5,5,19,0.2632,1,"{3512, 745, 807, 725, 206}"
576,1,221,0,0.213629,"\int \frac{\cos (c+d x)}{(a+b \tan (c+d x))^3} \, dx","Int[Cos[c + d*x]/(a + b*Tan[c + d*x])^3,x]","\frac{\cos (c+d x) (a \tan (c+d x)+b)}{d \left(a^2+b^2\right) (a+b \tan (c+d x))^2}+\frac{a b \left(2 a^2-13 b^2\right) \sec (c+d x)}{2 d \left(a^2+b^2\right)^3 (a+b \tan (c+d x))}+\frac{b \left(2 a^2-3 b^2\right) \sec (c+d x)}{2 d \left(a^2+b^2\right)^2 (a+b \tan (c+d x))^2}-\frac{3 b^2 \left(4 a^2-b^2\right) \cos (c+d x) \sqrt{\sec ^2(c+d x)} \tanh ^{-1}\left(\frac{b-a \tan (c+d x)}{\sqrt{a^2+b^2} \sqrt{\sec ^2(c+d x)}}\right)}{2 d \left(a^2+b^2\right)^{7/2}}","\frac{\cos (c+d x) (a \tan (c+d x)+b)}{d \left(a^2+b^2\right) (a+b \tan (c+d x))^2}+\frac{a b \left(2 a^2-13 b^2\right) \sec (c+d x)}{2 d \left(a^2+b^2\right)^3 (a+b \tan (c+d x))}+\frac{b \left(2 a^2-3 b^2\right) \sec (c+d x)}{2 d \left(a^2+b^2\right)^2 (a+b \tan (c+d x))^2}-\frac{3 b^2 \left(4 a^2-b^2\right) \cos (c+d x) \sqrt{\sec ^2(c+d x)} \tanh ^{-1}\left(\frac{b-a \tan (c+d x)}{\sqrt{a^2+b^2} \sqrt{\sec ^2(c+d x)}}\right)}{2 d \left(a^2+b^2\right)^{7/2}}",1,"(-3*b^2*(4*a^2 - b^2)*ArcTanh[(b - a*Tan[c + d*x])/(Sqrt[a^2 + b^2]*Sqrt[Sec[c + d*x]^2])]*Cos[c + d*x]*Sqrt[Sec[c + d*x]^2])/(2*(a^2 + b^2)^(7/2)*d) + (b*(2*a^2 - 3*b^2)*Sec[c + d*x])/(2*(a^2 + b^2)^2*d*(a + b*Tan[c + d*x])^2) + (Cos[c + d*x]*(b + a*Tan[c + d*x]))/((a^2 + b^2)*d*(a + b*Tan[c + d*x])^2) + (a*b*(2*a^2 - 13*b^2)*Sec[c + d*x])/(2*(a^2 + b^2)^3*d*(a + b*Tan[c + d*x]))","A",6,6,19,0.3158,1,"{3512, 741, 835, 807, 725, 206}"
577,1,310,0,0.3845315,"\int \frac{\cos ^3(c+d x)}{(a+b \tan (c+d x))^3} \, dx","Int[Cos[c + d*x]^3/(a + b*Tan[c + d*x])^3,x]","\frac{\cos ^3(c+d x) (a \tan (c+d x)+b)}{3 d \left(a^2+b^2\right) (a+b \tan (c+d x))^2}-\frac{\cos (c+d x) \left(b \left(2 a^2-5 b^2\right)-a \left(2 a^2+9 b^2\right) \tan (c+d x)\right)}{3 d \left(a^2+b^2\right)^2 (a+b \tan (c+d x))^2}+\frac{a b \left(28 a^2 b^2+4 a^4-81 b^4\right) \sec (c+d x)}{6 d \left(a^2+b^2\right)^4 (a+b \tan (c+d x))}+\frac{b \left(24 a^2 b^2+4 a^4-15 b^4\right) \sec (c+d x)}{6 d \left(a^2+b^2\right)^3 (a+b \tan (c+d x))^2}-\frac{5 b^4 \left(6 a^2-b^2\right) \cos (c+d x) \sqrt{\sec ^2(c+d x)} \tanh ^{-1}\left(\frac{b-a \tan (c+d x)}{\sqrt{a^2+b^2} \sqrt{\sec ^2(c+d x)}}\right)}{2 d \left(a^2+b^2\right)^{9/2}}","\frac{\cos ^3(c+d x) (a \tan (c+d x)+b)}{3 d \left(a^2+b^2\right) (a+b \tan (c+d x))^2}-\frac{\cos (c+d x) \left(b \left(2 a^2-5 b^2\right)-a \left(2 a^2+9 b^2\right) \tan (c+d x)\right)}{3 d \left(a^2+b^2\right)^2 (a+b \tan (c+d x))^2}+\frac{a b \left(28 a^2 b^2+4 a^4-81 b^4\right) \sec (c+d x)}{6 d \left(a^2+b^2\right)^4 (a+b \tan (c+d x))}+\frac{b \left(24 a^2 b^2+4 a^4-15 b^4\right) \sec (c+d x)}{6 d \left(a^2+b^2\right)^3 (a+b \tan (c+d x))^2}-\frac{5 b^4 \left(6 a^2-b^2\right) \cos (c+d x) \sqrt{\sec ^2(c+d x)} \tanh ^{-1}\left(\frac{b-a \tan (c+d x)}{\sqrt{a^2+b^2} \sqrt{\sec ^2(c+d x)}}\right)}{2 d \left(a^2+b^2\right)^{9/2}}",1,"(-5*b^4*(6*a^2 - b^2)*ArcTanh[(b - a*Tan[c + d*x])/(Sqrt[a^2 + b^2]*Sqrt[Sec[c + d*x]^2])]*Cos[c + d*x]*Sqrt[Sec[c + d*x]^2])/(2*(a^2 + b^2)^(9/2)*d) + (b*(4*a^4 + 24*a^2*b^2 - 15*b^4)*Sec[c + d*x])/(6*(a^2 + b^2)^3*d*(a + b*Tan[c + d*x])^2) + (Cos[c + d*x]^3*(b + a*Tan[c + d*x]))/(3*(a^2 + b^2)*d*(a + b*Tan[c + d*x])^2) + (a*b*(4*a^4 + 28*a^2*b^2 - 81*b^4)*Sec[c + d*x])/(6*(a^2 + b^2)^4*d*(a + b*Tan[c + d*x])) - (Cos[c + d*x]*(b*(2*a^2 - 5*b^2) - a*(2*a^2 + 9*b^2)*Tan[c + d*x]))/(3*(a^2 + b^2)^2*d*(a + b*Tan[c + d*x])^2)","A",7,7,21,0.3333,1,"{3512, 741, 823, 835, 807, 725, 206}"
578,1,121,0,0.0928726,"\int (d \sec (e+f x))^{7/2} (a+b \tan (e+f x)) \, dx","Int[(d*Sec[e + f*x])^(7/2)*(a + b*Tan[e + f*x]),x]","\frac{6 a d^3 \sin (e+f x) \sqrt{d \sec (e+f x)}}{5 f}-\frac{6 a d^4 E\left(\left.\frac{1}{2} (e+f x)\right|2\right)}{5 f \sqrt{\cos (e+f x)} \sqrt{d \sec (e+f x)}}+\frac{2 a d \sin (e+f x) (d \sec (e+f x))^{5/2}}{5 f}+\frac{2 b (d \sec (e+f x))^{7/2}}{7 f}","\frac{6 a d^3 \sin (e+f x) \sqrt{d \sec (e+f x)}}{5 f}-\frac{6 a d^4 E\left(\left.\frac{1}{2} (e+f x)\right|2\right)}{5 f \sqrt{\cos (e+f x)} \sqrt{d \sec (e+f x)}}+\frac{2 a d \sin (e+f x) (d \sec (e+f x))^{5/2}}{5 f}+\frac{2 b (d \sec (e+f x))^{7/2}}{7 f}",1,"(-6*a*d^4*EllipticE[(e + f*x)/2, 2])/(5*f*Sqrt[Cos[e + f*x]]*Sqrt[d*Sec[e + f*x]]) + (2*b*(d*Sec[e + f*x])^(7/2))/(7*f) + (6*a*d^3*Sqrt[d*Sec[e + f*x]]*Sin[e + f*x])/(5*f) + (2*a*d*(d*Sec[e + f*x])^(5/2)*Sin[e + f*x])/(5*f)","A",5,4,23,0.1739,1,"{3486, 3768, 3771, 2639}"
579,1,92,0,0.0691213,"\int (d \sec (e+f x))^{5/2} (a+b \tan (e+f x)) \, dx","Int[(d*Sec[e + f*x])^(5/2)*(a + b*Tan[e + f*x]),x]","\frac{2 a d^2 \sqrt{\cos (e+f x)} F\left(\left.\frac{1}{2} (e+f x)\right|2\right) \sqrt{d \sec (e+f x)}}{3 f}+\frac{2 a d \sin (e+f x) (d \sec (e+f x))^{3/2}}{3 f}+\frac{2 b (d \sec (e+f x))^{5/2}}{5 f}","\frac{2 a d^2 \sqrt{\cos (e+f x)} F\left(\left.\frac{1}{2} (e+f x)\right|2\right) \sqrt{d \sec (e+f x)}}{3 f}+\frac{2 a d \sin (e+f x) (d \sec (e+f x))^{3/2}}{3 f}+\frac{2 b (d \sec (e+f x))^{5/2}}{5 f}",1,"(2*a*d^2*Sqrt[Cos[e + f*x]]*EllipticF[(e + f*x)/2, 2]*Sqrt[d*Sec[e + f*x]])/(3*f) + (2*b*(d*Sec[e + f*x])^(5/2))/(5*f) + (2*a*d*(d*Sec[e + f*x])^(3/2)*Sin[e + f*x])/(3*f)","A",4,4,23,0.1739,1,"{3486, 3768, 3771, 2641}"
580,1,88,0,0.0694522,"\int (d \sec (e+f x))^{3/2} (a+b \tan (e+f x)) \, dx","Int[(d*Sec[e + f*x])^(3/2)*(a + b*Tan[e + f*x]),x]","-\frac{2 a d^2 E\left(\left.\frac{1}{2} (e+f x)\right|2\right)}{f \sqrt{\cos (e+f x)} \sqrt{d \sec (e+f x)}}+\frac{2 a d \sin (e+f x) \sqrt{d \sec (e+f x)}}{f}+\frac{2 b (d \sec (e+f x))^{3/2}}{3 f}","-\frac{2 a d^2 E\left(\left.\frac{1}{2} (e+f x)\right|2\right)}{f \sqrt{\cos (e+f x)} \sqrt{d \sec (e+f x)}}+\frac{2 a d \sin (e+f x) \sqrt{d \sec (e+f x)}}{f}+\frac{2 b (d \sec (e+f x))^{3/2}}{3 f}",1,"(-2*a*d^2*EllipticE[(e + f*x)/2, 2])/(f*Sqrt[Cos[e + f*x]]*Sqrt[d*Sec[e + f*x]]) + (2*b*(d*Sec[e + f*x])^(3/2))/(3*f) + (2*a*d*Sqrt[d*Sec[e + f*x]]*Sin[e + f*x])/f","A",4,4,23,0.1739,1,"{3486, 3768, 3771, 2639}"
581,1,58,0,0.0474153,"\int \sqrt{d \sec (e+f x)} (a+b \tan (e+f x)) \, dx","Int[Sqrt[d*Sec[e + f*x]]*(a + b*Tan[e + f*x]),x]","\frac{2 a \sqrt{\cos (e+f x)} F\left(\left.\frac{1}{2} (e+f x)\right|2\right) \sqrt{d \sec (e+f x)}}{f}+\frac{2 b \sqrt{d \sec (e+f x)}}{f}","\frac{2 a \sqrt{\cos (e+f x)} F\left(\left.\frac{1}{2} (e+f x)\right|2\right) \sqrt{d \sec (e+f x)}}{f}+\frac{2 b \sqrt{d \sec (e+f x)}}{f}",1,"(2*b*Sqrt[d*Sec[e + f*x]])/f + (2*a*Sqrt[Cos[e + f*x]]*EllipticF[(e + f*x)/2, 2]*Sqrt[d*Sec[e + f*x]])/f","A",3,3,23,0.1304,1,"{3486, 3771, 2641}"
582,1,58,0,0.0492027,"\int \frac{a+b \tan (e+f x)}{\sqrt{d \sec (e+f x)}} \, dx","Int[(a + b*Tan[e + f*x])/Sqrt[d*Sec[e + f*x]],x]","\frac{2 a E\left(\left.\frac{1}{2} (e+f x)\right|2\right)}{f \sqrt{\cos (e+f x)} \sqrt{d \sec (e+f x)}}-\frac{2 b}{f \sqrt{d \sec (e+f x)}}","\frac{2 a E\left(\left.\frac{1}{2} (e+f x)\right|2\right)}{f \sqrt{\cos (e+f x)} \sqrt{d \sec (e+f x)}}-\frac{2 b}{f \sqrt{d \sec (e+f x)}}",1,"(-2*b)/(f*Sqrt[d*Sec[e + f*x]]) + (2*a*EllipticE[(e + f*x)/2, 2])/(f*Sqrt[Cos[e + f*x]]*Sqrt[d*Sec[e + f*x]])","A",3,3,23,0.1304,1,"{3486, 3771, 2639}"
583,1,94,0,0.0693648,"\int \frac{a+b \tan (e+f x)}{(d \sec (e+f x))^{3/2}} \, dx","Int[(a + b*Tan[e + f*x])/(d*Sec[e + f*x])^(3/2),x]","\frac{2 a \sqrt{\cos (e+f x)} F\left(\left.\frac{1}{2} (e+f x)\right|2\right) \sqrt{d \sec (e+f x)}}{3 d^2 f}+\frac{2 a \sin (e+f x)}{3 d f \sqrt{d \sec (e+f x)}}-\frac{2 b}{3 f (d \sec (e+f x))^{3/2}}","\frac{2 a \sqrt{\cos (e+f x)} F\left(\left.\frac{1}{2} (e+f x)\right|2\right) \sqrt{d \sec (e+f x)}}{3 d^2 f}+\frac{2 a \sin (e+f x)}{3 d f \sqrt{d \sec (e+f x)}}-\frac{2 b}{3 f (d \sec (e+f x))^{3/2}}",1,"(-2*b)/(3*f*(d*Sec[e + f*x])^(3/2)) + (2*a*Sqrt[Cos[e + f*x]]*EllipticF[(e + f*x)/2, 2]*Sqrt[d*Sec[e + f*x]])/(3*d^2*f) + (2*a*Sin[e + f*x])/(3*d*f*Sqrt[d*Sec[e + f*x]])","A",4,4,23,0.1739,1,"{3486, 3769, 3771, 2641}"
584,1,94,0,0.0704951,"\int \frac{a+b \tan (e+f x)}{(d \sec (e+f x))^{5/2}} \, dx","Int[(a + b*Tan[e + f*x])/(d*Sec[e + f*x])^(5/2),x]","\frac{6 a E\left(\left.\frac{1}{2} (e+f x)\right|2\right)}{5 d^2 f \sqrt{\cos (e+f x)} \sqrt{d \sec (e+f x)}}+\frac{2 a \sin (e+f x)}{5 d f (d \sec (e+f x))^{3/2}}-\frac{2 b}{5 f (d \sec (e+f x))^{5/2}}","\frac{6 a E\left(\left.\frac{1}{2} (e+f x)\right|2\right)}{5 d^2 f \sqrt{\cos (e+f x)} \sqrt{d \sec (e+f x)}}+\frac{2 a \sin (e+f x)}{5 d f (d \sec (e+f x))^{3/2}}-\frac{2 b}{5 f (d \sec (e+f x))^{5/2}}",1,"(-2*b)/(5*f*(d*Sec[e + f*x])^(5/2)) + (6*a*EllipticE[(e + f*x)/2, 2])/(5*d^2*f*Sqrt[Cos[e + f*x]]*Sqrt[d*Sec[e + f*x]]) + (2*a*Sin[e + f*x])/(5*d*f*(d*Sec[e + f*x])^(3/2))","A",4,4,23,0.1739,1,"{3486, 3769, 3771, 2639}"
585,1,123,0,0.0905019,"\int \frac{a+b \tan (e+f x)}{(d \sec (e+f x))^{7/2}} \, dx","Int[(a + b*Tan[e + f*x])/(d*Sec[e + f*x])^(7/2),x]","\frac{10 a \sin (e+f x)}{21 d^3 f \sqrt{d \sec (e+f x)}}+\frac{10 a \sqrt{\cos (e+f x)} F\left(\left.\frac{1}{2} (e+f x)\right|2\right) \sqrt{d \sec (e+f x)}}{21 d^4 f}+\frac{2 a \sin (e+f x)}{7 d f (d \sec (e+f x))^{5/2}}-\frac{2 b}{7 f (d \sec (e+f x))^{7/2}}","\frac{10 a \sin (e+f x)}{21 d^3 f \sqrt{d \sec (e+f x)}}+\frac{10 a \sqrt{\cos (e+f x)} F\left(\left.\frac{1}{2} (e+f x)\right|2\right) \sqrt{d \sec (e+f x)}}{21 d^4 f}+\frac{2 a \sin (e+f x)}{7 d f (d \sec (e+f x))^{5/2}}-\frac{2 b}{7 f (d \sec (e+f x))^{7/2}}",1,"(-2*b)/(7*f*(d*Sec[e + f*x])^(7/2)) + (10*a*Sqrt[Cos[e + f*x]]*EllipticF[(e + f*x)/2, 2]*Sqrt[d*Sec[e + f*x]])/(21*d^4*f) + (2*a*Sin[e + f*x])/(7*d*f*(d*Sec[e + f*x])^(5/2)) + (10*a*Sin[e + f*x])/(21*d^3*f*Sqrt[d*Sec[e + f*x]])","A",5,4,23,0.1739,1,"{3486, 3769, 3771, 2641}"
586,1,143,0,0.1600026,"\int (d \sec (e+f x))^{5/2} (a+b \tan (e+f x))^2 \, dx","Int[(d*Sec[e + f*x])^(5/2)*(a + b*Tan[e + f*x])^2,x]","\frac{2 d^2 \left(7 a^2-2 b^2\right) \sqrt{\cos (e+f x)} F\left(\left.\frac{1}{2} (e+f x)\right|2\right) \sqrt{d \sec (e+f x)}}{21 f}+\frac{2 d \left(7 a^2-2 b^2\right) \sin (e+f x) (d \sec (e+f x))^{3/2}}{21 f}+\frac{18 a b (d \sec (e+f x))^{5/2}}{35 f}+\frac{2 b (d \sec (e+f x))^{5/2} (a+b \tan (e+f x))}{7 f}","\frac{2 d^2 \left(7 a^2-2 b^2\right) \sqrt{\cos (e+f x)} F\left(\left.\frac{1}{2} (e+f x)\right|2\right) \sqrt{d \sec (e+f x)}}{21 f}+\frac{2 d \left(7 a^2-2 b^2\right) \sin (e+f x) (d \sec (e+f x))^{3/2}}{21 f}+\frac{18 a b (d \sec (e+f x))^{5/2}}{35 f}+\frac{2 b (d \sec (e+f x))^{5/2} (a+b \tan (e+f x))}{7 f}",1,"(2*(7*a^2 - 2*b^2)*d^2*Sqrt[Cos[e + f*x]]*EllipticF[(e + f*x)/2, 2]*Sqrt[d*Sec[e + f*x]])/(21*f) + (18*a*b*(d*Sec[e + f*x])^(5/2))/(35*f) + (2*(7*a^2 - 2*b^2)*d*(d*Sec[e + f*x])^(3/2)*Sin[e + f*x])/(21*f) + (2*b*(d*Sec[e + f*x])^(5/2)*(a + b*Tan[e + f*x]))/(7*f)","A",5,5,25,0.2000,1,"{3508, 3486, 3768, 3771, 2641}"
587,1,143,0,0.1628746,"\int (d \sec (e+f x))^{3/2} (a+b \tan (e+f x))^2 \, dx","Int[(d*Sec[e + f*x])^(3/2)*(a + b*Tan[e + f*x])^2,x]","-\frac{2 d^2 \left(5 a^2-2 b^2\right) E\left(\left.\frac{1}{2} (e+f x)\right|2\right)}{5 f \sqrt{\cos (e+f x)} \sqrt{d \sec (e+f x)}}+\frac{2 d \left(5 a^2-2 b^2\right) \sin (e+f x) \sqrt{d \sec (e+f x)}}{5 f}+\frac{14 a b (d \sec (e+f x))^{3/2}}{15 f}+\frac{2 b (d \sec (e+f x))^{3/2} (a+b \tan (e+f x))}{5 f}","-\frac{2 d^2 \left(5 a^2-2 b^2\right) E\left(\left.\frac{1}{2} (e+f x)\right|2\right)}{5 f \sqrt{\cos (e+f x)} \sqrt{d \sec (e+f x)}}+\frac{2 d \left(5 a^2-2 b^2\right) \sin (e+f x) \sqrt{d \sec (e+f x)}}{5 f}+\frac{14 a b (d \sec (e+f x))^{3/2}}{15 f}+\frac{2 b (d \sec (e+f x))^{3/2} (a+b \tan (e+f x))}{5 f}",1,"(-2*(5*a^2 - 2*b^2)*d^2*EllipticE[(e + f*x)/2, 2])/(5*f*Sqrt[Cos[e + f*x]]*Sqrt[d*Sec[e + f*x]]) + (14*a*b*(d*Sec[e + f*x])^(3/2))/(15*f) + (2*(5*a^2 - 2*b^2)*d*Sqrt[d*Sec[e + f*x]]*Sin[e + f*x])/(5*f) + (2*b*(d*Sec[e + f*x])^(3/2)*(a + b*Tan[e + f*x]))/(5*f)","A",5,5,25,0.2000,1,"{3508, 3486, 3768, 3771, 2639}"
588,1,103,0,0.1233283,"\int \sqrt{d \sec (e+f x)} (a+b \tan (e+f x))^2 \, dx","Int[Sqrt[d*Sec[e + f*x]]*(a + b*Tan[e + f*x])^2,x]","\frac{2 \left(3 a^2-2 b^2\right) \sqrt{\cos (e+f x)} F\left(\left.\frac{1}{2} (e+f x)\right|2\right) \sqrt{d \sec (e+f x)}}{3 f}+\frac{10 a b \sqrt{d \sec (e+f x)}}{3 f}+\frac{2 b \sqrt{d \sec (e+f x)} (a+b \tan (e+f x))}{3 f}","\frac{2 \left(3 a^2-2 b^2\right) \sqrt{\cos (e+f x)} F\left(\left.\frac{1}{2} (e+f x)\right|2\right) \sqrt{d \sec (e+f x)}}{3 f}+\frac{10 a b \sqrt{d \sec (e+f x)}}{3 f}+\frac{2 b \sqrt{d \sec (e+f x)} (a+b \tan (e+f x))}{3 f}",1,"(10*a*b*Sqrt[d*Sec[e + f*x]])/(3*f) + (2*(3*a^2 - 2*b^2)*Sqrt[Cos[e + f*x]]*EllipticF[(e + f*x)/2, 2]*Sqrt[d*Sec[e + f*x]])/(3*f) + (2*b*Sqrt[d*Sec[e + f*x]]*(a + b*Tan[e + f*x]))/(3*f)","A",4,4,25,0.1600,1,"{3508, 3486, 3771, 2641}"
589,1,95,0,0.1255651,"\int \frac{(a+b \tan (e+f x))^2}{\sqrt{d \sec (e+f x)}} \, dx","Int[(a + b*Tan[e + f*x])^2/Sqrt[d*Sec[e + f*x]],x]","\frac{2 \left(a^2-2 b^2\right) E\left(\left.\frac{1}{2} (e+f x)\right|2\right)}{f \sqrt{\cos (e+f x)} \sqrt{d \sec (e+f x)}}-\frac{6 a b}{f \sqrt{d \sec (e+f x)}}+\frac{2 b (a+b \tan (e+f x))}{f \sqrt{d \sec (e+f x)}}","\frac{2 \left(a^2-2 b^2\right) E\left(\left.\frac{1}{2} (e+f x)\right|2\right)}{f \sqrt{\cos (e+f x)} \sqrt{d \sec (e+f x)}}-\frac{6 a b}{f \sqrt{d \sec (e+f x)}}+\frac{2 b (a+b \tan (e+f x))}{f \sqrt{d \sec (e+f x)}}",1,"(-6*a*b)/(f*Sqrt[d*Sec[e + f*x]]) + (2*(a^2 - 2*b^2)*EllipticE[(e + f*x)/2, 2])/(f*Sqrt[Cos[e + f*x]]*Sqrt[d*Sec[e + f*x]]) + (2*b*(a + b*Tan[e + f*x]))/(f*Sqrt[d*Sec[e + f*x]])","A",4,4,25,0.1600,1,"{3508, 3486, 3771, 2639}"
590,1,139,0,0.1624706,"\int \frac{(a+b \tan (e+f x))^2}{(d \sec (e+f x))^{3/2}} \, dx","Int[(a + b*Tan[e + f*x])^2/(d*Sec[e + f*x])^(3/2),x]","\frac{2 \left(a^2+2 b^2\right) \sqrt{\cos (e+f x)} F\left(\left.\frac{1}{2} (e+f x)\right|2\right) \sqrt{d \sec (e+f x)}}{3 d^2 f}+\frac{2 \left(a^2+2 b^2\right) \sin (e+f x)}{3 d f \sqrt{d \sec (e+f x)}}+\frac{2 a b}{3 f (d \sec (e+f x))^{3/2}}-\frac{2 b (a+b \tan (e+f x))}{f (d \sec (e+f x))^{3/2}}","\frac{2 \left(a^2+2 b^2\right) \sqrt{\cos (e+f x)} F\left(\left.\frac{1}{2} (e+f x)\right|2\right) \sqrt{d \sec (e+f x)}}{3 d^2 f}+\frac{2 \left(a^2+2 b^2\right) \sin (e+f x)}{3 d f \sqrt{d \sec (e+f x)}}+\frac{2 a b}{3 f (d \sec (e+f x))^{3/2}}-\frac{2 b (a+b \tan (e+f x))}{f (d \sec (e+f x))^{3/2}}",1,"(2*a*b)/(3*f*(d*Sec[e + f*x])^(3/2)) + (2*(a^2 + 2*b^2)*Sqrt[Cos[e + f*x]]*EllipticF[(e + f*x)/2, 2]*Sqrt[d*Sec[e + f*x]])/(3*d^2*f) + (2*(a^2 + 2*b^2)*Sin[e + f*x])/(3*d*f*Sqrt[d*Sec[e + f*x]]) - (2*b*(a + b*Tan[e + f*x]))/(f*(d*Sec[e + f*x])^(3/2))","A",5,5,25,0.2000,1,"{3508, 3486, 3769, 3771, 2641}"
591,1,145,0,0.1659577,"\int \frac{(a+b \tan (e+f x))^2}{(d \sec (e+f x))^{5/2}} \, dx","Int[(a + b*Tan[e + f*x])^2/(d*Sec[e + f*x])^(5/2),x]","\frac{2 \left(3 a^2+2 b^2\right) E\left(\left.\frac{1}{2} (e+f x)\right|2\right)}{5 d^2 f \sqrt{\cos (e+f x)} \sqrt{d \sec (e+f x)}}+\frac{2 \left(3 a^2+2 b^2\right) \sin (e+f x)}{15 d f (d \sec (e+f x))^{3/2}}-\frac{2 a b}{15 f (d \sec (e+f x))^{5/2}}-\frac{2 b (a+b \tan (e+f x))}{3 f (d \sec (e+f x))^{5/2}}","\frac{2 \left(3 a^2+2 b^2\right) E\left(\left.\frac{1}{2} (e+f x)\right|2\right)}{5 d^2 f \sqrt{\cos (e+f x)} \sqrt{d \sec (e+f x)}}+\frac{2 \left(3 a^2+2 b^2\right) \sin (e+f x)}{15 d f (d \sec (e+f x))^{3/2}}-\frac{2 a b}{15 f (d \sec (e+f x))^{5/2}}-\frac{2 b (a+b \tan (e+f x))}{3 f (d \sec (e+f x))^{5/2}}",1,"(-2*a*b)/(15*f*(d*Sec[e + f*x])^(5/2)) + (2*(3*a^2 + 2*b^2)*EllipticE[(e + f*x)/2, 2])/(5*d^2*f*Sqrt[Cos[e + f*x]]*Sqrt[d*Sec[e + f*x]]) + (2*(3*a^2 + 2*b^2)*Sin[e + f*x])/(15*d*f*(d*Sec[e + f*x])^(3/2)) - (2*b*(a + b*Tan[e + f*x]))/(3*f*(d*Sec[e + f*x])^(5/2))","A",5,5,25,0.2000,1,"{3508, 3486, 3769, 3771, 2639}"
592,1,184,0,0.1919035,"\int \frac{(a+b \tan (e+f x))^2}{(d \sec (e+f x))^{7/2}} \, dx","Int[(a + b*Tan[e + f*x])^2/(d*Sec[e + f*x])^(7/2),x]","\frac{2 \left(5 a^2+2 b^2\right) \sin (e+f x)}{21 d^3 f \sqrt{d \sec (e+f x)}}+\frac{2 \left(5 a^2+2 b^2\right) \sqrt{\cos (e+f x)} F\left(\left.\frac{1}{2} (e+f x)\right|2\right) \sqrt{d \sec (e+f x)}}{21 d^4 f}+\frac{2 \left(5 a^2+2 b^2\right) \sin (e+f x)}{35 d f (d \sec (e+f x))^{5/2}}-\frac{6 a b}{35 f (d \sec (e+f x))^{7/2}}-\frac{2 b (a+b \tan (e+f x))}{5 f (d \sec (e+f x))^{7/2}}","\frac{2 \left(5 a^2+2 b^2\right) \sin (e+f x)}{21 d^3 f \sqrt{d \sec (e+f x)}}+\frac{2 \left(5 a^2+2 b^2\right) \sqrt{\cos (e+f x)} F\left(\left.\frac{1}{2} (e+f x)\right|2\right) \sqrt{d \sec (e+f x)}}{21 d^4 f}+\frac{2 \left(5 a^2+2 b^2\right) \sin (e+f x)}{35 d f (d \sec (e+f x))^{5/2}}-\frac{6 a b}{35 f (d \sec (e+f x))^{7/2}}-\frac{2 b (a+b \tan (e+f x))}{5 f (d \sec (e+f x))^{7/2}}",1,"(-6*a*b)/(35*f*(d*Sec[e + f*x])^(7/2)) + (2*(5*a^2 + 2*b^2)*Sqrt[Cos[e + f*x]]*EllipticF[(e + f*x)/2, 2]*Sqrt[d*Sec[e + f*x]])/(21*d^4*f) + (2*(5*a^2 + 2*b^2)*Sin[e + f*x])/(35*d*f*(d*Sec[e + f*x])^(5/2)) + (2*(5*a^2 + 2*b^2)*Sin[e + f*x])/(21*d^3*f*Sqrt[d*Sec[e + f*x]]) - (2*b*(a + b*Tan[e + f*x]))/(5*f*(d*Sec[e + f*x])^(7/2))","A",6,5,25,0.2000,1,"{3508, 3486, 3769, 3771, 2641}"
593,1,184,0,0.1917638,"\int \frac{(a+b \tan (e+f x))^2}{(d \sec (e+f x))^{9/2}} \, dx","Int[(a + b*Tan[e + f*x])^2/(d*Sec[e + f*x])^(9/2),x]","\frac{2 \left(7 a^2+2 b^2\right) \sin (e+f x)}{45 d^3 f (d \sec (e+f x))^{3/2}}+\frac{2 \left(7 a^2+2 b^2\right) E\left(\left.\frac{1}{2} (e+f x)\right|2\right)}{15 d^4 f \sqrt{\cos (e+f x)} \sqrt{d \sec (e+f x)}}+\frac{2 \left(7 a^2+2 b^2\right) \sin (e+f x)}{63 d f (d \sec (e+f x))^{7/2}}-\frac{10 a b}{63 f (d \sec (e+f x))^{9/2}}-\frac{2 b (a+b \tan (e+f x))}{7 f (d \sec (e+f x))^{9/2}}","\frac{2 \left(7 a^2+2 b^2\right) \sin (e+f x)}{45 d^3 f (d \sec (e+f x))^{3/2}}+\frac{2 \left(7 a^2+2 b^2\right) E\left(\left.\frac{1}{2} (e+f x)\right|2\right)}{15 d^4 f \sqrt{\cos (e+f x)} \sqrt{d \sec (e+f x)}}+\frac{2 \left(7 a^2+2 b^2\right) \sin (e+f x)}{63 d f (d \sec (e+f x))^{7/2}}-\frac{10 a b}{63 f (d \sec (e+f x))^{9/2}}-\frac{2 b (a+b \tan (e+f x))}{7 f (d \sec (e+f x))^{9/2}}",1,"(-10*a*b)/(63*f*(d*Sec[e + f*x])^(9/2)) + (2*(7*a^2 + 2*b^2)*EllipticE[(e + f*x)/2, 2])/(15*d^4*f*Sqrt[Cos[e + f*x]]*Sqrt[d*Sec[e + f*x]]) + (2*(7*a^2 + 2*b^2)*Sin[e + f*x])/(63*d*f*(d*Sec[e + f*x])^(7/2)) + (2*(7*a^2 + 2*b^2)*Sin[e + f*x])/(45*d^3*f*(d*Sec[e + f*x])^(3/2)) - (2*b*(a + b*Tan[e + f*x]))/(7*f*(d*Sec[e + f*x])^(9/2))","A",6,5,25,0.2000,1,"{3508, 3486, 3769, 3771, 2639}"
594,1,198,0,0.1540408,"\int (d \sec (e+f x))^{5/2} (a+b \tan (e+f x))^3 \, dx","Int[(d*Sec[e + f*x])^(5/2)*(a + b*Tan[e + f*x])^3,x]","\frac{2 b d^2 \sec ^2(e+f x) \sqrt{d \sec (e+f x)} \left(14 \left(11 a^2-2 b^2\right)+65 a b \tan (e+f x)\right)}{315 f}+\frac{2 a d^2 \left(7 a^2-6 b^2\right) \tan (e+f x) \sqrt{d \sec (e+f x)}}{21 f}+\frac{2 a d^2 \left(7 a^2-6 b^2\right) \sqrt{d \sec (e+f x)} F\left(\left.\frac{1}{2} \tan ^{-1}(\tan (e+f x))\right|2\right)}{21 f \sqrt[4]{\sec ^2(e+f x)}}+\frac{2 b d^2 \sec ^2(e+f x) \sqrt{d \sec (e+f x)} (a+b \tan (e+f x))^2}{9 f}","\frac{2 b d^2 \sec ^2(e+f x) \sqrt{d \sec (e+f x)} \left(14 \left(11 a^2-2 b^2\right)+65 a b \tan (e+f x)\right)}{315 f}+\frac{2 a d^2 \left(7 a^2-6 b^2\right) \tan (e+f x) \sqrt{d \sec (e+f x)}}{21 f}+\frac{2 a d^2 \left(7 a^2-6 b^2\right) \sqrt{d \sec (e+f x)} F\left(\left.\frac{1}{2} \tan ^{-1}(\tan (e+f x))\right|2\right)}{21 f \sqrt[4]{\sec ^2(e+f x)}}+\frac{2 b d^2 \sec ^2(e+f x) \sqrt{d \sec (e+f x)} (a+b \tan (e+f x))^2}{9 f}",1,"(2*a*(7*a^2 - 6*b^2)*d^2*EllipticF[ArcTan[Tan[e + f*x]]/2, 2]*Sqrt[d*Sec[e + f*x]])/(21*f*(Sec[e + f*x]^2)^(1/4)) + (2*a*(7*a^2 - 6*b^2)*d^2*Sqrt[d*Sec[e + f*x]]*Tan[e + f*x])/(21*f) + (2*b*d^2*Sec[e + f*x]^2*Sqrt[d*Sec[e + f*x]]*(a + b*Tan[e + f*x])^2)/(9*f) + (2*b*d^2*Sec[e + f*x]^2*Sqrt[d*Sec[e + f*x]]*(14*(11*a^2 - 2*b^2) + 65*a*b*Tan[e + f*x]))/(315*f)","A",5,5,25,0.2000,1,"{3512, 743, 780, 195, 231}"
595,1,176,0,0.1455803,"\int (d \sec (e+f x))^{3/2} (a+b \tan (e+f x))^3 \, dx","Int[(d*Sec[e + f*x])^(3/2)*(a + b*Tan[e + f*x])^3,x]","\frac{2 b (d \sec (e+f x))^{3/2} \left(10 \left(9 a^2-2 b^2\right)+33 a b \tan (e+f x)\right)}{105 f}+\frac{2 a \left(5 a^2-6 b^2\right) \sin (e+f x) \cos (e+f x) (d \sec (e+f x))^{3/2}}{5 f}-\frac{2 a \left(5 a^2-6 b^2\right) (d \sec (e+f x))^{3/2} E\left(\left.\frac{1}{2} \tan ^{-1}(\tan (e+f x))\right|2\right)}{5 f \sec ^2(e+f x)^{3/4}}+\frac{2 b (d \sec (e+f x))^{3/2} (a+b \tan (e+f x))^2}{7 f}","\frac{2 b (d \sec (e+f x))^{3/2} \left(10 \left(9 a^2-2 b^2\right)+33 a b \tan (e+f x)\right)}{105 f}+\frac{2 a \left(5 a^2-6 b^2\right) \sin (e+f x) \cos (e+f x) (d \sec (e+f x))^{3/2}}{5 f}-\frac{2 a \left(5 a^2-6 b^2\right) (d \sec (e+f x))^{3/2} E\left(\left.\frac{1}{2} \tan ^{-1}(\tan (e+f x))\right|2\right)}{5 f \sec ^2(e+f x)^{3/4}}+\frac{2 b (d \sec (e+f x))^{3/2} (a+b \tan (e+f x))^2}{7 f}",1,"(-2*a*(5*a^2 - 6*b^2)*EllipticE[ArcTan[Tan[e + f*x]]/2, 2]*(d*Sec[e + f*x])^(3/2))/(5*f*(Sec[e + f*x]^2)^(3/4)) + (2*a*(5*a^2 - 6*b^2)*Cos[e + f*x]*(d*Sec[e + f*x])^(3/2)*Sin[e + f*x])/(5*f) + (2*b*(d*Sec[e + f*x])^(3/2)*(a + b*Tan[e + f*x])^2)/(7*f) + (2*b*(d*Sec[e + f*x])^(3/2)*(10*(9*a^2 - 2*b^2) + 33*a*b*Tan[e + f*x]))/(105*f)","A",5,5,25,0.2000,1,"{3512, 743, 780, 227, 196}"
596,1,129,0,0.1120888,"\int \sqrt{d \sec (e+f x)} (a+b \tan (e+f x))^3 \, dx","Int[Sqrt[d*Sec[e + f*x]]*(a + b*Tan[e + f*x])^3,x]","\frac{2 b \sqrt{d \sec (e+f x)} \left(2 \left(7 a^2-2 b^2\right)+3 a b \tan (e+f x)\right)}{5 f}+\frac{2 a \left(a^2-2 b^2\right) \sqrt{d \sec (e+f x)} F\left(\left.\frac{1}{2} \tan ^{-1}(\tan (e+f x))\right|2\right)}{f \sqrt[4]{\sec ^2(e+f x)}}+\frac{2 b \sqrt{d \sec (e+f x)} (a+b \tan (e+f x))^2}{5 f}","\frac{2 b \sqrt{d \sec (e+f x)} \left(2 \left(7 a^2-2 b^2\right)+3 a b \tan (e+f x)\right)}{5 f}+\frac{2 a \left(a^2-2 b^2\right) \sqrt{d \sec (e+f x)} F\left(\left.\frac{1}{2} \tan ^{-1}(\tan (e+f x))\right|2\right)}{f \sqrt[4]{\sec ^2(e+f x)}}+\frac{2 b \sqrt{d \sec (e+f x)} (a+b \tan (e+f x))^2}{5 f}",1,"(2*a*(a^2 - 2*b^2)*EllipticF[ArcTan[Tan[e + f*x]]/2, 2]*Sqrt[d*Sec[e + f*x]])/(f*(Sec[e + f*x]^2)^(1/4)) + (2*b*Sqrt[d*Sec[e + f*x]]*(a + b*Tan[e + f*x])^2)/(5*f) + (2*b*Sqrt[d*Sec[e + f*x]]*(2*(7*a^2 - 2*b^2) + 3*a*b*Tan[e + f*x]))/(5*f)","A",4,4,25,0.1600,1,"{3512, 743, 780, 231}"
597,1,178,0,0.1405786,"\int \frac{(a+b \tan (e+f x))^3}{\sqrt{d \sec (e+f x)}} \, dx","Int[(a + b*Tan[e + f*x])^3/Sqrt[d*Sec[e + f*x]],x]","-\frac{2 b \sec ^2(e+f x) \left(2 \left(3 a^2-2 b^2\right)+3 a b \tan (e+f x)\right)}{3 f \sqrt{d \sec (e+f x)}}-\frac{2 a \left(a^2-6 b^2\right) \tan (e+f x)}{f \sqrt{d \sec (e+f x)}}+\frac{2 a \left(a^2-6 b^2\right) \sqrt[4]{\sec ^2(e+f x)} E\left(\left.\frac{1}{2} \tan ^{-1}(\tan (e+f x))\right|2\right)}{f \sqrt{d \sec (e+f x)}}-\frac{2 (b-a \tan (e+f x)) (a+b \tan (e+f x))^2}{f \sqrt{d \sec (e+f x)}}","-\frac{2 b \sec ^2(e+f x) \left(2 \left(3 a^2-2 b^2\right)+3 a b \tan (e+f x)\right)}{3 f \sqrt{d \sec (e+f x)}}-\frac{2 a \left(a^2-6 b^2\right) \tan (e+f x)}{f \sqrt{d \sec (e+f x)}}+\frac{2 a \left(a^2-6 b^2\right) \sqrt[4]{\sec ^2(e+f x)} E\left(\left.\frac{1}{2} \tan ^{-1}(\tan (e+f x))\right|2\right)}{f \sqrt{d \sec (e+f x)}}-\frac{2 (b-a \tan (e+f x)) (a+b \tan (e+f x))^2}{f \sqrt{d \sec (e+f x)}}",1,"(2*a*(a^2 - 6*b^2)*EllipticE[ArcTan[Tan[e + f*x]]/2, 2]*(Sec[e + f*x]^2)^(1/4))/(f*Sqrt[d*Sec[e + f*x]]) - (2*a*(a^2 - 6*b^2)*Tan[e + f*x])/(f*Sqrt[d*Sec[e + f*x]]) - (2*(b - a*Tan[e + f*x])*(a + b*Tan[e + f*x])^2)/(f*Sqrt[d*Sec[e + f*x]]) - (2*b*Sec[e + f*x]^2*(2*(3*a^2 - 2*b^2) + 3*a*b*Tan[e + f*x]))/(3*f*Sqrt[d*Sec[e + f*x]])","A",5,5,25,0.2000,1,"{3512, 739, 780, 227, 196}"
598,1,146,0,0.1244663,"\int \frac{(a+b \tan (e+f x))^3}{(d \sec (e+f x))^{3/2}} \, dx","Int[(a + b*Tan[e + f*x])^3/(d*Sec[e + f*x])^(3/2),x]","-\frac{2 b \sec ^2(e+f x) \left(2 \left(a^2-2 b^2\right)+a b \tan (e+f x)\right)}{3 f (d \sec (e+f x))^{3/2}}+\frac{2 a \left(a^2+6 b^2\right) \sec ^2(e+f x)^{3/4} F\left(\left.\frac{1}{2} \tan ^{-1}(\tan (e+f x))\right|2\right)}{3 f (d \sec (e+f x))^{3/2}}-\frac{2 (b-a \tan (e+f x)) (a+b \tan (e+f x))^2}{3 f (d \sec (e+f x))^{3/2}}","-\frac{2 b \sec ^2(e+f x) \left(2 \left(a^2-2 b^2\right)+a b \tan (e+f x)\right)}{3 f (d \sec (e+f x))^{3/2}}+\frac{2 a \left(a^2+6 b^2\right) \sec ^2(e+f x)^{3/4} F\left(\left.\frac{1}{2} \tan ^{-1}(\tan (e+f x))\right|2\right)}{3 f (d \sec (e+f x))^{3/2}}-\frac{2 (b-a \tan (e+f x)) (a+b \tan (e+f x))^2}{3 f (d \sec (e+f x))^{3/2}}",1,"(2*a*(a^2 + 6*b^2)*EllipticF[ArcTan[Tan[e + f*x]]/2, 2]*(Sec[e + f*x]^2)^(3/4))/(3*f*(d*Sec[e + f*x])^(3/2)) - (2*(b - a*Tan[e + f*x])*(a + b*Tan[e + f*x])^2)/(3*f*(d*Sec[e + f*x])^(3/2)) - (2*b*Sec[e + f*x]^2*(2*(a^2 - 2*b^2) + a*b*Tan[e + f*x]))/(3*f*(d*Sec[e + f*x])^(3/2))","A",4,4,25,0.1600,1,"{3512, 739, 780, 231}"
599,1,204,0,0.1573257,"\int \frac{(a+b \tan (e+f x))^3}{(d \sec (e+f x))^{5/2}} \, dx","Int[(a + b*Tan[e + f*x])^3/(d*Sec[e + f*x])^(5/2),x]","-\frac{6 a \left(a^2+2 b^2\right) \tan (e+f x)}{5 d^2 f \sqrt{d \sec (e+f x)}}-\frac{2 \left(2 b \left(a^2+2 b^2\right)-a \left(3 a^2+5 b^2\right) \tan (e+f x)\right)}{5 d^2 f \sqrt{d \sec (e+f x)}}+\frac{6 a \left(a^2+2 b^2\right) \sqrt[4]{\sec ^2(e+f x)} E\left(\left.\frac{1}{2} \tan ^{-1}(\tan (e+f x))\right|2\right)}{5 d^2 f \sqrt{d \sec (e+f x)}}-\frac{2 \cos ^2(e+f x) (b-a \tan (e+f x)) (a+b \tan (e+f x))^2}{5 d^2 f \sqrt{d \sec (e+f x)}}","-\frac{6 a \left(a^2+2 b^2\right) \tan (e+f x)}{5 d^2 f \sqrt{d \sec (e+f x)}}-\frac{2 \left(2 b \left(a^2+2 b^2\right)-a \left(3 a^2+5 b^2\right) \tan (e+f x)\right)}{5 d^2 f \sqrt{d \sec (e+f x)}}+\frac{6 a \left(a^2+2 b^2\right) \sqrt[4]{\sec ^2(e+f x)} E\left(\left.\frac{1}{2} \tan ^{-1}(\tan (e+f x))\right|2\right)}{5 d^2 f \sqrt{d \sec (e+f x)}}-\frac{2 \cos ^2(e+f x) (b-a \tan (e+f x)) (a+b \tan (e+f x))^2}{5 d^2 f \sqrt{d \sec (e+f x)}}",1,"(6*a*(a^2 + 2*b^2)*EllipticE[ArcTan[Tan[e + f*x]]/2, 2]*(Sec[e + f*x]^2)^(1/4))/(5*d^2*f*Sqrt[d*Sec[e + f*x]]) - (6*a*(a^2 + 2*b^2)*Tan[e + f*x])/(5*d^2*f*Sqrt[d*Sec[e + f*x]]) - (2*Cos[e + f*x]^2*(b - a*Tan[e + f*x])*(a + b*Tan[e + f*x])^2)/(5*d^2*f*Sqrt[d*Sec[e + f*x]]) - (2*(2*b*(a^2 + 2*b^2) - a*(3*a^2 + 5*b^2)*Tan[e + f*x]))/(5*d^2*f*Sqrt[d*Sec[e + f*x]])","A",5,5,25,0.2000,1,"{3512, 739, 778, 227, 196}"
600,1,170,0,0.142954,"\int \frac{(a+b \tan (e+f x))^3}{(d \sec (e+f x))^{7/2}} \, dx","Int[(a + b*Tan[e + f*x])^3/(d*Sec[e + f*x])^(7/2),x]","-\frac{2 \left(2 b \left(3 a^2+2 b^2\right)-a \left(5 a^2+3 b^2\right) \tan (e+f x)\right)}{21 d^2 f (d \sec (e+f x))^{3/2}}+\frac{2 a \left(5 a^2+6 b^2\right) \sec ^2(e+f x)^{3/4} F\left(\left.\frac{1}{2} \tan ^{-1}(\tan (e+f x))\right|2\right)}{21 d^2 f (d \sec (e+f x))^{3/2}}-\frac{2 \cos ^2(e+f x) (b-a \tan (e+f x)) (a+b \tan (e+f x))^2}{7 d^2 f (d \sec (e+f x))^{3/2}}","-\frac{2 \left(2 b \left(3 a^2+2 b^2\right)-a \left(5 a^2+3 b^2\right) \tan (e+f x)\right)}{21 d^2 f (d \sec (e+f x))^{3/2}}+\frac{2 a \left(5 a^2+6 b^2\right) \sec ^2(e+f x)^{3/4} F\left(\left.\frac{1}{2} \tan ^{-1}(\tan (e+f x))\right|2\right)}{21 d^2 f (d \sec (e+f x))^{3/2}}-\frac{2 \cos ^2(e+f x) (b-a \tan (e+f x)) (a+b \tan (e+f x))^2}{7 d^2 f (d \sec (e+f x))^{3/2}}",1,"(2*a*(5*a^2 + 6*b^2)*EllipticF[ArcTan[Tan[e + f*x]]/2, 2]*(Sec[e + f*x]^2)^(3/4))/(21*d^2*f*(d*Sec[e + f*x])^(3/2)) - (2*Cos[e + f*x]^2*(b - a*Tan[e + f*x])*(a + b*Tan[e + f*x])^2)/(7*d^2*f*(d*Sec[e + f*x])^(3/2)) - (2*(2*b*(3*a^2 + 2*b^2) - a*(5*a^2 + 3*b^2)*Tan[e + f*x]))/(21*d^2*f*(d*Sec[e + f*x])^(3/2))","A",4,4,25,0.1600,1,"{3512, 739, 778, 231}"
601,1,176,0,0.1394756,"\int \frac{(a+b \tan (e+f x))^3}{(d \sec (e+f x))^{9/2}} \, dx","Int[(a + b*Tan[e + f*x])^3/(d*Sec[e + f*x])^(9/2),x]","-\frac{2 \cos ^2(e+f x) \left(2 b \left(5 a^2+2 b^2\right)-a \left(7 a^2+b^2\right) \tan (e+f x)\right)}{45 d^4 f \sqrt{d \sec (e+f x)}}+\frac{2 a \left(7 a^2+6 b^2\right) \sqrt[4]{\sec ^2(e+f x)} E\left(\left.\frac{1}{2} \tan ^{-1}(\tan (e+f x))\right|2\right)}{15 d^4 f \sqrt{d \sec (e+f x)}}-\frac{2 \cos ^4(e+f x) (b-a \tan (e+f x)) (a+b \tan (e+f x))^2}{9 d^4 f \sqrt{d \sec (e+f x)}}","-\frac{2 \cos ^2(e+f x) \left(2 b \left(5 a^2+2 b^2\right)-a \left(7 a^2+b^2\right) \tan (e+f x)\right)}{45 d^4 f \sqrt{d \sec (e+f x)}}+\frac{2 a \left(7 a^2+6 b^2\right) \sqrt[4]{\sec ^2(e+f x)} E\left(\left.\frac{1}{2} \tan ^{-1}(\tan (e+f x))\right|2\right)}{15 d^4 f \sqrt{d \sec (e+f x)}}-\frac{2 \cos ^4(e+f x) (b-a \tan (e+f x)) (a+b \tan (e+f x))^2}{9 d^4 f \sqrt{d \sec (e+f x)}}",1,"(2*a*(7*a^2 + 6*b^2)*EllipticE[ArcTan[Tan[e + f*x]]/2, 2]*(Sec[e + f*x]^2)^(1/4))/(15*d^4*f*Sqrt[d*Sec[e + f*x]]) - (2*Cos[e + f*x]^4*(b - a*Tan[e + f*x])*(a + b*Tan[e + f*x])^2)/(9*d^4*f*Sqrt[d*Sec[e + f*x]]) - (2*Cos[e + f*x]^2*(2*b*(5*a^2 + 2*b^2) - a*(7*a^2 + b^2)*Tan[e + f*x]))/(45*d^4*f*Sqrt[d*Sec[e + f*x]])","A",4,4,25,0.1600,1,"{3512, 739, 778, 196}"
602,1,218,0,0.1668016,"\int \frac{(a+b \tan (e+f x))^3}{(d \sec (e+f x))^{11/2}} \, dx","Int[(a + b*Tan[e + f*x])^3/(d*Sec[e + f*x])^(11/2),x]","\frac{10 a \left(3 a^2+2 b^2\right) \tan (e+f x)}{77 d^4 f (d \sec (e+f x))^{3/2}}-\frac{2 \cos ^2(e+f x) \left(2 b \left(7 a^2+2 b^2\right)-a \left(9 a^2-b^2\right) \tan (e+f x)\right)}{77 d^4 f (d \sec (e+f x))^{3/2}}+\frac{10 a \left(3 a^2+2 b^2\right) \sec ^2(e+f x)^{3/4} F\left(\left.\frac{1}{2} \tan ^{-1}(\tan (e+f x))\right|2\right)}{77 d^4 f (d \sec (e+f x))^{3/2}}-\frac{2 \cos ^4(e+f x) (b-a \tan (e+f x)) (a+b \tan (e+f x))^2}{11 d^4 f (d \sec (e+f x))^{3/2}}","\frac{10 a \left(3 a^2+2 b^2\right) \tan (e+f x)}{77 d^4 f (d \sec (e+f x))^{3/2}}-\frac{2 \cos ^2(e+f x) \left(2 b \left(7 a^2+2 b^2\right)-a \left(9 a^2-b^2\right) \tan (e+f x)\right)}{77 d^4 f (d \sec (e+f x))^{3/2}}+\frac{10 a \left(3 a^2+2 b^2\right) \sec ^2(e+f x)^{3/4} F\left(\left.\frac{1}{2} \tan ^{-1}(\tan (e+f x))\right|2\right)}{77 d^4 f (d \sec (e+f x))^{3/2}}-\frac{2 \cos ^4(e+f x) (b-a \tan (e+f x)) (a+b \tan (e+f x))^2}{11 d^4 f (d \sec (e+f x))^{3/2}}",1,"(10*a*(3*a^2 + 2*b^2)*EllipticF[ArcTan[Tan[e + f*x]]/2, 2]*(Sec[e + f*x]^2)^(3/4))/(77*d^4*f*(d*Sec[e + f*x])^(3/2)) + (10*a*(3*a^2 + 2*b^2)*Tan[e + f*x])/(77*d^4*f*(d*Sec[e + f*x])^(3/2)) - (2*Cos[e + f*x]^4*(b - a*Tan[e + f*x])*(a + b*Tan[e + f*x])^2)/(11*d^4*f*(d*Sec[e + f*x])^(3/2)) - (2*Cos[e + f*x]^2*(2*b*(7*a^2 + 2*b^2) - a*(9*a^2 - b^2)*Tan[e + f*x]))/(77*d^4*f*(d*Sec[e + f*x])^(3/2))","A",5,5,25,0.2000,1,"{3512, 739, 778, 199, 231}"
603,1,456,0,0.4084578,"\int \frac{(d \sec (e+f x))^{7/2}}{a+b \tan (e+f x)} \, dx","Int[(d*Sec[e + f*x])^(7/2)/(a + b*Tan[e + f*x]),x]","\frac{d^2 \left(a^2+b^2\right)^{3/4} (d \sec (e+f x))^{3/2} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt[4]{\sec ^2(e+f x)}}{\sqrt[4]{a^2+b^2}}\right)}{b^{5/2} f \sec ^2(e+f x)^{3/4}}-\frac{d^2 \left(a^2+b^2\right)^{3/4} (d \sec (e+f x))^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt[4]{\sec ^2(e+f x)}}{\sqrt[4]{a^2+b^2}}\right)}{b^{5/2} f \sec ^2(e+f x)^{3/4}}-\frac{a d^2 \sqrt{a^2+b^2} \sqrt{-\tan ^2(e+f x)} \cot (e+f x) (d \sec (e+f x))^{3/2} \Pi \left(-\frac{b}{\sqrt{a^2+b^2}};\left.\sin ^{-1}\left(\sqrt[4]{\sec ^2(e+f x)}\right)\right|-1\right)}{b^3 f \sec ^2(e+f x)^{3/4}}+\frac{a d^2 \sqrt{a^2+b^2} \sqrt{-\tan ^2(e+f x)} \cot (e+f x) (d \sec (e+f x))^{3/2} \Pi \left(\frac{b}{\sqrt{a^2+b^2}};\left.\sin ^{-1}\left(\sqrt[4]{\sec ^2(e+f x)}\right)\right|-1\right)}{b^3 f \sec ^2(e+f x)^{3/4}}-\frac{2 a d^2 \sin (e+f x) \cos (e+f x) (d \sec (e+f x))^{3/2}}{b^2 f}+\frac{2 a d^2 (d \sec (e+f x))^{3/2} E\left(\left.\frac{1}{2} \tan ^{-1}(\tan (e+f x))\right|2\right)}{b^2 f \sec ^2(e+f x)^{3/4}}+\frac{2 d^2 (d \sec (e+f x))^{3/2}}{3 b f}","\frac{d^2 \left(a^2+b^2\right)^{3/4} (d \sec (e+f x))^{3/2} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt[4]{\sec ^2(e+f x)}}{\sqrt[4]{a^2+b^2}}\right)}{b^{5/2} f \sec ^2(e+f x)^{3/4}}-\frac{d^2 \left(a^2+b^2\right)^{3/4} (d \sec (e+f x))^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt[4]{\sec ^2(e+f x)}}{\sqrt[4]{a^2+b^2}}\right)}{b^{5/2} f \sec ^2(e+f x)^{3/4}}-\frac{a d^2 \sqrt{a^2+b^2} \sqrt{-\tan ^2(e+f x)} \cot (e+f x) (d \sec (e+f x))^{3/2} \Pi \left(-\frac{b}{\sqrt{a^2+b^2}};\left.\sin ^{-1}\left(\sqrt[4]{\sec ^2(e+f x)}\right)\right|-1\right)}{b^3 f \sec ^2(e+f x)^{3/4}}+\frac{a d^2 \sqrt{a^2+b^2} \sqrt{-\tan ^2(e+f x)} \cot (e+f x) (d \sec (e+f x))^{3/2} \Pi \left(\frac{b}{\sqrt{a^2+b^2}};\left.\sin ^{-1}\left(\sqrt[4]{\sec ^2(e+f x)}\right)\right|-1\right)}{b^3 f \sec ^2(e+f x)^{3/4}}-\frac{2 a d^2 \sin (e+f x) \cos (e+f x) (d \sec (e+f x))^{3/2}}{b^2 f}+\frac{2 a d^2 (d \sec (e+f x))^{3/2} E\left(\left.\frac{1}{2} \tan ^{-1}(\tan (e+f x))\right|2\right)}{b^2 f \sec ^2(e+f x)^{3/4}}+\frac{2 d^2 (d \sec (e+f x))^{3/2}}{3 b f}",1,"(2*d^2*(d*Sec[e + f*x])^(3/2))/(3*b*f) + ((a^2 + b^2)^(3/4)*d^2*ArcTan[(Sqrt[b]*(Sec[e + f*x]^2)^(1/4))/(a^2 + b^2)^(1/4)]*(d*Sec[e + f*x])^(3/2))/(b^(5/2)*f*(Sec[e + f*x]^2)^(3/4)) - ((a^2 + b^2)^(3/4)*d^2*ArcTanh[(Sqrt[b]*(Sec[e + f*x]^2)^(1/4))/(a^2 + b^2)^(1/4)]*(d*Sec[e + f*x])^(3/2))/(b^(5/2)*f*(Sec[e + f*x]^2)^(3/4)) + (2*a*d^2*EllipticE[ArcTan[Tan[e + f*x]]/2, 2]*(d*Sec[e + f*x])^(3/2))/(b^2*f*(Sec[e + f*x]^2)^(3/4)) - (2*a*d^2*Cos[e + f*x]*(d*Sec[e + f*x])^(3/2)*Sin[e + f*x])/(b^2*f) - (a*Sqrt[a^2 + b^2]*d^2*Cot[e + f*x]*EllipticPi[-(b/Sqrt[a^2 + b^2]), ArcSin[(Sec[e + f*x]^2)^(1/4)], -1]*(d*Sec[e + f*x])^(3/2)*Sqrt[-Tan[e + f*x]^2])/(b^3*f*(Sec[e + f*x]^2)^(3/4)) + (a*Sqrt[a^2 + b^2]*d^2*Cot[e + f*x]*EllipticPi[b/Sqrt[a^2 + b^2], ArcSin[(Sec[e + f*x]^2)^(1/4)], -1]*(d*Sec[e + f*x])^(3/2)*Sqrt[-Tan[e + f*x]^2])/(b^3*f*(Sec[e + f*x]^2)^(3/4))","A",17,15,25,0.6000,1,"{3512, 735, 844, 227, 196, 746, 399, 490, 1213, 537, 444, 63, 298, 205, 208}"
604,1,396,0,0.3840027,"\int \frac{(d \sec (e+f x))^{5/2}}{a+b \tan (e+f x)} \, dx","Int[(d*Sec[e + f*x])^(5/2)/(a + b*Tan[e + f*x]),x]","-\frac{d^2 \sqrt[4]{a^2+b^2} \sqrt{d \sec (e+f x)} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt[4]{\sec ^2(e+f x)}}{\sqrt[4]{a^2+b^2}}\right)}{b^{3/2} f \sqrt[4]{\sec ^2(e+f x)}}-\frac{d^2 \sqrt[4]{a^2+b^2} \sqrt{d \sec (e+f x)} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt[4]{\sec ^2(e+f x)}}{\sqrt[4]{a^2+b^2}}\right)}{b^{3/2} f \sqrt[4]{\sec ^2(e+f x)}}+\frac{a d^2 \sqrt{-\tan ^2(e+f x)} \cot (e+f x) \sqrt{d \sec (e+f x)} \Pi \left(-\frac{b}{\sqrt{a^2+b^2}};\left.\sin ^{-1}\left(\sqrt[4]{\sec ^2(e+f x)}\right)\right|-1\right)}{b^2 f \sqrt[4]{\sec ^2(e+f x)}}+\frac{a d^2 \sqrt{-\tan ^2(e+f x)} \cot (e+f x) \sqrt{d \sec (e+f x)} \Pi \left(\frac{b}{\sqrt{a^2+b^2}};\left.\sin ^{-1}\left(\sqrt[4]{\sec ^2(e+f x)}\right)\right|-1\right)}{b^2 f \sqrt[4]{\sec ^2(e+f x)}}-\frac{2 a d^2 \sqrt{d \sec (e+f x)} F\left(\left.\frac{1}{2} \tan ^{-1}(\tan (e+f x))\right|2\right)}{b^2 f \sqrt[4]{\sec ^2(e+f x)}}+\frac{2 d^2 \sqrt{d \sec (e+f x)}}{b f}","-\frac{d^2 \sqrt[4]{a^2+b^2} \sqrt{d \sec (e+f x)} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt[4]{\sec ^2(e+f x)}}{\sqrt[4]{a^2+b^2}}\right)}{b^{3/2} f \sqrt[4]{\sec ^2(e+f x)}}-\frac{d^2 \sqrt[4]{a^2+b^2} \sqrt{d \sec (e+f x)} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt[4]{\sec ^2(e+f x)}}{\sqrt[4]{a^2+b^2}}\right)}{b^{3/2} f \sqrt[4]{\sec ^2(e+f x)}}+\frac{a d^2 \sqrt{-\tan ^2(e+f x)} \cot (e+f x) \sqrt{d \sec (e+f x)} \Pi \left(-\frac{b}{\sqrt{a^2+b^2}};\left.\sin ^{-1}\left(\sqrt[4]{\sec ^2(e+f x)}\right)\right|-1\right)}{b^2 f \sqrt[4]{\sec ^2(e+f x)}}+\frac{a d^2 \sqrt{-\tan ^2(e+f x)} \cot (e+f x) \sqrt{d \sec (e+f x)} \Pi \left(\frac{b}{\sqrt{a^2+b^2}};\left.\sin ^{-1}\left(\sqrt[4]{\sec ^2(e+f x)}\right)\right|-1\right)}{b^2 f \sqrt[4]{\sec ^2(e+f x)}}-\frac{2 a d^2 \sqrt{d \sec (e+f x)} F\left(\left.\frac{1}{2} \tan ^{-1}(\tan (e+f x))\right|2\right)}{b^2 f \sqrt[4]{\sec ^2(e+f x)}}+\frac{2 d^2 \sqrt{d \sec (e+f x)}}{b f}",1,"(2*d^2*Sqrt[d*Sec[e + f*x]])/(b*f) - ((a^2 + b^2)^(1/4)*d^2*ArcTan[(Sqrt[b]*(Sec[e + f*x]^2)^(1/4))/(a^2 + b^2)^(1/4)]*Sqrt[d*Sec[e + f*x]])/(b^(3/2)*f*(Sec[e + f*x]^2)^(1/4)) - ((a^2 + b^2)^(1/4)*d^2*ArcTanh[(Sqrt[b]*(Sec[e + f*x]^2)^(1/4))/(a^2 + b^2)^(1/4)]*Sqrt[d*Sec[e + f*x]])/(b^(3/2)*f*(Sec[e + f*x]^2)^(1/4)) - (2*a*d^2*EllipticF[ArcTan[Tan[e + f*x]]/2, 2]*Sqrt[d*Sec[e + f*x]])/(b^2*f*(Sec[e + f*x]^2)^(1/4)) + (a*d^2*Cot[e + f*x]*EllipticPi[-(b/Sqrt[a^2 + b^2]), ArcSin[(Sec[e + f*x]^2)^(1/4)], -1]*Sqrt[d*Sec[e + f*x]]*Sqrt[-Tan[e + f*x]^2])/(b^2*f*(Sec[e + f*x]^2)^(1/4)) + (a*d^2*Cot[e + f*x]*EllipticPi[b/Sqrt[a^2 + b^2], ArcSin[(Sec[e + f*x]^2)^(1/4)], -1]*Sqrt[d*Sec[e + f*x]]*Sqrt[-Tan[e + f*x]^2])/(b^2*f*(Sec[e + f*x]^2)^(1/4))","A",17,15,25,0.6000,1,"{3512, 735, 844, 231, 747, 401, 108, 409, 1213, 537, 444, 63, 212, 208, 205}"
605,1,334,0,0.2942342,"\int \frac{(d \sec (e+f x))^{3/2}}{a+b \tan (e+f x)} \, dx","Int[(d*Sec[e + f*x])^(3/2)/(a + b*Tan[e + f*x]),x]","\frac{(d \sec (e+f x))^{3/2} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt[4]{\sec ^2(e+f x)}}{\sqrt[4]{a^2+b^2}}\right)}{\sqrt{b} f \sqrt[4]{a^2+b^2} \sec ^2(e+f x)^{3/4}}-\frac{(d \sec (e+f x))^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt[4]{\sec ^2(e+f x)}}{\sqrt[4]{a^2+b^2}}\right)}{\sqrt{b} f \sqrt[4]{a^2+b^2} \sec ^2(e+f x)^{3/4}}-\frac{a \sqrt{-\tan ^2(e+f x)} \cot (e+f x) (d \sec (e+f x))^{3/2} \Pi \left(-\frac{b}{\sqrt{a^2+b^2}};\left.\sin ^{-1}\left(\sqrt[4]{\sec ^2(e+f x)}\right)\right|-1\right)}{b f \sqrt{a^2+b^2} \sec ^2(e+f x)^{3/4}}+\frac{a \sqrt{-\tan ^2(e+f x)} \cot (e+f x) (d \sec (e+f x))^{3/2} \Pi \left(\frac{b}{\sqrt{a^2+b^2}};\left.\sin ^{-1}\left(\sqrt[4]{\sec ^2(e+f x)}\right)\right|-1\right)}{b f \sqrt{a^2+b^2} \sec ^2(e+f x)^{3/4}}","\frac{(d \sec (e+f x))^{3/2} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt[4]{\sec ^2(e+f x)}}{\sqrt[4]{a^2+b^2}}\right)}{\sqrt{b} f \sqrt[4]{a^2+b^2} \sec ^2(e+f x)^{3/4}}-\frac{(d \sec (e+f x))^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt[4]{\sec ^2(e+f x)}}{\sqrt[4]{a^2+b^2}}\right)}{\sqrt{b} f \sqrt[4]{a^2+b^2} \sec ^2(e+f x)^{3/4}}-\frac{a \sqrt{-\tan ^2(e+f x)} \cot (e+f x) (d \sec (e+f x))^{3/2} \Pi \left(-\frac{b}{\sqrt{a^2+b^2}};\left.\sin ^{-1}\left(\sqrt[4]{\sec ^2(e+f x)}\right)\right|-1\right)}{b f \sqrt{a^2+b^2} \sec ^2(e+f x)^{3/4}}+\frac{a \sqrt{-\tan ^2(e+f x)} \cot (e+f x) (d \sec (e+f x))^{3/2} \Pi \left(\frac{b}{\sqrt{a^2+b^2}};\left.\sin ^{-1}\left(\sqrt[4]{\sec ^2(e+f x)}\right)\right|-1\right)}{b f \sqrt{a^2+b^2} \sec ^2(e+f x)^{3/4}}",1,"(ArcTan[(Sqrt[b]*(Sec[e + f*x]^2)^(1/4))/(a^2 + b^2)^(1/4)]*(d*Sec[e + f*x])^(3/2))/(Sqrt[b]*(a^2 + b^2)^(1/4)*f*(Sec[e + f*x]^2)^(3/4)) - (ArcTanh[(Sqrt[b]*(Sec[e + f*x]^2)^(1/4))/(a^2 + b^2)^(1/4)]*(d*Sec[e + f*x])^(3/2))/(Sqrt[b]*(a^2 + b^2)^(1/4)*f*(Sec[e + f*x]^2)^(3/4)) - (a*Cot[e + f*x]*EllipticPi[-(b/Sqrt[a^2 + b^2]), ArcSin[(Sec[e + f*x]^2)^(1/4)], -1]*(d*Sec[e + f*x])^(3/2)*Sqrt[-Tan[e + f*x]^2])/(b*Sqrt[a^2 + b^2]*f*(Sec[e + f*x]^2)^(3/4)) + (a*Cot[e + f*x]*EllipticPi[b/Sqrt[a^2 + b^2], ArcSin[(Sec[e + f*x]^2)^(1/4)], -1]*(d*Sec[e + f*x])^(3/2)*Sqrt[-Tan[e + f*x]^2])/(b*Sqrt[a^2 + b^2]*f*(Sec[e + f*x]^2)^(3/4))","A",13,11,25,0.4400,1,"{3512, 746, 399, 490, 1213, 537, 444, 63, 298, 205, 208}"
606,1,324,0,0.3012194,"\int \frac{\sqrt{d \sec (e+f x)}}{a+b \tan (e+f x)} \, dx","Int[Sqrt[d*Sec[e + f*x]]/(a + b*Tan[e + f*x]),x]","-\frac{\sqrt{b} \sqrt{d \sec (e+f x)} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt[4]{\sec ^2(e+f x)}}{\sqrt[4]{a^2+b^2}}\right)}{f \left(a^2+b^2\right)^{3/4} \sqrt[4]{\sec ^2(e+f x)}}-\frac{\sqrt{b} \sqrt{d \sec (e+f x)} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt[4]{\sec ^2(e+f x)}}{\sqrt[4]{a^2+b^2}}\right)}{f \left(a^2+b^2\right)^{3/4} \sqrt[4]{\sec ^2(e+f x)}}+\frac{a \sqrt{-\tan ^2(e+f x)} \cot (e+f x) \sqrt{d \sec (e+f x)} \Pi \left(-\frac{b}{\sqrt{a^2+b^2}};\left.\sin ^{-1}\left(\sqrt[4]{\sec ^2(e+f x)}\right)\right|-1\right)}{f \left(a^2+b^2\right) \sqrt[4]{\sec ^2(e+f x)}}+\frac{a \sqrt{-\tan ^2(e+f x)} \cot (e+f x) \sqrt{d \sec (e+f x)} \Pi \left(\frac{b}{\sqrt{a^2+b^2}};\left.\sin ^{-1}\left(\sqrt[4]{\sec ^2(e+f x)}\right)\right|-1\right)}{f \left(a^2+b^2\right) \sqrt[4]{\sec ^2(e+f x)}}","-\frac{\sqrt{b} \sqrt{d \sec (e+f x)} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt[4]{\sec ^2(e+f x)}}{\sqrt[4]{a^2+b^2}}\right)}{f \left(a^2+b^2\right)^{3/4} \sqrt[4]{\sec ^2(e+f x)}}-\frac{\sqrt{b} \sqrt{d \sec (e+f x)} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt[4]{\sec ^2(e+f x)}}{\sqrt[4]{a^2+b^2}}\right)}{f \left(a^2+b^2\right)^{3/4} \sqrt[4]{\sec ^2(e+f x)}}+\frac{a \sqrt{-\tan ^2(e+f x)} \cot (e+f x) \sqrt{d \sec (e+f x)} \Pi \left(-\frac{b}{\sqrt{a^2+b^2}};\left.\sin ^{-1}\left(\sqrt[4]{\sec ^2(e+f x)}\right)\right|-1\right)}{f \left(a^2+b^2\right) \sqrt[4]{\sec ^2(e+f x)}}+\frac{a \sqrt{-\tan ^2(e+f x)} \cot (e+f x) \sqrt{d \sec (e+f x)} \Pi \left(\frac{b}{\sqrt{a^2+b^2}};\left.\sin ^{-1}\left(\sqrt[4]{\sec ^2(e+f x)}\right)\right|-1\right)}{f \left(a^2+b^2\right) \sqrt[4]{\sec ^2(e+f x)}}",1,"-((Sqrt[b]*ArcTan[(Sqrt[b]*(Sec[e + f*x]^2)^(1/4))/(a^2 + b^2)^(1/4)]*Sqrt[d*Sec[e + f*x]])/((a^2 + b^2)^(3/4)*f*(Sec[e + f*x]^2)^(1/4))) - (Sqrt[b]*ArcTanh[(Sqrt[b]*(Sec[e + f*x]^2)^(1/4))/(a^2 + b^2)^(1/4)]*Sqrt[d*Sec[e + f*x]])/((a^2 + b^2)^(3/4)*f*(Sec[e + f*x]^2)^(1/4)) + (a*Cot[e + f*x]*EllipticPi[-(b/Sqrt[a^2 + b^2]), ArcSin[(Sec[e + f*x]^2)^(1/4)], -1]*Sqrt[d*Sec[e + f*x]]*Sqrt[-Tan[e + f*x]^2])/((a^2 + b^2)*f*(Sec[e + f*x]^2)^(1/4)) + (a*Cot[e + f*x]*EllipticPi[b/Sqrt[a^2 + b^2], ArcSin[(Sec[e + f*x]^2)^(1/4)], -1]*Sqrt[d*Sec[e + f*x]]*Sqrt[-Tan[e + f*x]^2])/((a^2 + b^2)*f*(Sec[e + f*x]^2)^(1/4))","A",14,12,25,0.4800,1,"{3512, 747, 401, 108, 409, 1213, 537, 444, 63, 212, 208, 205}"
607,1,451,0,0.4227545,"\int \frac{1}{\sqrt{d \sec (e+f x)} (a+b \tan (e+f x))} \, dx","Int[1/(Sqrt[d*Sec[e + f*x]]*(a + b*Tan[e + f*x])),x]","\frac{b^{3/2} \sqrt[4]{\sec ^2(e+f x)} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt[4]{\sec ^2(e+f x)}}{\sqrt[4]{a^2+b^2}}\right)}{f \left(a^2+b^2\right)^{5/4} \sqrt{d \sec (e+f x)}}-\frac{b^{3/2} \sqrt[4]{\sec ^2(e+f x)} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt[4]{\sec ^2(e+f x)}}{\sqrt[4]{a^2+b^2}}\right)}{f \left(a^2+b^2\right)^{5/4} \sqrt{d \sec (e+f x)}}-\frac{2 a \tan (e+f x)}{f \left(a^2+b^2\right) \sqrt{d \sec (e+f x)}}+\frac{2 (a \tan (e+f x)+b)}{f \left(a^2+b^2\right) \sqrt{d \sec (e+f x)}}+\frac{2 a \sqrt[4]{\sec ^2(e+f x)} E\left(\left.\frac{1}{2} \tan ^{-1}(\tan (e+f x))\right|2\right)}{f \left(a^2+b^2\right) \sqrt{d \sec (e+f x)}}-\frac{a b \sqrt{-\tan ^2(e+f x)} \cot (e+f x) \sqrt[4]{\sec ^2(e+f x)} \Pi \left(-\frac{b}{\sqrt{a^2+b^2}};\left.\sin ^{-1}\left(\sqrt[4]{\sec ^2(e+f x)}\right)\right|-1\right)}{f \left(a^2+b^2\right)^{3/2} \sqrt{d \sec (e+f x)}}+\frac{a b \sqrt{-\tan ^2(e+f x)} \cot (e+f x) \sqrt[4]{\sec ^2(e+f x)} \Pi \left(\frac{b}{\sqrt{a^2+b^2}};\left.\sin ^{-1}\left(\sqrt[4]{\sec ^2(e+f x)}\right)\right|-1\right)}{f \left(a^2+b^2\right)^{3/2} \sqrt{d \sec (e+f x)}}","\frac{b^{3/2} \sqrt[4]{\sec ^2(e+f x)} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt[4]{\sec ^2(e+f x)}}{\sqrt[4]{a^2+b^2}}\right)}{f \left(a^2+b^2\right)^{5/4} \sqrt{d \sec (e+f x)}}-\frac{b^{3/2} \sqrt[4]{\sec ^2(e+f x)} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt[4]{\sec ^2(e+f x)}}{\sqrt[4]{a^2+b^2}}\right)}{f \left(a^2+b^2\right)^{5/4} \sqrt{d \sec (e+f x)}}-\frac{2 a \tan (e+f x)}{f \left(a^2+b^2\right) \sqrt{d \sec (e+f x)}}+\frac{2 (a \tan (e+f x)+b)}{f \left(a^2+b^2\right) \sqrt{d \sec (e+f x)}}+\frac{2 a \sqrt[4]{\sec ^2(e+f x)} E\left(\left.\frac{1}{2} \tan ^{-1}(\tan (e+f x))\right|2\right)}{f \left(a^2+b^2\right) \sqrt{d \sec (e+f x)}}-\frac{a b \sqrt{-\tan ^2(e+f x)} \cot (e+f x) \sqrt[4]{\sec ^2(e+f x)} \Pi \left(-\frac{b}{\sqrt{a^2+b^2}};\left.\sin ^{-1}\left(\sqrt[4]{\sec ^2(e+f x)}\right)\right|-1\right)}{f \left(a^2+b^2\right)^{3/2} \sqrt{d \sec (e+f x)}}+\frac{a b \sqrt{-\tan ^2(e+f x)} \cot (e+f x) \sqrt[4]{\sec ^2(e+f x)} \Pi \left(\frac{b}{\sqrt{a^2+b^2}};\left.\sin ^{-1}\left(\sqrt[4]{\sec ^2(e+f x)}\right)\right|-1\right)}{f \left(a^2+b^2\right)^{3/2} \sqrt{d \sec (e+f x)}}",1,"(b^(3/2)*ArcTan[(Sqrt[b]*(Sec[e + f*x]^2)^(1/4))/(a^2 + b^2)^(1/4)]*(Sec[e + f*x]^2)^(1/4))/((a^2 + b^2)^(5/4)*f*Sqrt[d*Sec[e + f*x]]) - (b^(3/2)*ArcTanh[(Sqrt[b]*(Sec[e + f*x]^2)^(1/4))/(a^2 + b^2)^(1/4)]*(Sec[e + f*x]^2)^(1/4))/((a^2 + b^2)^(5/4)*f*Sqrt[d*Sec[e + f*x]]) + (2*a*EllipticE[ArcTan[Tan[e + f*x]]/2, 2]*(Sec[e + f*x]^2)^(1/4))/((a^2 + b^2)*f*Sqrt[d*Sec[e + f*x]]) - (2*a*Tan[e + f*x])/((a^2 + b^2)*f*Sqrt[d*Sec[e + f*x]]) - (a*b*Cot[e + f*x]*EllipticPi[-(b/Sqrt[a^2 + b^2]), ArcSin[(Sec[e + f*x]^2)^(1/4)], -1]*(Sec[e + f*x]^2)^(1/4)*Sqrt[-Tan[e + f*x]^2])/((a^2 + b^2)^(3/2)*f*Sqrt[d*Sec[e + f*x]]) + (a*b*Cot[e + f*x]*EllipticPi[b/Sqrt[a^2 + b^2], ArcSin[(Sec[e + f*x]^2)^(1/4)], -1]*(Sec[e + f*x]^2)^(1/4)*Sqrt[-Tan[e + f*x]^2])/((a^2 + b^2)^(3/2)*f*Sqrt[d*Sec[e + f*x]]) + (2*(b + a*Tan[e + f*x]))/((a^2 + b^2)*f*Sqrt[d*Sec[e + f*x]])","A",17,15,25,0.6000,1,"{3512, 741, 844, 227, 196, 746, 399, 490, 1213, 537, 444, 63, 298, 205, 208}"
608,1,422,0,0.4319163,"\int \frac{1}{(d \sec (e+f x))^{3/2} (a+b \tan (e+f x))} \, dx","Int[1/((d*Sec[e + f*x])^(3/2)*(a + b*Tan[e + f*x])),x]","-\frac{b^{5/2} \sec ^2(e+f x)^{3/4} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt[4]{\sec ^2(e+f x)}}{\sqrt[4]{a^2+b^2}}\right)}{f \left(a^2+b^2\right)^{7/4} (d \sec (e+f x))^{3/2}}-\frac{b^{5/2} \sec ^2(e+f x)^{3/4} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt[4]{\sec ^2(e+f x)}}{\sqrt[4]{a^2+b^2}}\right)}{f \left(a^2+b^2\right)^{7/4} (d \sec (e+f x))^{3/2}}+\frac{2 (a \tan (e+f x)+b)}{3 f \left(a^2+b^2\right) (d \sec (e+f x))^{3/2}}+\frac{2 a \sec ^2(e+f x)^{3/4} F\left(\left.\frac{1}{2} \tan ^{-1}(\tan (e+f x))\right|2\right)}{3 f \left(a^2+b^2\right) (d \sec (e+f x))^{3/2}}+\frac{a b^2 \sqrt{-\tan ^2(e+f x)} \cot (e+f x) \sec ^2(e+f x)^{3/4} \Pi \left(-\frac{b}{\sqrt{a^2+b^2}};\left.\sin ^{-1}\left(\sqrt[4]{\sec ^2(e+f x)}\right)\right|-1\right)}{f \left(a^2+b^2\right)^2 (d \sec (e+f x))^{3/2}}+\frac{a b^2 \sqrt{-\tan ^2(e+f x)} \cot (e+f x) \sec ^2(e+f x)^{3/4} \Pi \left(\frac{b}{\sqrt{a^2+b^2}};\left.\sin ^{-1}\left(\sqrt[4]{\sec ^2(e+f x)}\right)\right|-1\right)}{f \left(a^2+b^2\right)^2 (d \sec (e+f x))^{3/2}}","-\frac{b^{5/2} \sec ^2(e+f x)^{3/4} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt[4]{\sec ^2(e+f x)}}{\sqrt[4]{a^2+b^2}}\right)}{f \left(a^2+b^2\right)^{7/4} (d \sec (e+f x))^{3/2}}-\frac{b^{5/2} \sec ^2(e+f x)^{3/4} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt[4]{\sec ^2(e+f x)}}{\sqrt[4]{a^2+b^2}}\right)}{f \left(a^2+b^2\right)^{7/4} (d \sec (e+f x))^{3/2}}+\frac{2 (a \tan (e+f x)+b)}{3 f \left(a^2+b^2\right) (d \sec (e+f x))^{3/2}}+\frac{2 a \sec ^2(e+f x)^{3/4} F\left(\left.\frac{1}{2} \tan ^{-1}(\tan (e+f x))\right|2\right)}{3 f \left(a^2+b^2\right) (d \sec (e+f x))^{3/2}}+\frac{a b^2 \sqrt{-\tan ^2(e+f x)} \cot (e+f x) \sec ^2(e+f x)^{3/4} \Pi \left(-\frac{b}{\sqrt{a^2+b^2}};\left.\sin ^{-1}\left(\sqrt[4]{\sec ^2(e+f x)}\right)\right|-1\right)}{f \left(a^2+b^2\right)^2 (d \sec (e+f x))^{3/2}}+\frac{a b^2 \sqrt{-\tan ^2(e+f x)} \cot (e+f x) \sec ^2(e+f x)^{3/4} \Pi \left(\frac{b}{\sqrt{a^2+b^2}};\left.\sin ^{-1}\left(\sqrt[4]{\sec ^2(e+f x)}\right)\right|-1\right)}{f \left(a^2+b^2\right)^2 (d \sec (e+f x))^{3/2}}",1,"-((b^(5/2)*ArcTan[(Sqrt[b]*(Sec[e + f*x]^2)^(1/4))/(a^2 + b^2)^(1/4)]*(Sec[e + f*x]^2)^(3/4))/((a^2 + b^2)^(7/4)*f*(d*Sec[e + f*x])^(3/2))) - (b^(5/2)*ArcTanh[(Sqrt[b]*(Sec[e + f*x]^2)^(1/4))/(a^2 + b^2)^(1/4)]*(Sec[e + f*x]^2)^(3/4))/((a^2 + b^2)^(7/4)*f*(d*Sec[e + f*x])^(3/2)) + (2*a*EllipticF[ArcTan[Tan[e + f*x]]/2, 2]*(Sec[e + f*x]^2)^(3/4))/(3*(a^2 + b^2)*f*(d*Sec[e + f*x])^(3/2)) + (a*b^2*Cot[e + f*x]*EllipticPi[-(b/Sqrt[a^2 + b^2]), ArcSin[(Sec[e + f*x]^2)^(1/4)], -1]*(Sec[e + f*x]^2)^(3/4)*Sqrt[-Tan[e + f*x]^2])/((a^2 + b^2)^2*f*(d*Sec[e + f*x])^(3/2)) + (a*b^2*Cot[e + f*x]*EllipticPi[b/Sqrt[a^2 + b^2], ArcSin[(Sec[e + f*x]^2)^(1/4)], -1]*(Sec[e + f*x]^2)^(3/4)*Sqrt[-Tan[e + f*x]^2])/((a^2 + b^2)^2*f*(d*Sec[e + f*x])^(3/2)) + (2*(b + a*Tan[e + f*x]))/(3*(a^2 + b^2)*f*(d*Sec[e + f*x])^(3/2))","A",17,15,25,0.6000,1,"{3512, 741, 844, 231, 747, 401, 108, 409, 1213, 537, 444, 63, 212, 208, 205}"
609,1,568,0,0.6085002,"\int \frac{1}{(d \sec (e+f x))^{5/2} (a+b \tan (e+f x))} \, dx","Int[1/((d*Sec[e + f*x])^(5/2)*(a + b*Tan[e + f*x])),x]","\frac{b^{7/2} \sqrt[4]{\sec ^2(e+f x)} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt[4]{\sec ^2(e+f x)}}{\sqrt[4]{a^2+b^2}}\right)}{d^2 f \left(a^2+b^2\right)^{9/4} \sqrt{d \sec (e+f x)}}-\frac{b^{7/2} \sqrt[4]{\sec ^2(e+f x)} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt[4]{\sec ^2(e+f x)}}{\sqrt[4]{a^2+b^2}}\right)}{d^2 f \left(a^2+b^2\right)^{9/4} \sqrt{d \sec (e+f x)}}-\frac{2 a \left(3 a^2+8 b^2\right) \tan (e+f x)}{5 d^2 f \left(a^2+b^2\right)^2 \sqrt{d \sec (e+f x)}}+\frac{2 \left(a \left(3 a^2+8 b^2\right) \tan (e+f x)+5 b^3\right)}{5 d^2 f \left(a^2+b^2\right)^2 \sqrt{d \sec (e+f x)}}+\frac{2 \cos ^2(e+f x) (a \tan (e+f x)+b)}{5 d^2 f \left(a^2+b^2\right) \sqrt{d \sec (e+f x)}}+\frac{2 a \left(3 a^2+8 b^2\right) \sqrt[4]{\sec ^2(e+f x)} E\left(\left.\frac{1}{2} \tan ^{-1}(\tan (e+f x))\right|2\right)}{5 d^2 f \left(a^2+b^2\right)^2 \sqrt{d \sec (e+f x)}}-\frac{a b^3 \sqrt{-\tan ^2(e+f x)} \cot (e+f x) \sqrt[4]{\sec ^2(e+f x)} \Pi \left(-\frac{b}{\sqrt{a^2+b^2}};\left.\sin ^{-1}\left(\sqrt[4]{\sec ^2(e+f x)}\right)\right|-1\right)}{d^2 f \left(a^2+b^2\right)^{5/2} \sqrt{d \sec (e+f x)}}+\frac{a b^3 \sqrt{-\tan ^2(e+f x)} \cot (e+f x) \sqrt[4]{\sec ^2(e+f x)} \Pi \left(\frac{b}{\sqrt{a^2+b^2}};\left.\sin ^{-1}\left(\sqrt[4]{\sec ^2(e+f x)}\right)\right|-1\right)}{d^2 f \left(a^2+b^2\right)^{5/2} \sqrt{d \sec (e+f x)}}","\frac{b^{7/2} \sqrt[4]{\sec ^2(e+f x)} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt[4]{\sec ^2(e+f x)}}{\sqrt[4]{a^2+b^2}}\right)}{d^2 f \left(a^2+b^2\right)^{9/4} \sqrt{d \sec (e+f x)}}-\frac{b^{7/2} \sqrt[4]{\sec ^2(e+f x)} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt[4]{\sec ^2(e+f x)}}{\sqrt[4]{a^2+b^2}}\right)}{d^2 f \left(a^2+b^2\right)^{9/4} \sqrt{d \sec (e+f x)}}-\frac{2 a \left(3 a^2+8 b^2\right) \tan (e+f x)}{5 d^2 f \left(a^2+b^2\right)^2 \sqrt{d \sec (e+f x)}}+\frac{2 \left(a \left(3 a^2+8 b^2\right) \tan (e+f x)+5 b^3\right)}{5 d^2 f \left(a^2+b^2\right)^2 \sqrt{d \sec (e+f x)}}+\frac{2 \cos ^2(e+f x) (a \tan (e+f x)+b)}{5 d^2 f \left(a^2+b^2\right) \sqrt{d \sec (e+f x)}}+\frac{2 a \left(3 a^2+8 b^2\right) \sqrt[4]{\sec ^2(e+f x)} E\left(\left.\frac{1}{2} \tan ^{-1}(\tan (e+f x))\right|2\right)}{5 d^2 f \left(a^2+b^2\right)^2 \sqrt{d \sec (e+f x)}}-\frac{a b^3 \sqrt{-\tan ^2(e+f x)} \cot (e+f x) \sqrt[4]{\sec ^2(e+f x)} \Pi \left(-\frac{b}{\sqrt{a^2+b^2}};\left.\sin ^{-1}\left(\sqrt[4]{\sec ^2(e+f x)}\right)\right|-1\right)}{d^2 f \left(a^2+b^2\right)^{5/2} \sqrt{d \sec (e+f x)}}+\frac{a b^3 \sqrt{-\tan ^2(e+f x)} \cot (e+f x) \sqrt[4]{\sec ^2(e+f x)} \Pi \left(\frac{b}{\sqrt{a^2+b^2}};\left.\sin ^{-1}\left(\sqrt[4]{\sec ^2(e+f x)}\right)\right|-1\right)}{d^2 f \left(a^2+b^2\right)^{5/2} \sqrt{d \sec (e+f x)}}",1,"(b^(7/2)*ArcTan[(Sqrt[b]*(Sec[e + f*x]^2)^(1/4))/(a^2 + b^2)^(1/4)]*(Sec[e + f*x]^2)^(1/4))/((a^2 + b^2)^(9/4)*d^2*f*Sqrt[d*Sec[e + f*x]]) - (b^(7/2)*ArcTanh[(Sqrt[b]*(Sec[e + f*x]^2)^(1/4))/(a^2 + b^2)^(1/4)]*(Sec[e + f*x]^2)^(1/4))/((a^2 + b^2)^(9/4)*d^2*f*Sqrt[d*Sec[e + f*x]]) + (2*a*(3*a^2 + 8*b^2)*EllipticE[ArcTan[Tan[e + f*x]]/2, 2]*(Sec[e + f*x]^2)^(1/4))/(5*(a^2 + b^2)^2*d^2*f*Sqrt[d*Sec[e + f*x]]) - (2*a*(3*a^2 + 8*b^2)*Tan[e + f*x])/(5*(a^2 + b^2)^2*d^2*f*Sqrt[d*Sec[e + f*x]]) - (a*b^3*Cot[e + f*x]*EllipticPi[-(b/Sqrt[a^2 + b^2]), ArcSin[(Sec[e + f*x]^2)^(1/4)], -1]*(Sec[e + f*x]^2)^(1/4)*Sqrt[-Tan[e + f*x]^2])/((a^2 + b^2)^(5/2)*d^2*f*Sqrt[d*Sec[e + f*x]]) + (a*b^3*Cot[e + f*x]*EllipticPi[b/Sqrt[a^2 + b^2], ArcSin[(Sec[e + f*x]^2)^(1/4)], -1]*(Sec[e + f*x]^2)^(1/4)*Sqrt[-Tan[e + f*x]^2])/((a^2 + b^2)^(5/2)*d^2*f*Sqrt[d*Sec[e + f*x]]) + (2*Cos[e + f*x]^2*(b + a*Tan[e + f*x]))/(5*(a^2 + b^2)*d^2*f*Sqrt[d*Sec[e + f*x]]) + (2*(5*b^3 + a*(3*a^2 + 8*b^2)*Tan[e + f*x]))/(5*(a^2 + b^2)^2*d^2*f*Sqrt[d*Sec[e + f*x]])","A",18,16,25,0.6400,1,"{3512, 741, 823, 844, 227, 196, 746, 399, 490, 1213, 537, 444, 63, 298, 205, 208}"
610,1,480,0,0.3822187,"\int \frac{(d \sec (e+f x))^{7/2}}{(a+b \tan (e+f x))^2} \, dx","Int[(d*Sec[e + f*x])^(7/2)/(a + b*Tan[e + f*x])^2,x]","-\frac{3 a d^2 (d \sec (e+f x))^{3/2} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt[4]{\sec ^2(e+f x)}}{\sqrt[4]{a^2+b^2}}\right)}{2 b^{5/2} f \sqrt[4]{a^2+b^2} \sec ^2(e+f x)^{3/4}}+\frac{3 a d^2 (d \sec (e+f x))^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt[4]{\sec ^2(e+f x)}}{\sqrt[4]{a^2+b^2}}\right)}{2 b^{5/2} f \sqrt[4]{a^2+b^2} \sec ^2(e+f x)^{3/4}}+\frac{3 a^2 d^2 \sqrt{-\tan ^2(e+f x)} \cot (e+f x) (d \sec (e+f x))^{3/2} \Pi \left(-\frac{b}{\sqrt{a^2+b^2}};\left.\sin ^{-1}\left(\sqrt[4]{\sec ^2(e+f x)}\right)\right|-1\right)}{2 b^3 f \sqrt{a^2+b^2} \sec ^2(e+f x)^{3/4}}-\frac{3 a^2 d^2 \sqrt{-\tan ^2(e+f x)} \cot (e+f x) (d \sec (e+f x))^{3/2} \Pi \left(\frac{b}{\sqrt{a^2+b^2}};\left.\sin ^{-1}\left(\sqrt[4]{\sec ^2(e+f x)}\right)\right|-1\right)}{2 b^3 f \sqrt{a^2+b^2} \sec ^2(e+f x)^{3/4}}-\frac{d^2 (d \sec (e+f x))^{3/2}}{b f (a+b \tan (e+f x))}+\frac{3 d^2 \sin (e+f x) \cos (e+f x) (d \sec (e+f x))^{3/2}}{b^2 f}-\frac{3 d^2 (d \sec (e+f x))^{3/2} E\left(\left.\frac{1}{2} \tan ^{-1}(\tan (e+f x))\right|2\right)}{b^2 f \sec ^2(e+f x)^{3/4}}","-\frac{3 a d^2 (d \sec (e+f x))^{3/2} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt[4]{\sec ^2(e+f x)}}{\sqrt[4]{a^2+b^2}}\right)}{2 b^{5/2} f \sqrt[4]{a^2+b^2} \sec ^2(e+f x)^{3/4}}+\frac{3 a d^2 (d \sec (e+f x))^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt[4]{\sec ^2(e+f x)}}{\sqrt[4]{a^2+b^2}}\right)}{2 b^{5/2} f \sqrt[4]{a^2+b^2} \sec ^2(e+f x)^{3/4}}+\frac{3 a^2 d^2 \sqrt{-\tan ^2(e+f x)} \cot (e+f x) (d \sec (e+f x))^{3/2} \Pi \left(-\frac{b}{\sqrt{a^2+b^2}};\left.\sin ^{-1}\left(\sqrt[4]{\sec ^2(e+f x)}\right)\right|-1\right)}{2 b^3 f \sqrt{a^2+b^2} \sec ^2(e+f x)^{3/4}}-\frac{3 a^2 d^2 \sqrt{-\tan ^2(e+f x)} \cot (e+f x) (d \sec (e+f x))^{3/2} \Pi \left(\frac{b}{\sqrt{a^2+b^2}};\left.\sin ^{-1}\left(\sqrt[4]{\sec ^2(e+f x)}\right)\right|-1\right)}{2 b^3 f \sqrt{a^2+b^2} \sec ^2(e+f x)^{3/4}}-\frac{d^2 (d \sec (e+f x))^{3/2}}{b f (a+b \tan (e+f x))}+\frac{3 d^2 \sin (e+f x) \cos (e+f x) (d \sec (e+f x))^{3/2}}{b^2 f}-\frac{3 d^2 (d \sec (e+f x))^{3/2} E\left(\left.\frac{1}{2} \tan ^{-1}(\tan (e+f x))\right|2\right)}{b^2 f \sec ^2(e+f x)^{3/4}}",1,"(-3*a*d^2*ArcTan[(Sqrt[b]*(Sec[e + f*x]^2)^(1/4))/(a^2 + b^2)^(1/4)]*(d*Sec[e + f*x])^(3/2))/(2*b^(5/2)*(a^2 + b^2)^(1/4)*f*(Sec[e + f*x]^2)^(3/4)) + (3*a*d^2*ArcTanh[(Sqrt[b]*(Sec[e + f*x]^2)^(1/4))/(a^2 + b^2)^(1/4)]*(d*Sec[e + f*x])^(3/2))/(2*b^(5/2)*(a^2 + b^2)^(1/4)*f*(Sec[e + f*x]^2)^(3/4)) - (3*d^2*EllipticE[ArcTan[Tan[e + f*x]]/2, 2]*(d*Sec[e + f*x])^(3/2))/(b^2*f*(Sec[e + f*x]^2)^(3/4)) + (3*d^2*Cos[e + f*x]*(d*Sec[e + f*x])^(3/2)*Sin[e + f*x])/(b^2*f) + (3*a^2*d^2*Cot[e + f*x]*EllipticPi[-(b/Sqrt[a^2 + b^2]), ArcSin[(Sec[e + f*x]^2)^(1/4)], -1]*(d*Sec[e + f*x])^(3/2)*Sqrt[-Tan[e + f*x]^2])/(2*b^3*Sqrt[a^2 + b^2]*f*(Sec[e + f*x]^2)^(3/4)) - (3*a^2*d^2*Cot[e + f*x]*EllipticPi[b/Sqrt[a^2 + b^2], ArcSin[(Sec[e + f*x]^2)^(1/4)], -1]*(d*Sec[e + f*x])^(3/2)*Sqrt[-Tan[e + f*x]^2])/(2*b^3*Sqrt[a^2 + b^2]*f*(Sec[e + f*x]^2)^(3/4)) - (d^2*(d*Sec[e + f*x])^(3/2))/(b*f*(a + b*Tan[e + f*x]))","A",17,15,25,0.6000,1,"{3512, 733, 844, 227, 196, 746, 399, 490, 1213, 537, 444, 63, 298, 205, 208}"
611,1,440,0,0.3947532,"\int \frac{(d \sec (e+f x))^{5/2}}{(a+b \tan (e+f x))^2} \, dx","Int[(d*Sec[e + f*x])^(5/2)/(a + b*Tan[e + f*x])^2,x]","\frac{a d^2 \sqrt{d \sec (e+f x)} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt[4]{\sec ^2(e+f x)}}{\sqrt[4]{a^2+b^2}}\right)}{2 b^{3/2} f \left(a^2+b^2\right)^{3/4} \sqrt[4]{\sec ^2(e+f x)}}+\frac{a d^2 \sqrt{d \sec (e+f x)} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt[4]{\sec ^2(e+f x)}}{\sqrt[4]{a^2+b^2}}\right)}{2 b^{3/2} f \left(a^2+b^2\right)^{3/4} \sqrt[4]{\sec ^2(e+f x)}}-\frac{a^2 d^2 \sqrt{-\tan ^2(e+f x)} \cot (e+f x) \sqrt{d \sec (e+f x)} \Pi \left(-\frac{b}{\sqrt{a^2+b^2}};\left.\sin ^{-1}\left(\sqrt[4]{\sec ^2(e+f x)}\right)\right|-1\right)}{2 b^2 f \left(a^2+b^2\right) \sqrt[4]{\sec ^2(e+f x)}}-\frac{a^2 d^2 \sqrt{-\tan ^2(e+f x)} \cot (e+f x) \sqrt{d \sec (e+f x)} \Pi \left(\frac{b}{\sqrt{a^2+b^2}};\left.\sin ^{-1}\left(\sqrt[4]{\sec ^2(e+f x)}\right)\right|-1\right)}{2 b^2 f \left(a^2+b^2\right) \sqrt[4]{\sec ^2(e+f x)}}-\frac{d^2 \sqrt{d \sec (e+f x)}}{b f (a+b \tan (e+f x))}+\frac{d^2 \sqrt{d \sec (e+f x)} F\left(\left.\frac{1}{2} \tan ^{-1}(\tan (e+f x))\right|2\right)}{b^2 f \sqrt[4]{\sec ^2(e+f x)}}","\frac{a d^2 \sqrt{d \sec (e+f x)} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt[4]{\sec ^2(e+f x)}}{\sqrt[4]{a^2+b^2}}\right)}{2 b^{3/2} f \left(a^2+b^2\right)^{3/4} \sqrt[4]{\sec ^2(e+f x)}}+\frac{a d^2 \sqrt{d \sec (e+f x)} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt[4]{\sec ^2(e+f x)}}{\sqrt[4]{a^2+b^2}}\right)}{2 b^{3/2} f \left(a^2+b^2\right)^{3/4} \sqrt[4]{\sec ^2(e+f x)}}-\frac{a^2 d^2 \sqrt{-\tan ^2(e+f x)} \cot (e+f x) \sqrt{d \sec (e+f x)} \Pi \left(-\frac{b}{\sqrt{a^2+b^2}};\left.\sin ^{-1}\left(\sqrt[4]{\sec ^2(e+f x)}\right)\right|-1\right)}{2 b^2 f \left(a^2+b^2\right) \sqrt[4]{\sec ^2(e+f x)}}-\frac{a^2 d^2 \sqrt{-\tan ^2(e+f x)} \cot (e+f x) \sqrt{d \sec (e+f x)} \Pi \left(\frac{b}{\sqrt{a^2+b^2}};\left.\sin ^{-1}\left(\sqrt[4]{\sec ^2(e+f x)}\right)\right|-1\right)}{2 b^2 f \left(a^2+b^2\right) \sqrt[4]{\sec ^2(e+f x)}}-\frac{d^2 \sqrt{d \sec (e+f x)}}{b f (a+b \tan (e+f x))}+\frac{d^2 \sqrt{d \sec (e+f x)} F\left(\left.\frac{1}{2} \tan ^{-1}(\tan (e+f x))\right|2\right)}{b^2 f \sqrt[4]{\sec ^2(e+f x)}}",1,"(a*d^2*ArcTan[(Sqrt[b]*(Sec[e + f*x]^2)^(1/4))/(a^2 + b^2)^(1/4)]*Sqrt[d*Sec[e + f*x]])/(2*b^(3/2)*(a^2 + b^2)^(3/4)*f*(Sec[e + f*x]^2)^(1/4)) + (a*d^2*ArcTanh[(Sqrt[b]*(Sec[e + f*x]^2)^(1/4))/(a^2 + b^2)^(1/4)]*Sqrt[d*Sec[e + f*x]])/(2*b^(3/2)*(a^2 + b^2)^(3/4)*f*(Sec[e + f*x]^2)^(1/4)) + (d^2*EllipticF[ArcTan[Tan[e + f*x]]/2, 2]*Sqrt[d*Sec[e + f*x]])/(b^2*f*(Sec[e + f*x]^2)^(1/4)) - (a^2*d^2*Cot[e + f*x]*EllipticPi[-(b/Sqrt[a^2 + b^2]), ArcSin[(Sec[e + f*x]^2)^(1/4)], -1]*Sqrt[d*Sec[e + f*x]]*Sqrt[-Tan[e + f*x]^2])/(2*b^2*(a^2 + b^2)*f*(Sec[e + f*x]^2)^(1/4)) - (a^2*d^2*Cot[e + f*x]*EllipticPi[b/Sqrt[a^2 + b^2], ArcSin[(Sec[e + f*x]^2)^(1/4)], -1]*Sqrt[d*Sec[e + f*x]]*Sqrt[-Tan[e + f*x]^2])/(2*b^2*(a^2 + b^2)*f*(Sec[e + f*x]^2)^(1/4)) - (d^2*Sqrt[d*Sec[e + f*x]])/(b*f*(a + b*Tan[e + f*x]))","A",17,15,25,0.6000,1,"{3512, 733, 844, 231, 747, 401, 108, 409, 1213, 537, 444, 63, 212, 208, 205}"
612,1,477,0,0.3852052,"\int \frac{(d \sec (e+f x))^{3/2}}{(a+b \tan (e+f x))^2} \, dx","Int[(d*Sec[e + f*x])^(3/2)/(a + b*Tan[e + f*x])^2,x]","\frac{a (d \sec (e+f x))^{3/2} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt[4]{\sec ^2(e+f x)}}{\sqrt[4]{a^2+b^2}}\right)}{2 \sqrt{b} f \left(a^2+b^2\right)^{5/4} \sec ^2(e+f x)^{3/4}}-\frac{a (d \sec (e+f x))^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt[4]{\sec ^2(e+f x)}}{\sqrt[4]{a^2+b^2}}\right)}{2 \sqrt{b} f \left(a^2+b^2\right)^{5/4} \sec ^2(e+f x)^{3/4}}-\frac{b (d \sec (e+f x))^{3/2}}{f \left(a^2+b^2\right) (a+b \tan (e+f x))}+\frac{\sin (e+f x) \cos (e+f x) (d \sec (e+f x))^{3/2}}{f \left(a^2+b^2\right)}-\frac{(d \sec (e+f x))^{3/2} E\left(\left.\frac{1}{2} \tan ^{-1}(\tan (e+f x))\right|2\right)}{f \left(a^2+b^2\right) \sec ^2(e+f x)^{3/4}}-\frac{a^2 \sqrt{-\tan ^2(e+f x)} \cot (e+f x) (d \sec (e+f x))^{3/2} \Pi \left(-\frac{b}{\sqrt{a^2+b^2}};\left.\sin ^{-1}\left(\sqrt[4]{\sec ^2(e+f x)}\right)\right|-1\right)}{2 b f \left(a^2+b^2\right)^{3/2} \sec ^2(e+f x)^{3/4}}+\frac{a^2 \sqrt{-\tan ^2(e+f x)} \cot (e+f x) (d \sec (e+f x))^{3/2} \Pi \left(\frac{b}{\sqrt{a^2+b^2}};\left.\sin ^{-1}\left(\sqrt[4]{\sec ^2(e+f x)}\right)\right|-1\right)}{2 b f \left(a^2+b^2\right)^{3/2} \sec ^2(e+f x)^{3/4}}","\frac{a (d \sec (e+f x))^{3/2} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt[4]{\sec ^2(e+f x)}}{\sqrt[4]{a^2+b^2}}\right)}{2 \sqrt{b} f \left(a^2+b^2\right)^{5/4} \sec ^2(e+f x)^{3/4}}-\frac{a (d \sec (e+f x))^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt[4]{\sec ^2(e+f x)}}{\sqrt[4]{a^2+b^2}}\right)}{2 \sqrt{b} f \left(a^2+b^2\right)^{5/4} \sec ^2(e+f x)^{3/4}}-\frac{b (d \sec (e+f x))^{3/2}}{f \left(a^2+b^2\right) (a+b \tan (e+f x))}+\frac{\sin (e+f x) \cos (e+f x) (d \sec (e+f x))^{3/2}}{f \left(a^2+b^2\right)}-\frac{(d \sec (e+f x))^{3/2} E\left(\left.\frac{1}{2} \tan ^{-1}(\tan (e+f x))\right|2\right)}{f \left(a^2+b^2\right) \sec ^2(e+f x)^{3/4}}-\frac{a^2 \sqrt{-\tan ^2(e+f x)} \cot (e+f x) (d \sec (e+f x))^{3/2} \Pi \left(-\frac{b}{\sqrt{a^2+b^2}};\left.\sin ^{-1}\left(\sqrt[4]{\sec ^2(e+f x)}\right)\right|-1\right)}{2 b f \left(a^2+b^2\right)^{3/2} \sec ^2(e+f x)^{3/4}}+\frac{a^2 \sqrt{-\tan ^2(e+f x)} \cot (e+f x) (d \sec (e+f x))^{3/2} \Pi \left(\frac{b}{\sqrt{a^2+b^2}};\left.\sin ^{-1}\left(\sqrt[4]{\sec ^2(e+f x)}\right)\right|-1\right)}{2 b f \left(a^2+b^2\right)^{3/2} \sec ^2(e+f x)^{3/4}}",1,"(a*ArcTan[(Sqrt[b]*(Sec[e + f*x]^2)^(1/4))/(a^2 + b^2)^(1/4)]*(d*Sec[e + f*x])^(3/2))/(2*Sqrt[b]*(a^2 + b^2)^(5/4)*f*(Sec[e + f*x]^2)^(3/4)) - (a*ArcTanh[(Sqrt[b]*(Sec[e + f*x]^2)^(1/4))/(a^2 + b^2)^(1/4)]*(d*Sec[e + f*x])^(3/2))/(2*Sqrt[b]*(a^2 + b^2)^(5/4)*f*(Sec[e + f*x]^2)^(3/4)) - (EllipticE[ArcTan[Tan[e + f*x]]/2, 2]*(d*Sec[e + f*x])^(3/2))/((a^2 + b^2)*f*(Sec[e + f*x]^2)^(3/4)) + (Cos[e + f*x]*(d*Sec[e + f*x])^(3/2)*Sin[e + f*x])/((a^2 + b^2)*f) - (a^2*Cot[e + f*x]*EllipticPi[-(b/Sqrt[a^2 + b^2]), ArcSin[(Sec[e + f*x]^2)^(1/4)], -1]*(d*Sec[e + f*x])^(3/2)*Sqrt[-Tan[e + f*x]^2])/(2*b*(a^2 + b^2)^(3/2)*f*(Sec[e + f*x]^2)^(3/4)) + (a^2*Cot[e + f*x]*EllipticPi[b/Sqrt[a^2 + b^2], ArcSin[(Sec[e + f*x]^2)^(1/4)], -1]*(d*Sec[e + f*x])^(3/2)*Sqrt[-Tan[e + f*x]^2])/(2*b*(a^2 + b^2)^(3/2)*f*(Sec[e + f*x]^2)^(3/4)) - (b*(d*Sec[e + f*x])^(3/2))/((a^2 + b^2)*f*(a + b*Tan[e + f*x]))","A",17,15,25,0.6000,1,"{3512, 745, 844, 227, 196, 746, 399, 490, 1213, 537, 444, 63, 298, 205, 208}"
613,1,430,0,0.3799903,"\int \frac{\sqrt{d \sec (e+f x)}}{(a+b \tan (e+f x))^2} \, dx","Int[Sqrt[d*Sec[e + f*x]]/(a + b*Tan[e + f*x])^2,x]","-\frac{3 a \sqrt{b} \sqrt{d \sec (e+f x)} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt[4]{\sec ^2(e+f x)}}{\sqrt[4]{a^2+b^2}}\right)}{2 f \left(a^2+b^2\right)^{7/4} \sqrt[4]{\sec ^2(e+f x)}}-\frac{3 a \sqrt{b} \sqrt{d \sec (e+f x)} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt[4]{\sec ^2(e+f x)}}{\sqrt[4]{a^2+b^2}}\right)}{2 f \left(a^2+b^2\right)^{7/4} \sqrt[4]{\sec ^2(e+f x)}}-\frac{b \sqrt{d \sec (e+f x)}}{f \left(a^2+b^2\right) (a+b \tan (e+f x))}-\frac{\sqrt{d \sec (e+f x)} F\left(\left.\frac{1}{2} \tan ^{-1}(\tan (e+f x))\right|2\right)}{f \left(a^2+b^2\right) \sqrt[4]{\sec ^2(e+f x)}}+\frac{3 a^2 \sqrt{-\tan ^2(e+f x)} \cot (e+f x) \sqrt{d \sec (e+f x)} \Pi \left(-\frac{b}{\sqrt{a^2+b^2}};\left.\sin ^{-1}\left(\sqrt[4]{\sec ^2(e+f x)}\right)\right|-1\right)}{2 f \left(a^2+b^2\right)^2 \sqrt[4]{\sec ^2(e+f x)}}+\frac{3 a^2 \sqrt{-\tan ^2(e+f x)} \cot (e+f x) \sqrt{d \sec (e+f x)} \Pi \left(\frac{b}{\sqrt{a^2+b^2}};\left.\sin ^{-1}\left(\sqrt[4]{\sec ^2(e+f x)}\right)\right|-1\right)}{2 f \left(a^2+b^2\right)^2 \sqrt[4]{\sec ^2(e+f x)}}","-\frac{3 a \sqrt{b} \sqrt{d \sec (e+f x)} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt[4]{\sec ^2(e+f x)}}{\sqrt[4]{a^2+b^2}}\right)}{2 f \left(a^2+b^2\right)^{7/4} \sqrt[4]{\sec ^2(e+f x)}}-\frac{3 a \sqrt{b} \sqrt{d \sec (e+f x)} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt[4]{\sec ^2(e+f x)}}{\sqrt[4]{a^2+b^2}}\right)}{2 f \left(a^2+b^2\right)^{7/4} \sqrt[4]{\sec ^2(e+f x)}}-\frac{b \sqrt{d \sec (e+f x)}}{f \left(a^2+b^2\right) (a+b \tan (e+f x))}-\frac{\sqrt{d \sec (e+f x)} F\left(\left.\frac{1}{2} \tan ^{-1}(\tan (e+f x))\right|2\right)}{f \left(a^2+b^2\right) \sqrt[4]{\sec ^2(e+f x)}}+\frac{3 a^2 \sqrt{-\tan ^2(e+f x)} \cot (e+f x) \sqrt{d \sec (e+f x)} \Pi \left(-\frac{b}{\sqrt{a^2+b^2}};\left.\sin ^{-1}\left(\sqrt[4]{\sec ^2(e+f x)}\right)\right|-1\right)}{2 f \left(a^2+b^2\right)^2 \sqrt[4]{\sec ^2(e+f x)}}+\frac{3 a^2 \sqrt{-\tan ^2(e+f x)} \cot (e+f x) \sqrt{d \sec (e+f x)} \Pi \left(\frac{b}{\sqrt{a^2+b^2}};\left.\sin ^{-1}\left(\sqrt[4]{\sec ^2(e+f x)}\right)\right|-1\right)}{2 f \left(a^2+b^2\right)^2 \sqrt[4]{\sec ^2(e+f x)}}",1,"(-3*a*Sqrt[b]*ArcTan[(Sqrt[b]*(Sec[e + f*x]^2)^(1/4))/(a^2 + b^2)^(1/4)]*Sqrt[d*Sec[e + f*x]])/(2*(a^2 + b^2)^(7/4)*f*(Sec[e + f*x]^2)^(1/4)) - (3*a*Sqrt[b]*ArcTanh[(Sqrt[b]*(Sec[e + f*x]^2)^(1/4))/(a^2 + b^2)^(1/4)]*Sqrt[d*Sec[e + f*x]])/(2*(a^2 + b^2)^(7/4)*f*(Sec[e + f*x]^2)^(1/4)) - (EllipticF[ArcTan[Tan[e + f*x]]/2, 2]*Sqrt[d*Sec[e + f*x]])/((a^2 + b^2)*f*(Sec[e + f*x]^2)^(1/4)) + (3*a^2*Cot[e + f*x]*EllipticPi[-(b/Sqrt[a^2 + b^2]), ArcSin[(Sec[e + f*x]^2)^(1/4)], -1]*Sqrt[d*Sec[e + f*x]]*Sqrt[-Tan[e + f*x]^2])/(2*(a^2 + b^2)^2*f*(Sec[e + f*x]^2)^(1/4)) + (3*a^2*Cot[e + f*x]*EllipticPi[b/Sqrt[a^2 + b^2], ArcSin[(Sec[e + f*x]^2)^(1/4)], -1]*Sqrt[d*Sec[e + f*x]]*Sqrt[-Tan[e + f*x]^2])/(2*(a^2 + b^2)^2*f*(Sec[e + f*x]^2)^(1/4)) - (b*Sqrt[d*Sec[e + f*x]])/((a^2 + b^2)*f*(a + b*Tan[e + f*x]))","A",17,15,25,0.6000,1,"{3512, 745, 844, 231, 747, 401, 108, 409, 1213, 537, 444, 63, 212, 208, 205}"
614,1,555,0,0.5372437,"\int \frac{1}{\sqrt{d \sec (e+f x)} (a+b \tan (e+f x))^2} \, dx","Int[1/(Sqrt[d*Sec[e + f*x]]*(a + b*Tan[e + f*x])^2),x]","\frac{5 a b^{3/2} \sqrt[4]{\sec ^2(e+f x)} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt[4]{\sec ^2(e+f x)}}{\sqrt[4]{a^2+b^2}}\right)}{2 f \left(a^2+b^2\right)^{9/4} \sqrt{d \sec (e+f x)}}+\frac{b \left(2 a^2-3 b^2\right) \sec ^2(e+f x)}{f \left(a^2+b^2\right)^2 \sqrt{d \sec (e+f x)} (a+b \tan (e+f x))}-\frac{5 a b^{3/2} \sqrt[4]{\sec ^2(e+f x)} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt[4]{\sec ^2(e+f x)}}{\sqrt[4]{a^2+b^2}}\right)}{2 f \left(a^2+b^2\right)^{9/4} \sqrt{d \sec (e+f x)}}-\frac{\left(2 a^2-3 b^2\right) \tan (e+f x)}{f \left(a^2+b^2\right)^2 \sqrt{d \sec (e+f x)}}+\frac{2 (a \tan (e+f x)+b)}{f \left(a^2+b^2\right) \sqrt{d \sec (e+f x)} (a+b \tan (e+f x))}+\frac{\left(2 a^2-3 b^2\right) \sqrt[4]{\sec ^2(e+f x)} E\left(\left.\frac{1}{2} \tan ^{-1}(\tan (e+f x))\right|2\right)}{f \left(a^2+b^2\right)^2 \sqrt{d \sec (e+f x)}}-\frac{5 a^2 b \sqrt{-\tan ^2(e+f x)} \cot (e+f x) \sqrt[4]{\sec ^2(e+f x)} \Pi \left(-\frac{b}{\sqrt{a^2+b^2}};\left.\sin ^{-1}\left(\sqrt[4]{\sec ^2(e+f x)}\right)\right|-1\right)}{2 f \left(a^2+b^2\right)^{5/2} \sqrt{d \sec (e+f x)}}+\frac{5 a^2 b \sqrt{-\tan ^2(e+f x)} \cot (e+f x) \sqrt[4]{\sec ^2(e+f x)} \Pi \left(\frac{b}{\sqrt{a^2+b^2}};\left.\sin ^{-1}\left(\sqrt[4]{\sec ^2(e+f x)}\right)\right|-1\right)}{2 f \left(a^2+b^2\right)^{5/2} \sqrt{d \sec (e+f x)}}","\frac{5 a b^{3/2} \sqrt[4]{\sec ^2(e+f x)} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt[4]{\sec ^2(e+f x)}}{\sqrt[4]{a^2+b^2}}\right)}{2 f \left(a^2+b^2\right)^{9/4} \sqrt{d \sec (e+f x)}}+\frac{b \left(2 a^2-3 b^2\right) \sec ^2(e+f x)}{f \left(a^2+b^2\right)^2 \sqrt{d \sec (e+f x)} (a+b \tan (e+f x))}-\frac{5 a b^{3/2} \sqrt[4]{\sec ^2(e+f x)} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt[4]{\sec ^2(e+f x)}}{\sqrt[4]{a^2+b^2}}\right)}{2 f \left(a^2+b^2\right)^{9/4} \sqrt{d \sec (e+f x)}}-\frac{\left(2 a^2-3 b^2\right) \tan (e+f x)}{f \left(a^2+b^2\right)^2 \sqrt{d \sec (e+f x)}}+\frac{2 (a \tan (e+f x)+b)}{f \left(a^2+b^2\right) \sqrt{d \sec (e+f x)} (a+b \tan (e+f x))}+\frac{\left(2 a^2-3 b^2\right) \sqrt[4]{\sec ^2(e+f x)} E\left(\left.\frac{1}{2} \tan ^{-1}(\tan (e+f x))\right|2\right)}{f \left(a^2+b^2\right)^2 \sqrt{d \sec (e+f x)}}-\frac{5 a^2 b \sqrt{-\tan ^2(e+f x)} \cot (e+f x) \sqrt[4]{\sec ^2(e+f x)} \Pi \left(-\frac{b}{\sqrt{a^2+b^2}};\left.\sin ^{-1}\left(\sqrt[4]{\sec ^2(e+f x)}\right)\right|-1\right)}{2 f \left(a^2+b^2\right)^{5/2} \sqrt{d \sec (e+f x)}}+\frac{5 a^2 b \sqrt{-\tan ^2(e+f x)} \cot (e+f x) \sqrt[4]{\sec ^2(e+f x)} \Pi \left(\frac{b}{\sqrt{a^2+b^2}};\left.\sin ^{-1}\left(\sqrt[4]{\sec ^2(e+f x)}\right)\right|-1\right)}{2 f \left(a^2+b^2\right)^{5/2} \sqrt{d \sec (e+f x)}}",1,"(5*a*b^(3/2)*ArcTan[(Sqrt[b]*(Sec[e + f*x]^2)^(1/4))/(a^2 + b^2)^(1/4)]*(Sec[e + f*x]^2)^(1/4))/(2*(a^2 + b^2)^(9/4)*f*Sqrt[d*Sec[e + f*x]]) - (5*a*b^(3/2)*ArcTanh[(Sqrt[b]*(Sec[e + f*x]^2)^(1/4))/(a^2 + b^2)^(1/4)]*(Sec[e + f*x]^2)^(1/4))/(2*(a^2 + b^2)^(9/4)*f*Sqrt[d*Sec[e + f*x]]) + ((2*a^2 - 3*b^2)*EllipticE[ArcTan[Tan[e + f*x]]/2, 2]*(Sec[e + f*x]^2)^(1/4))/((a^2 + b^2)^2*f*Sqrt[d*Sec[e + f*x]]) - ((2*a^2 - 3*b^2)*Tan[e + f*x])/((a^2 + b^2)^2*f*Sqrt[d*Sec[e + f*x]]) - (5*a^2*b*Cot[e + f*x]*EllipticPi[-(b/Sqrt[a^2 + b^2]), ArcSin[(Sec[e + f*x]^2)^(1/4)], -1]*(Sec[e + f*x]^2)^(1/4)*Sqrt[-Tan[e + f*x]^2])/(2*(a^2 + b^2)^(5/2)*f*Sqrt[d*Sec[e + f*x]]) + (5*a^2*b*Cot[e + f*x]*EllipticPi[b/Sqrt[a^2 + b^2], ArcSin[(Sec[e + f*x]^2)^(1/4)], -1]*(Sec[e + f*x]^2)^(1/4)*Sqrt[-Tan[e + f*x]^2])/(2*(a^2 + b^2)^(5/2)*f*Sqrt[d*Sec[e + f*x]]) + (b*(2*a^2 - 3*b^2)*Sec[e + f*x]^2)/((a^2 + b^2)^2*f*Sqrt[d*Sec[e + f*x]]*(a + b*Tan[e + f*x])) + (2*(b + a*Tan[e + f*x]))/((a^2 + b^2)*f*Sqrt[d*Sec[e + f*x]]*(a + b*Tan[e + f*x]))","A",18,16,25,0.6400,1,"{3512, 741, 835, 844, 227, 196, 746, 399, 490, 1213, 537, 444, 63, 298, 205, 208}"
615,1,520,0,0.5660931,"\int \frac{1}{(d \sec (e+f x))^{3/2} (a+b \tan (e+f x))^2} \, dx","Int[1/((d*Sec[e + f*x])^(3/2)*(a + b*Tan[e + f*x])^2),x]","-\frac{7 a b^{5/2} \sec ^2(e+f x)^{3/4} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt[4]{\sec ^2(e+f x)}}{\sqrt[4]{a^2+b^2}}\right)}{2 f \left(a^2+b^2\right)^{11/4} (d \sec (e+f x))^{3/2}}+\frac{b \left(2 a^2-5 b^2\right) \sec ^2(e+f x)}{3 f \left(a^2+b^2\right)^2 (d \sec (e+f x))^{3/2} (a+b \tan (e+f x))}-\frac{7 a b^{5/2} \sec ^2(e+f x)^{3/4} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt[4]{\sec ^2(e+f x)}}{\sqrt[4]{a^2+b^2}}\right)}{2 f \left(a^2+b^2\right)^{11/4} (d \sec (e+f x))^{3/2}}+\frac{2 (a \tan (e+f x)+b)}{3 f \left(a^2+b^2\right) (d \sec (e+f x))^{3/2} (a+b \tan (e+f x))}+\frac{\left(2 a^2-5 b^2\right) \sec ^2(e+f x)^{3/4} F\left(\left.\frac{1}{2} \tan ^{-1}(\tan (e+f x))\right|2\right)}{3 f \left(a^2+b^2\right)^2 (d \sec (e+f x))^{3/2}}+\frac{7 a^2 b^2 \sqrt{-\tan ^2(e+f x)} \cot (e+f x) \sec ^2(e+f x)^{3/4} \Pi \left(-\frac{b}{\sqrt{a^2+b^2}};\left.\sin ^{-1}\left(\sqrt[4]{\sec ^2(e+f x)}\right)\right|-1\right)}{2 f \left(a^2+b^2\right)^3 (d \sec (e+f x))^{3/2}}+\frac{7 a^2 b^2 \sqrt{-\tan ^2(e+f x)} \cot (e+f x) \sec ^2(e+f x)^{3/4} \Pi \left(\frac{b}{\sqrt{a^2+b^2}};\left.\sin ^{-1}\left(\sqrt[4]{\sec ^2(e+f x)}\right)\right|-1\right)}{2 f \left(a^2+b^2\right)^3 (d \sec (e+f x))^{3/2}}","-\frac{7 a b^{5/2} \sec ^2(e+f x)^{3/4} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt[4]{\sec ^2(e+f x)}}{\sqrt[4]{a^2+b^2}}\right)}{2 f \left(a^2+b^2\right)^{11/4} (d \sec (e+f x))^{3/2}}+\frac{b \left(2 a^2-5 b^2\right) \sec ^2(e+f x)}{3 f \left(a^2+b^2\right)^2 (d \sec (e+f x))^{3/2} (a+b \tan (e+f x))}-\frac{7 a b^{5/2} \sec ^2(e+f x)^{3/4} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt[4]{\sec ^2(e+f x)}}{\sqrt[4]{a^2+b^2}}\right)}{2 f \left(a^2+b^2\right)^{11/4} (d \sec (e+f x))^{3/2}}+\frac{2 (a \tan (e+f x)+b)}{3 f \left(a^2+b^2\right) (d \sec (e+f x))^{3/2} (a+b \tan (e+f x))}+\frac{\left(2 a^2-5 b^2\right) \sec ^2(e+f x)^{3/4} F\left(\left.\frac{1}{2} \tan ^{-1}(\tan (e+f x))\right|2\right)}{3 f \left(a^2+b^2\right)^2 (d \sec (e+f x))^{3/2}}+\frac{7 a^2 b^2 \sqrt{-\tan ^2(e+f x)} \cot (e+f x) \sec ^2(e+f x)^{3/4} \Pi \left(-\frac{b}{\sqrt{a^2+b^2}};\left.\sin ^{-1}\left(\sqrt[4]{\sec ^2(e+f x)}\right)\right|-1\right)}{2 f \left(a^2+b^2\right)^3 (d \sec (e+f x))^{3/2}}+\frac{7 a^2 b^2 \sqrt{-\tan ^2(e+f x)} \cot (e+f x) \sec ^2(e+f x)^{3/4} \Pi \left(\frac{b}{\sqrt{a^2+b^2}};\left.\sin ^{-1}\left(\sqrt[4]{\sec ^2(e+f x)}\right)\right|-1\right)}{2 f \left(a^2+b^2\right)^3 (d \sec (e+f x))^{3/2}}",1,"(-7*a*b^(5/2)*ArcTan[(Sqrt[b]*(Sec[e + f*x]^2)^(1/4))/(a^2 + b^2)^(1/4)]*(Sec[e + f*x]^2)^(3/4))/(2*(a^2 + b^2)^(11/4)*f*(d*Sec[e + f*x])^(3/2)) - (7*a*b^(5/2)*ArcTanh[(Sqrt[b]*(Sec[e + f*x]^2)^(1/4))/(a^2 + b^2)^(1/4)]*(Sec[e + f*x]^2)^(3/4))/(2*(a^2 + b^2)^(11/4)*f*(d*Sec[e + f*x])^(3/2)) + ((2*a^2 - 5*b^2)*EllipticF[ArcTan[Tan[e + f*x]]/2, 2]*(Sec[e + f*x]^2)^(3/4))/(3*(a^2 + b^2)^2*f*(d*Sec[e + f*x])^(3/2)) + (7*a^2*b^2*Cot[e + f*x]*EllipticPi[-(b/Sqrt[a^2 + b^2]), ArcSin[(Sec[e + f*x]^2)^(1/4)], -1]*(Sec[e + f*x]^2)^(3/4)*Sqrt[-Tan[e + f*x]^2])/(2*(a^2 + b^2)^3*f*(d*Sec[e + f*x])^(3/2)) + (7*a^2*b^2*Cot[e + f*x]*EllipticPi[b/Sqrt[a^2 + b^2], ArcSin[(Sec[e + f*x]^2)^(1/4)], -1]*(Sec[e + f*x]^2)^(3/4)*Sqrt[-Tan[e + f*x]^2])/(2*(a^2 + b^2)^3*f*(d*Sec[e + f*x])^(3/2)) + (b*(2*a^2 - 5*b^2)*Sec[e + f*x]^2)/(3*(a^2 + b^2)^2*f*(d*Sec[e + f*x])^(3/2)*(a + b*Tan[e + f*x])) + (2*(b + a*Tan[e + f*x]))/(3*(a^2 + b^2)*f*(d*Sec[e + f*x])^(3/2)*(a + b*Tan[e + f*x]))","A",18,16,25,0.6400,1,"{3512, 741, 835, 844, 231, 747, 401, 108, 409, 1213, 537, 444, 63, 212, 208, 205}"
616,1,700,0,0.7140321,"\int \frac{1}{(d \sec (e+f x))^{5/2} (a+b \tan (e+f x))^2} \, dx","Int[1/((d*Sec[e + f*x])^(5/2)*(a + b*Tan[e + f*x])^2),x]","\frac{9 a b^{7/2} \sqrt[4]{\sec ^2(e+f x)} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt[4]{\sec ^2(e+f x)}}{\sqrt[4]{a^2+b^2}}\right)}{2 d^2 f \left(a^2+b^2\right)^{13/4} \sqrt{d \sec (e+f x)}}+\frac{3 b \left(10 a^2 b^2+2 a^4-7 b^4\right) \sec ^2(e+f x)}{5 d^2 f \left(a^2+b^2\right)^3 \sqrt{d \sec (e+f x)} (a+b \tan (e+f x))}-\frac{9 a b^{7/2} \sqrt[4]{\sec ^2(e+f x)} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt[4]{\sec ^2(e+f x)}}{\sqrt[4]{a^2+b^2}}\right)}{2 d^2 f \left(a^2+b^2\right)^{13/4} \sqrt{d \sec (e+f x)}}-\frac{3 \left(10 a^2 b^2+2 a^4-7 b^4\right) \tan (e+f x)}{5 d^2 f \left(a^2+b^2\right)^3 \sqrt{d \sec (e+f x)}}-\frac{2 \left(b \left(2 a^2-7 b^2\right)-3 a \left(a^2+4 b^2\right) \tan (e+f x)\right)}{5 d^2 f \left(a^2+b^2\right)^2 \sqrt{d \sec (e+f x)} (a+b \tan (e+f x))}+\frac{2 \cos ^2(e+f x) (a \tan (e+f x)+b)}{5 d^2 f \left(a^2+b^2\right) \sqrt{d \sec (e+f x)} (a+b \tan (e+f x))}+\frac{3 \left(10 a^2 b^2+2 a^4-7 b^4\right) \sqrt[4]{\sec ^2(e+f x)} E\left(\left.\frac{1}{2} \tan ^{-1}(\tan (e+f x))\right|2\right)}{5 d^2 f \left(a^2+b^2\right)^3 \sqrt{d \sec (e+f x)}}-\frac{9 a^2 b^3 \sqrt{-\tan ^2(e+f x)} \cot (e+f x) \sqrt[4]{\sec ^2(e+f x)} \Pi \left(-\frac{b}{\sqrt{a^2+b^2}};\left.\sin ^{-1}\left(\sqrt[4]{\sec ^2(e+f x)}\right)\right|-1\right)}{2 d^2 f \left(a^2+b^2\right)^{7/2} \sqrt{d \sec (e+f x)}}+\frac{9 a^2 b^3 \sqrt{-\tan ^2(e+f x)} \cot (e+f x) \sqrt[4]{\sec ^2(e+f x)} \Pi \left(\frac{b}{\sqrt{a^2+b^2}};\left.\sin ^{-1}\left(\sqrt[4]{\sec ^2(e+f x)}\right)\right|-1\right)}{2 d^2 f \left(a^2+b^2\right)^{7/2} \sqrt{d \sec (e+f x)}}","\frac{9 a b^{7/2} \sqrt[4]{\sec ^2(e+f x)} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt[4]{\sec ^2(e+f x)}}{\sqrt[4]{a^2+b^2}}\right)}{2 d^2 f \left(a^2+b^2\right)^{13/4} \sqrt{d \sec (e+f x)}}+\frac{3 b \left(10 a^2 b^2+2 a^4-7 b^4\right) \sec ^2(e+f x)}{5 d^2 f \left(a^2+b^2\right)^3 \sqrt{d \sec (e+f x)} (a+b \tan (e+f x))}-\frac{9 a b^{7/2} \sqrt[4]{\sec ^2(e+f x)} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt[4]{\sec ^2(e+f x)}}{\sqrt[4]{a^2+b^2}}\right)}{2 d^2 f \left(a^2+b^2\right)^{13/4} \sqrt{d \sec (e+f x)}}-\frac{3 \left(10 a^2 b^2+2 a^4-7 b^4\right) \tan (e+f x)}{5 d^2 f \left(a^2+b^2\right)^3 \sqrt{d \sec (e+f x)}}-\frac{2 \left(b \left(2 a^2-7 b^2\right)-3 a \left(a^2+4 b^2\right) \tan (e+f x)\right)}{5 d^2 f \left(a^2+b^2\right)^2 \sqrt{d \sec (e+f x)} (a+b \tan (e+f x))}+\frac{2 \cos ^2(e+f x) (a \tan (e+f x)+b)}{5 d^2 f \left(a^2+b^2\right) \sqrt{d \sec (e+f x)} (a+b \tan (e+f x))}+\frac{3 \left(10 a^2 b^2+2 a^4-7 b^4\right) \sqrt[4]{\sec ^2(e+f x)} E\left(\left.\frac{1}{2} \tan ^{-1}(\tan (e+f x))\right|2\right)}{5 d^2 f \left(a^2+b^2\right)^3 \sqrt{d \sec (e+f x)}}-\frac{9 a^2 b^3 \sqrt{-\tan ^2(e+f x)} \cot (e+f x) \sqrt[4]{\sec ^2(e+f x)} \Pi \left(-\frac{b}{\sqrt{a^2+b^2}};\left.\sin ^{-1}\left(\sqrt[4]{\sec ^2(e+f x)}\right)\right|-1\right)}{2 d^2 f \left(a^2+b^2\right)^{7/2} \sqrt{d \sec (e+f x)}}+\frac{9 a^2 b^3 \sqrt{-\tan ^2(e+f x)} \cot (e+f x) \sqrt[4]{\sec ^2(e+f x)} \Pi \left(\frac{b}{\sqrt{a^2+b^2}};\left.\sin ^{-1}\left(\sqrt[4]{\sec ^2(e+f x)}\right)\right|-1\right)}{2 d^2 f \left(a^2+b^2\right)^{7/2} \sqrt{d \sec (e+f x)}}",1,"(9*a*b^(7/2)*ArcTan[(Sqrt[b]*(Sec[e + f*x]^2)^(1/4))/(a^2 + b^2)^(1/4)]*(Sec[e + f*x]^2)^(1/4))/(2*(a^2 + b^2)^(13/4)*d^2*f*Sqrt[d*Sec[e + f*x]]) - (9*a*b^(7/2)*ArcTanh[(Sqrt[b]*(Sec[e + f*x]^2)^(1/4))/(a^2 + b^2)^(1/4)]*(Sec[e + f*x]^2)^(1/4))/(2*(a^2 + b^2)^(13/4)*d^2*f*Sqrt[d*Sec[e + f*x]]) + (3*(2*a^4 + 10*a^2*b^2 - 7*b^4)*EllipticE[ArcTan[Tan[e + f*x]]/2, 2]*(Sec[e + f*x]^2)^(1/4))/(5*(a^2 + b^2)^3*d^2*f*Sqrt[d*Sec[e + f*x]]) - (3*(2*a^4 + 10*a^2*b^2 - 7*b^4)*Tan[e + f*x])/(5*(a^2 + b^2)^3*d^2*f*Sqrt[d*Sec[e + f*x]]) - (9*a^2*b^3*Cot[e + f*x]*EllipticPi[-(b/Sqrt[a^2 + b^2]), ArcSin[(Sec[e + f*x]^2)^(1/4)], -1]*(Sec[e + f*x]^2)^(1/4)*Sqrt[-Tan[e + f*x]^2])/(2*(a^2 + b^2)^(7/2)*d^2*f*Sqrt[d*Sec[e + f*x]]) + (9*a^2*b^3*Cot[e + f*x]*EllipticPi[b/Sqrt[a^2 + b^2], ArcSin[(Sec[e + f*x]^2)^(1/4)], -1]*(Sec[e + f*x]^2)^(1/4)*Sqrt[-Tan[e + f*x]^2])/(2*(a^2 + b^2)^(7/2)*d^2*f*Sqrt[d*Sec[e + f*x]]) + (3*b*(2*a^4 + 10*a^2*b^2 - 7*b^4)*Sec[e + f*x]^2)/(5*(a^2 + b^2)^3*d^2*f*Sqrt[d*Sec[e + f*x]]*(a + b*Tan[e + f*x])) + (2*Cos[e + f*x]^2*(b + a*Tan[e + f*x]))/(5*(a^2 + b^2)*d^2*f*Sqrt[d*Sec[e + f*x]]*(a + b*Tan[e + f*x])) - (2*(b*(2*a^2 - 7*b^2) - 3*a*(a^2 + 4*b^2)*Tan[e + f*x]))/(5*(a^2 + b^2)^2*d^2*f*Sqrt[d*Sec[e + f*x]]*(a + b*Tan[e + f*x]))","A",19,17,25,0.6800,1,"{3512, 741, 823, 835, 844, 227, 196, 746, 399, 490, 1213, 537, 444, 63, 298, 205, 208}"
617,1,583,0,0.5170928,"\int \frac{(d \sec (e+f x))^{7/2}}{(a+b \tan (e+f x))^3} \, dx","Int[(d*Sec[e + f*x])^(7/2)/(a + b*Tan[e + f*x])^3,x]","\frac{3 d^2 \left(a^2+2 b^2\right) (d \sec (e+f x))^{3/2} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt[4]{\sec ^2(e+f x)}}{\sqrt[4]{a^2+b^2}}\right)}{8 b^{5/2} f \left(a^2+b^2\right)^{5/4} \sec ^2(e+f x)^{3/4}}-\frac{3 d^2 \left(a^2+2 b^2\right) (d \sec (e+f x))^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt[4]{\sec ^2(e+f x)}}{\sqrt[4]{a^2+b^2}}\right)}{8 b^{5/2} f \left(a^2+b^2\right)^{5/4} \sec ^2(e+f x)^{3/4}}+\frac{3 a d^2 (d \sec (e+f x))^{3/2}}{4 b f \left(a^2+b^2\right) (a+b \tan (e+f x))}-\frac{3 a d^2 \sin (e+f x) \cos (e+f x) (d \sec (e+f x))^{3/2}}{4 b^2 f \left(a^2+b^2\right)}+\frac{3 a d^2 (d \sec (e+f x))^{3/2} E\left(\left.\frac{1}{2} \tan ^{-1}(\tan (e+f x))\right|2\right)}{4 b^2 f \left(a^2+b^2\right) \sec ^2(e+f x)^{3/4}}-\frac{3 a d^2 \left(a^2+2 b^2\right) \sqrt{-\tan ^2(e+f x)} \cot (e+f x) (d \sec (e+f x))^{3/2} \Pi \left(-\frac{b}{\sqrt{a^2+b^2}};\left.\sin ^{-1}\left(\sqrt[4]{\sec ^2(e+f x)}\right)\right|-1\right)}{8 b^3 f \left(a^2+b^2\right)^{3/2} \sec ^2(e+f x)^{3/4}}+\frac{3 a d^2 \left(a^2+2 b^2\right) \sqrt{-\tan ^2(e+f x)} \cot (e+f x) (d \sec (e+f x))^{3/2} \Pi \left(\frac{b}{\sqrt{a^2+b^2}};\left.\sin ^{-1}\left(\sqrt[4]{\sec ^2(e+f x)}\right)\right|-1\right)}{8 b^3 f \left(a^2+b^2\right)^{3/2} \sec ^2(e+f x)^{3/4}}-\frac{d^2 (d \sec (e+f x))^{3/2}}{2 b f (a+b \tan (e+f x))^2}","\frac{3 d^2 \left(a^2+2 b^2\right) (d \sec (e+f x))^{3/2} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt[4]{\sec ^2(e+f x)}}{\sqrt[4]{a^2+b^2}}\right)}{8 b^{5/2} f \left(a^2+b^2\right)^{5/4} \sec ^2(e+f x)^{3/4}}-\frac{3 d^2 \left(a^2+2 b^2\right) (d \sec (e+f x))^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt[4]{\sec ^2(e+f x)}}{\sqrt[4]{a^2+b^2}}\right)}{8 b^{5/2} f \left(a^2+b^2\right)^{5/4} \sec ^2(e+f x)^{3/4}}+\frac{3 a d^2 (d \sec (e+f x))^{3/2}}{4 b f \left(a^2+b^2\right) (a+b \tan (e+f x))}-\frac{3 a d^2 \sin (e+f x) \cos (e+f x) (d \sec (e+f x))^{3/2}}{4 b^2 f \left(a^2+b^2\right)}+\frac{3 a d^2 (d \sec (e+f x))^{3/2} E\left(\left.\frac{1}{2} \tan ^{-1}(\tan (e+f x))\right|2\right)}{4 b^2 f \left(a^2+b^2\right) \sec ^2(e+f x)^{3/4}}-\frac{3 a d^2 \left(a^2+2 b^2\right) \sqrt{-\tan ^2(e+f x)} \cot (e+f x) (d \sec (e+f x))^{3/2} \Pi \left(-\frac{b}{\sqrt{a^2+b^2}};\left.\sin ^{-1}\left(\sqrt[4]{\sec ^2(e+f x)}\right)\right|-1\right)}{8 b^3 f \left(a^2+b^2\right)^{3/2} \sec ^2(e+f x)^{3/4}}+\frac{3 a d^2 \left(a^2+2 b^2\right) \sqrt{-\tan ^2(e+f x)} \cot (e+f x) (d \sec (e+f x))^{3/2} \Pi \left(\frac{b}{\sqrt{a^2+b^2}};\left.\sin ^{-1}\left(\sqrt[4]{\sec ^2(e+f x)}\right)\right|-1\right)}{8 b^3 f \left(a^2+b^2\right)^{3/2} \sec ^2(e+f x)^{3/4}}-\frac{d^2 (d \sec (e+f x))^{3/2}}{2 b f (a+b \tan (e+f x))^2}",1,"(3*(a^2 + 2*b^2)*d^2*ArcTan[(Sqrt[b]*(Sec[e + f*x]^2)^(1/4))/(a^2 + b^2)^(1/4)]*(d*Sec[e + f*x])^(3/2))/(8*b^(5/2)*(a^2 + b^2)^(5/4)*f*(Sec[e + f*x]^2)^(3/4)) - (3*(a^2 + 2*b^2)*d^2*ArcTanh[(Sqrt[b]*(Sec[e + f*x]^2)^(1/4))/(a^2 + b^2)^(1/4)]*(d*Sec[e + f*x])^(3/2))/(8*b^(5/2)*(a^2 + b^2)^(5/4)*f*(Sec[e + f*x]^2)^(3/4)) + (3*a*d^2*EllipticE[ArcTan[Tan[e + f*x]]/2, 2]*(d*Sec[e + f*x])^(3/2))/(4*b^2*(a^2 + b^2)*f*(Sec[e + f*x]^2)^(3/4)) - (3*a*d^2*Cos[e + f*x]*(d*Sec[e + f*x])^(3/2)*Sin[e + f*x])/(4*b^2*(a^2 + b^2)*f) - (3*a*(a^2 + 2*b^2)*d^2*Cot[e + f*x]*EllipticPi[-(b/Sqrt[a^2 + b^2]), ArcSin[(Sec[e + f*x]^2)^(1/4)], -1]*(d*Sec[e + f*x])^(3/2)*Sqrt[-Tan[e + f*x]^2])/(8*b^3*(a^2 + b^2)^(3/2)*f*(Sec[e + f*x]^2)^(3/4)) + (3*a*(a^2 + 2*b^2)*d^2*Cot[e + f*x]*EllipticPi[b/Sqrt[a^2 + b^2], ArcSin[(Sec[e + f*x]^2)^(1/4)], -1]*(d*Sec[e + f*x])^(3/2)*Sqrt[-Tan[e + f*x]^2])/(8*b^3*(a^2 + b^2)^(3/2)*f*(Sec[e + f*x]^2)^(3/4)) - (d^2*(d*Sec[e + f*x])^(3/2))/(2*b*f*(a + b*Tan[e + f*x])^2) + (3*a*d^2*(d*Sec[e + f*x])^(3/2))/(4*b*(a^2 + b^2)*f*(a + b*Tan[e + f*x]))","A",18,16,25,0.6400,1,"{3512, 733, 835, 844, 227, 196, 746, 399, 490, 1213, 537, 444, 63, 298, 205, 208}"
618,1,532,0,0.4975271,"\int \frac{(d \sec (e+f x))^{5/2}}{(a+b \tan (e+f x))^3} \, dx","Int[(d*Sec[e + f*x])^(5/2)/(a + b*Tan[e + f*x])^3,x]","\frac{d^2 \left(a^2-2 b^2\right) \sqrt{d \sec (e+f x)} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt[4]{\sec ^2(e+f x)}}{\sqrt[4]{a^2+b^2}}\right)}{8 b^{3/2} f \left(a^2+b^2\right)^{7/4} \sqrt[4]{\sec ^2(e+f x)}}+\frac{d^2 \left(a^2-2 b^2\right) \sqrt{d \sec (e+f x)} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt[4]{\sec ^2(e+f x)}}{\sqrt[4]{a^2+b^2}}\right)}{8 b^{3/2} f \left(a^2+b^2\right)^{7/4} \sqrt[4]{\sec ^2(e+f x)}}+\frac{a d^2 \sqrt{d \sec (e+f x)}}{4 b f \left(a^2+b^2\right) (a+b \tan (e+f x))}+\frac{a d^2 \sqrt{d \sec (e+f x)} F\left(\left.\frac{1}{2} \tan ^{-1}(\tan (e+f x))\right|2\right)}{4 b^2 f \left(a^2+b^2\right) \sqrt[4]{\sec ^2(e+f x)}}-\frac{a d^2 \left(a^2-2 b^2\right) \sqrt{-\tan ^2(e+f x)} \cot (e+f x) \sqrt{d \sec (e+f x)} \Pi \left(-\frac{b}{\sqrt{a^2+b^2}};\left.\sin ^{-1}\left(\sqrt[4]{\sec ^2(e+f x)}\right)\right|-1\right)}{8 b^2 f \left(a^2+b^2\right)^2 \sqrt[4]{\sec ^2(e+f x)}}-\frac{a d^2 \left(a^2-2 b^2\right) \sqrt{-\tan ^2(e+f x)} \cot (e+f x) \sqrt{d \sec (e+f x)} \Pi \left(\frac{b}{\sqrt{a^2+b^2}};\left.\sin ^{-1}\left(\sqrt[4]{\sec ^2(e+f x)}\right)\right|-1\right)}{8 b^2 f \left(a^2+b^2\right)^2 \sqrt[4]{\sec ^2(e+f x)}}-\frac{d^2 \sqrt{d \sec (e+f x)}}{2 b f (a+b \tan (e+f x))^2}","\frac{d^2 \left(a^2-2 b^2\right) \sqrt{d \sec (e+f x)} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt[4]{\sec ^2(e+f x)}}{\sqrt[4]{a^2+b^2}}\right)}{8 b^{3/2} f \left(a^2+b^2\right)^{7/4} \sqrt[4]{\sec ^2(e+f x)}}+\frac{d^2 \left(a^2-2 b^2\right) \sqrt{d \sec (e+f x)} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt[4]{\sec ^2(e+f x)}}{\sqrt[4]{a^2+b^2}}\right)}{8 b^{3/2} f \left(a^2+b^2\right)^{7/4} \sqrt[4]{\sec ^2(e+f x)}}+\frac{a d^2 \sqrt{d \sec (e+f x)}}{4 b f \left(a^2+b^2\right) (a+b \tan (e+f x))}+\frac{a d^2 \sqrt{d \sec (e+f x)} F\left(\left.\frac{1}{2} \tan ^{-1}(\tan (e+f x))\right|2\right)}{4 b^2 f \left(a^2+b^2\right) \sqrt[4]{\sec ^2(e+f x)}}-\frac{a d^2 \left(a^2-2 b^2\right) \sqrt{-\tan ^2(e+f x)} \cot (e+f x) \sqrt{d \sec (e+f x)} \Pi \left(-\frac{b}{\sqrt{a^2+b^2}};\left.\sin ^{-1}\left(\sqrt[4]{\sec ^2(e+f x)}\right)\right|-1\right)}{8 b^2 f \left(a^2+b^2\right)^2 \sqrt[4]{\sec ^2(e+f x)}}-\frac{a d^2 \left(a^2-2 b^2\right) \sqrt{-\tan ^2(e+f x)} \cot (e+f x) \sqrt{d \sec (e+f x)} \Pi \left(\frac{b}{\sqrt{a^2+b^2}};\left.\sin ^{-1}\left(\sqrt[4]{\sec ^2(e+f x)}\right)\right|-1\right)}{8 b^2 f \left(a^2+b^2\right)^2 \sqrt[4]{\sec ^2(e+f x)}}-\frac{d^2 \sqrt{d \sec (e+f x)}}{2 b f (a+b \tan (e+f x))^2}",1,"((a^2 - 2*b^2)*d^2*ArcTan[(Sqrt[b]*(Sec[e + f*x]^2)^(1/4))/(a^2 + b^2)^(1/4)]*Sqrt[d*Sec[e + f*x]])/(8*b^(3/2)*(a^2 + b^2)^(7/4)*f*(Sec[e + f*x]^2)^(1/4)) + ((a^2 - 2*b^2)*d^2*ArcTanh[(Sqrt[b]*(Sec[e + f*x]^2)^(1/4))/(a^2 + b^2)^(1/4)]*Sqrt[d*Sec[e + f*x]])/(8*b^(3/2)*(a^2 + b^2)^(7/4)*f*(Sec[e + f*x]^2)^(1/4)) + (a*d^2*EllipticF[ArcTan[Tan[e + f*x]]/2, 2]*Sqrt[d*Sec[e + f*x]])/(4*b^2*(a^2 + b^2)*f*(Sec[e + f*x]^2)^(1/4)) - (a*(a^2 - 2*b^2)*d^2*Cot[e + f*x]*EllipticPi[-(b/Sqrt[a^2 + b^2]), ArcSin[(Sec[e + f*x]^2)^(1/4)], -1]*Sqrt[d*Sec[e + f*x]]*Sqrt[-Tan[e + f*x]^2])/(8*b^2*(a^2 + b^2)^2*f*(Sec[e + f*x]^2)^(1/4)) - (a*(a^2 - 2*b^2)*d^2*Cot[e + f*x]*EllipticPi[b/Sqrt[a^2 + b^2], ArcSin[(Sec[e + f*x]^2)^(1/4)], -1]*Sqrt[d*Sec[e + f*x]]*Sqrt[-Tan[e + f*x]^2])/(8*b^2*(a^2 + b^2)^2*f*(Sec[e + f*x]^2)^(1/4)) - (d^2*Sqrt[d*Sec[e + f*x]])/(2*b*f*(a + b*Tan[e + f*x])^2) + (a*d^2*Sqrt[d*Sec[e + f*x]])/(4*b*(a^2 + b^2)*f*(a + b*Tan[e + f*x]))","A",18,16,25,0.6400,1,"{3512, 733, 835, 844, 231, 747, 401, 108, 409, 1213, 537, 444, 63, 212, 208, 205}"
619,1,566,0,0.5391624,"\int \frac{(d \sec (e+f x))^{3/2}}{(a+b \tan (e+f x))^3} \, dx","Int[(d*Sec[e + f*x])^(3/2)/(a + b*Tan[e + f*x])^3,x]","\frac{\left(3 a^2-2 b^2\right) (d \sec (e+f x))^{3/2} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt[4]{\sec ^2(e+f x)}}{\sqrt[4]{a^2+b^2}}\right)}{8 \sqrt{b} f \left(a^2+b^2\right)^{9/4} \sec ^2(e+f x)^{3/4}}-\frac{\left(3 a^2-2 b^2\right) (d \sec (e+f x))^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt[4]{\sec ^2(e+f x)}}{\sqrt[4]{a^2+b^2}}\right)}{8 \sqrt{b} f \left(a^2+b^2\right)^{9/4} \sec ^2(e+f x)^{3/4}}-\frac{5 a b (d \sec (e+f x))^{3/2}}{4 f \left(a^2+b^2\right)^2 (a+b \tan (e+f x))}-\frac{b (d \sec (e+f x))^{3/2}}{2 f \left(a^2+b^2\right) (a+b \tan (e+f x))^2}+\frac{5 a \sin (e+f x) \cos (e+f x) (d \sec (e+f x))^{3/2}}{4 f \left(a^2+b^2\right)^2}-\frac{5 a (d \sec (e+f x))^{3/2} E\left(\left.\frac{1}{2} \tan ^{-1}(\tan (e+f x))\right|2\right)}{4 f \left(a^2+b^2\right)^2 \sec ^2(e+f x)^{3/4}}-\frac{a \left(3 a^2-2 b^2\right) \sqrt{-\tan ^2(e+f x)} \cot (e+f x) (d \sec (e+f x))^{3/2} \Pi \left(-\frac{b}{\sqrt{a^2+b^2}};\left.\sin ^{-1}\left(\sqrt[4]{\sec ^2(e+f x)}\right)\right|-1\right)}{8 b f \left(a^2+b^2\right)^{5/2} \sec ^2(e+f x)^{3/4}}+\frac{a \left(3 a^2-2 b^2\right) \sqrt{-\tan ^2(e+f x)} \cot (e+f x) (d \sec (e+f x))^{3/2} \Pi \left(\frac{b}{\sqrt{a^2+b^2}};\left.\sin ^{-1}\left(\sqrt[4]{\sec ^2(e+f x)}\right)\right|-1\right)}{8 b f \left(a^2+b^2\right)^{5/2} \sec ^2(e+f x)^{3/4}}","\frac{\left(3 a^2-2 b^2\right) (d \sec (e+f x))^{3/2} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt[4]{\sec ^2(e+f x)}}{\sqrt[4]{a^2+b^2}}\right)}{8 \sqrt{b} f \left(a^2+b^2\right)^{9/4} \sec ^2(e+f x)^{3/4}}-\frac{\left(3 a^2-2 b^2\right) (d \sec (e+f x))^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt[4]{\sec ^2(e+f x)}}{\sqrt[4]{a^2+b^2}}\right)}{8 \sqrt{b} f \left(a^2+b^2\right)^{9/4} \sec ^2(e+f x)^{3/4}}-\frac{5 a b (d \sec (e+f x))^{3/2}}{4 f \left(a^2+b^2\right)^2 (a+b \tan (e+f x))}-\frac{b (d \sec (e+f x))^{3/2}}{2 f \left(a^2+b^2\right) (a+b \tan (e+f x))^2}+\frac{5 a \sin (e+f x) \cos (e+f x) (d \sec (e+f x))^{3/2}}{4 f \left(a^2+b^2\right)^2}-\frac{5 a (d \sec (e+f x))^{3/2} E\left(\left.\frac{1}{2} \tan ^{-1}(\tan (e+f x))\right|2\right)}{4 f \left(a^2+b^2\right)^2 \sec ^2(e+f x)^{3/4}}-\frac{a \left(3 a^2-2 b^2\right) \sqrt{-\tan ^2(e+f x)} \cot (e+f x) (d \sec (e+f x))^{3/2} \Pi \left(-\frac{b}{\sqrt{a^2+b^2}};\left.\sin ^{-1}\left(\sqrt[4]{\sec ^2(e+f x)}\right)\right|-1\right)}{8 b f \left(a^2+b^2\right)^{5/2} \sec ^2(e+f x)^{3/4}}+\frac{a \left(3 a^2-2 b^2\right) \sqrt{-\tan ^2(e+f x)} \cot (e+f x) (d \sec (e+f x))^{3/2} \Pi \left(\frac{b}{\sqrt{a^2+b^2}};\left.\sin ^{-1}\left(\sqrt[4]{\sec ^2(e+f x)}\right)\right|-1\right)}{8 b f \left(a^2+b^2\right)^{5/2} \sec ^2(e+f x)^{3/4}}",1,"((3*a^2 - 2*b^2)*ArcTan[(Sqrt[b]*(Sec[e + f*x]^2)^(1/4))/(a^2 + b^2)^(1/4)]*(d*Sec[e + f*x])^(3/2))/(8*Sqrt[b]*(a^2 + b^2)^(9/4)*f*(Sec[e + f*x]^2)^(3/4)) - ((3*a^2 - 2*b^2)*ArcTanh[(Sqrt[b]*(Sec[e + f*x]^2)^(1/4))/(a^2 + b^2)^(1/4)]*(d*Sec[e + f*x])^(3/2))/(8*Sqrt[b]*(a^2 + b^2)^(9/4)*f*(Sec[e + f*x]^2)^(3/4)) - (5*a*EllipticE[ArcTan[Tan[e + f*x]]/2, 2]*(d*Sec[e + f*x])^(3/2))/(4*(a^2 + b^2)^2*f*(Sec[e + f*x]^2)^(3/4)) + (5*a*Cos[e + f*x]*(d*Sec[e + f*x])^(3/2)*Sin[e + f*x])/(4*(a^2 + b^2)^2*f) - (a*(3*a^2 - 2*b^2)*Cot[e + f*x]*EllipticPi[-(b/Sqrt[a^2 + b^2]), ArcSin[(Sec[e + f*x]^2)^(1/4)], -1]*(d*Sec[e + f*x])^(3/2)*Sqrt[-Tan[e + f*x]^2])/(8*b*(a^2 + b^2)^(5/2)*f*(Sec[e + f*x]^2)^(3/4)) + (a*(3*a^2 - 2*b^2)*Cot[e + f*x]*EllipticPi[b/Sqrt[a^2 + b^2], ArcSin[(Sec[e + f*x]^2)^(1/4)], -1]*(d*Sec[e + f*x])^(3/2)*Sqrt[-Tan[e + f*x]^2])/(8*b*(a^2 + b^2)^(5/2)*f*(Sec[e + f*x]^2)^(3/4)) - (b*(d*Sec[e + f*x])^(3/2))/(2*(a^2 + b^2)*f*(a + b*Tan[e + f*x])^2) - (5*a*b*(d*Sec[e + f*x])^(3/2))/(4*(a^2 + b^2)^2*f*(a + b*Tan[e + f*x]))","A",18,16,25,0.6400,1,"{3512, 745, 835, 844, 227, 196, 746, 399, 490, 1213, 537, 444, 63, 298, 205, 208}"
620,1,515,0,0.5219281,"\int \frac{\sqrt{d \sec (e+f x)}}{(a+b \tan (e+f x))^3} \, dx","Int[Sqrt[d*Sec[e + f*x]]/(a + b*Tan[e + f*x])^3,x]","-\frac{3 \sqrt{b} \left(5 a^2-2 b^2\right) \sqrt{d \sec (e+f x)} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt[4]{\sec ^2(e+f x)}}{\sqrt[4]{a^2+b^2}}\right)}{8 f \left(a^2+b^2\right)^{11/4} \sqrt[4]{\sec ^2(e+f x)}}-\frac{3 \sqrt{b} \left(5 a^2-2 b^2\right) \sqrt{d \sec (e+f x)} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt[4]{\sec ^2(e+f x)}}{\sqrt[4]{a^2+b^2}}\right)}{8 f \left(a^2+b^2\right)^{11/4} \sqrt[4]{\sec ^2(e+f x)}}-\frac{7 a b \sqrt{d \sec (e+f x)}}{4 f \left(a^2+b^2\right)^2 (a+b \tan (e+f x))}-\frac{b \sqrt{d \sec (e+f x)}}{2 f \left(a^2+b^2\right) (a+b \tan (e+f x))^2}-\frac{7 a \sqrt{d \sec (e+f x)} F\left(\left.\frac{1}{2} \tan ^{-1}(\tan (e+f x))\right|2\right)}{4 f \left(a^2+b^2\right)^2 \sqrt[4]{\sec ^2(e+f x)}}+\frac{3 a \left(5 a^2-2 b^2\right) \sqrt{-\tan ^2(e+f x)} \cot (e+f x) \sqrt{d \sec (e+f x)} \Pi \left(-\frac{b}{\sqrt{a^2+b^2}};\left.\sin ^{-1}\left(\sqrt[4]{\sec ^2(e+f x)}\right)\right|-1\right)}{8 f \left(a^2+b^2\right)^3 \sqrt[4]{\sec ^2(e+f x)}}+\frac{3 a \left(5 a^2-2 b^2\right) \sqrt{-\tan ^2(e+f x)} \cot (e+f x) \sqrt{d \sec (e+f x)} \Pi \left(\frac{b}{\sqrt{a^2+b^2}};\left.\sin ^{-1}\left(\sqrt[4]{\sec ^2(e+f x)}\right)\right|-1\right)}{8 f \left(a^2+b^2\right)^3 \sqrt[4]{\sec ^2(e+f x)}}","-\frac{3 \sqrt{b} \left(5 a^2-2 b^2\right) \sqrt{d \sec (e+f x)} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt[4]{\sec ^2(e+f x)}}{\sqrt[4]{a^2+b^2}}\right)}{8 f \left(a^2+b^2\right)^{11/4} \sqrt[4]{\sec ^2(e+f x)}}-\frac{3 \sqrt{b} \left(5 a^2-2 b^2\right) \sqrt{d \sec (e+f x)} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt[4]{\sec ^2(e+f x)}}{\sqrt[4]{a^2+b^2}}\right)}{8 f \left(a^2+b^2\right)^{11/4} \sqrt[4]{\sec ^2(e+f x)}}-\frac{7 a b \sqrt{d \sec (e+f x)}}{4 f \left(a^2+b^2\right)^2 (a+b \tan (e+f x))}-\frac{b \sqrt{d \sec (e+f x)}}{2 f \left(a^2+b^2\right) (a+b \tan (e+f x))^2}-\frac{7 a \sqrt{d \sec (e+f x)} F\left(\left.\frac{1}{2} \tan ^{-1}(\tan (e+f x))\right|2\right)}{4 f \left(a^2+b^2\right)^2 \sqrt[4]{\sec ^2(e+f x)}}+\frac{3 a \left(5 a^2-2 b^2\right) \sqrt{-\tan ^2(e+f x)} \cot (e+f x) \sqrt{d \sec (e+f x)} \Pi \left(-\frac{b}{\sqrt{a^2+b^2}};\left.\sin ^{-1}\left(\sqrt[4]{\sec ^2(e+f x)}\right)\right|-1\right)}{8 f \left(a^2+b^2\right)^3 \sqrt[4]{\sec ^2(e+f x)}}+\frac{3 a \left(5 a^2-2 b^2\right) \sqrt{-\tan ^2(e+f x)} \cot (e+f x) \sqrt{d \sec (e+f x)} \Pi \left(\frac{b}{\sqrt{a^2+b^2}};\left.\sin ^{-1}\left(\sqrt[4]{\sec ^2(e+f x)}\right)\right|-1\right)}{8 f \left(a^2+b^2\right)^3 \sqrt[4]{\sec ^2(e+f x)}}",1,"(-3*Sqrt[b]*(5*a^2 - 2*b^2)*ArcTan[(Sqrt[b]*(Sec[e + f*x]^2)^(1/4))/(a^2 + b^2)^(1/4)]*Sqrt[d*Sec[e + f*x]])/(8*(a^2 + b^2)^(11/4)*f*(Sec[e + f*x]^2)^(1/4)) - (3*Sqrt[b]*(5*a^2 - 2*b^2)*ArcTanh[(Sqrt[b]*(Sec[e + f*x]^2)^(1/4))/(a^2 + b^2)^(1/4)]*Sqrt[d*Sec[e + f*x]])/(8*(a^2 + b^2)^(11/4)*f*(Sec[e + f*x]^2)^(1/4)) - (7*a*EllipticF[ArcTan[Tan[e + f*x]]/2, 2]*Sqrt[d*Sec[e + f*x]])/(4*(a^2 + b^2)^2*f*(Sec[e + f*x]^2)^(1/4)) + (3*a*(5*a^2 - 2*b^2)*Cot[e + f*x]*EllipticPi[-(b/Sqrt[a^2 + b^2]), ArcSin[(Sec[e + f*x]^2)^(1/4)], -1]*Sqrt[d*Sec[e + f*x]]*Sqrt[-Tan[e + f*x]^2])/(8*(a^2 + b^2)^3*f*(Sec[e + f*x]^2)^(1/4)) + (3*a*(5*a^2 - 2*b^2)*Cot[e + f*x]*EllipticPi[b/Sqrt[a^2 + b^2], ArcSin[(Sec[e + f*x]^2)^(1/4)], -1]*Sqrt[d*Sec[e + f*x]]*Sqrt[-Tan[e + f*x]^2])/(8*(a^2 + b^2)^3*f*(Sec[e + f*x]^2)^(1/4)) - (b*Sqrt[d*Sec[e + f*x]])/(2*(a^2 + b^2)*f*(a + b*Tan[e + f*x])^2) - (7*a*b*Sqrt[d*Sec[e + f*x]])/(4*(a^2 + b^2)^2*f*(a + b*Tan[e + f*x]))","A",18,16,25,0.6400,1,"{3512, 745, 835, 844, 231, 747, 401, 108, 409, 1213, 537, 444, 63, 212, 208, 205}"
621,1,664,0,0.7610363,"\int \frac{1}{\sqrt{d \sec (e+f x)} (a+b \tan (e+f x))^3} \, dx","Int[1/(Sqrt[d*Sec[e + f*x]]*(a + b*Tan[e + f*x])^3),x]","\frac{5 b^{3/2} \left(7 a^2-2 b^2\right) \sqrt[4]{\sec ^2(e+f x)} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt[4]{\sec ^2(e+f x)}}{\sqrt[4]{a^2+b^2}}\right)}{8 f \left(a^2+b^2\right)^{13/4} \sqrt{d \sec (e+f x)}}+\frac{a b \left(8 a^2-37 b^2\right) \sec ^2(e+f x)}{4 f \left(a^2+b^2\right)^3 \sqrt{d \sec (e+f x)} (a+b \tan (e+f x))}+\frac{b \left(4 a^2-5 b^2\right) \sec ^2(e+f x)}{2 f \left(a^2+b^2\right)^2 \sqrt{d \sec (e+f x)} (a+b \tan (e+f x))^2}-\frac{5 b^{3/2} \left(7 a^2-2 b^2\right) \sqrt[4]{\sec ^2(e+f x)} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt[4]{\sec ^2(e+f x)}}{\sqrt[4]{a^2+b^2}}\right)}{8 f \left(a^2+b^2\right)^{13/4} \sqrt{d \sec (e+f x)}}-\frac{a \left(8 a^2-37 b^2\right) \tan (e+f x)}{4 f \left(a^2+b^2\right)^3 \sqrt{d \sec (e+f x)}}+\frac{2 (a \tan (e+f x)+b)}{f \left(a^2+b^2\right) \sqrt{d \sec (e+f x)} (a+b \tan (e+f x))^2}+\frac{a \left(8 a^2-37 b^2\right) \sqrt[4]{\sec ^2(e+f x)} E\left(\left.\frac{1}{2} \tan ^{-1}(\tan (e+f x))\right|2\right)}{4 f \left(a^2+b^2\right)^3 \sqrt{d \sec (e+f x)}}-\frac{5 a b \left(7 a^2-2 b^2\right) \sqrt{-\tan ^2(e+f x)} \cot (e+f x) \sqrt[4]{\sec ^2(e+f x)} \Pi \left(-\frac{b}{\sqrt{a^2+b^2}};\left.\sin ^{-1}\left(\sqrt[4]{\sec ^2(e+f x)}\right)\right|-1\right)}{8 f \left(a^2+b^2\right)^{7/2} \sqrt{d \sec (e+f x)}}+\frac{5 a b \left(7 a^2-2 b^2\right) \sqrt{-\tan ^2(e+f x)} \cot (e+f x) \sqrt[4]{\sec ^2(e+f x)} \Pi \left(\frac{b}{\sqrt{a^2+b^2}};\left.\sin ^{-1}\left(\sqrt[4]{\sec ^2(e+f x)}\right)\right|-1\right)}{8 f \left(a^2+b^2\right)^{7/2} \sqrt{d \sec (e+f x)}}","\frac{5 b^{3/2} \left(7 a^2-2 b^2\right) \sqrt[4]{\sec ^2(e+f x)} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt[4]{\sec ^2(e+f x)}}{\sqrt[4]{a^2+b^2}}\right)}{8 f \left(a^2+b^2\right)^{13/4} \sqrt{d \sec (e+f x)}}+\frac{a b \left(8 a^2-37 b^2\right) \sec ^2(e+f x)}{4 f \left(a^2+b^2\right)^3 \sqrt{d \sec (e+f x)} (a+b \tan (e+f x))}+\frac{b \left(4 a^2-5 b^2\right) \sec ^2(e+f x)}{2 f \left(a^2+b^2\right)^2 \sqrt{d \sec (e+f x)} (a+b \tan (e+f x))^2}-\frac{5 b^{3/2} \left(7 a^2-2 b^2\right) \sqrt[4]{\sec ^2(e+f x)} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt[4]{\sec ^2(e+f x)}}{\sqrt[4]{a^2+b^2}}\right)}{8 f \left(a^2+b^2\right)^{13/4} \sqrt{d \sec (e+f x)}}-\frac{a \left(8 a^2-37 b^2\right) \tan (e+f x)}{4 f \left(a^2+b^2\right)^3 \sqrt{d \sec (e+f x)}}+\frac{2 (a \tan (e+f x)+b)}{f \left(a^2+b^2\right) \sqrt{d \sec (e+f x)} (a+b \tan (e+f x))^2}+\frac{a \left(8 a^2-37 b^2\right) \sqrt[4]{\sec ^2(e+f x)} E\left(\left.\frac{1}{2} \tan ^{-1}(\tan (e+f x))\right|2\right)}{4 f \left(a^2+b^2\right)^3 \sqrt{d \sec (e+f x)}}-\frac{5 a b \left(7 a^2-2 b^2\right) \sqrt{-\tan ^2(e+f x)} \cot (e+f x) \sqrt[4]{\sec ^2(e+f x)} \Pi \left(-\frac{b}{\sqrt{a^2+b^2}};\left.\sin ^{-1}\left(\sqrt[4]{\sec ^2(e+f x)}\right)\right|-1\right)}{8 f \left(a^2+b^2\right)^{7/2} \sqrt{d \sec (e+f x)}}+\frac{5 a b \left(7 a^2-2 b^2\right) \sqrt{-\tan ^2(e+f x)} \cot (e+f x) \sqrt[4]{\sec ^2(e+f x)} \Pi \left(\frac{b}{\sqrt{a^2+b^2}};\left.\sin ^{-1}\left(\sqrt[4]{\sec ^2(e+f x)}\right)\right|-1\right)}{8 f \left(a^2+b^2\right)^{7/2} \sqrt{d \sec (e+f x)}}",1,"(5*b^(3/2)*(7*a^2 - 2*b^2)*ArcTan[(Sqrt[b]*(Sec[e + f*x]^2)^(1/4))/(a^2 + b^2)^(1/4)]*(Sec[e + f*x]^2)^(1/4))/(8*(a^2 + b^2)^(13/4)*f*Sqrt[d*Sec[e + f*x]]) - (5*b^(3/2)*(7*a^2 - 2*b^2)*ArcTanh[(Sqrt[b]*(Sec[e + f*x]^2)^(1/4))/(a^2 + b^2)^(1/4)]*(Sec[e + f*x]^2)^(1/4))/(8*(a^2 + b^2)^(13/4)*f*Sqrt[d*Sec[e + f*x]]) + (a*(8*a^2 - 37*b^2)*EllipticE[ArcTan[Tan[e + f*x]]/2, 2]*(Sec[e + f*x]^2)^(1/4))/(4*(a^2 + b^2)^3*f*Sqrt[d*Sec[e + f*x]]) - (a*(8*a^2 - 37*b^2)*Tan[e + f*x])/(4*(a^2 + b^2)^3*f*Sqrt[d*Sec[e + f*x]]) - (5*a*b*(7*a^2 - 2*b^2)*Cot[e + f*x]*EllipticPi[-(b/Sqrt[a^2 + b^2]), ArcSin[(Sec[e + f*x]^2)^(1/4)], -1]*(Sec[e + f*x]^2)^(1/4)*Sqrt[-Tan[e + f*x]^2])/(8*(a^2 + b^2)^(7/2)*f*Sqrt[d*Sec[e + f*x]]) + (5*a*b*(7*a^2 - 2*b^2)*Cot[e + f*x]*EllipticPi[b/Sqrt[a^2 + b^2], ArcSin[(Sec[e + f*x]^2)^(1/4)], -1]*(Sec[e + f*x]^2)^(1/4)*Sqrt[-Tan[e + f*x]^2])/(8*(a^2 + b^2)^(7/2)*f*Sqrt[d*Sec[e + f*x]]) + (b*(4*a^2 - 5*b^2)*Sec[e + f*x]^2)/(2*(a^2 + b^2)^2*f*Sqrt[d*Sec[e + f*x]]*(a + b*Tan[e + f*x])^2) + (2*(b + a*Tan[e + f*x]))/((a^2 + b^2)*f*Sqrt[d*Sec[e + f*x]]*(a + b*Tan[e + f*x])^2) + (a*b*(8*a^2 - 37*b^2)*Sec[e + f*x]^2)/(4*(a^2 + b^2)^3*f*Sqrt[d*Sec[e + f*x]]*(a + b*Tan[e + f*x]))","A",19,16,25,0.6400,1,"{3512, 741, 835, 844, 227, 196, 746, 399, 490, 1213, 537, 444, 63, 298, 205, 208}"
622,1,620,0,0.7586692,"\int \frac{1}{(d \sec (e+f x))^{3/2} (a+b \tan (e+f x))^3} \, dx","Int[1/((d*Sec[e + f*x])^(3/2)*(a + b*Tan[e + f*x])^3),x]","-\frac{7 b^{5/2} \left(9 a^2-2 b^2\right) \sec ^2(e+f x)^{3/4} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt[4]{\sec ^2(e+f x)}}{\sqrt[4]{a^2+b^2}}\right)}{8 f \left(a^2+b^2\right)^{15/4} (d \sec (e+f x))^{3/2}}+\frac{a b \left(8 a^2-69 b^2\right) \sec ^2(e+f x)}{12 f \left(a^2+b^2\right)^3 (d \sec (e+f x))^{3/2} (a+b \tan (e+f x))}+\frac{b \left(4 a^2-7 b^2\right) \sec ^2(e+f x)}{6 f \left(a^2+b^2\right)^2 (d \sec (e+f x))^{3/2} (a+b \tan (e+f x))^2}-\frac{7 b^{5/2} \left(9 a^2-2 b^2\right) \sec ^2(e+f x)^{3/4} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt[4]{\sec ^2(e+f x)}}{\sqrt[4]{a^2+b^2}}\right)}{8 f \left(a^2+b^2\right)^{15/4} (d \sec (e+f x))^{3/2}}+\frac{2 (a \tan (e+f x)+b)}{3 f \left(a^2+b^2\right) (d \sec (e+f x))^{3/2} (a+b \tan (e+f x))^2}+\frac{a \left(8 a^2-69 b^2\right) \sec ^2(e+f x)^{3/4} F\left(\left.\frac{1}{2} \tan ^{-1}(\tan (e+f x))\right|2\right)}{12 f \left(a^2+b^2\right)^3 (d \sec (e+f x))^{3/2}}+\frac{7 a b^2 \left(9 a^2-2 b^2\right) \sqrt{-\tan ^2(e+f x)} \cot (e+f x) \sec ^2(e+f x)^{3/4} \Pi \left(-\frac{b}{\sqrt{a^2+b^2}};\left.\sin ^{-1}\left(\sqrt[4]{\sec ^2(e+f x)}\right)\right|-1\right)}{8 f \left(a^2+b^2\right)^4 (d \sec (e+f x))^{3/2}}+\frac{7 a b^2 \left(9 a^2-2 b^2\right) \sqrt{-\tan ^2(e+f x)} \cot (e+f x) \sec ^2(e+f x)^{3/4} \Pi \left(\frac{b}{\sqrt{a^2+b^2}};\left.\sin ^{-1}\left(\sqrt[4]{\sec ^2(e+f x)}\right)\right|-1\right)}{8 f \left(a^2+b^2\right)^4 (d \sec (e+f x))^{3/2}}","-\frac{7 b^{5/2} \left(9 a^2-2 b^2\right) \sec ^2(e+f x)^{3/4} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt[4]{\sec ^2(e+f x)}}{\sqrt[4]{a^2+b^2}}\right)}{8 f \left(a^2+b^2\right)^{15/4} (d \sec (e+f x))^{3/2}}+\frac{a b \left(8 a^2-69 b^2\right) \sec ^2(e+f x)}{12 f \left(a^2+b^2\right)^3 (d \sec (e+f x))^{3/2} (a+b \tan (e+f x))}+\frac{b \left(4 a^2-7 b^2\right) \sec ^2(e+f x)}{6 f \left(a^2+b^2\right)^2 (d \sec (e+f x))^{3/2} (a+b \tan (e+f x))^2}-\frac{7 b^{5/2} \left(9 a^2-2 b^2\right) \sec ^2(e+f x)^{3/4} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt[4]{\sec ^2(e+f x)}}{\sqrt[4]{a^2+b^2}}\right)}{8 f \left(a^2+b^2\right)^{15/4} (d \sec (e+f x))^{3/2}}+\frac{2 (a \tan (e+f x)+b)}{3 f \left(a^2+b^2\right) (d \sec (e+f x))^{3/2} (a+b \tan (e+f x))^2}+\frac{a \left(8 a^2-69 b^2\right) \sec ^2(e+f x)^{3/4} F\left(\left.\frac{1}{2} \tan ^{-1}(\tan (e+f x))\right|2\right)}{12 f \left(a^2+b^2\right)^3 (d \sec (e+f x))^{3/2}}+\frac{7 a b^2 \left(9 a^2-2 b^2\right) \sqrt{-\tan ^2(e+f x)} \cot (e+f x) \sec ^2(e+f x)^{3/4} \Pi \left(-\frac{b}{\sqrt{a^2+b^2}};\left.\sin ^{-1}\left(\sqrt[4]{\sec ^2(e+f x)}\right)\right|-1\right)}{8 f \left(a^2+b^2\right)^4 (d \sec (e+f x))^{3/2}}+\frac{7 a b^2 \left(9 a^2-2 b^2\right) \sqrt{-\tan ^2(e+f x)} \cot (e+f x) \sec ^2(e+f x)^{3/4} \Pi \left(\frac{b}{\sqrt{a^2+b^2}};\left.\sin ^{-1}\left(\sqrt[4]{\sec ^2(e+f x)}\right)\right|-1\right)}{8 f \left(a^2+b^2\right)^4 (d \sec (e+f x))^{3/2}}",1,"(-7*b^(5/2)*(9*a^2 - 2*b^2)*ArcTan[(Sqrt[b]*(Sec[e + f*x]^2)^(1/4))/(a^2 + b^2)^(1/4)]*(Sec[e + f*x]^2)^(3/4))/(8*(a^2 + b^2)^(15/4)*f*(d*Sec[e + f*x])^(3/2)) - (7*b^(5/2)*(9*a^2 - 2*b^2)*ArcTanh[(Sqrt[b]*(Sec[e + f*x]^2)^(1/4))/(a^2 + b^2)^(1/4)]*(Sec[e + f*x]^2)^(3/4))/(8*(a^2 + b^2)^(15/4)*f*(d*Sec[e + f*x])^(3/2)) + (a*(8*a^2 - 69*b^2)*EllipticF[ArcTan[Tan[e + f*x]]/2, 2]*(Sec[e + f*x]^2)^(3/4))/(12*(a^2 + b^2)^3*f*(d*Sec[e + f*x])^(3/2)) + (7*a*b^2*(9*a^2 - 2*b^2)*Cot[e + f*x]*EllipticPi[-(b/Sqrt[a^2 + b^2]), ArcSin[(Sec[e + f*x]^2)^(1/4)], -1]*(Sec[e + f*x]^2)^(3/4)*Sqrt[-Tan[e + f*x]^2])/(8*(a^2 + b^2)^4*f*(d*Sec[e + f*x])^(3/2)) + (7*a*b^2*(9*a^2 - 2*b^2)*Cot[e + f*x]*EllipticPi[b/Sqrt[a^2 + b^2], ArcSin[(Sec[e + f*x]^2)^(1/4)], -1]*(Sec[e + f*x]^2)^(3/4)*Sqrt[-Tan[e + f*x]^2])/(8*(a^2 + b^2)^4*f*(d*Sec[e + f*x])^(3/2)) + (b*(4*a^2 - 7*b^2)*Sec[e + f*x]^2)/(6*(a^2 + b^2)^2*f*(d*Sec[e + f*x])^(3/2)*(a + b*Tan[e + f*x])^2) + (2*(b + a*Tan[e + f*x]))/(3*(a^2 + b^2)*f*(d*Sec[e + f*x])^(3/2)*(a + b*Tan[e + f*x])^2) + (a*b*(8*a^2 - 69*b^2)*Sec[e + f*x]^2)/(12*(a^2 + b^2)^3*f*(d*Sec[e + f*x])^(3/2)*(a + b*Tan[e + f*x]))","A",19,16,25,0.6400,1,"{3512, 741, 835, 844, 231, 747, 401, 108, 409, 1213, 537, 444, 63, 212, 208, 205}"
623,1,814,0,0.9153025,"\int \frac{1}{(d \sec (e+f x))^{5/2} (a+b \tan (e+f x))^3} \, dx","Int[1/((d*Sec[e + f*x])^(5/2)*(a + b*Tan[e + f*x])^3),x]","\frac{9 \left(11 a^2-2 b^2\right) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt[4]{\sec ^2(e+f x)}}{\sqrt[4]{a^2+b^2}}\right) \sqrt[4]{\sec ^2(e+f x)} b^{7/2}}{8 \left(a^2+b^2\right)^{17/4} d^2 f \sqrt{d \sec (e+f x)}}-\frac{9 \left(11 a^2-2 b^2\right) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt[4]{\sec ^2(e+f x)}}{\sqrt[4]{a^2+b^2}}\right) \sqrt[4]{\sec ^2(e+f x)} b^{7/2}}{8 \left(a^2+b^2\right)^{17/4} d^2 f \sqrt{d \sec (e+f x)}}-\frac{9 a \left(11 a^2-2 b^2\right) \cot (e+f x) \Pi \left(-\frac{b}{\sqrt{a^2+b^2}};\left.\sin ^{-1}\left(\sqrt[4]{\sec ^2(e+f x)}\right)\right|-1\right) \sqrt[4]{\sec ^2(e+f x)} \sqrt{-\tan ^2(e+f x)} b^3}{8 \left(a^2+b^2\right)^{9/2} d^2 f \sqrt{d \sec (e+f x)}}+\frac{9 a \left(11 a^2-2 b^2\right) \cot (e+f x) \Pi \left(\frac{b}{\sqrt{a^2+b^2}};\left.\sin ^{-1}\left(\sqrt[4]{\sec ^2(e+f x)}\right)\right|-1\right) \sqrt[4]{\sec ^2(e+f x)} \sqrt{-\tan ^2(e+f x)} b^3}{8 \left(a^2+b^2\right)^{9/2} d^2 f \sqrt{d \sec (e+f x)}}+\frac{3 a \left(8 a^4+64 b^2 a^2-139 b^4\right) \sec ^2(e+f x) b}{20 \left(a^2+b^2\right)^4 d^2 f \sqrt{d \sec (e+f x)} (a+b \tan (e+f x))}+\frac{3 \left(4 a^4+28 b^2 a^2-15 b^4\right) \sec ^2(e+f x) b}{10 \left(a^2+b^2\right)^3 d^2 f \sqrt{d \sec (e+f x)} (a+b \tan (e+f x))^2}-\frac{3 a \left(8 a^4+64 b^2 a^2-139 b^4\right) \tan (e+f x)}{20 \left(a^2+b^2\right)^4 d^2 f \sqrt{d \sec (e+f x)}}-\frac{2 \left(b \left(4 a^2-9 b^2\right)-a \left(3 a^2+16 b^2\right) \tan (e+f x)\right)}{5 \left(a^2+b^2\right)^2 d^2 f \sqrt{d \sec (e+f x)} (a+b \tan (e+f x))^2}+\frac{3 a \left(8 a^4+64 b^2 a^2-139 b^4\right) E\left(\left.\frac{1}{2} \tan ^{-1}(\tan (e+f x))\right|2\right) \sqrt[4]{\sec ^2(e+f x)}}{20 \left(a^2+b^2\right)^4 d^2 f \sqrt{d \sec (e+f x)}}+\frac{2 \cos ^2(e+f x) (b+a \tan (e+f x))}{5 \left(a^2+b^2\right) d^2 f \sqrt{d \sec (e+f x)} (a+b \tan (e+f x))^2}","\frac{9 \left(11 a^2-2 b^2\right) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt[4]{\sec ^2(e+f x)}}{\sqrt[4]{a^2+b^2}}\right) \sqrt[4]{\sec ^2(e+f x)} b^{7/2}}{8 \left(a^2+b^2\right)^{17/4} d^2 f \sqrt{d \sec (e+f x)}}-\frac{9 \left(11 a^2-2 b^2\right) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt[4]{\sec ^2(e+f x)}}{\sqrt[4]{a^2+b^2}}\right) \sqrt[4]{\sec ^2(e+f x)} b^{7/2}}{8 \left(a^2+b^2\right)^{17/4} d^2 f \sqrt{d \sec (e+f x)}}-\frac{9 a \left(11 a^2-2 b^2\right) \cot (e+f x) \Pi \left(-\frac{b}{\sqrt{a^2+b^2}};\left.\sin ^{-1}\left(\sqrt[4]{\sec ^2(e+f x)}\right)\right|-1\right) \sqrt[4]{\sec ^2(e+f x)} \sqrt{-\tan ^2(e+f x)} b^3}{8 \left(a^2+b^2\right)^{9/2} d^2 f \sqrt{d \sec (e+f x)}}+\frac{9 a \left(11 a^2-2 b^2\right) \cot (e+f x) \Pi \left(\frac{b}{\sqrt{a^2+b^2}};\left.\sin ^{-1}\left(\sqrt[4]{\sec ^2(e+f x)}\right)\right|-1\right) \sqrt[4]{\sec ^2(e+f x)} \sqrt{-\tan ^2(e+f x)} b^3}{8 \left(a^2+b^2\right)^{9/2} d^2 f \sqrt{d \sec (e+f x)}}+\frac{3 a \left(8 a^4+64 b^2 a^2-139 b^4\right) \sec ^2(e+f x) b}{20 \left(a^2+b^2\right)^4 d^2 f \sqrt{d \sec (e+f x)} (a+b \tan (e+f x))}+\frac{3 \left(4 a^4+28 b^2 a^2-15 b^4\right) \sec ^2(e+f x) b}{10 \left(a^2+b^2\right)^3 d^2 f \sqrt{d \sec (e+f x)} (a+b \tan (e+f x))^2}-\frac{3 a \left(8 a^4+64 b^2 a^2-139 b^4\right) \tan (e+f x)}{20 \left(a^2+b^2\right)^4 d^2 f \sqrt{d \sec (e+f x)}}-\frac{2 \left(b \left(4 a^2-9 b^2\right)-a \left(3 a^2+16 b^2\right) \tan (e+f x)\right)}{5 \left(a^2+b^2\right)^2 d^2 f \sqrt{d \sec (e+f x)} (a+b \tan (e+f x))^2}+\frac{3 a \left(8 a^4+64 b^2 a^2-139 b^4\right) E\left(\left.\frac{1}{2} \tan ^{-1}(\tan (e+f x))\right|2\right) \sqrt[4]{\sec ^2(e+f x)}}{20 \left(a^2+b^2\right)^4 d^2 f \sqrt{d \sec (e+f x)}}+\frac{2 \cos ^2(e+f x) (b+a \tan (e+f x))}{5 \left(a^2+b^2\right) d^2 f \sqrt{d \sec (e+f x)} (a+b \tan (e+f x))^2}",1,"(9*b^(7/2)*(11*a^2 - 2*b^2)*ArcTan[(Sqrt[b]*(Sec[e + f*x]^2)^(1/4))/(a^2 + b^2)^(1/4)]*(Sec[e + f*x]^2)^(1/4))/(8*(a^2 + b^2)^(17/4)*d^2*f*Sqrt[d*Sec[e + f*x]]) - (9*b^(7/2)*(11*a^2 - 2*b^2)*ArcTanh[(Sqrt[b]*(Sec[e + f*x]^2)^(1/4))/(a^2 + b^2)^(1/4)]*(Sec[e + f*x]^2)^(1/4))/(8*(a^2 + b^2)^(17/4)*d^2*f*Sqrt[d*Sec[e + f*x]]) + (3*a*(8*a^4 + 64*a^2*b^2 - 139*b^4)*EllipticE[ArcTan[Tan[e + f*x]]/2, 2]*(Sec[e + f*x]^2)^(1/4))/(20*(a^2 + b^2)^4*d^2*f*Sqrt[d*Sec[e + f*x]]) - (3*a*(8*a^4 + 64*a^2*b^2 - 139*b^4)*Tan[e + f*x])/(20*(a^2 + b^2)^4*d^2*f*Sqrt[d*Sec[e + f*x]]) - (9*a*b^3*(11*a^2 - 2*b^2)*Cot[e + f*x]*EllipticPi[-(b/Sqrt[a^2 + b^2]), ArcSin[(Sec[e + f*x]^2)^(1/4)], -1]*(Sec[e + f*x]^2)^(1/4)*Sqrt[-Tan[e + f*x]^2])/(8*(a^2 + b^2)^(9/2)*d^2*f*Sqrt[d*Sec[e + f*x]]) + (9*a*b^3*(11*a^2 - 2*b^2)*Cot[e + f*x]*EllipticPi[b/Sqrt[a^2 + b^2], ArcSin[(Sec[e + f*x]^2)^(1/4)], -1]*(Sec[e + f*x]^2)^(1/4)*Sqrt[-Tan[e + f*x]^2])/(8*(a^2 + b^2)^(9/2)*d^2*f*Sqrt[d*Sec[e + f*x]]) + (3*b*(4*a^4 + 28*a^2*b^2 - 15*b^4)*Sec[e + f*x]^2)/(10*(a^2 + b^2)^3*d^2*f*Sqrt[d*Sec[e + f*x]]*(a + b*Tan[e + f*x])^2) + (2*Cos[e + f*x]^2*(b + a*Tan[e + f*x]))/(5*(a^2 + b^2)*d^2*f*Sqrt[d*Sec[e + f*x]]*(a + b*Tan[e + f*x])^2) + (3*a*b*(8*a^4 + 64*a^2*b^2 - 139*b^4)*Sec[e + f*x]^2)/(20*(a^2 + b^2)^4*d^2*f*Sqrt[d*Sec[e + f*x]]*(a + b*Tan[e + f*x])) - (2*(b*(4*a^2 - 9*b^2) - a*(3*a^2 + 16*b^2)*Tan[e + f*x]))/(5*(a^2 + b^2)^2*d^2*f*Sqrt[d*Sec[e + f*x]]*(a + b*Tan[e + f*x])^2)","A",20,17,25,0.6800,1,"{3512, 741, 823, 835, 844, 227, 196, 746, 399, 490, 1213, 537, 444, 63, 298, 205, 208}"
624,1,78,0,0.0642202,"\int (d \sec (e+f x))^{5/3} (a+b \tan (e+f x)) \, dx","Int[(d*Sec[e + f*x])^(5/3)*(a + b*Tan[e + f*x]),x]","\frac{3 a d \sin (e+f x) (d \sec (e+f x))^{2/3} \text{Hypergeometric2F1}\left(-\frac{1}{3},\frac{1}{2},\frac{2}{3},\cos ^2(e+f x)\right)}{2 f \sqrt{\sin ^2(e+f x)}}+\frac{3 b (d \sec (e+f x))^{5/3}}{5 f}","\frac{3 a d \sin (e+f x) (d \sec (e+f x))^{2/3} \text{Hypergeometric2F1}\left(-\frac{1}{3},\frac{1}{2},\frac{2}{3},\cos ^2(e+f x)\right)}{2 f \sqrt{\sin ^2(e+f x)}}+\frac{3 b (d \sec (e+f x))^{5/3}}{5 f}",1,"(3*b*(d*Sec[e + f*x])^(5/3))/(5*f) + (3*a*d*Hypergeometric2F1[-1/3, 1/2, 2/3, Cos[e + f*x]^2]*(d*Sec[e + f*x])^(2/3)*Sin[e + f*x])/(2*f*Sqrt[Sin[e + f*x]^2])","A",3,3,23,0.1304,1,"{3486, 3772, 2643}"
625,1,76,0,0.0598606,"\int \sqrt[3]{d \sec (e+f x)} (a+b \tan (e+f x)) \, dx","Int[(d*Sec[e + f*x])^(1/3)*(a + b*Tan[e + f*x]),x]","\frac{3 b \sqrt[3]{d \sec (e+f x)}}{f}-\frac{3 a d \sin (e+f x) \text{Hypergeometric2F1}\left(\frac{1}{3},\frac{1}{2},\frac{4}{3},\cos ^2(e+f x)\right)}{2 f \sqrt{\sin ^2(e+f x)} (d \sec (e+f x))^{2/3}}","\frac{3 b \sqrt[3]{d \sec (e+f x)}}{f}-\frac{3 a d \sin (e+f x) \text{Hypergeometric2F1}\left(\frac{1}{3},\frac{1}{2},\frac{4}{3},\cos ^2(e+f x)\right)}{2 f \sqrt{\sin ^2(e+f x)} (d \sec (e+f x))^{2/3}}",1,"(3*b*(d*Sec[e + f*x])^(1/3))/f - (3*a*d*Hypergeometric2F1[1/3, 1/2, 4/3, Cos[e + f*x]^2]*Sin[e + f*x])/(2*f*(d*Sec[e + f*x])^(2/3)*Sqrt[Sin[e + f*x]^2])","A",3,3,23,0.1304,1,"{3486, 3772, 2643}"
626,1,76,0,0.0598214,"\int \frac{a+b \tan (e+f x)}{\sqrt[3]{d \sec (e+f x)}} \, dx","Int[(a + b*Tan[e + f*x])/(d*Sec[e + f*x])^(1/3),x]","-\frac{3 a d \sin (e+f x) \text{Hypergeometric2F1}\left(\frac{1}{2},\frac{2}{3},\frac{5}{3},\cos ^2(e+f x)\right)}{4 f \sqrt{\sin ^2(e+f x)} (d \sec (e+f x))^{4/3}}-\frac{3 b}{f \sqrt[3]{d \sec (e+f x)}}","-\frac{3 a d \sin (e+f x) \text{Hypergeometric2F1}\left(\frac{1}{2},\frac{2}{3},\frac{5}{3},\cos ^2(e+f x)\right)}{4 f \sqrt{\sin ^2(e+f x)} (d \sec (e+f x))^{4/3}}-\frac{3 b}{f \sqrt[3]{d \sec (e+f x)}}",1,"(-3*b)/(f*(d*Sec[e + f*x])^(1/3)) - (3*a*d*Hypergeometric2F1[1/2, 2/3, 5/3, Cos[e + f*x]^2]*Sin[e + f*x])/(4*f*(d*Sec[e + f*x])^(4/3)*Sqrt[Sin[e + f*x]^2])","A",3,3,23,0.1304,1,"{3486, 3772, 2643}"
627,1,78,0,0.0639063,"\int \frac{a+b \tan (e+f x)}{(d \sec (e+f x))^{5/3}} \, dx","Int[(a + b*Tan[e + f*x])/(d*Sec[e + f*x])^(5/3),x]","-\frac{3 a d \sin (e+f x) \text{Hypergeometric2F1}\left(\frac{1}{2},\frac{4}{3},\frac{7}{3},\cos ^2(e+f x)\right)}{8 f \sqrt{\sin ^2(e+f x)} (d \sec (e+f x))^{8/3}}-\frac{3 b}{5 f (d \sec (e+f x))^{5/3}}","-\frac{3 a d \sin (e+f x) \text{Hypergeometric2F1}\left(\frac{1}{2},\frac{4}{3},\frac{7}{3},\cos ^2(e+f x)\right)}{8 f \sqrt{\sin ^2(e+f x)} (d \sec (e+f x))^{8/3}}-\frac{3 b}{5 f (d \sec (e+f x))^{5/3}}",1,"(-3*b)/(5*f*(d*Sec[e + f*x])^(5/3)) - (3*a*d*Hypergeometric2F1[1/2, 4/3, 7/3, Cos[e + f*x]^2]*Sin[e + f*x])/(8*f*(d*Sec[e + f*x])^(8/3)*Sqrt[Sin[e + f*x]^2])","A",3,3,23,0.1304,1,"{3486, 3772, 2643}"
628,1,119,0,0.1523438,"\int (d \sec (e+f x))^{5/3} (a+b \tan (e+f x))^2 \, dx","Int[(d*Sec[e + f*x])^(5/3)*(a + b*Tan[e + f*x])^2,x]","\frac{3 d \left(8 a^2-3 b^2\right) \sin (e+f x) (d \sec (e+f x))^{2/3} \text{Hypergeometric2F1}\left(-\frac{1}{3},\frac{1}{2},\frac{2}{3},\cos ^2(e+f x)\right)}{16 f \sqrt{\sin ^2(e+f x)}}+\frac{33 a b (d \sec (e+f x))^{5/3}}{40 f}+\frac{3 b (d \sec (e+f x))^{5/3} (a+b \tan (e+f x))}{8 f}","\frac{3 d \left(8 a^2-3 b^2\right) \sin (e+f x) (d \sec (e+f x))^{2/3} \text{Hypergeometric2F1}\left(-\frac{1}{3},\frac{1}{2},\frac{2}{3},\cos ^2(e+f x)\right)}{16 f \sqrt{\sin ^2(e+f x)}}+\frac{33 a b (d \sec (e+f x))^{5/3}}{40 f}+\frac{3 b (d \sec (e+f x))^{5/3} (a+b \tan (e+f x))}{8 f}",1,"(33*a*b*(d*Sec[e + f*x])^(5/3))/(40*f) + (3*(8*a^2 - 3*b^2)*d*Hypergeometric2F1[-1/3, 1/2, 2/3, Cos[e + f*x]^2]*(d*Sec[e + f*x])^(2/3)*Sin[e + f*x])/(16*f*Sqrt[Sin[e + f*x]^2]) + (3*b*(d*Sec[e + f*x])^(5/3)*(a + b*Tan[e + f*x]))/(8*f)","A",4,4,25,0.1600,1,"{3508, 3486, 3772, 2643}"
629,1,119,0,0.1363988,"\int \sqrt[3]{d \sec (e+f x)} (a+b \tan (e+f x))^2 \, dx","Int[(d*Sec[e + f*x])^(1/3)*(a + b*Tan[e + f*x])^2,x]","-\frac{3 d \left(4 a^2-3 b^2\right) \sin (e+f x) \text{Hypergeometric2F1}\left(\frac{1}{3},\frac{1}{2},\frac{4}{3},\cos ^2(e+f x)\right)}{8 f \sqrt{\sin ^2(e+f x)} (d \sec (e+f x))^{2/3}}+\frac{21 a b \sqrt[3]{d \sec (e+f x)}}{4 f}+\frac{3 b \sqrt[3]{d \sec (e+f x)} (a+b \tan (e+f x))}{4 f}","-\frac{3 d \left(4 a^2-3 b^2\right) \sin (e+f x) \text{Hypergeometric2F1}\left(\frac{1}{3},\frac{1}{2},\frac{4}{3},\cos ^2(e+f x)\right)}{8 f \sqrt{\sin ^2(e+f x)} (d \sec (e+f x))^{2/3}}+\frac{21 a b \sqrt[3]{d \sec (e+f x)}}{4 f}+\frac{3 b \sqrt[3]{d \sec (e+f x)} (a+b \tan (e+f x))}{4 f}",1,"(21*a*b*(d*Sec[e + f*x])^(1/3))/(4*f) - (3*(4*a^2 - 3*b^2)*d*Hypergeometric2F1[1/3, 1/2, 4/3, Cos[e + f*x]^2]*Sin[e + f*x])/(8*f*(d*Sec[e + f*x])^(2/3)*Sqrt[Sin[e + f*x]^2]) + (3*b*(d*Sec[e + f*x])^(1/3)*(a + b*Tan[e + f*x]))/(4*f)","A",4,4,25,0.1600,1,"{3508, 3486, 3772, 2643}"
630,1,119,0,0.1428239,"\int \frac{(a+b \tan (e+f x))^2}{\sqrt[3]{d \sec (e+f x)}} \, dx","Int[(a + b*Tan[e + f*x])^2/(d*Sec[e + f*x])^(1/3),x]","-\frac{3 d \left(2 a^2-3 b^2\right) \sin (e+f x) \text{Hypergeometric2F1}\left(\frac{1}{2},\frac{2}{3},\frac{5}{3},\cos ^2(e+f x)\right)}{8 f \sqrt{\sin ^2(e+f x)} (d \sec (e+f x))^{4/3}}-\frac{15 a b}{2 f \sqrt[3]{d \sec (e+f x)}}+\frac{3 b (a+b \tan (e+f x))}{2 f \sqrt[3]{d \sec (e+f x)}}","-\frac{3 d \left(2 a^2-3 b^2\right) \sin (e+f x) \text{Hypergeometric2F1}\left(\frac{1}{2},\frac{2}{3},\frac{5}{3},\cos ^2(e+f x)\right)}{8 f \sqrt{\sin ^2(e+f x)} (d \sec (e+f x))^{4/3}}-\frac{15 a b}{2 f \sqrt[3]{d \sec (e+f x)}}+\frac{3 b (a+b \tan (e+f x))}{2 f \sqrt[3]{d \sec (e+f x)}}",1,"(-15*a*b)/(2*f*(d*Sec[e + f*x])^(1/3)) - (3*(2*a^2 - 3*b^2)*d*Hypergeometric2F1[1/2, 2/3, 5/3, Cos[e + f*x]^2]*Sin[e + f*x])/(8*f*(d*Sec[e + f*x])^(4/3)*Sqrt[Sin[e + f*x]^2]) + (3*b*(a + b*Tan[e + f*x]))/(2*f*(d*Sec[e + f*x])^(1/3))","A",4,4,25,0.1600,1,"{3508, 3486, 3772, 2643}"
631,1,119,0,0.1536472,"\int \frac{(a+b \tan (e+f x))^2}{(d \sec (e+f x))^{5/3}} \, dx","Int[(a + b*Tan[e + f*x])^2/(d*Sec[e + f*x])^(5/3),x]","-\frac{3 d \left(2 a^2+3 b^2\right) \sin (e+f x) \text{Hypergeometric2F1}\left(\frac{1}{2},\frac{4}{3},\frac{7}{3},\cos ^2(e+f x)\right)}{16 f \sqrt{\sin ^2(e+f x)} (d \sec (e+f x))^{8/3}}+\frac{3 a b}{10 f (d \sec (e+f x))^{5/3}}-\frac{3 b (a+b \tan (e+f x))}{2 f (d \sec (e+f x))^{5/3}}","-\frac{3 d \left(2 a^2+3 b^2\right) \sin (e+f x) \text{Hypergeometric2F1}\left(\frac{1}{2},\frac{4}{3},\frac{7}{3},\cos ^2(e+f x)\right)}{16 f \sqrt{\sin ^2(e+f x)} (d \sec (e+f x))^{8/3}}+\frac{3 a b}{10 f (d \sec (e+f x))^{5/3}}-\frac{3 b (a+b \tan (e+f x))}{2 f (d \sec (e+f x))^{5/3}}",1,"(3*a*b)/(10*f*(d*Sec[e + f*x])^(5/3)) - (3*(2*a^2 + 3*b^2)*d*Hypergeometric2F1[1/2, 4/3, 7/3, Cos[e + f*x]^2]*Sin[e + f*x])/(16*f*(d*Sec[e + f*x])^(8/3)*Sqrt[Sin[e + f*x]^2]) - (3*b*(a + b*Tan[e + f*x]))/(2*f*(d*Sec[e + f*x])^(5/3))","A",4,4,25,0.1600,1,"{3508, 3486, 3772, 2643}"
632,1,552,0,0.8494204,"\int \frac{(d \sec (e+f x))^{5/3}}{a+b \tan (e+f x)} \, dx","Int[(d*Sec[e + f*x])^(5/3)/(a + b*Tan[e + f*x]),x]","\frac{\tan (e+f x) (d \sec (e+f x))^{5/3} F_1\left(\frac{1}{2};1,\frac{1}{6};\frac{3}{2};\frac{b^2 \tan ^2(e+f x)}{a^2},-\tan ^2(e+f x)\right)}{a f \sec ^2(e+f x)^{5/6}}+\frac{(d \sec (e+f x))^{5/3} \log \left(-\sqrt[3]{b} \sqrt[6]{a^2+b^2} \sqrt[6]{\sec ^2(e+f x)}+\sqrt[3]{a^2+b^2}+b^{2/3} \sqrt[3]{\sec ^2(e+f x)}\right)}{4 b^{2/3} f \sqrt[6]{a^2+b^2} \sec ^2(e+f x)^{5/6}}-\frac{(d \sec (e+f x))^{5/3} \log \left(\sqrt[3]{b} \sqrt[6]{a^2+b^2} \sqrt[6]{\sec ^2(e+f x)}+\sqrt[3]{a^2+b^2}+b^{2/3} \sqrt[3]{\sec ^2(e+f x)}\right)}{4 b^{2/3} f \sqrt[6]{a^2+b^2} \sec ^2(e+f x)^{5/6}}-\frac{\sqrt{3} (d \sec (e+f x))^{5/3} \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[3]{b} \sqrt[6]{\sec ^2(e+f x)}}{\sqrt{3} \sqrt[6]{a^2+b^2}}\right)}{2 b^{2/3} f \sqrt[6]{a^2+b^2} \sec ^2(e+f x)^{5/6}}+\frac{\sqrt{3} (d \sec (e+f x))^{5/3} \tan ^{-1}\left(\frac{2 \sqrt[3]{b} \sqrt[6]{\sec ^2(e+f x)}}{\sqrt{3} \sqrt[6]{a^2+b^2}}+\frac{1}{\sqrt{3}}\right)}{2 b^{2/3} f \sqrt[6]{a^2+b^2} \sec ^2(e+f x)^{5/6}}-\frac{(d \sec (e+f x))^{5/3} \tanh ^{-1}\left(\frac{\sqrt[3]{b} \sqrt[6]{\sec ^2(e+f x)}}{\sqrt[6]{a^2+b^2}}\right)}{b^{2/3} f \sqrt[6]{a^2+b^2} \sec ^2(e+f x)^{5/6}}","\frac{\tan (e+f x) (d \sec (e+f x))^{5/3} F_1\left(\frac{1}{2};1,\frac{1}{6};\frac{3}{2};\frac{b^2 \tan ^2(e+f x)}{a^2},-\tan ^2(e+f x)\right)}{a f \sec ^2(e+f x)^{5/6}}+\frac{(d \sec (e+f x))^{5/3} \log \left(-\sqrt[3]{b} \sqrt[6]{a^2+b^2} \sqrt[6]{\sec ^2(e+f x)}+\sqrt[3]{a^2+b^2}+b^{2/3} \sqrt[3]{\sec ^2(e+f x)}\right)}{4 b^{2/3} f \sqrt[6]{a^2+b^2} \sec ^2(e+f x)^{5/6}}-\frac{(d \sec (e+f x))^{5/3} \log \left(\sqrt[3]{b} \sqrt[6]{a^2+b^2} \sqrt[6]{\sec ^2(e+f x)}+\sqrt[3]{a^2+b^2}+b^{2/3} \sqrt[3]{\sec ^2(e+f x)}\right)}{4 b^{2/3} f \sqrt[6]{a^2+b^2} \sec ^2(e+f x)^{5/6}}-\frac{\sqrt{3} (d \sec (e+f x))^{5/3} \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[3]{b} \sqrt[6]{\sec ^2(e+f x)}}{\sqrt{3} \sqrt[6]{a^2+b^2}}\right)}{2 b^{2/3} f \sqrt[6]{a^2+b^2} \sec ^2(e+f x)^{5/6}}+\frac{\sqrt{3} (d \sec (e+f x))^{5/3} \tan ^{-1}\left(\frac{2 \sqrt[3]{b} \sqrt[6]{\sec ^2(e+f x)}}{\sqrt{3} \sqrt[6]{a^2+b^2}}+\frac{1}{\sqrt{3}}\right)}{2 b^{2/3} f \sqrt[6]{a^2+b^2} \sec ^2(e+f x)^{5/6}}-\frac{(d \sec (e+f x))^{5/3} \tanh ^{-1}\left(\frac{\sqrt[3]{b} \sqrt[6]{\sec ^2(e+f x)}}{\sqrt[6]{a^2+b^2}}\right)}{b^{2/3} f \sqrt[6]{a^2+b^2} \sec ^2(e+f x)^{5/6}}",1,"-(Sqrt[3]*ArcTan[1/Sqrt[3] - (2*b^(1/3)*(Sec[e + f*x]^2)^(1/6))/(Sqrt[3]*(a^2 + b^2)^(1/6))]*(d*Sec[e + f*x])^(5/3))/(2*b^(2/3)*(a^2 + b^2)^(1/6)*f*(Sec[e + f*x]^2)^(5/6)) + (Sqrt[3]*ArcTan[1/Sqrt[3] + (2*b^(1/3)*(Sec[e + f*x]^2)^(1/6))/(Sqrt[3]*(a^2 + b^2)^(1/6))]*(d*Sec[e + f*x])^(5/3))/(2*b^(2/3)*(a^2 + b^2)^(1/6)*f*(Sec[e + f*x]^2)^(5/6)) - (ArcTanh[(b^(1/3)*(Sec[e + f*x]^2)^(1/6))/(a^2 + b^2)^(1/6)]*(d*Sec[e + f*x])^(5/3))/(b^(2/3)*(a^2 + b^2)^(1/6)*f*(Sec[e + f*x]^2)^(5/6)) + (Log[(a^2 + b^2)^(1/3) - b^(1/3)*(a^2 + b^2)^(1/6)*(Sec[e + f*x]^2)^(1/6) + b^(2/3)*(Sec[e + f*x]^2)^(1/3)]*(d*Sec[e + f*x])^(5/3))/(4*b^(2/3)*(a^2 + b^2)^(1/6)*f*(Sec[e + f*x]^2)^(5/6)) - (Log[(a^2 + b^2)^(1/3) + b^(1/3)*(a^2 + b^2)^(1/6)*(Sec[e + f*x]^2)^(1/6) + b^(2/3)*(Sec[e + f*x]^2)^(1/3)]*(d*Sec[e + f*x])^(5/3))/(4*b^(2/3)*(a^2 + b^2)^(1/6)*f*(Sec[e + f*x]^2)^(5/6)) + (AppellF1[1/2, 1, 1/6, 3/2, (b^2*Tan[e + f*x]^2)/a^2, -Tan[e + f*x]^2]*(d*Sec[e + f*x])^(5/3)*Tan[e + f*x])/(a*f*(Sec[e + f*x]^2)^(5/6))","A",16,11,25,0.4400,1,"{3512, 757, 429, 444, 63, 296, 634, 618, 204, 628, 208}"
633,1,552,0,0.7685535,"\int \frac{\sqrt[3]{d \sec (e+f x)}}{a+b \tan (e+f x)} \, dx","Int[(d*Sec[e + f*x])^(1/3)/(a + b*Tan[e + f*x]),x]","\frac{\tan (e+f x) \sqrt[3]{d \sec (e+f x)} F_1\left(\frac{1}{2};1,\frac{5}{6};\frac{3}{2};\frac{b^2 \tan ^2(e+f x)}{a^2},-\tan ^2(e+f x)\right)}{a f \sqrt[6]{\sec ^2(e+f x)}}+\frac{b^{2/3} \sqrt[3]{d \sec (e+f x)} \log \left(-\sqrt[3]{b} \sqrt[6]{a^2+b^2} \sqrt[6]{\sec ^2(e+f x)}+\sqrt[3]{a^2+b^2}+b^{2/3} \sqrt[3]{\sec ^2(e+f x)}\right)}{4 f \left(a^2+b^2\right)^{5/6} \sqrt[6]{\sec ^2(e+f x)}}-\frac{b^{2/3} \sqrt[3]{d \sec (e+f x)} \log \left(\sqrt[3]{b} \sqrt[6]{a^2+b^2} \sqrt[6]{\sec ^2(e+f x)}+\sqrt[3]{a^2+b^2}+b^{2/3} \sqrt[3]{\sec ^2(e+f x)}\right)}{4 f \left(a^2+b^2\right)^{5/6} \sqrt[6]{\sec ^2(e+f x)}}+\frac{\sqrt{3} b^{2/3} \sqrt[3]{d \sec (e+f x)} \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[3]{b} \sqrt[6]{\sec ^2(e+f x)}}{\sqrt{3} \sqrt[6]{a^2+b^2}}\right)}{2 f \left(a^2+b^2\right)^{5/6} \sqrt[6]{\sec ^2(e+f x)}}-\frac{\sqrt{3} b^{2/3} \sqrt[3]{d \sec (e+f x)} \tan ^{-1}\left(\frac{2 \sqrt[3]{b} \sqrt[6]{\sec ^2(e+f x)}}{\sqrt{3} \sqrt[6]{a^2+b^2}}+\frac{1}{\sqrt{3}}\right)}{2 f \left(a^2+b^2\right)^{5/6} \sqrt[6]{\sec ^2(e+f x)}}-\frac{b^{2/3} \sqrt[3]{d \sec (e+f x)} \tanh ^{-1}\left(\frac{\sqrt[3]{b} \sqrt[6]{\sec ^2(e+f x)}}{\sqrt[6]{a^2+b^2}}\right)}{f \left(a^2+b^2\right)^{5/6} \sqrt[6]{\sec ^2(e+f x)}}","\frac{\tan (e+f x) \sqrt[3]{d \sec (e+f x)} F_1\left(\frac{1}{2};1,\frac{5}{6};\frac{3}{2};\frac{b^2 \tan ^2(e+f x)}{a^2},-\tan ^2(e+f x)\right)}{a f \sqrt[6]{\sec ^2(e+f x)}}+\frac{b^{2/3} \sqrt[3]{d \sec (e+f x)} \log \left(-\sqrt[3]{b} \sqrt[6]{a^2+b^2} \sqrt[6]{\sec ^2(e+f x)}+\sqrt[3]{a^2+b^2}+b^{2/3} \sqrt[3]{\sec ^2(e+f x)}\right)}{4 f \left(a^2+b^2\right)^{5/6} \sqrt[6]{\sec ^2(e+f x)}}-\frac{b^{2/3} \sqrt[3]{d \sec (e+f x)} \log \left(\sqrt[3]{b} \sqrt[6]{a^2+b^2} \sqrt[6]{\sec ^2(e+f x)}+\sqrt[3]{a^2+b^2}+b^{2/3} \sqrt[3]{\sec ^2(e+f x)}\right)}{4 f \left(a^2+b^2\right)^{5/6} \sqrt[6]{\sec ^2(e+f x)}}+\frac{\sqrt{3} b^{2/3} \sqrt[3]{d \sec (e+f x)} \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[3]{b} \sqrt[6]{\sec ^2(e+f x)}}{\sqrt{3} \sqrt[6]{a^2+b^2}}\right)}{2 f \left(a^2+b^2\right)^{5/6} \sqrt[6]{\sec ^2(e+f x)}}-\frac{\sqrt{3} b^{2/3} \sqrt[3]{d \sec (e+f x)} \tan ^{-1}\left(\frac{2 \sqrt[3]{b} \sqrt[6]{\sec ^2(e+f x)}}{\sqrt{3} \sqrt[6]{a^2+b^2}}+\frac{1}{\sqrt{3}}\right)}{2 f \left(a^2+b^2\right)^{5/6} \sqrt[6]{\sec ^2(e+f x)}}-\frac{b^{2/3} \sqrt[3]{d \sec (e+f x)} \tanh ^{-1}\left(\frac{\sqrt[3]{b} \sqrt[6]{\sec ^2(e+f x)}}{\sqrt[6]{a^2+b^2}}\right)}{f \left(a^2+b^2\right)^{5/6} \sqrt[6]{\sec ^2(e+f x)}}",1,"(Sqrt[3]*b^(2/3)*ArcTan[1/Sqrt[3] - (2*b^(1/3)*(Sec[e + f*x]^2)^(1/6))/(Sqrt[3]*(a^2 + b^2)^(1/6))]*(d*Sec[e + f*x])^(1/3))/(2*(a^2 + b^2)^(5/6)*f*(Sec[e + f*x]^2)^(1/6)) - (Sqrt[3]*b^(2/3)*ArcTan[1/Sqrt[3] + (2*b^(1/3)*(Sec[e + f*x]^2)^(1/6))/(Sqrt[3]*(a^2 + b^2)^(1/6))]*(d*Sec[e + f*x])^(1/3))/(2*(a^2 + b^2)^(5/6)*f*(Sec[e + f*x]^2)^(1/6)) - (b^(2/3)*ArcTanh[(b^(1/3)*(Sec[e + f*x]^2)^(1/6))/(a^2 + b^2)^(1/6)]*(d*Sec[e + f*x])^(1/3))/((a^2 + b^2)^(5/6)*f*(Sec[e + f*x]^2)^(1/6)) + (b^(2/3)*Log[(a^2 + b^2)^(1/3) - b^(1/3)*(a^2 + b^2)^(1/6)*(Sec[e + f*x]^2)^(1/6) + b^(2/3)*(Sec[e + f*x]^2)^(1/3)]*(d*Sec[e + f*x])^(1/3))/(4*(a^2 + b^2)^(5/6)*f*(Sec[e + f*x]^2)^(1/6)) - (b^(2/3)*Log[(a^2 + b^2)^(1/3) + b^(1/3)*(a^2 + b^2)^(1/6)*(Sec[e + f*x]^2)^(1/6) + b^(2/3)*(Sec[e + f*x]^2)^(1/3)]*(d*Sec[e + f*x])^(1/3))/(4*(a^2 + b^2)^(5/6)*f*(Sec[e + f*x]^2)^(1/6)) + (AppellF1[1/2, 1, 5/6, 3/2, (b^2*Tan[e + f*x]^2)/a^2, -Tan[e + f*x]^2]*(d*Sec[e + f*x])^(1/3)*Tan[e + f*x])/(a*f*(Sec[e + f*x]^2)^(1/6))","A",16,11,25,0.4400,1,"{3512, 757, 429, 444, 63, 210, 634, 618, 204, 628, 208}"
634,1,579,0,0.850136,"\int \frac{1}{\sqrt[3]{d \sec (e+f x)} (a+b \tan (e+f x))} \, dx","Int[1/((d*Sec[e + f*x])^(1/3)*(a + b*Tan[e + f*x])),x]","\frac{\tan (e+f x) \sqrt[6]{\sec ^2(e+f x)} F_1\left(\frac{1}{2};1,\frac{7}{6};\frac{3}{2};\frac{b^2 \tan ^2(e+f x)}{a^2},-\tan ^2(e+f x)\right)}{a f \sqrt[3]{d \sec (e+f x)}}+\frac{3 b}{f \left(a^2+b^2\right) \sqrt[3]{d \sec (e+f x)}}+\frac{b^{4/3} \sqrt[6]{\sec ^2(e+f x)} \log \left(-\sqrt[3]{b} \sqrt[6]{a^2+b^2} \sqrt[6]{\sec ^2(e+f x)}+\sqrt[3]{a^2+b^2}+b^{2/3} \sqrt[3]{\sec ^2(e+f x)}\right)}{4 f \left(a^2+b^2\right)^{7/6} \sqrt[3]{d \sec (e+f x)}}-\frac{b^{4/3} \sqrt[6]{\sec ^2(e+f x)} \log \left(\sqrt[3]{b} \sqrt[6]{a^2+b^2} \sqrt[6]{\sec ^2(e+f x)}+\sqrt[3]{a^2+b^2}+b^{2/3} \sqrt[3]{\sec ^2(e+f x)}\right)}{4 f \left(a^2+b^2\right)^{7/6} \sqrt[3]{d \sec (e+f x)}}-\frac{\sqrt{3} b^{4/3} \sqrt[6]{\sec ^2(e+f x)} \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[3]{b} \sqrt[6]{\sec ^2(e+f x)}}{\sqrt{3} \sqrt[6]{a^2+b^2}}\right)}{2 f \left(a^2+b^2\right)^{7/6} \sqrt[3]{d \sec (e+f x)}}+\frac{\sqrt{3} b^{4/3} \sqrt[6]{\sec ^2(e+f x)} \tan ^{-1}\left(\frac{2 \sqrt[3]{b} \sqrt[6]{\sec ^2(e+f x)}}{\sqrt{3} \sqrt[6]{a^2+b^2}}+\frac{1}{\sqrt{3}}\right)}{2 f \left(a^2+b^2\right)^{7/6} \sqrt[3]{d \sec (e+f x)}}-\frac{b^{4/3} \sqrt[6]{\sec ^2(e+f x)} \tanh ^{-1}\left(\frac{\sqrt[3]{b} \sqrt[6]{\sec ^2(e+f x)}}{\sqrt[6]{a^2+b^2}}\right)}{f \left(a^2+b^2\right)^{7/6} \sqrt[3]{d \sec (e+f x)}}","\frac{\tan (e+f x) \sqrt[6]{\sec ^2(e+f x)} F_1\left(\frac{1}{2};1,\frac{7}{6};\frac{3}{2};\frac{b^2 \tan ^2(e+f x)}{a^2},-\tan ^2(e+f x)\right)}{a f \sqrt[3]{d \sec (e+f x)}}+\frac{3 b}{f \left(a^2+b^2\right) \sqrt[3]{d \sec (e+f x)}}+\frac{b^{4/3} \sqrt[6]{\sec ^2(e+f x)} \log \left(-\sqrt[3]{b} \sqrt[6]{a^2+b^2} \sqrt[6]{\sec ^2(e+f x)}+\sqrt[3]{a^2+b^2}+b^{2/3} \sqrt[3]{\sec ^2(e+f x)}\right)}{4 f \left(a^2+b^2\right)^{7/6} \sqrt[3]{d \sec (e+f x)}}-\frac{b^{4/3} \sqrt[6]{\sec ^2(e+f x)} \log \left(\sqrt[3]{b} \sqrt[6]{a^2+b^2} \sqrt[6]{\sec ^2(e+f x)}+\sqrt[3]{a^2+b^2}+b^{2/3} \sqrt[3]{\sec ^2(e+f x)}\right)}{4 f \left(a^2+b^2\right)^{7/6} \sqrt[3]{d \sec (e+f x)}}-\frac{\sqrt{3} b^{4/3} \sqrt[6]{\sec ^2(e+f x)} \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[3]{b} \sqrt[6]{\sec ^2(e+f x)}}{\sqrt{3} \sqrt[6]{a^2+b^2}}\right)}{2 f \left(a^2+b^2\right)^{7/6} \sqrt[3]{d \sec (e+f x)}}+\frac{\sqrt{3} b^{4/3} \sqrt[6]{\sec ^2(e+f x)} \tan ^{-1}\left(\frac{2 \sqrt[3]{b} \sqrt[6]{\sec ^2(e+f x)}}{\sqrt{3} \sqrt[6]{a^2+b^2}}+\frac{1}{\sqrt{3}}\right)}{2 f \left(a^2+b^2\right)^{7/6} \sqrt[3]{d \sec (e+f x)}}-\frac{b^{4/3} \sqrt[6]{\sec ^2(e+f x)} \tanh ^{-1}\left(\frac{\sqrt[3]{b} \sqrt[6]{\sec ^2(e+f x)}}{\sqrt[6]{a^2+b^2}}\right)}{f \left(a^2+b^2\right)^{7/6} \sqrt[3]{d \sec (e+f x)}}",1,"(3*b)/((a^2 + b^2)*f*(d*Sec[e + f*x])^(1/3)) - (Sqrt[3]*b^(4/3)*ArcTan[1/Sqrt[3] - (2*b^(1/3)*(Sec[e + f*x]^2)^(1/6))/(Sqrt[3]*(a^2 + b^2)^(1/6))]*(Sec[e + f*x]^2)^(1/6))/(2*(a^2 + b^2)^(7/6)*f*(d*Sec[e + f*x])^(1/3)) + (Sqrt[3]*b^(4/3)*ArcTan[1/Sqrt[3] + (2*b^(1/3)*(Sec[e + f*x]^2)^(1/6))/(Sqrt[3]*(a^2 + b^2)^(1/6))]*(Sec[e + f*x]^2)^(1/6))/(2*(a^2 + b^2)^(7/6)*f*(d*Sec[e + f*x])^(1/3)) - (b^(4/3)*ArcTanh[(b^(1/3)*(Sec[e + f*x]^2)^(1/6))/(a^2 + b^2)^(1/6)]*(Sec[e + f*x]^2)^(1/6))/((a^2 + b^2)^(7/6)*f*(d*Sec[e + f*x])^(1/3)) + (b^(4/3)*Log[(a^2 + b^2)^(1/3) - b^(1/3)*(a^2 + b^2)^(1/6)*(Sec[e + f*x]^2)^(1/6) + b^(2/3)*(Sec[e + f*x]^2)^(1/3)]*(Sec[e + f*x]^2)^(1/6))/(4*(a^2 + b^2)^(7/6)*f*(d*Sec[e + f*x])^(1/3)) - (b^(4/3)*Log[(a^2 + b^2)^(1/3) + b^(1/3)*(a^2 + b^2)^(1/6)*(Sec[e + f*x]^2)^(1/6) + b^(2/3)*(Sec[e + f*x]^2)^(1/3)]*(Sec[e + f*x]^2)^(1/6))/(4*(a^2 + b^2)^(7/6)*f*(d*Sec[e + f*x])^(1/3)) + (AppellF1[1/2, 1, 7/6, 3/2, (b^2*Tan[e + f*x]^2)/a^2, -Tan[e + f*x]^2]*(Sec[e + f*x]^2)^(1/6)*Tan[e + f*x])/(a*f*(d*Sec[e + f*x])^(1/3))","A",17,12,25,0.4800,1,"{3512, 757, 429, 444, 51, 63, 296, 634, 618, 204, 628, 208}"
635,1,581,0,0.8192245,"\int \frac{1}{(d \sec (e+f x))^{5/3} (a+b \tan (e+f x))} \, dx","Int[1/((d*Sec[e + f*x])^(5/3)*(a + b*Tan[e + f*x])),x]","\frac{\tan (e+f x) \sec ^2(e+f x)^{5/6} F_1\left(\frac{1}{2};1,\frac{11}{6};\frac{3}{2};\frac{b^2 \tan ^2(e+f x)}{a^2},-\tan ^2(e+f x)\right)}{a f (d \sec (e+f x))^{5/3}}+\frac{3 b}{5 f \left(a^2+b^2\right) (d \sec (e+f x))^{5/3}}+\frac{b^{8/3} \sec ^2(e+f x)^{5/6} \log \left(-\sqrt[3]{b} \sqrt[6]{a^2+b^2} \sqrt[6]{\sec ^2(e+f x)}+\sqrt[3]{a^2+b^2}+b^{2/3} \sqrt[3]{\sec ^2(e+f x)}\right)}{4 f \left(a^2+b^2\right)^{11/6} (d \sec (e+f x))^{5/3}}-\frac{b^{8/3} \sec ^2(e+f x)^{5/6} \log \left(\sqrt[3]{b} \sqrt[6]{a^2+b^2} \sqrt[6]{\sec ^2(e+f x)}+\sqrt[3]{a^2+b^2}+b^{2/3} \sqrt[3]{\sec ^2(e+f x)}\right)}{4 f \left(a^2+b^2\right)^{11/6} (d \sec (e+f x))^{5/3}}+\frac{\sqrt{3} b^{8/3} \sec ^2(e+f x)^{5/6} \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[3]{b} \sqrt[6]{\sec ^2(e+f x)}}{\sqrt{3} \sqrt[6]{a^2+b^2}}\right)}{2 f \left(a^2+b^2\right)^{11/6} (d \sec (e+f x))^{5/3}}-\frac{\sqrt{3} b^{8/3} \sec ^2(e+f x)^{5/6} \tan ^{-1}\left(\frac{2 \sqrt[3]{b} \sqrt[6]{\sec ^2(e+f x)}}{\sqrt{3} \sqrt[6]{a^2+b^2}}+\frac{1}{\sqrt{3}}\right)}{2 f \left(a^2+b^2\right)^{11/6} (d \sec (e+f x))^{5/3}}-\frac{b^{8/3} \sec ^2(e+f x)^{5/6} \tanh ^{-1}\left(\frac{\sqrt[3]{b} \sqrt[6]{\sec ^2(e+f x)}}{\sqrt[6]{a^2+b^2}}\right)}{f \left(a^2+b^2\right)^{11/6} (d \sec (e+f x))^{5/3}}","\frac{\tan (e+f x) \sec ^2(e+f x)^{5/6} F_1\left(\frac{1}{2};1,\frac{11}{6};\frac{3}{2};\frac{b^2 \tan ^2(e+f x)}{a^2},-\tan ^2(e+f x)\right)}{a f (d \sec (e+f x))^{5/3}}+\frac{3 b}{5 f \left(a^2+b^2\right) (d \sec (e+f x))^{5/3}}+\frac{b^{8/3} \sec ^2(e+f x)^{5/6} \log \left(-\sqrt[3]{b} \sqrt[6]{a^2+b^2} \sqrt[6]{\sec ^2(e+f x)}+\sqrt[3]{a^2+b^2}+b^{2/3} \sqrt[3]{\sec ^2(e+f x)}\right)}{4 f \left(a^2+b^2\right)^{11/6} (d \sec (e+f x))^{5/3}}-\frac{b^{8/3} \sec ^2(e+f x)^{5/6} \log \left(\sqrt[3]{b} \sqrt[6]{a^2+b^2} \sqrt[6]{\sec ^2(e+f x)}+\sqrt[3]{a^2+b^2}+b^{2/3} \sqrt[3]{\sec ^2(e+f x)}\right)}{4 f \left(a^2+b^2\right)^{11/6} (d \sec (e+f x))^{5/3}}+\frac{\sqrt{3} b^{8/3} \sec ^2(e+f x)^{5/6} \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[3]{b} \sqrt[6]{\sec ^2(e+f x)}}{\sqrt{3} \sqrt[6]{a^2+b^2}}\right)}{2 f \left(a^2+b^2\right)^{11/6} (d \sec (e+f x))^{5/3}}-\frac{\sqrt{3} b^{8/3} \sec ^2(e+f x)^{5/6} \tan ^{-1}\left(\frac{2 \sqrt[3]{b} \sqrt[6]{\sec ^2(e+f x)}}{\sqrt{3} \sqrt[6]{a^2+b^2}}+\frac{1}{\sqrt{3}}\right)}{2 f \left(a^2+b^2\right)^{11/6} (d \sec (e+f x))^{5/3}}-\frac{b^{8/3} \sec ^2(e+f x)^{5/6} \tanh ^{-1}\left(\frac{\sqrt[3]{b} \sqrt[6]{\sec ^2(e+f x)}}{\sqrt[6]{a^2+b^2}}\right)}{f \left(a^2+b^2\right)^{11/6} (d \sec (e+f x))^{5/3}}",1,"(3*b)/(5*(a^2 + b^2)*f*(d*Sec[e + f*x])^(5/3)) + (Sqrt[3]*b^(8/3)*ArcTan[1/Sqrt[3] - (2*b^(1/3)*(Sec[e + f*x]^2)^(1/6))/(Sqrt[3]*(a^2 + b^2)^(1/6))]*(Sec[e + f*x]^2)^(5/6))/(2*(a^2 + b^2)^(11/6)*f*(d*Sec[e + f*x])^(5/3)) - (Sqrt[3]*b^(8/3)*ArcTan[1/Sqrt[3] + (2*b^(1/3)*(Sec[e + f*x]^2)^(1/6))/(Sqrt[3]*(a^2 + b^2)^(1/6))]*(Sec[e + f*x]^2)^(5/6))/(2*(a^2 + b^2)^(11/6)*f*(d*Sec[e + f*x])^(5/3)) - (b^(8/3)*ArcTanh[(b^(1/3)*(Sec[e + f*x]^2)^(1/6))/(a^2 + b^2)^(1/6)]*(Sec[e + f*x]^2)^(5/6))/((a^2 + b^2)^(11/6)*f*(d*Sec[e + f*x])^(5/3)) + (b^(8/3)*Log[(a^2 + b^2)^(1/3) - b^(1/3)*(a^2 + b^2)^(1/6)*(Sec[e + f*x]^2)^(1/6) + b^(2/3)*(Sec[e + f*x]^2)^(1/3)]*(Sec[e + f*x]^2)^(5/6))/(4*(a^2 + b^2)^(11/6)*f*(d*Sec[e + f*x])^(5/3)) - (b^(8/3)*Log[(a^2 + b^2)^(1/3) + b^(1/3)*(a^2 + b^2)^(1/6)*(Sec[e + f*x]^2)^(1/6) + b^(2/3)*(Sec[e + f*x]^2)^(1/3)]*(Sec[e + f*x]^2)^(5/6))/(4*(a^2 + b^2)^(11/6)*f*(d*Sec[e + f*x])^(5/3)) + (AppellF1[1/2, 1, 11/6, 3/2, (b^2*Tan[e + f*x]^2)/a^2, -Tan[e + f*x]^2]*(Sec[e + f*x]^2)^(5/6)*Tan[e + f*x])/(a*f*(d*Sec[e + f*x])^(5/3))","A",17,12,25,0.4800,1,"{3512, 757, 429, 444, 51, 63, 210, 634, 618, 204, 628, 208}"
636,1,687,0,0.944485,"\int \frac{(d \sec (e+f x))^{5/3}}{(a+b \tan (e+f x))^2} \, dx","Int[(d*Sec[e + f*x])^(5/3)/(a + b*Tan[e + f*x])^2,x]","\frac{b^2 \tan ^3(e+f x) (d \sec (e+f x))^{5/3} F_1\left(\frac{3}{2};2,\frac{1}{6};\frac{5}{2};\frac{b^2 \tan ^2(e+f x)}{a^2},-\tan ^2(e+f x)\right)}{3 a^4 f \sec ^2(e+f x)^{5/6}}+\frac{\tan (e+f x) (d \sec (e+f x))^{5/3} F_1\left(\frac{1}{2};2,\frac{1}{6};\frac{3}{2};\frac{b^2 \tan ^2(e+f x)}{a^2},-\tan ^2(e+f x)\right)}{a^2 f \sec ^2(e+f x)^{5/6}}+\frac{a (d \sec (e+f x))^{5/3} \log \left(-\sqrt[3]{b} \sqrt[6]{a^2+b^2} \sqrt[6]{\sec ^2(e+f x)}+\sqrt[3]{a^2+b^2}+b^{2/3} \sqrt[3]{\sec ^2(e+f x)}\right)}{12 b^{2/3} f \left(a^2+b^2\right)^{7/6} \sec ^2(e+f x)^{5/6}}-\frac{a (d \sec (e+f x))^{5/3} \log \left(\sqrt[3]{b} \sqrt[6]{a^2+b^2} \sqrt[6]{\sec ^2(e+f x)}+\sqrt[3]{a^2+b^2}+b^{2/3} \sqrt[3]{\sec ^2(e+f x)}\right)}{12 b^{2/3} f \left(a^2+b^2\right)^{7/6} \sec ^2(e+f x)^{5/6}}-\frac{a (d \sec (e+f x))^{5/3} \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[3]{b} \sqrt[6]{\sec ^2(e+f x)}}{\sqrt{3} \sqrt[6]{a^2+b^2}}\right)}{2 \sqrt{3} b^{2/3} f \left(a^2+b^2\right)^{7/6} \sec ^2(e+f x)^{5/6}}+\frac{a (d \sec (e+f x))^{5/3} \tan ^{-1}\left(\frac{2 \sqrt[3]{b} \sqrt[6]{\sec ^2(e+f x)}}{\sqrt{3} \sqrt[6]{a^2+b^2}}+\frac{1}{\sqrt{3}}\right)}{2 \sqrt{3} b^{2/3} f \left(a^2+b^2\right)^{7/6} \sec ^2(e+f x)^{5/6}}-\frac{a (d \sec (e+f x))^{5/3} \tanh ^{-1}\left(\frac{\sqrt[3]{b} \sqrt[6]{\sec ^2(e+f x)}}{\sqrt[6]{a^2+b^2}}\right)}{3 b^{2/3} f \left(a^2+b^2\right)^{7/6} \sec ^2(e+f x)^{5/6}}-\frac{a b (d \sec (e+f x))^{5/3}}{f \left(a^2+b^2\right) \left(a^2-b^2 \tan ^2(e+f x)\right)}","\frac{b^2 \tan ^3(e+f x) (d \sec (e+f x))^{5/3} F_1\left(\frac{3}{2};2,\frac{1}{6};\frac{5}{2};\frac{b^2 \tan ^2(e+f x)}{a^2},-\tan ^2(e+f x)\right)}{3 a^4 f \sec ^2(e+f x)^{5/6}}+\frac{\tan (e+f x) (d \sec (e+f x))^{5/3} F_1\left(\frac{1}{2};2,\frac{1}{6};\frac{3}{2};\frac{b^2 \tan ^2(e+f x)}{a^2},-\tan ^2(e+f x)\right)}{a^2 f \sec ^2(e+f x)^{5/6}}+\frac{a (d \sec (e+f x))^{5/3} \log \left(-\sqrt[3]{b} \sqrt[6]{a^2+b^2} \sqrt[6]{\sec ^2(e+f x)}+\sqrt[3]{a^2+b^2}+b^{2/3} \sqrt[3]{\sec ^2(e+f x)}\right)}{12 b^{2/3} f \left(a^2+b^2\right)^{7/6} \sec ^2(e+f x)^{5/6}}-\frac{a (d \sec (e+f x))^{5/3} \log \left(\sqrt[3]{b} \sqrt[6]{a^2+b^2} \sqrt[6]{\sec ^2(e+f x)}+\sqrt[3]{a^2+b^2}+b^{2/3} \sqrt[3]{\sec ^2(e+f x)}\right)}{12 b^{2/3} f \left(a^2+b^2\right)^{7/6} \sec ^2(e+f x)^{5/6}}-\frac{a (d \sec (e+f x))^{5/3} \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[3]{b} \sqrt[6]{\sec ^2(e+f x)}}{\sqrt{3} \sqrt[6]{a^2+b^2}}\right)}{2 \sqrt{3} b^{2/3} f \left(a^2+b^2\right)^{7/6} \sec ^2(e+f x)^{5/6}}+\frac{a (d \sec (e+f x))^{5/3} \tan ^{-1}\left(\frac{2 \sqrt[3]{b} \sqrt[6]{\sec ^2(e+f x)}}{\sqrt{3} \sqrt[6]{a^2+b^2}}+\frac{1}{\sqrt{3}}\right)}{2 \sqrt{3} b^{2/3} f \left(a^2+b^2\right)^{7/6} \sec ^2(e+f x)^{5/6}}-\frac{a (d \sec (e+f x))^{5/3} \tanh ^{-1}\left(\frac{\sqrt[3]{b} \sqrt[6]{\sec ^2(e+f x)}}{\sqrt[6]{a^2+b^2}}\right)}{3 b^{2/3} f \left(a^2+b^2\right)^{7/6} \sec ^2(e+f x)^{5/6}}-\frac{a b (d \sec (e+f x))^{5/3}}{f \left(a^2+b^2\right) \left(a^2-b^2 \tan ^2(e+f x)\right)}",1,"-(a*ArcTan[1/Sqrt[3] - (2*b^(1/3)*(Sec[e + f*x]^2)^(1/6))/(Sqrt[3]*(a^2 + b^2)^(1/6))]*(d*Sec[e + f*x])^(5/3))/(2*Sqrt[3]*b^(2/3)*(a^2 + b^2)^(7/6)*f*(Sec[e + f*x]^2)^(5/6)) + (a*ArcTan[1/Sqrt[3] + (2*b^(1/3)*(Sec[e + f*x]^2)^(1/6))/(Sqrt[3]*(a^2 + b^2)^(1/6))]*(d*Sec[e + f*x])^(5/3))/(2*Sqrt[3]*b^(2/3)*(a^2 + b^2)^(7/6)*f*(Sec[e + f*x]^2)^(5/6)) - (a*ArcTanh[(b^(1/3)*(Sec[e + f*x]^2)^(1/6))/(a^2 + b^2)^(1/6)]*(d*Sec[e + f*x])^(5/3))/(3*b^(2/3)*(a^2 + b^2)^(7/6)*f*(Sec[e + f*x]^2)^(5/6)) + (a*Log[(a^2 + b^2)^(1/3) - b^(1/3)*(a^2 + b^2)^(1/6)*(Sec[e + f*x]^2)^(1/6) + b^(2/3)*(Sec[e + f*x]^2)^(1/3)]*(d*Sec[e + f*x])^(5/3))/(12*b^(2/3)*(a^2 + b^2)^(7/6)*f*(Sec[e + f*x]^2)^(5/6)) - (a*Log[(a^2 + b^2)^(1/3) + b^(1/3)*(a^2 + b^2)^(1/6)*(Sec[e + f*x]^2)^(1/6) + b^(2/3)*(Sec[e + f*x]^2)^(1/3)]*(d*Sec[e + f*x])^(5/3))/(12*b^(2/3)*(a^2 + b^2)^(7/6)*f*(Sec[e + f*x]^2)^(5/6)) + (AppellF1[1/2, 2, 1/6, 3/2, (b^2*Tan[e + f*x]^2)/a^2, -Tan[e + f*x]^2]*(d*Sec[e + f*x])^(5/3)*Tan[e + f*x])/(a^2*f*(Sec[e + f*x]^2)^(5/6)) + (b^2*AppellF1[3/2, 2, 1/6, 5/2, (b^2*Tan[e + f*x]^2)/a^2, -Tan[e + f*x]^2]*(d*Sec[e + f*x])^(5/3)*Tan[e + f*x]^3)/(3*a^4*f*(Sec[e + f*x]^2)^(5/6)) - (a*b*(d*Sec[e + f*x])^(5/3))/((a^2 + b^2)*f*(a^2 - b^2*Tan[e + f*x]^2))","A",18,13,25,0.5200,1,"{3512, 757, 429, 444, 51, 63, 296, 634, 618, 204, 628, 208, 510}"
637,1,687,0,0.8839178,"\int \frac{\sqrt[3]{d \sec (e+f x)}}{(a+b \tan (e+f x))^2} \, dx","Int[(d*Sec[e + f*x])^(1/3)/(a + b*Tan[e + f*x])^2,x]","\frac{b^2 \tan ^3(e+f x) \sqrt[3]{d \sec (e+f x)} F_1\left(\frac{3}{2};2,\frac{5}{6};\frac{5}{2};\frac{b^2 \tan ^2(e+f x)}{a^2},-\tan ^2(e+f x)\right)}{3 a^4 f \sqrt[6]{\sec ^2(e+f x)}}+\frac{\tan (e+f x) \sqrt[3]{d \sec (e+f x)} F_1\left(\frac{1}{2};2,\frac{5}{6};\frac{3}{2};\frac{b^2 \tan ^2(e+f x)}{a^2},-\tan ^2(e+f x)\right)}{a^2 f \sqrt[6]{\sec ^2(e+f x)}}+\frac{5 a b^{2/3} \sqrt[3]{d \sec (e+f x)} \log \left(-\sqrt[3]{b} \sqrt[6]{a^2+b^2} \sqrt[6]{\sec ^2(e+f x)}+\sqrt[3]{a^2+b^2}+b^{2/3} \sqrt[3]{\sec ^2(e+f x)}\right)}{12 f \left(a^2+b^2\right)^{11/6} \sqrt[6]{\sec ^2(e+f x)}}-\frac{5 a b^{2/3} \sqrt[3]{d \sec (e+f x)} \log \left(\sqrt[3]{b} \sqrt[6]{a^2+b^2} \sqrt[6]{\sec ^2(e+f x)}+\sqrt[3]{a^2+b^2}+b^{2/3} \sqrt[3]{\sec ^2(e+f x)}\right)}{12 f \left(a^2+b^2\right)^{11/6} \sqrt[6]{\sec ^2(e+f x)}}+\frac{5 a b^{2/3} \sqrt[3]{d \sec (e+f x)} \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[3]{b} \sqrt[6]{\sec ^2(e+f x)}}{\sqrt{3} \sqrt[6]{a^2+b^2}}\right)}{2 \sqrt{3} f \left(a^2+b^2\right)^{11/6} \sqrt[6]{\sec ^2(e+f x)}}-\frac{5 a b^{2/3} \sqrt[3]{d \sec (e+f x)} \tan ^{-1}\left(\frac{2 \sqrt[3]{b} \sqrt[6]{\sec ^2(e+f x)}}{\sqrt{3} \sqrt[6]{a^2+b^2}}+\frac{1}{\sqrt{3}}\right)}{2 \sqrt{3} f \left(a^2+b^2\right)^{11/6} \sqrt[6]{\sec ^2(e+f x)}}-\frac{5 a b^{2/3} \sqrt[3]{d \sec (e+f x)} \tanh ^{-1}\left(\frac{\sqrt[3]{b} \sqrt[6]{\sec ^2(e+f x)}}{\sqrt[6]{a^2+b^2}}\right)}{3 f \left(a^2+b^2\right)^{11/6} \sqrt[6]{\sec ^2(e+f x)}}-\frac{a b \sqrt[3]{d \sec (e+f x)}}{f \left(a^2+b^2\right) \left(a^2-b^2 \tan ^2(e+f x)\right)}","\frac{b^2 \tan ^3(e+f x) \sqrt[3]{d \sec (e+f x)} F_1\left(\frac{3}{2};2,\frac{5}{6};\frac{5}{2};\frac{b^2 \tan ^2(e+f x)}{a^2},-\tan ^2(e+f x)\right)}{3 a^4 f \sqrt[6]{\sec ^2(e+f x)}}+\frac{\tan (e+f x) \sqrt[3]{d \sec (e+f x)} F_1\left(\frac{1}{2};2,\frac{5}{6};\frac{3}{2};\frac{b^2 \tan ^2(e+f x)}{a^2},-\tan ^2(e+f x)\right)}{a^2 f \sqrt[6]{\sec ^2(e+f x)}}+\frac{5 a b^{2/3} \sqrt[3]{d \sec (e+f x)} \log \left(-\sqrt[3]{b} \sqrt[6]{a^2+b^2} \sqrt[6]{\sec ^2(e+f x)}+\sqrt[3]{a^2+b^2}+b^{2/3} \sqrt[3]{\sec ^2(e+f x)}\right)}{12 f \left(a^2+b^2\right)^{11/6} \sqrt[6]{\sec ^2(e+f x)}}-\frac{5 a b^{2/3} \sqrt[3]{d \sec (e+f x)} \log \left(\sqrt[3]{b} \sqrt[6]{a^2+b^2} \sqrt[6]{\sec ^2(e+f x)}+\sqrt[3]{a^2+b^2}+b^{2/3} \sqrt[3]{\sec ^2(e+f x)}\right)}{12 f \left(a^2+b^2\right)^{11/6} \sqrt[6]{\sec ^2(e+f x)}}+\frac{5 a b^{2/3} \sqrt[3]{d \sec (e+f x)} \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[3]{b} \sqrt[6]{\sec ^2(e+f x)}}{\sqrt{3} \sqrt[6]{a^2+b^2}}\right)}{2 \sqrt{3} f \left(a^2+b^2\right)^{11/6} \sqrt[6]{\sec ^2(e+f x)}}-\frac{5 a b^{2/3} \sqrt[3]{d \sec (e+f x)} \tan ^{-1}\left(\frac{2 \sqrt[3]{b} \sqrt[6]{\sec ^2(e+f x)}}{\sqrt{3} \sqrt[6]{a^2+b^2}}+\frac{1}{\sqrt{3}}\right)}{2 \sqrt{3} f \left(a^2+b^2\right)^{11/6} \sqrt[6]{\sec ^2(e+f x)}}-\frac{5 a b^{2/3} \sqrt[3]{d \sec (e+f x)} \tanh ^{-1}\left(\frac{\sqrt[3]{b} \sqrt[6]{\sec ^2(e+f x)}}{\sqrt[6]{a^2+b^2}}\right)}{3 f \left(a^2+b^2\right)^{11/6} \sqrt[6]{\sec ^2(e+f x)}}-\frac{a b \sqrt[3]{d \sec (e+f x)}}{f \left(a^2+b^2\right) \left(a^2-b^2 \tan ^2(e+f x)\right)}",1,"(5*a*b^(2/3)*ArcTan[1/Sqrt[3] - (2*b^(1/3)*(Sec[e + f*x]^2)^(1/6))/(Sqrt[3]*(a^2 + b^2)^(1/6))]*(d*Sec[e + f*x])^(1/3))/(2*Sqrt[3]*(a^2 + b^2)^(11/6)*f*(Sec[e + f*x]^2)^(1/6)) - (5*a*b^(2/3)*ArcTan[1/Sqrt[3] + (2*b^(1/3)*(Sec[e + f*x]^2)^(1/6))/(Sqrt[3]*(a^2 + b^2)^(1/6))]*(d*Sec[e + f*x])^(1/3))/(2*Sqrt[3]*(a^2 + b^2)^(11/6)*f*(Sec[e + f*x]^2)^(1/6)) - (5*a*b^(2/3)*ArcTanh[(b^(1/3)*(Sec[e + f*x]^2)^(1/6))/(a^2 + b^2)^(1/6)]*(d*Sec[e + f*x])^(1/3))/(3*(a^2 + b^2)^(11/6)*f*(Sec[e + f*x]^2)^(1/6)) + (5*a*b^(2/3)*Log[(a^2 + b^2)^(1/3) - b^(1/3)*(a^2 + b^2)^(1/6)*(Sec[e + f*x]^2)^(1/6) + b^(2/3)*(Sec[e + f*x]^2)^(1/3)]*(d*Sec[e + f*x])^(1/3))/(12*(a^2 + b^2)^(11/6)*f*(Sec[e + f*x]^2)^(1/6)) - (5*a*b^(2/3)*Log[(a^2 + b^2)^(1/3) + b^(1/3)*(a^2 + b^2)^(1/6)*(Sec[e + f*x]^2)^(1/6) + b^(2/3)*(Sec[e + f*x]^2)^(1/3)]*(d*Sec[e + f*x])^(1/3))/(12*(a^2 + b^2)^(11/6)*f*(Sec[e + f*x]^2)^(1/6)) + (AppellF1[1/2, 2, 5/6, 3/2, (b^2*Tan[e + f*x]^2)/a^2, -Tan[e + f*x]^2]*(d*Sec[e + f*x])^(1/3)*Tan[e + f*x])/(a^2*f*(Sec[e + f*x]^2)^(1/6)) + (b^2*AppellF1[3/2, 2, 5/6, 5/2, (b^2*Tan[e + f*x]^2)/a^2, -Tan[e + f*x]^2]*(d*Sec[e + f*x])^(1/3)*Tan[e + f*x]^3)/(3*a^4*f*(Sec[e + f*x]^2)^(1/6)) - (a*b*(d*Sec[e + f*x])^(1/3))/((a^2 + b^2)*f*(a^2 - b^2*Tan[e + f*x]^2))","A",18,13,25,0.5200,1,"{3512, 757, 429, 444, 51, 63, 210, 634, 618, 204, 628, 208, 510}"
638,1,715,0,0.9943695,"\int \frac{1}{\sqrt[3]{d \sec (e+f x)} (a+b \tan (e+f x))^2} \, dx","Int[1/((d*Sec[e + f*x])^(1/3)*(a + b*Tan[e + f*x])^2),x]","\frac{b^2 \tan ^3(e+f x) \sqrt[6]{\sec ^2(e+f x)} F_1\left(\frac{3}{2};2,\frac{7}{6};\frac{5}{2};\frac{b^2 \tan ^2(e+f x)}{a^2},-\tan ^2(e+f x)\right)}{3 a^4 f \sqrt[3]{d \sec (e+f x)}}+\frac{\tan (e+f x) \sqrt[6]{\sec ^2(e+f x)} F_1\left(\frac{1}{2};2,\frac{7}{6};\frac{3}{2};\frac{b^2 \tan ^2(e+f x)}{a^2},-\tan ^2(e+f x)\right)}{a^2 f \sqrt[3]{d \sec (e+f x)}}+\frac{7 a b}{f \left(a^2+b^2\right)^2 \sqrt[3]{d \sec (e+f x)}}+\frac{7 a b^{4/3} \sqrt[6]{\sec ^2(e+f x)} \log \left(-\sqrt[3]{b} \sqrt[6]{a^2+b^2} \sqrt[6]{\sec ^2(e+f x)}+\sqrt[3]{a^2+b^2}+b^{2/3} \sqrt[3]{\sec ^2(e+f x)}\right)}{12 f \left(a^2+b^2\right)^{13/6} \sqrt[3]{d \sec (e+f x)}}-\frac{7 a b^{4/3} \sqrt[6]{\sec ^2(e+f x)} \log \left(\sqrt[3]{b} \sqrt[6]{a^2+b^2} \sqrt[6]{\sec ^2(e+f x)}+\sqrt[3]{a^2+b^2}+b^{2/3} \sqrt[3]{\sec ^2(e+f x)}\right)}{12 f \left(a^2+b^2\right)^{13/6} \sqrt[3]{d \sec (e+f x)}}-\frac{7 a b^{4/3} \sqrt[6]{\sec ^2(e+f x)} \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[3]{b} \sqrt[6]{\sec ^2(e+f x)}}{\sqrt{3} \sqrt[6]{a^2+b^2}}\right)}{2 \sqrt{3} f \left(a^2+b^2\right)^{13/6} \sqrt[3]{d \sec (e+f x)}}+\frac{7 a b^{4/3} \sqrt[6]{\sec ^2(e+f x)} \tan ^{-1}\left(\frac{2 \sqrt[3]{b} \sqrt[6]{\sec ^2(e+f x)}}{\sqrt{3} \sqrt[6]{a^2+b^2}}+\frac{1}{\sqrt{3}}\right)}{2 \sqrt{3} f \left(a^2+b^2\right)^{13/6} \sqrt[3]{d \sec (e+f x)}}-\frac{7 a b^{4/3} \sqrt[6]{\sec ^2(e+f x)} \tanh ^{-1}\left(\frac{\sqrt[3]{b} \sqrt[6]{\sec ^2(e+f x)}}{\sqrt[6]{a^2+b^2}}\right)}{3 f \left(a^2+b^2\right)^{13/6} \sqrt[3]{d \sec (e+f x)}}-\frac{a b}{f \left(a^2+b^2\right) \sqrt[3]{d \sec (e+f x)} \left(a^2-b^2 \tan ^2(e+f x)\right)}","\frac{b^2 \tan ^3(e+f x) \sqrt[6]{\sec ^2(e+f x)} F_1\left(\frac{3}{2};2,\frac{7}{6};\frac{5}{2};\frac{b^2 \tan ^2(e+f x)}{a^2},-\tan ^2(e+f x)\right)}{3 a^4 f \sqrt[3]{d \sec (e+f x)}}+\frac{\tan (e+f x) \sqrt[6]{\sec ^2(e+f x)} F_1\left(\frac{1}{2};2,\frac{7}{6};\frac{3}{2};\frac{b^2 \tan ^2(e+f x)}{a^2},-\tan ^2(e+f x)\right)}{a^2 f \sqrt[3]{d \sec (e+f x)}}+\frac{7 a b}{f \left(a^2+b^2\right)^2 \sqrt[3]{d \sec (e+f x)}}+\frac{7 a b^{4/3} \sqrt[6]{\sec ^2(e+f x)} \log \left(-\sqrt[3]{b} \sqrt[6]{a^2+b^2} \sqrt[6]{\sec ^2(e+f x)}+\sqrt[3]{a^2+b^2}+b^{2/3} \sqrt[3]{\sec ^2(e+f x)}\right)}{12 f \left(a^2+b^2\right)^{13/6} \sqrt[3]{d \sec (e+f x)}}-\frac{7 a b^{4/3} \sqrt[6]{\sec ^2(e+f x)} \log \left(\sqrt[3]{b} \sqrt[6]{a^2+b^2} \sqrt[6]{\sec ^2(e+f x)}+\sqrt[3]{a^2+b^2}+b^{2/3} \sqrt[3]{\sec ^2(e+f x)}\right)}{12 f \left(a^2+b^2\right)^{13/6} \sqrt[3]{d \sec (e+f x)}}-\frac{7 a b^{4/3} \sqrt[6]{\sec ^2(e+f x)} \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[3]{b} \sqrt[6]{\sec ^2(e+f x)}}{\sqrt{3} \sqrt[6]{a^2+b^2}}\right)}{2 \sqrt{3} f \left(a^2+b^2\right)^{13/6} \sqrt[3]{d \sec (e+f x)}}+\frac{7 a b^{4/3} \sqrt[6]{\sec ^2(e+f x)} \tan ^{-1}\left(\frac{2 \sqrt[3]{b} \sqrt[6]{\sec ^2(e+f x)}}{\sqrt{3} \sqrt[6]{a^2+b^2}}+\frac{1}{\sqrt{3}}\right)}{2 \sqrt{3} f \left(a^2+b^2\right)^{13/6} \sqrt[3]{d \sec (e+f x)}}-\frac{7 a b^{4/3} \sqrt[6]{\sec ^2(e+f x)} \tanh ^{-1}\left(\frac{\sqrt[3]{b} \sqrt[6]{\sec ^2(e+f x)}}{\sqrt[6]{a^2+b^2}}\right)}{3 f \left(a^2+b^2\right)^{13/6} \sqrt[3]{d \sec (e+f x)}}-\frac{a b}{f \left(a^2+b^2\right) \sqrt[3]{d \sec (e+f x)} \left(a^2-b^2 \tan ^2(e+f x)\right)}",1,"(7*a*b)/((a^2 + b^2)^2*f*(d*Sec[e + f*x])^(1/3)) - (7*a*b^(4/3)*ArcTan[1/Sqrt[3] - (2*b^(1/3)*(Sec[e + f*x]^2)^(1/6))/(Sqrt[3]*(a^2 + b^2)^(1/6))]*(Sec[e + f*x]^2)^(1/6))/(2*Sqrt[3]*(a^2 + b^2)^(13/6)*f*(d*Sec[e + f*x])^(1/3)) + (7*a*b^(4/3)*ArcTan[1/Sqrt[3] + (2*b^(1/3)*(Sec[e + f*x]^2)^(1/6))/(Sqrt[3]*(a^2 + b^2)^(1/6))]*(Sec[e + f*x]^2)^(1/6))/(2*Sqrt[3]*(a^2 + b^2)^(13/6)*f*(d*Sec[e + f*x])^(1/3)) - (7*a*b^(4/3)*ArcTanh[(b^(1/3)*(Sec[e + f*x]^2)^(1/6))/(a^2 + b^2)^(1/6)]*(Sec[e + f*x]^2)^(1/6))/(3*(a^2 + b^2)^(13/6)*f*(d*Sec[e + f*x])^(1/3)) + (7*a*b^(4/3)*Log[(a^2 + b^2)^(1/3) - b^(1/3)*(a^2 + b^2)^(1/6)*(Sec[e + f*x]^2)^(1/6) + b^(2/3)*(Sec[e + f*x]^2)^(1/3)]*(Sec[e + f*x]^2)^(1/6))/(12*(a^2 + b^2)^(13/6)*f*(d*Sec[e + f*x])^(1/3)) - (7*a*b^(4/3)*Log[(a^2 + b^2)^(1/3) + b^(1/3)*(a^2 + b^2)^(1/6)*(Sec[e + f*x]^2)^(1/6) + b^(2/3)*(Sec[e + f*x]^2)^(1/3)]*(Sec[e + f*x]^2)^(1/6))/(12*(a^2 + b^2)^(13/6)*f*(d*Sec[e + f*x])^(1/3)) + (AppellF1[1/2, 2, 7/6, 3/2, (b^2*Tan[e + f*x]^2)/a^2, -Tan[e + f*x]^2]*(Sec[e + f*x]^2)^(1/6)*Tan[e + f*x])/(a^2*f*(d*Sec[e + f*x])^(1/3)) + (b^2*AppellF1[3/2, 2, 7/6, 5/2, (b^2*Tan[e + f*x]^2)/a^2, -Tan[e + f*x]^2]*(Sec[e + f*x]^2)^(1/6)*Tan[e + f*x]^3)/(3*a^4*f*(d*Sec[e + f*x])^(1/3)) - (a*b)/((a^2 + b^2)*f*(d*Sec[e + f*x])^(1/3)*(a^2 - b^2*Tan[e + f*x]^2))","A",19,13,25,0.5200,1,"{3512, 757, 429, 444, 51, 63, 296, 634, 618, 204, 628, 208, 510}"
639,1,717,0,0.9688494,"\int \frac{1}{(d \sec (e+f x))^{5/3} (a+b \tan (e+f x))^2} \, dx","Int[1/((d*Sec[e + f*x])^(5/3)*(a + b*Tan[e + f*x])^2),x]","\frac{b^2 \tan ^3(e+f x) \sec ^2(e+f x)^{5/6} F_1\left(\frac{3}{2};2,\frac{11}{6};\frac{5}{2};\frac{b^2 \tan ^2(e+f x)}{a^2},-\tan ^2(e+f x)\right)}{3 a^4 f (d \sec (e+f x))^{5/3}}+\frac{\tan (e+f x) \sec ^2(e+f x)^{5/6} F_1\left(\frac{1}{2};2,\frac{11}{6};\frac{3}{2};\frac{b^2 \tan ^2(e+f x)}{a^2},-\tan ^2(e+f x)\right)}{a^2 f (d \sec (e+f x))^{5/3}}+\frac{11 a b}{5 f \left(a^2+b^2\right)^2 (d \sec (e+f x))^{5/3}}+\frac{11 a b^{8/3} \sec ^2(e+f x)^{5/6} \log \left(-\sqrt[3]{b} \sqrt[6]{a^2+b^2} \sqrt[6]{\sec ^2(e+f x)}+\sqrt[3]{a^2+b^2}+b^{2/3} \sqrt[3]{\sec ^2(e+f x)}\right)}{12 f \left(a^2+b^2\right)^{17/6} (d \sec (e+f x))^{5/3}}-\frac{11 a b^{8/3} \sec ^2(e+f x)^{5/6} \log \left(\sqrt[3]{b} \sqrt[6]{a^2+b^2} \sqrt[6]{\sec ^2(e+f x)}+\sqrt[3]{a^2+b^2}+b^{2/3} \sqrt[3]{\sec ^2(e+f x)}\right)}{12 f \left(a^2+b^2\right)^{17/6} (d \sec (e+f x))^{5/3}}+\frac{11 a b^{8/3} \sec ^2(e+f x)^{5/6} \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[3]{b} \sqrt[6]{\sec ^2(e+f x)}}{\sqrt{3} \sqrt[6]{a^2+b^2}}\right)}{2 \sqrt{3} f \left(a^2+b^2\right)^{17/6} (d \sec (e+f x))^{5/3}}-\frac{11 a b^{8/3} \sec ^2(e+f x)^{5/6} \tan ^{-1}\left(\frac{2 \sqrt[3]{b} \sqrt[6]{\sec ^2(e+f x)}}{\sqrt{3} \sqrt[6]{a^2+b^2}}+\frac{1}{\sqrt{3}}\right)}{2 \sqrt{3} f \left(a^2+b^2\right)^{17/6} (d \sec (e+f x))^{5/3}}-\frac{11 a b^{8/3} \sec ^2(e+f x)^{5/6} \tanh ^{-1}\left(\frac{\sqrt[3]{b} \sqrt[6]{\sec ^2(e+f x)}}{\sqrt[6]{a^2+b^2}}\right)}{3 f \left(a^2+b^2\right)^{17/6} (d \sec (e+f x))^{5/3}}-\frac{a b}{f \left(a^2+b^2\right) (d \sec (e+f x))^{5/3} \left(a^2-b^2 \tan ^2(e+f x)\right)}","\frac{b^2 \tan ^3(e+f x) \sec ^2(e+f x)^{5/6} F_1\left(\frac{3}{2};2,\frac{11}{6};\frac{5}{2};\frac{b^2 \tan ^2(e+f x)}{a^2},-\tan ^2(e+f x)\right)}{3 a^4 f (d \sec (e+f x))^{5/3}}+\frac{\tan (e+f x) \sec ^2(e+f x)^{5/6} F_1\left(\frac{1}{2};2,\frac{11}{6};\frac{3}{2};\frac{b^2 \tan ^2(e+f x)}{a^2},-\tan ^2(e+f x)\right)}{a^2 f (d \sec (e+f x))^{5/3}}+\frac{11 a b}{5 f \left(a^2+b^2\right)^2 (d \sec (e+f x))^{5/3}}+\frac{11 a b^{8/3} \sec ^2(e+f x)^{5/6} \log \left(-\sqrt[3]{b} \sqrt[6]{a^2+b^2} \sqrt[6]{\sec ^2(e+f x)}+\sqrt[3]{a^2+b^2}+b^{2/3} \sqrt[3]{\sec ^2(e+f x)}\right)}{12 f \left(a^2+b^2\right)^{17/6} (d \sec (e+f x))^{5/3}}-\frac{11 a b^{8/3} \sec ^2(e+f x)^{5/6} \log \left(\sqrt[3]{b} \sqrt[6]{a^2+b^2} \sqrt[6]{\sec ^2(e+f x)}+\sqrt[3]{a^2+b^2}+b^{2/3} \sqrt[3]{\sec ^2(e+f x)}\right)}{12 f \left(a^2+b^2\right)^{17/6} (d \sec (e+f x))^{5/3}}+\frac{11 a b^{8/3} \sec ^2(e+f x)^{5/6} \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[3]{b} \sqrt[6]{\sec ^2(e+f x)}}{\sqrt{3} \sqrt[6]{a^2+b^2}}\right)}{2 \sqrt{3} f \left(a^2+b^2\right)^{17/6} (d \sec (e+f x))^{5/3}}-\frac{11 a b^{8/3} \sec ^2(e+f x)^{5/6} \tan ^{-1}\left(\frac{2 \sqrt[3]{b} \sqrt[6]{\sec ^2(e+f x)}}{\sqrt{3} \sqrt[6]{a^2+b^2}}+\frac{1}{\sqrt{3}}\right)}{2 \sqrt{3} f \left(a^2+b^2\right)^{17/6} (d \sec (e+f x))^{5/3}}-\frac{11 a b^{8/3} \sec ^2(e+f x)^{5/6} \tanh ^{-1}\left(\frac{\sqrt[3]{b} \sqrt[6]{\sec ^2(e+f x)}}{\sqrt[6]{a^2+b^2}}\right)}{3 f \left(a^2+b^2\right)^{17/6} (d \sec (e+f x))^{5/3}}-\frac{a b}{f \left(a^2+b^2\right) (d \sec (e+f x))^{5/3} \left(a^2-b^2 \tan ^2(e+f x)\right)}",1,"(11*a*b)/(5*(a^2 + b^2)^2*f*(d*Sec[e + f*x])^(5/3)) + (11*a*b^(8/3)*ArcTan[1/Sqrt[3] - (2*b^(1/3)*(Sec[e + f*x]^2)^(1/6))/(Sqrt[3]*(a^2 + b^2)^(1/6))]*(Sec[e + f*x]^2)^(5/6))/(2*Sqrt[3]*(a^2 + b^2)^(17/6)*f*(d*Sec[e + f*x])^(5/3)) - (11*a*b^(8/3)*ArcTan[1/Sqrt[3] + (2*b^(1/3)*(Sec[e + f*x]^2)^(1/6))/(Sqrt[3]*(a^2 + b^2)^(1/6))]*(Sec[e + f*x]^2)^(5/6))/(2*Sqrt[3]*(a^2 + b^2)^(17/6)*f*(d*Sec[e + f*x])^(5/3)) - (11*a*b^(8/3)*ArcTanh[(b^(1/3)*(Sec[e + f*x]^2)^(1/6))/(a^2 + b^2)^(1/6)]*(Sec[e + f*x]^2)^(5/6))/(3*(a^2 + b^2)^(17/6)*f*(d*Sec[e + f*x])^(5/3)) + (11*a*b^(8/3)*Log[(a^2 + b^2)^(1/3) - b^(1/3)*(a^2 + b^2)^(1/6)*(Sec[e + f*x]^2)^(1/6) + b^(2/3)*(Sec[e + f*x]^2)^(1/3)]*(Sec[e + f*x]^2)^(5/6))/(12*(a^2 + b^2)^(17/6)*f*(d*Sec[e + f*x])^(5/3)) - (11*a*b^(8/3)*Log[(a^2 + b^2)^(1/3) + b^(1/3)*(a^2 + b^2)^(1/6)*(Sec[e + f*x]^2)^(1/6) + b^(2/3)*(Sec[e + f*x]^2)^(1/3)]*(Sec[e + f*x]^2)^(5/6))/(12*(a^2 + b^2)^(17/6)*f*(d*Sec[e + f*x])^(5/3)) + (AppellF1[1/2, 2, 11/6, 3/2, (b^2*Tan[e + f*x]^2)/a^2, -Tan[e + f*x]^2]*(Sec[e + f*x]^2)^(5/6)*Tan[e + f*x])/(a^2*f*(d*Sec[e + f*x])^(5/3)) + (b^2*AppellF1[3/2, 2, 11/6, 5/2, (b^2*Tan[e + f*x]^2)/a^2, -Tan[e + f*x]^2]*(Sec[e + f*x]^2)^(5/6)*Tan[e + f*x]^3)/(3*a^4*f*(d*Sec[e + f*x])^(5/3)) - (a*b)/((a^2 + b^2)*f*(d*Sec[e + f*x])^(5/3)*(a^2 - b^2*Tan[e + f*x]^2))","A",19,13,25,0.5200,1,"{3512, 757, 429, 444, 51, 63, 210, 634, 618, 204, 628, 208, 510}"
640,1,167,0,0.1966204,"\int (d \sec (e+f x))^m (a+b \tan (e+f x))^3 \, dx","Int[(d*Sec[e + f*x])^m*(a + b*Tan[e + f*x])^3,x]","\frac{a \left(a^2-\frac{3 b^2}{m+1}\right) \tan (e+f x) \sec ^2(e+f x)^{-m/2} (d \sec (e+f x))^m \, _2F_1\left(\frac{1}{2},1-\frac{m}{2};\frac{3}{2};-\tan ^2(e+f x)\right)}{f}-\frac{b (d \sec (e+f x))^m \left(2 (m+1) \left(b^2-a^2 (m+3)\right)-a b m (m+4) \tan (e+f x)\right)}{f m \left(m^2+3 m+2\right)}+\frac{b (a+b \tan (e+f x))^2 (d \sec (e+f x))^m}{f (m+2)}","-\frac{a \left(3 b^2-a^2 (m+1)\right) \tan (e+f x) \sec ^2(e+f x)^{-m/2} (d \sec (e+f x))^m \, _2F_1\left(\frac{1}{2},1-\frac{m}{2};\frac{3}{2};-\tan ^2(e+f x)\right)}{f (m+1)}-\frac{b (d \sec (e+f x))^m \left(2 (m+1) \left(b^2-a^2 (m+3)\right)-a b m (m+4) \tan (e+f x)\right)}{f m \left(m^2+3 m+2\right)}+\frac{b (a+b \tan (e+f x))^2 (d \sec (e+f x))^m}{f (m+2)}",1,"(a*(a^2 - (3*b^2)/(1 + m))*Hypergeometric2F1[1/2, 1 - m/2, 3/2, -Tan[e + f*x]^2]*(d*Sec[e + f*x])^m*Tan[e + f*x])/(f*(Sec[e + f*x]^2)^(m/2)) + (b*(d*Sec[e + f*x])^m*(a + b*Tan[e + f*x])^2)/(f*(2 + m)) - (b*(d*Sec[e + f*x])^m*(2*(1 + m)*(b^2 - a^2*(3 + m)) - a*b*m*(4 + m)*Tan[e + f*x]))/(f*m*(2 + 3*m + m^2))","A",4,4,23,0.1739,1,"{3512, 743, 780, 245}"
641,1,147,0,0.1662413,"\int (d \sec (e+f x))^m (a+b \tan (e+f x))^2 \, dx","Int[(d*Sec[e + f*x])^m*(a + b*Tan[e + f*x])^2,x]","\frac{d \left(b^2-a^2 (m+1)\right) \sin (e+f x) (d \sec (e+f x))^{m-1} \, _2F_1\left(\frac{1}{2},\frac{1-m}{2};\frac{3-m}{2};\cos ^2(e+f x)\right)}{f (1-m) (m+1) \sqrt{\sin ^2(e+f x)}}+\frac{a b (m+2) (d \sec (e+f x))^m}{f m (m+1)}+\frac{b (a+b \tan (e+f x)) (d \sec (e+f x))^m}{f (m+1)}","\frac{d \left(b^2-a^2 (m+1)\right) \sin (e+f x) (d \sec (e+f x))^{m-1} \, _2F_1\left(\frac{1}{2},\frac{1-m}{2};\frac{3-m}{2};\cos ^2(e+f x)\right)}{f (1-m) (m+1) \sqrt{\sin ^2(e+f x)}}+\frac{a b (m+2) (d \sec (e+f x))^m}{f m (m+1)}+\frac{b (a+b \tan (e+f x)) (d \sec (e+f x))^m}{f (m+1)}",1,"(a*b*(2 + m)*(d*Sec[e + f*x])^m)/(f*m*(1 + m)) + (d*(b^2 - a^2*(1 + m))*Hypergeometric2F1[1/2, (1 - m)/2, (3 - m)/2, Cos[e + f*x]^2]*(d*Sec[e + f*x])^(-1 + m)*Sin[e + f*x])/(f*(1 - m)*(1 + m)*Sqrt[Sin[e + f*x]^2]) + (b*(d*Sec[e + f*x])^m*(a + b*Tan[e + f*x]))/(f*(1 + m))","A",4,4,23,0.1739,1,"{3508, 3486, 3772, 2643}"
642,1,93,0,0.0615625,"\int (d \sec (e+f x))^m (a+b \tan (e+f x)) \, dx","Int[(d*Sec[e + f*x])^m*(a + b*Tan[e + f*x]),x]","\frac{b (d \sec (e+f x))^m}{f m}-\frac{a d \sin (e+f x) (d \sec (e+f x))^{m-1} \, _2F_1\left(\frac{1}{2},\frac{1-m}{2};\frac{3-m}{2};\cos ^2(e+f x)\right)}{f (1-m) \sqrt{\sin ^2(e+f x)}}","\frac{b (d \sec (e+f x))^m}{f m}-\frac{a d \sin (e+f x) (d \sec (e+f x))^{m-1} \, _2F_1\left(\frac{1}{2},\frac{1-m}{2};\frac{3-m}{2};\cos ^2(e+f x)\right)}{f (1-m) \sqrt{\sin ^2(e+f x)}}",1,"(b*(d*Sec[e + f*x])^m)/(f*m) - (a*d*Hypergeometric2F1[1/2, (1 - m)/2, (3 - m)/2, Cos[e + f*x]^2]*(d*Sec[e + f*x])^(-1 + m)*Sin[e + f*x])/(f*(1 - m)*Sqrt[Sin[e + f*x]^2])","A",3,3,21,0.1429,1,"{3486, 3772, 2643}"
643,1,141,0,0.1574471,"\int \frac{(d \sec (e+f x))^m}{a+b \tan (e+f x)} \, dx","Int[(d*Sec[e + f*x])^m/(a + b*Tan[e + f*x]),x]","\frac{\tan (e+f x) \sec ^2(e+f x)^{-m/2} (d \sec (e+f x))^m F_1\left(\frac{1}{2};1,1-\frac{m}{2};\frac{3}{2};\frac{b^2 \tan ^2(e+f x)}{a^2},-\tan ^2(e+f x)\right)}{a f}-\frac{b (d \sec (e+f x))^m \, _2F_1\left(1,\frac{m}{2};\frac{m+2}{2};\frac{b^2 \sec ^2(e+f x)}{a^2+b^2}\right)}{f m \left(a^2+b^2\right)}","\frac{\tan (e+f x) \sec ^2(e+f x)^{-m/2} (d \sec (e+f x))^m F_1\left(\frac{1}{2};1,1-\frac{m}{2};\frac{3}{2};\frac{b^2 \tan ^2(e+f x)}{a^2},-\tan ^2(e+f x)\right)}{a f}-\frac{b (d \sec (e+f x))^m \, _2F_1\left(1,\frac{m}{2};\frac{m+2}{2};\frac{b^2 \sec ^2(e+f x)}{a^2+b^2}\right)}{f m \left(a^2+b^2\right)}",1,"-((b*Hypergeometric2F1[1, m/2, (2 + m)/2, (b^2*Sec[e + f*x]^2)/(a^2 + b^2)]*(d*Sec[e + f*x])^m)/((a^2 + b^2)*f*m)) + (AppellF1[1/2, 1, 1 - m/2, 3/2, (b^2*Tan[e + f*x]^2)/a^2, -Tan[e + f*x]^2]*(d*Sec[e + f*x])^m*Tan[e + f*x])/(a*f*(Sec[e + f*x]^2)^(m/2))","A",6,5,23,0.2174,1,"{3512, 757, 429, 444, 68}"
644,1,227,0,0.1976269,"\int \frac{(d \sec (e+f x))^m}{(a+b \tan (e+f x))^2} \, dx","Int[(d*Sec[e + f*x])^m/(a + b*Tan[e + f*x])^2,x]","\frac{b^2 \tan ^3(e+f x) \sec ^2(e+f x)^{-m/2} (d \sec (e+f x))^m F_1\left(\frac{3}{2};2,1-\frac{m}{2};\frac{5}{2};\frac{b^2 \tan ^2(e+f x)}{a^2},-\tan ^2(e+f x)\right)}{3 a^4 f}+\frac{\tan (e+f x) \sec ^2(e+f x)^{-m/2} (d \sec (e+f x))^m F_1\left(\frac{1}{2};2,1-\frac{m}{2};\frac{3}{2};\frac{b^2 \tan ^2(e+f x)}{a^2},-\tan ^2(e+f x)\right)}{a^2 f}-\frac{2 a b (d \sec (e+f x))^m \, _2F_1\left(2,\frac{m}{2};\frac{m+2}{2};\frac{b^2 \sec ^2(e+f x)}{a^2+b^2}\right)}{f m \left(a^2+b^2\right)^2}","\frac{b^2 \tan ^3(e+f x) \sec ^2(e+f x)^{-m/2} (d \sec (e+f x))^m F_1\left(\frac{3}{2};2,1-\frac{m}{2};\frac{5}{2};\frac{b^2 \tan ^2(e+f x)}{a^2},-\tan ^2(e+f x)\right)}{3 a^4 f}+\frac{\tan (e+f x) \sec ^2(e+f x)^{-m/2} (d \sec (e+f x))^m F_1\left(\frac{1}{2};2,1-\frac{m}{2};\frac{3}{2};\frac{b^2 \tan ^2(e+f x)}{a^2},-\tan ^2(e+f x)\right)}{a^2 f}-\frac{2 a b (d \sec (e+f x))^m \, _2F_1\left(2,\frac{m}{2};\frac{m+2}{2};\frac{b^2 \sec ^2(e+f x)}{a^2+b^2}\right)}{f m \left(a^2+b^2\right)^2}",1,"(-2*a*b*Hypergeometric2F1[2, m/2, (2 + m)/2, (b^2*Sec[e + f*x]^2)/(a^2 + b^2)]*(d*Sec[e + f*x])^m)/((a^2 + b^2)^2*f*m) + (AppellF1[1/2, 2, 1 - m/2, 3/2, (b^2*Tan[e + f*x]^2)/a^2, -Tan[e + f*x]^2]*(d*Sec[e + f*x])^m*Tan[e + f*x])/(a^2*f*(Sec[e + f*x]^2)^(m/2)) + (b^2*AppellF1[3/2, 2, 1 - m/2, 5/2, (b^2*Tan[e + f*x]^2)/a^2, -Tan[e + f*x]^2]*(d*Sec[e + f*x])^m*Tan[e + f*x]^3)/(3*a^4*f*(Sec[e + f*x]^2)^(m/2))","A",7,6,23,0.2609,1,"{3512, 757, 429, 444, 68, 510}"
645,1,187,0,0.1678577,"\int (d \sec (e+f x))^m (a+b \tan (e+f x))^n \, dx","Int[(d*Sec[e + f*x])^m*(a + b*Tan[e + f*x])^n,x]","\frac{\cos ^2(e+f x) (d \sec (e+f x))^m \left(1-\frac{a+b \tan (e+f x)}{a-\sqrt{-b^2}}\right)^{1-\frac{m}{2}} \left(1-\frac{a+b \tan (e+f x)}{a+\sqrt{-b^2}}\right)^{1-\frac{m}{2}} (a+b \tan (e+f x))^{n+1} F_1\left(n+1;1-\frac{m}{2},1-\frac{m}{2};n+2;\frac{a+b \tan (e+f x)}{a-\sqrt{-b^2}},\frac{a+b \tan (e+f x)}{a+\sqrt{-b^2}}\right)}{b f (n+1)}","\frac{b (d \sec (e+f x))^m \left(\frac{a+b \tan (e+f x)}{\sqrt{-b^2}-a}+1\right)^{-m/2} \left(1-\frac{a+b \tan (e+f x)}{a+\sqrt{-b^2}}\right)^{-m/2} (a+b \tan (e+f x))^{n+1} F_1\left(n+1;1-\frac{m}{2},1-\frac{m}{2};n+2;\frac{a+b \tan (e+f x)}{a+\sqrt{-b^2}},\frac{a+b \tan (e+f x)}{a-\sqrt{-b^2}}\right)}{f (n+1) \left(a^2+b^2\right)}",1,"(AppellF1[1 + n, 1 - m/2, 1 - m/2, 2 + n, (a + b*Tan[e + f*x])/(a - Sqrt[-b^2]), (a + b*Tan[e + f*x])/(a + Sqrt[-b^2])]*Cos[e + f*x]^2*(d*Sec[e + f*x])^m*(a + b*Tan[e + f*x])^(1 + n)*(1 - (a + b*Tan[e + f*x])/(a - Sqrt[-b^2]))^(1 - m/2)*(1 - (a + b*Tan[e + f*x])/(a + Sqrt[-b^2]))^(1 - m/2))/(b*f*(1 + n))","A",3,3,23,0.1304,0,"{3512, 760, 133}"
646,1,161,0,0.1234856,"\int \sec ^6(c+d x) (a+b \tan (c+d x))^n \, dx","Int[Sec[c + d*x]^6*(a + b*Tan[c + d*x])^n,x]","\frac{\left(a^2+b^2\right)^2 (a+b \tan (c+d x))^{n+1}}{b^5 d (n+1)}-\frac{4 a \left(a^2+b^2\right) (a+b \tan (c+d x))^{n+2}}{b^5 d (n+2)}+\frac{2 \left(3 a^2+b^2\right) (a+b \tan (c+d x))^{n+3}}{b^5 d (n+3)}-\frac{4 a (a+b \tan (c+d x))^{n+4}}{b^5 d (n+4)}+\frac{(a+b \tan (c+d x))^{n+5}}{b^5 d (n+5)}","\frac{\left(a^2+b^2\right)^2 (a+b \tan (c+d x))^{n+1}}{b^5 d (n+1)}-\frac{4 a \left(a^2+b^2\right) (a+b \tan (c+d x))^{n+2}}{b^5 d (n+2)}+\frac{2 \left(3 a^2+b^2\right) (a+b \tan (c+d x))^{n+3}}{b^5 d (n+3)}-\frac{4 a (a+b \tan (c+d x))^{n+4}}{b^5 d (n+4)}+\frac{(a+b \tan (c+d x))^{n+5}}{b^5 d (n+5)}",1,"((a^2 + b^2)^2*(a + b*Tan[c + d*x])^(1 + n))/(b^5*d*(1 + n)) - (4*a*(a^2 + b^2)*(a + b*Tan[c + d*x])^(2 + n))/(b^5*d*(2 + n)) + (2*(3*a^2 + b^2)*(a + b*Tan[c + d*x])^(3 + n))/(b^5*d*(3 + n)) - (4*a*(a + b*Tan[c + d*x])^(4 + n))/(b^5*d*(4 + n)) + (a + b*Tan[c + d*x])^(5 + n)/(b^5*d*(5 + n))","A",3,2,21,0.09524,1,"{3506, 697}"
647,1,88,0,0.0764361,"\int \sec ^4(c+d x) (a+b \tan (c+d x))^n \, dx","Int[Sec[c + d*x]^4*(a + b*Tan[c + d*x])^n,x]","\frac{\left(a^2+b^2\right) (a+b \tan (c+d x))^{n+1}}{b^3 d (n+1)}-\frac{2 a (a+b \tan (c+d x))^{n+2}}{b^3 d (n+2)}+\frac{(a+b \tan (c+d x))^{n+3}}{b^3 d (n+3)}","\frac{\left(a^2+b^2\right) (a+b \tan (c+d x))^{n+1}}{b^3 d (n+1)}-\frac{2 a (a+b \tan (c+d x))^{n+2}}{b^3 d (n+2)}+\frac{(a+b \tan (c+d x))^{n+3}}{b^3 d (n+3)}",1,"((a^2 + b^2)*(a + b*Tan[c + d*x])^(1 + n))/(b^3*d*(1 + n)) - (2*a*(a + b*Tan[c + d*x])^(2 + n))/(b^3*d*(2 + n)) + (a + b*Tan[c + d*x])^(3 + n)/(b^3*d*(3 + n))","A",3,2,21,0.09524,1,"{3506, 697}"
648,1,26,0,0.0435077,"\int \sec ^2(c+d x) (a+b \tan (c+d x))^n \, dx","Int[Sec[c + d*x]^2*(a + b*Tan[c + d*x])^n,x]","\frac{(a+b \tan (c+d x))^{n+1}}{b d (n+1)}","\frac{(a+b \tan (c+d x))^{n+1}}{b d (n+1)}",1,"(a + b*Tan[c + d*x])^(1 + n)/(b*d*(1 + n))","A",2,2,21,0.09524,1,"{3506, 32}"
649,1,272,0,0.4573962,"\int \cos ^2(c+d x) (a+b \tan (c+d x))^n \, dx","Int[Cos[c + d*x]^2*(a + b*Tan[c + d*x])^n,x]","-\frac{\left(\sqrt{-b^2} \left(\frac{a^2}{b^2}-n+1\right)-a n\right) (a+b \tan (c+d x))^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{a+b \tan (c+d x)}{a-\sqrt{-b^2}}\right)}{4 b d (n+1) \left(\frac{a^2}{b^2}+1\right) \left(a-\sqrt{-b^2}\right)}+\frac{b \left(\sqrt{-b^2} \left(\frac{a^2}{b^2}-n+1\right)+a n\right) (a+b \tan (c+d x))^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{a+b \tan (c+d x)}{a+\sqrt{-b^2}}\right)}{4 d (n+1) \left(a^2+b^2\right) \left(a+\sqrt{-b^2}\right)}+\frac{\cos ^2(c+d x) (a \tan (c+d x)+b) (a+b \tan (c+d x))^{n+1}}{2 d \left(a^2+b^2\right)}","-\frac{\left(\sqrt{-b^2} \left(\frac{a^2}{b^2}-n+1\right)-a n\right) (a+b \tan (c+d x))^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{a+b \tan (c+d x)}{a-\sqrt{-b^2}}\right)}{4 b d (n+1) \left(\frac{a^2}{b^2}+1\right) \left(a-\sqrt{-b^2}\right)}+\frac{b \left(\sqrt{-b^2} \left(\frac{a^2}{b^2}-n+1\right)+a n\right) (a+b \tan (c+d x))^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{a+b \tan (c+d x)}{a+\sqrt{-b^2}}\right)}{4 d (n+1) \left(a^2+b^2\right) \left(a+\sqrt{-b^2}\right)}+\frac{\cos ^2(c+d x) (a \tan (c+d x)+b) (a+b \tan (c+d x))^{n+1}}{2 d \left(a^2+b^2\right)}",1,"-((Sqrt[-b^2]*(1 + a^2/b^2 - n) - a*n)*Hypergeometric2F1[1, 1 + n, 2 + n, (a + b*Tan[c + d*x])/(a - Sqrt[-b^2])]*(a + b*Tan[c + d*x])^(1 + n))/(4*(1 + a^2/b^2)*b*(a - Sqrt[-b^2])*d*(1 + n)) + (b*(Sqrt[-b^2]*(1 + a^2/b^2 - n) + a*n)*Hypergeometric2F1[1, 1 + n, 2 + n, (a + b*Tan[c + d*x])/(a + Sqrt[-b^2])]*(a + b*Tan[c + d*x])^(1 + n))/(4*(a^2 + b^2)*(a + Sqrt[-b^2])*d*(1 + n)) + (Cos[c + d*x]^2*(b + a*Tan[c + d*x])*(a + b*Tan[c + d*x])^(1 + n))/(2*(a^2 + b^2)*d)","A",6,4,21,0.1905,1,"{3506, 741, 831, 68}"
650,1,434,0,0.6867674,"\int \cos ^4(c+d x) (a+b \tan (c+d x))^n \, dx","Int[Cos[c + d*x]^4*(a + b*Tan[c + d*x])^n,x]","\frac{b \left(\frac{a n \left(\frac{3 a^2}{b^2}-2 n+5\right)}{b^2}-\frac{\sqrt{-b^2} \left(a^2 b^2 \left(-n^2-2 n+6\right)+3 a^4+b^4 \left(n^2-4 n+3\right)\right)}{b^6}\right) (a+b \tan (c+d x))^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{a+b \tan (c+d x)}{a-\sqrt{-b^2}}\right)}{16 d (n+1) \left(\frac{a^2}{b^2}+1\right)^2 \left(a-\sqrt{-b^2}\right)}+\frac{b \left(\frac{\sqrt{-b^2} \left(a^2 b^2 \left(-n^2-2 n+6\right)+3 a^4+b^4 \left(n^2-4 n+3\right)\right)}{b^6}+\frac{a n \left(\frac{3 a^2}{b^2}-2 n+5\right)}{b^2}\right) (a+b \tan (c+d x))^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{a+b \tan (c+d x)}{a+\sqrt{-b^2}}\right)}{16 d (n+1) \left(\frac{a^2}{b^2}+1\right)^2 \left(a+\sqrt{-b^2}\right)}+\frac{\cos ^4(c+d x) (a \tan (c+d x)+b) (a+b \tan (c+d x))^{n+1}}{4 d \left(a^2+b^2\right)}+\frac{b \cos ^2(c+d x) \left(a b \left(\frac{3 a^2}{b^2}-2 n+5\right) \tan (c+d x)+a^2 (n+1)+b^2 (3-n)\right) (a+b \tan (c+d x))^{n+1}}{8 d \left(a^2+b^2\right)^2}","\frac{b \left(\frac{a n \left(\frac{3 a^2}{b^2}-2 n+5\right)}{b^2}-\frac{\sqrt{-b^2} \left(a^2 b^2 \left(-n^2-2 n+6\right)+3 a^4+b^4 \left(n^2-4 n+3\right)\right)}{b^6}\right) (a+b \tan (c+d x))^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{a+b \tan (c+d x)}{a-\sqrt{-b^2}}\right)}{16 d (n+1) \left(\frac{a^2}{b^2}+1\right)^2 \left(a-\sqrt{-b^2}\right)}+\frac{b \left(\frac{\sqrt{-b^2} \left(a^2 b^2 \left(-n^2-2 n+6\right)+3 a^4+b^4 \left(n^2-4 n+3\right)\right)}{b^6}+\frac{a n \left(\frac{3 a^2}{b^2}-2 n+5\right)}{b^2}\right) (a+b \tan (c+d x))^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{a+b \tan (c+d x)}{a+\sqrt{-b^2}}\right)}{16 d (n+1) \left(\frac{a^2}{b^2}+1\right)^2 \left(a+\sqrt{-b^2}\right)}+\frac{\cos ^4(c+d x) (a \tan (c+d x)+b) (a+b \tan (c+d x))^{n+1}}{4 d \left(a^2+b^2\right)}+\frac{b \cos ^2(c+d x) \left(a b \left(\frac{3 a^2}{b^2}-2 n+5\right) \tan (c+d x)+a^2 (n+1)+b^2 (3-n)\right) (a+b \tan (c+d x))^{n+1}}{8 d \left(a^2+b^2\right)^2}",1,"(b*((a*(5 + (3*a^2)/b^2 - 2*n)*n)/b^2 - (Sqrt[-b^2]*(3*a^4 + a^2*b^2*(6 - 2*n - n^2) + b^4*(3 - 4*n + n^2)))/b^6)*Hypergeometric2F1[1, 1 + n, 2 + n, (a + b*Tan[c + d*x])/(a - Sqrt[-b^2])]*(a + b*Tan[c + d*x])^(1 + n))/(16*(1 + a^2/b^2)^2*(a - Sqrt[-b^2])*d*(1 + n)) + (b*((a*(5 + (3*a^2)/b^2 - 2*n)*n)/b^2 + (Sqrt[-b^2]*(3*a^4 + a^2*b^2*(6 - 2*n - n^2) + b^4*(3 - 4*n + n^2)))/b^6)*Hypergeometric2F1[1, 1 + n, 2 + n, (a + b*Tan[c + d*x])/(a + Sqrt[-b^2])]*(a + b*Tan[c + d*x])^(1 + n))/(16*(1 + a^2/b^2)^2*(a + Sqrt[-b^2])*d*(1 + n)) + (Cos[c + d*x]^4*(b + a*Tan[c + d*x])*(a + b*Tan[c + d*x])^(1 + n))/(4*(a^2 + b^2)*d) + (b*Cos[c + d*x]^2*(a + b*Tan[c + d*x])^(1 + n)*(b^2*(3 - n) + a^2*(1 + n) + a*b*(5 + (3*a^2)/b^2 - 2*n)*Tan[c + d*x]))/(8*(a^2 + b^2)^2*d)","A",7,5,21,0.2381,1,"{3506, 741, 823, 831, 68}"
651,1,159,0,0.1636873,"\int \sec ^3(c+d x) (a+b \tan (c+d x))^n \, dx","Int[Sec[c + d*x]^3*(a + b*Tan[c + d*x])^n,x]","\frac{\sec (c+d x) (a+b \tan (c+d x))^{n+1} F_1\left(n+1;-\frac{1}{2},-\frac{1}{2};n+2;\frac{a+b \tan (c+d x)}{a-\sqrt{-b^2}},\frac{a+b \tan (c+d x)}{a+\sqrt{-b^2}}\right)}{b d (n+1) \sqrt{1-\frac{a+b \tan (c+d x)}{a-\sqrt{-b^2}}} \sqrt{1-\frac{a+b \tan (c+d x)}{a+\sqrt{-b^2}}}}","\frac{\sec (c+d x) (a+b \tan (c+d x))^{n+1} F_1\left(n+1;-\frac{1}{2},-\frac{1}{2};n+2;\frac{a+b \tan (c+d x)}{a-\sqrt{-b^2}},\frac{a+b \tan (c+d x)}{a+\sqrt{-b^2}}\right)}{b d (n+1) \sqrt{1-\frac{a+b \tan (c+d x)}{a-\sqrt{-b^2}}} \sqrt{1-\frac{a+b \tan (c+d x)}{a+\sqrt{-b^2}}}}",1,"(AppellF1[1 + n, -1/2, -1/2, 2 + n, (a + b*Tan[c + d*x])/(a - Sqrt[-b^2]), (a + b*Tan[c + d*x])/(a + Sqrt[-b^2])]*Sec[c + d*x]*(a + b*Tan[c + d*x])^(1 + n))/(b*d*(1 + n)*Sqrt[1 - (a + b*Tan[c + d*x])/(a - Sqrt[-b^2])]*Sqrt[1 - (a + b*Tan[c + d*x])/(a + Sqrt[-b^2])])","A",3,3,21,0.1429,1,"{3512, 760, 133}"
652,1,159,0,0.1133229,"\int \sec (c+d x) (a+b \tan (c+d x))^n \, dx","Int[Sec[c + d*x]*(a + b*Tan[c + d*x])^n,x]","\frac{\cos (c+d x) \sqrt{1-\frac{a+b \tan (c+d x)}{a-\sqrt{-b^2}}} \sqrt{1-\frac{a+b \tan (c+d x)}{a+\sqrt{-b^2}}} (a+b \tan (c+d x))^{n+1} F_1\left(n+1;\frac{1}{2},\frac{1}{2};n+2;\frac{a+b \tan (c+d x)}{a-\sqrt{-b^2}},\frac{a+b \tan (c+d x)}{a+\sqrt{-b^2}}\right)}{b d (n+1)}","\frac{\cos (c+d x) \sqrt{1-\frac{a+b \tan (c+d x)}{a-\sqrt{-b^2}}} \sqrt{1-\frac{a+b \tan (c+d x)}{a+\sqrt{-b^2}}} (a+b \tan (c+d x))^{n+1} F_1\left(n+1;\frac{1}{2},\frac{1}{2};n+2;\frac{a+b \tan (c+d x)}{a-\sqrt{-b^2}},\frac{a+b \tan (c+d x)}{a+\sqrt{-b^2}}\right)}{b d (n+1)}",1,"(AppellF1[1 + n, 1/2, 1/2, 2 + n, (a + b*Tan[c + d*x])/(a - Sqrt[-b^2]), (a + b*Tan[c + d*x])/(a + Sqrt[-b^2])]*Cos[c + d*x]*(a + b*Tan[c + d*x])^(1 + n)*Sqrt[1 - (a + b*Tan[c + d*x])/(a - Sqrt[-b^2])]*Sqrt[1 - (a + b*Tan[c + d*x])/(a + Sqrt[-b^2])])/(b*d*(1 + n))","A",3,3,19,0.1579,1,"{3512, 760, 133}"
653,1,161,0,0.1249671,"\int \cos (c+d x) (a+b \tan (c+d x))^n \, dx","Int[Cos[c + d*x]*(a + b*Tan[c + d*x])^n,x]","\frac{\cos ^3(c+d x) \left(1-\frac{a+b \tan (c+d x)}{a-\sqrt{-b^2}}\right)^{3/2} \left(1-\frac{a+b \tan (c+d x)}{a+\sqrt{-b^2}}\right)^{3/2} (a+b \tan (c+d x))^{n+1} F_1\left(n+1;\frac{3}{2},\frac{3}{2};n+2;\frac{a+b \tan (c+d x)}{a-\sqrt{-b^2}},\frac{a+b \tan (c+d x)}{a+\sqrt{-b^2}}\right)}{b d (n+1)}","\frac{\cos ^3(c+d x) \left(1-\frac{a+b \tan (c+d x)}{a-\sqrt{-b^2}}\right)^{3/2} \left(1-\frac{a+b \tan (c+d x)}{a+\sqrt{-b^2}}\right)^{3/2} (a+b \tan (c+d x))^{n+1} F_1\left(n+1;\frac{3}{2},\frac{3}{2};n+2;\frac{a+b \tan (c+d x)}{a-\sqrt{-b^2}},\frac{a+b \tan (c+d x)}{a+\sqrt{-b^2}}\right)}{b d (n+1)}",1,"(AppellF1[1 + n, 3/2, 3/2, 2 + n, (a + b*Tan[c + d*x])/(a - Sqrt[-b^2]), (a + b*Tan[c + d*x])/(a + Sqrt[-b^2])]*Cos[c + d*x]^3*(a + b*Tan[c + d*x])^(1 + n)*(1 - (a + b*Tan[c + d*x])/(a - Sqrt[-b^2]))^(3/2)*(1 - (a + b*Tan[c + d*x])/(a + Sqrt[-b^2]))^(3/2))/(b*d*(1 + n))","A",3,3,19,0.1579,1,"{3512, 760, 133}"
654,1,161,0,0.1341215,"\int \cos ^3(c+d x) (a+b \tan (c+d x))^n \, dx","Int[Cos[c + d*x]^3*(a + b*Tan[c + d*x])^n,x]","\frac{\cos ^5(c+d x) \left(1-\frac{a+b \tan (c+d x)}{a-\sqrt{-b^2}}\right)^{5/2} \left(1-\frac{a+b \tan (c+d x)}{a+\sqrt{-b^2}}\right)^{5/2} (a+b \tan (c+d x))^{n+1} F_1\left(n+1;\frac{5}{2},\frac{5}{2};n+2;\frac{a+b \tan (c+d x)}{a-\sqrt{-b^2}},\frac{a+b \tan (c+d x)}{a+\sqrt{-b^2}}\right)}{b d (n+1)}","\frac{\cos ^5(c+d x) \left(1-\frac{a+b \tan (c+d x)}{a-\sqrt{-b^2}}\right)^{5/2} \left(1-\frac{a+b \tan (c+d x)}{a+\sqrt{-b^2}}\right)^{5/2} (a+b \tan (c+d x))^{n+1} F_1\left(n+1;\frac{5}{2},\frac{5}{2};n+2;\frac{a+b \tan (c+d x)}{a-\sqrt{-b^2}},\frac{a+b \tan (c+d x)}{a+\sqrt{-b^2}}\right)}{b d (n+1)}",1,"(AppellF1[1 + n, 5/2, 5/2, 2 + n, (a + b*Tan[c + d*x])/(a - Sqrt[-b^2]), (a + b*Tan[c + d*x])/(a + Sqrt[-b^2])]*Cos[c + d*x]^5*(a + b*Tan[c + d*x])^(1 + n)*(1 - (a + b*Tan[c + d*x])/(a - Sqrt[-b^2]))^(5/2)*(1 - (a + b*Tan[c + d*x])/(a + Sqrt[-b^2]))^(5/2))/(b*d*(1 + n))","A",3,3,21,0.1429,1,"{3512, 760, 133}"
655,1,124,0,0.1354201,"\int (e \cos (c+d x))^{7/2} (a+i a \tan (c+d x)) \, dx","Int[(e*Cos[c + d*x])^(7/2)*(a + I*a*Tan[c + d*x]),x]","-\frac{2 i a (e \cos (c+d x))^{7/2}}{7 d}+\frac{10 a F\left(\left.\frac{1}{2} (c+d x)\right|2\right) (e \cos (c+d x))^{7/2}}{21 d \cos ^{\frac{7}{2}}(c+d x)}+\frac{2 a \tan (c+d x) (e \cos (c+d x))^{7/2}}{7 d}+\frac{10 a \tan (c+d x) \sec ^2(c+d x) (e \cos (c+d x))^{7/2}}{21 d}","-\frac{2 i a (e \cos (c+d x))^{7/2}}{7 d}+\frac{10 a F\left(\left.\frac{1}{2} (c+d x)\right|2\right) (e \cos (c+d x))^{7/2}}{21 d \cos ^{\frac{7}{2}}(c+d x)}+\frac{2 a \tan (c+d x) (e \cos (c+d x))^{7/2}}{7 d}+\frac{10 a \tan (c+d x) \sec ^2(c+d x) (e \cos (c+d x))^{7/2}}{21 d}",1,"(((-2*I)/7)*a*(e*Cos[c + d*x])^(7/2))/d + (10*a*(e*Cos[c + d*x])^(7/2)*EllipticF[(c + d*x)/2, 2])/(21*d*Cos[c + d*x]^(7/2)) + (2*a*(e*Cos[c + d*x])^(7/2)*Tan[c + d*x])/(7*d) + (10*a*(e*Cos[c + d*x])^(7/2)*Sec[c + d*x]^2*Tan[c + d*x])/(21*d)","A",6,5,26,0.1923,1,"{3515, 3486, 3769, 3771, 2641}"
656,1,90,0,0.1113527,"\int (e \cos (c+d x))^{5/2} (a+i a \tan (c+d x)) \, dx","Int[(e*Cos[c + d*x])^(5/2)*(a + I*a*Tan[c + d*x]),x]","-\frac{2 i a (e \cos (c+d x))^{5/2}}{5 d}+\frac{6 a E\left(\left.\frac{1}{2} (c+d x)\right|2\right) (e \cos (c+d x))^{5/2}}{5 d \cos ^{\frac{5}{2}}(c+d x)}+\frac{2 a \tan (c+d x) (e \cos (c+d x))^{5/2}}{5 d}","-\frac{2 i a (e \cos (c+d x))^{5/2}}{5 d}+\frac{6 a E\left(\left.\frac{1}{2} (c+d x)\right|2\right) (e \cos (c+d x))^{5/2}}{5 d \cos ^{\frac{5}{2}}(c+d x)}+\frac{2 a \tan (c+d x) (e \cos (c+d x))^{5/2}}{5 d}",1,"(((-2*I)/5)*a*(e*Cos[c + d*x])^(5/2))/d + (6*a*(e*Cos[c + d*x])^(5/2)*EllipticE[(c + d*x)/2, 2])/(5*d*Cos[c + d*x]^(5/2)) + (2*a*(e*Cos[c + d*x])^(5/2)*Tan[c + d*x])/(5*d)","A",5,5,26,0.1923,1,"{3515, 3486, 3769, 3771, 2639}"
657,1,90,0,0.1093136,"\int (e \cos (c+d x))^{3/2} (a+i a \tan (c+d x)) \, dx","Int[(e*Cos[c + d*x])^(3/2)*(a + I*a*Tan[c + d*x]),x]","-\frac{2 i a (e \cos (c+d x))^{3/2}}{3 d}+\frac{2 a F\left(\left.\frac{1}{2} (c+d x)\right|2\right) (e \cos (c+d x))^{3/2}}{3 d \cos ^{\frac{3}{2}}(c+d x)}+\frac{2 a \tan (c+d x) (e \cos (c+d x))^{3/2}}{3 d}","-\frac{2 i a (e \cos (c+d x))^{3/2}}{3 d}+\frac{2 a F\left(\left.\frac{1}{2} (c+d x)\right|2\right) (e \cos (c+d x))^{3/2}}{3 d \cos ^{\frac{3}{2}}(c+d x)}+\frac{2 a \tan (c+d x) (e \cos (c+d x))^{3/2}}{3 d}",1,"(((-2*I)/3)*a*(e*Cos[c + d*x])^(3/2))/d + (2*a*(e*Cos[c + d*x])^(3/2)*EllipticF[(c + d*x)/2, 2])/(3*d*Cos[c + d*x]^(3/2)) + (2*a*(e*Cos[c + d*x])^(3/2)*Tan[c + d*x])/(3*d)","A",5,5,26,0.1923,1,"{3515, 3486, 3769, 3771, 2641}"
658,1,60,0,0.0782001,"\int \sqrt{e \cos (c+d x)} (a+i a \tan (c+d x)) \, dx","Int[Sqrt[e*Cos[c + d*x]]*(a + I*a*Tan[c + d*x]),x]","\frac{2 a E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{e \cos (c+d x)}}{d \sqrt{\cos (c+d x)}}-\frac{2 i a \sqrt{e \cos (c+d x)}}{d}","\frac{2 a E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{e \cos (c+d x)}}{d \sqrt{\cos (c+d x)}}-\frac{2 i a \sqrt{e \cos (c+d x)}}{d}",1,"((-2*I)*a*Sqrt[e*Cos[c + d*x]])/d + (2*a*Sqrt[e*Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2])/(d*Sqrt[Cos[c + d*x]])","A",4,4,26,0.1538,1,"{3515, 3486, 3771, 2639}"
659,1,60,0,0.0793143,"\int \frac{a+i a \tan (c+d x)}{\sqrt{e \cos (c+d x)}} \, dx","Int[(a + I*a*Tan[c + d*x])/Sqrt[e*Cos[c + d*x]],x]","\frac{2 a \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{d \sqrt{e \cos (c+d x)}}+\frac{2 i a}{d \sqrt{e \cos (c+d x)}}","\frac{2 a \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{d \sqrt{e \cos (c+d x)}}+\frac{2 i a}{d \sqrt{e \cos (c+d x)}}",1,"((2*I)*a)/(d*Sqrt[e*Cos[c + d*x]]) + (2*a*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2])/(d*Sqrt[e*Cos[c + d*x]])","A",4,4,26,0.1538,1,"{3515, 3486, 3771, 2641}"
660,1,92,0,0.1047109,"\int \frac{a+i a \tan (c+d x)}{(e \cos (c+d x))^{3/2}} \, dx","Int[(a + I*a*Tan[c + d*x])/(e*Cos[c + d*x])^(3/2),x]","\frac{2 i a}{3 d (e \cos (c+d x))^{3/2}}-\frac{2 a \cos ^{\frac{3}{2}}(c+d x) E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{d (e \cos (c+d x))^{3/2}}+\frac{2 a \sin (c+d x) \cos (c+d x)}{d (e \cos (c+d x))^{3/2}}","\frac{2 i a}{3 d (e \cos (c+d x))^{3/2}}-\frac{2 a \cos ^{\frac{3}{2}}(c+d x) E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{d (e \cos (c+d x))^{3/2}}+\frac{2 a \sin (c+d x)}{d e \sqrt{e \cos (c+d x)}}",1,"(((2*I)/3)*a)/(d*(e*Cos[c + d*x])^(3/2)) - (2*a*Cos[c + d*x]^(3/2)*EllipticE[(c + d*x)/2, 2])/(d*(e*Cos[c + d*x])^(3/2)) + (2*a*Cos[c + d*x]*Sin[c + d*x])/(d*(e*Cos[c + d*x])^(3/2))","A",5,5,26,0.1923,1,"{3515, 3486, 3768, 3771, 2639}"
661,1,96,0,0.1037492,"\int \frac{a+i a \tan (c+d x)}{(e \cos (c+d x))^{5/2}} \, dx","Int[(a + I*a*Tan[c + d*x])/(e*Cos[c + d*x])^(5/2),x]","\frac{2 i a}{5 d (e \cos (c+d x))^{5/2}}+\frac{2 a \cos ^{\frac{5}{2}}(c+d x) F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{3 d (e \cos (c+d x))^{5/2}}+\frac{2 a \sin (c+d x) \cos (c+d x)}{3 d (e \cos (c+d x))^{5/2}}","\frac{2 i a}{5 d (e \cos (c+d x))^{5/2}}+\frac{2 a \cos ^{\frac{5}{2}}(c+d x) F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{3 d (e \cos (c+d x))^{5/2}}+\frac{2 a \sin (c+d x) \cos (c+d x)}{3 d (e \cos (c+d x))^{5/2}}",1,"(((2*I)/5)*a)/(d*(e*Cos[c + d*x])^(5/2)) + (2*a*Cos[c + d*x]^(5/2)*EllipticF[(c + d*x)/2, 2])/(3*d*(e*Cos[c + d*x])^(5/2)) + (2*a*Cos[c + d*x]*Sin[c + d*x])/(3*d*(e*Cos[c + d*x])^(5/2))","A",5,5,26,0.1923,1,"{3515, 3486, 3768, 3771, 2641}"
662,1,130,0,0.1273111,"\int \frac{a+i a \tan (c+d x)}{(e \cos (c+d x))^{7/2}} \, dx","Int[(a + I*a*Tan[c + d*x])/(e*Cos[c + d*x])^(7/2),x]","\frac{2 i a}{7 d (e \cos (c+d x))^{7/2}}+\frac{6 a \sin (c+d x) \cos ^3(c+d x)}{5 d (e \cos (c+d x))^{7/2}}-\frac{6 a \cos ^{\frac{7}{2}}(c+d x) E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{5 d (e \cos (c+d x))^{7/2}}+\frac{2 a \sin (c+d x) \cos (c+d x)}{5 d (e \cos (c+d x))^{7/2}}","\frac{2 i a}{7 d (e \cos (c+d x))^{7/2}}+\frac{6 a \sin (c+d x) \cos ^3(c+d x)}{5 d (e \cos (c+d x))^{7/2}}-\frac{6 a \cos ^{\frac{7}{2}}(c+d x) E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{5 d (e \cos (c+d x))^{7/2}}+\frac{2 a \sin (c+d x) \cos (c+d x)}{5 d (e \cos (c+d x))^{7/2}}",1,"(((2*I)/7)*a)/(d*(e*Cos[c + d*x])^(7/2)) - (6*a*Cos[c + d*x]^(7/2)*EllipticE[(c + d*x)/2, 2])/(5*d*(e*Cos[c + d*x])^(7/2)) + (2*a*Cos[c + d*x]*Sin[c + d*x])/(5*d*(e*Cos[c + d*x])^(7/2)) + (6*a*Cos[c + d*x]^3*Sin[c + d*x])/(5*d*(e*Cos[c + d*x])^(7/2))","A",6,5,26,0.1923,1,"{3515, 3486, 3768, 3771, 2639}"
663,1,190,0,0.220811,"\int \frac{(e \cos (c+d x))^{7/2}}{(a+i a \tan (c+d x))^2} \, dx","Int[(e*Cos[c + d*x])^(7/2)/(a + I*a*Tan[c + d*x])^2,x]","\frac{4 i \cos ^2(c+d x) (e \cos (c+d x))^{7/2}}{15 d \left(a^2+i a^2 \tan (c+d x)\right)}+\frac{2 F\left(\left.\frac{1}{2} (c+d x)\right|2\right) (e \cos (c+d x))^{7/2}}{7 a^2 d \cos ^{\frac{7}{2}}(c+d x)}+\frac{2 \sin (c+d x) \cos (c+d x) (e \cos (c+d x))^{7/2}}{15 a^2 d}+\frac{6 \tan (c+d x) (e \cos (c+d x))^{7/2}}{35 a^2 d}+\frac{2 \tan (c+d x) \sec ^2(c+d x) (e \cos (c+d x))^{7/2}}{7 a^2 d}","\frac{4 i \cos ^2(c+d x) (e \cos (c+d x))^{7/2}}{15 d \left(a^2+i a^2 \tan (c+d x)\right)}+\frac{2 F\left(\left.\frac{1}{2} (c+d x)\right|2\right) (e \cos (c+d x))^{7/2}}{7 a^2 d \cos ^{\frac{7}{2}}(c+d x)}+\frac{2 \sin (c+d x) \cos (c+d x) (e \cos (c+d x))^{7/2}}{15 a^2 d}+\frac{6 \tan (c+d x) (e \cos (c+d x))^{7/2}}{35 a^2 d}+\frac{2 \tan (c+d x) \sec ^2(c+d x) (e \cos (c+d x))^{7/2}}{7 a^2 d}",1,"(2*(e*Cos[c + d*x])^(7/2)*EllipticF[(c + d*x)/2, 2])/(7*a^2*d*Cos[c + d*x]^(7/2)) + (2*Cos[c + d*x]*(e*Cos[c + d*x])^(7/2)*Sin[c + d*x])/(15*a^2*d) + (6*(e*Cos[c + d*x])^(7/2)*Tan[c + d*x])/(35*a^2*d) + (2*(e*Cos[c + d*x])^(7/2)*Sec[c + d*x]^2*Tan[c + d*x])/(7*a^2*d) + (((4*I)/15)*Cos[c + d*x]^2*(e*Cos[c + d*x])^(7/2))/(d*(a^2 + I*a^2*Tan[c + d*x]))","A",7,5,28,0.1786,1,"{3515, 3500, 3769, 3771, 2641}"
664,1,154,0,0.1913695,"\int \frac{(e \cos (c+d x))^{5/2}}{(a+i a \tan (c+d x))^2} \, dx","Int[(e*Cos[c + d*x])^(5/2)/(a + I*a*Tan[c + d*x])^2,x]","\frac{4 i \cos ^2(c+d x) (e \cos (c+d x))^{5/2}}{13 d \left(a^2+i a^2 \tan (c+d x)\right)}+\frac{42 E\left(\left.\frac{1}{2} (c+d x)\right|2\right) (e \cos (c+d x))^{5/2}}{65 a^2 d \cos ^{\frac{5}{2}}(c+d x)}+\frac{2 \sin (c+d x) \cos (c+d x) (e \cos (c+d x))^{5/2}}{13 a^2 d}+\frac{14 \tan (c+d x) (e \cos (c+d x))^{5/2}}{65 a^2 d}","\frac{4 i \cos ^2(c+d x) (e \cos (c+d x))^{5/2}}{13 d \left(a^2+i a^2 \tan (c+d x)\right)}+\frac{42 E\left(\left.\frac{1}{2} (c+d x)\right|2\right) (e \cos (c+d x))^{5/2}}{65 a^2 d \cos ^{\frac{5}{2}}(c+d x)}+\frac{2 \sin (c+d x) \cos (c+d x) (e \cos (c+d x))^{5/2}}{13 a^2 d}+\frac{14 \tan (c+d x) (e \cos (c+d x))^{5/2}}{65 a^2 d}",1,"(42*(e*Cos[c + d*x])^(5/2)*EllipticE[(c + d*x)/2, 2])/(65*a^2*d*Cos[c + d*x]^(5/2)) + (2*Cos[c + d*x]*(e*Cos[c + d*x])^(5/2)*Sin[c + d*x])/(13*a^2*d) + (14*(e*Cos[c + d*x])^(5/2)*Tan[c + d*x])/(65*a^2*d) + (((4*I)/13)*Cos[c + d*x]^2*(e*Cos[c + d*x])^(5/2))/(d*(a^2 + I*a^2*Tan[c + d*x]))","A",6,5,28,0.1786,1,"{3515, 3500, 3769, 3771, 2639}"
665,1,154,0,0.1983618,"\int \frac{(e \cos (c+d x))^{3/2}}{(a+i a \tan (c+d x))^2} \, dx","Int[(e*Cos[c + d*x])^(3/2)/(a + I*a*Tan[c + d*x])^2,x]","\frac{4 i \cos ^2(c+d x) (e \cos (c+d x))^{3/2}}{11 d \left(a^2+i a^2 \tan (c+d x)\right)}+\frac{10 F\left(\left.\frac{1}{2} (c+d x)\right|2\right) (e \cos (c+d x))^{3/2}}{33 a^2 d \cos ^{\frac{3}{2}}(c+d x)}+\frac{2 \sin (c+d x) \cos (c+d x) (e \cos (c+d x))^{3/2}}{11 a^2 d}+\frac{10 \tan (c+d x) (e \cos (c+d x))^{3/2}}{33 a^2 d}","\frac{4 i \cos ^2(c+d x) (e \cos (c+d x))^{3/2}}{11 d \left(a^2+i a^2 \tan (c+d x)\right)}+\frac{10 F\left(\left.\frac{1}{2} (c+d x)\right|2\right) (e \cos (c+d x))^{3/2}}{33 a^2 d \cos ^{\frac{3}{2}}(c+d x)}+\frac{2 \sin (c+d x) \cos (c+d x) (e \cos (c+d x))^{3/2}}{11 a^2 d}+\frac{10 \tan (c+d x) (e \cos (c+d x))^{3/2}}{33 a^2 d}",1,"(10*(e*Cos[c + d*x])^(3/2)*EllipticF[(c + d*x)/2, 2])/(33*a^2*d*Cos[c + d*x]^(3/2)) + (2*Cos[c + d*x]*(e*Cos[c + d*x])^(3/2)*Sin[c + d*x])/(11*a^2*d) + (10*(e*Cos[c + d*x])^(3/2)*Tan[c + d*x])/(33*a^2*d) + (((4*I)/11)*Cos[c + d*x]^2*(e*Cos[c + d*x])^(3/2))/(d*(a^2 + I*a^2*Tan[c + d*x]))","A",6,5,28,0.1786,1,"{3515, 3500, 3769, 3771, 2641}"
666,1,126,0,0.167294,"\int \frac{\sqrt{e \cos (c+d x)}}{(a+i a \tan (c+d x))^2} \, dx","Int[Sqrt[e*Cos[c + d*x]]/(a + I*a*Tan[c + d*x])^2,x]","\frac{4 i \cos ^2(c+d x) \sqrt{e \cos (c+d x)}}{9 d \left(a^2+i a^2 \tan (c+d x)\right)}+\frac{2 \sin (c+d x) \cos (c+d x) \sqrt{e \cos (c+d x)}}{9 a^2 d}+\frac{2 E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{e \cos (c+d x)}}{3 a^2 d \sqrt{\cos (c+d x)}}","\frac{2 i \sqrt{e \cos (c+d x)}}{9 d \left(a^2+i a^2 \tan (c+d x)\right)}+\frac{2 E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{e \cos (c+d x)}}{3 a^2 d \sqrt{\cos (c+d x)}}+\frac{2 i \sqrt{e \cos (c+d x)}}{9 d (a+i a \tan (c+d x))^2}",1,"(2*Sqrt[e*Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2])/(3*a^2*d*Sqrt[Cos[c + d*x]]) + (2*Cos[c + d*x]*Sqrt[e*Cos[c + d*x]]*Sin[c + d*x])/(9*a^2*d) + (((4*I)/9)*Cos[c + d*x]^2*Sqrt[e*Cos[c + d*x]])/(d*(a^2 + I*a^2*Tan[c + d*x]))","A",5,5,28,0.1786,1,"{3515, 3500, 3769, 3771, 2639}"
667,1,126,0,0.1584035,"\int \frac{1}{\sqrt{e \cos (c+d x)} (a+i a \tan (c+d x))^2} \, dx","Int[1/(Sqrt[e*Cos[c + d*x]]*(a + I*a*Tan[c + d*x])^2),x]","\frac{4 i \cos ^2(c+d x)}{7 d \left(a^2+i a^2 \tan (c+d x)\right) \sqrt{e \cos (c+d x)}}+\frac{2 \sin (c+d x) \cos (c+d x)}{7 a^2 d \sqrt{e \cos (c+d x)}}+\frac{2 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{7 a^2 d \sqrt{e \cos (c+d x)}}","\frac{2 i}{7 d \left(a^2+i a^2 \tan (c+d x)\right) \sqrt{e \cos (c+d x)}}+\frac{2 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{7 a^2 d \sqrt{e \cos (c+d x)}}+\frac{2 i}{7 d (a+i a \tan (c+d x))^2 \sqrt{e \cos (c+d x)}}",1,"(2*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2])/(7*a^2*d*Sqrt[e*Cos[c + d*x]]) + (2*Cos[c + d*x]*Sin[c + d*x])/(7*a^2*d*Sqrt[e*Cos[c + d*x]]) + (((4*I)/7)*Cos[c + d*x]^2)/(d*Sqrt[e*Cos[c + d*x]]*(a^2 + I*a^2*Tan[c + d*x]))","A",5,5,28,0.1786,1,"{3515, 3500, 3769, 3771, 2641}"
668,1,92,0,0.1542201,"\int \frac{1}{(e \cos (c+d x))^{3/2} (a+i a \tan (c+d x))^2} \, dx","Int[1/((e*Cos[c + d*x])^(3/2)*(a + I*a*Tan[c + d*x])^2),x]","\frac{2 \cos ^{\frac{3}{2}}(c+d x) E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{5 a^2 d (e \cos (c+d x))^{3/2}}+\frac{4 i \cos ^2(c+d x)}{5 d \left(a^2+i a^2 \tan (c+d x)\right) (e \cos (c+d x))^{3/2}}","\frac{2 \cos ^{\frac{3}{2}}(c+d x) E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{5 a^2 d (e \cos (c+d x))^{3/2}}+\frac{4 i \cos ^2(c+d x)}{5 d \left(a^2+i a^2 \tan (c+d x)\right) (e \cos (c+d x))^{3/2}}",1,"(2*Cos[c + d*x]^(3/2)*EllipticE[(c + d*x)/2, 2])/(5*a^2*d*(e*Cos[c + d*x])^(3/2)) + (((4*I)/5)*Cos[c + d*x]^2)/(d*(e*Cos[c + d*x])^(3/2)*(a^2 + I*a^2*Tan[c + d*x]))","A",4,4,28,0.1429,1,"{3515, 3500, 3771, 2639}"
669,1,92,0,0.1499404,"\int \frac{1}{(e \cos (c+d x))^{5/2} (a+i a \tan (c+d x))^2} \, dx","Int[1/((e*Cos[c + d*x])^(5/2)*(a + I*a*Tan[c + d*x])^2),x]","-\frac{2 \cos ^{\frac{5}{2}}(c+d x) F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{3 a^2 d (e \cos (c+d x))^{5/2}}+\frac{4 i \cos ^2(c+d x)}{3 d \left(a^2+i a^2 \tan (c+d x)\right) (e \cos (c+d x))^{5/2}}","-\frac{2 \cos ^{\frac{5}{2}}(c+d x) F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{3 a^2 d (e \cos (c+d x))^{5/2}}+\frac{4 i \cos ^2(c+d x)}{3 d \left(a^2+i a^2 \tan (c+d x)\right) (e \cos (c+d x))^{5/2}}",1,"(-2*Cos[c + d*x]^(5/2)*EllipticF[(c + d*x)/2, 2])/(3*a^2*d*(e*Cos[c + d*x])^(5/2)) + (((4*I)/3)*Cos[c + d*x]^2)/(d*(e*Cos[c + d*x])^(5/2)*(a^2 + I*a^2*Tan[c + d*x]))","A",4,4,28,0.1429,1,"{3515, 3500, 3771, 2641}"
670,1,122,0,0.1710091,"\int \frac{1}{(e \cos (c+d x))^{7/2} (a+i a \tan (c+d x))^2} \, dx","Int[1/((e*Cos[c + d*x])^(7/2)*(a + I*a*Tan[c + d*x])^2),x]","-\frac{6 \sin (c+d x) \cos ^3(c+d x)}{a^2 d (e \cos (c+d x))^{7/2}}+\frac{4 i \cos ^2(c+d x)}{d \left(a^2+i a^2 \tan (c+d x)\right) (e \cos (c+d x))^{7/2}}+\frac{6 \cos ^{\frac{7}{2}}(c+d x) E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{a^2 d (e \cos (c+d x))^{7/2}}","-\frac{6 \sin (c+d x) \cos ^3(c+d x)}{a^2 d (e \cos (c+d x))^{7/2}}+\frac{4 i \cos ^2(c+d x)}{d \left(a^2+i a^2 \tan (c+d x)\right) (e \cos (c+d x))^{7/2}}+\frac{6 \cos ^{\frac{7}{2}}(c+d x) E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{a^2 d (e \cos (c+d x))^{7/2}}",1,"(6*Cos[c + d*x]^(7/2)*EllipticE[(c + d*x)/2, 2])/(a^2*d*(e*Cos[c + d*x])^(7/2)) - (6*Cos[c + d*x]^3*Sin[c + d*x])/(a^2*d*(e*Cos[c + d*x])^(7/2)) + ((4*I)*Cos[c + d*x]^2)/(d*(e*Cos[c + d*x])^(7/2)*(a^2 + I*a^2*Tan[c + d*x]))","A",5,5,28,0.1786,1,"{3515, 3500, 3768, 3771, 2639}"
671,1,126,0,0.1723229,"\int \frac{1}{(e \cos (c+d x))^{9/2} (a+i a \tan (c+d x))^2} \, dx","Int[1/((e*Cos[c + d*x])^(9/2)*(a + I*a*Tan[c + d*x])^2),x]","\frac{10 \sin (c+d x) \cos ^3(c+d x)}{3 a^2 d (e \cos (c+d x))^{9/2}}-\frac{4 i \cos ^2(c+d x)}{d \left(a^2+i a^2 \tan (c+d x)\right) (e \cos (c+d x))^{9/2}}+\frac{10 \cos ^{\frac{9}{2}}(c+d x) F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{3 a^2 d (e \cos (c+d x))^{9/2}}","\frac{10 \sin (c+d x) \cos ^3(c+d x)}{3 a^2 d (e \cos (c+d x))^{9/2}}-\frac{4 i \cos ^2(c+d x)}{d \left(a^2+i a^2 \tan (c+d x)\right) (e \cos (c+d x))^{9/2}}+\frac{10 \cos ^{\frac{9}{2}}(c+d x) F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{3 a^2 d (e \cos (c+d x))^{9/2}}",1,"(10*Cos[c + d*x]^(9/2)*EllipticF[(c + d*x)/2, 2])/(3*a^2*d*(e*Cos[c + d*x])^(9/2)) + (10*Cos[c + d*x]^3*Sin[c + d*x])/(3*a^2*d*(e*Cos[c + d*x])^(9/2)) - ((4*I)*Cos[c + d*x]^2)/(d*(e*Cos[c + d*x])^(9/2)*(a^2 + I*a^2*Tan[c + d*x]))","A",5,5,28,0.1786,1,"{3515, 3500, 3768, 3771, 2641}"
672,1,164,0,0.1908077,"\int \frac{1}{(e \cos (c+d x))^{11/2} (a+i a \tan (c+d x))^2} \, dx","Int[1/((e*Cos[c + d*x])^(11/2)*(a + I*a*Tan[c + d*x])^2),x]","\frac{14 \sin (c+d x) \cos ^5(c+d x)}{5 a^2 d (e \cos (c+d x))^{11/2}}+\frac{14 \sin (c+d x) \cos ^3(c+d x)}{15 a^2 d (e \cos (c+d x))^{11/2}}-\frac{4 i \cos ^2(c+d x)}{3 d \left(a^2+i a^2 \tan (c+d x)\right) (e \cos (c+d x))^{11/2}}-\frac{14 \cos ^{\frac{11}{2}}(c+d x) E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{5 a^2 d (e \cos (c+d x))^{11/2}}","\frac{14 \sin (c+d x) \cos ^5(c+d x)}{5 a^2 d (e \cos (c+d x))^{11/2}}+\frac{14 \sin (c+d x) \cos ^3(c+d x)}{15 a^2 d (e \cos (c+d x))^{11/2}}-\frac{4 i \cos ^2(c+d x)}{3 d \left(a^2+i a^2 \tan (c+d x)\right) (e \cos (c+d x))^{11/2}}-\frac{14 \cos ^{\frac{11}{2}}(c+d x) E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{5 a^2 d (e \cos (c+d x))^{11/2}}",1,"(-14*Cos[c + d*x]^(11/2)*EllipticE[(c + d*x)/2, 2])/(5*a^2*d*(e*Cos[c + d*x])^(11/2)) + (14*Cos[c + d*x]^3*Sin[c + d*x])/(15*a^2*d*(e*Cos[c + d*x])^(11/2)) + (14*Cos[c + d*x]^5*Sin[c + d*x])/(5*a^2*d*(e*Cos[c + d*x])^(11/2)) - (((4*I)/3)*Cos[c + d*x]^2)/(d*(e*Cos[c + d*x])^(11/2)*(a^2 + I*a^2*Tan[c + d*x]))","A",6,5,28,0.1786,1,"{3515, 3500, 3768, 3771, 2639}"
673,1,179,0,0.3826535,"\int (e \cos (c+d x))^{7/2} \sqrt{a+i a \tan (c+d x)} \, dx","Int[(e*Cos[c + d*x])^(7/2)*Sqrt[a + I*a*Tan[c + d*x]],x]","-\frac{2 i \sqrt{a+i a \tan (c+d x)} (e \cos (c+d x))^{7/2}}{7 d}+\frac{32 i a \sec ^4(c+d x) (e \cos (c+d x))^{7/2}}{35 d \sqrt{a+i a \tan (c+d x)}}-\frac{16 i \sec ^2(c+d x) \sqrt{a+i a \tan (c+d x)} (e \cos (c+d x))^{7/2}}{35 d}+\frac{12 i a \sec ^2(c+d x) (e \cos (c+d x))^{7/2}}{35 d \sqrt{a+i a \tan (c+d x)}}","-\frac{2 i \sqrt{a+i a \tan (c+d x)} (e \cos (c+d x))^{7/2}}{7 d}+\frac{32 i a \sec ^4(c+d x) (e \cos (c+d x))^{7/2}}{35 d \sqrt{a+i a \tan (c+d x)}}-\frac{16 i \sec ^2(c+d x) \sqrt{a+i a \tan (c+d x)} (e \cos (c+d x))^{7/2}}{35 d}+\frac{12 i a \sec ^2(c+d x) (e \cos (c+d x))^{7/2}}{35 d \sqrt{a+i a \tan (c+d x)}}",1,"(((12*I)/35)*a*(e*Cos[c + d*x])^(7/2)*Sec[c + d*x]^2)/(d*Sqrt[a + I*a*Tan[c + d*x]]) + (((32*I)/35)*a*(e*Cos[c + d*x])^(7/2)*Sec[c + d*x]^4)/(d*Sqrt[a + I*a*Tan[c + d*x]]) - (((2*I)/7)*(e*Cos[c + d*x])^(7/2)*Sqrt[a + I*a*Tan[c + d*x]])/d - (((16*I)/35)*(e*Cos[c + d*x])^(7/2)*Sec[c + d*x]^2*Sqrt[a + I*a*Tan[c + d*x]])/d","A",5,4,30,0.1333,1,"{3515, 3497, 3502, 3488}"
674,1,132,0,0.2880114,"\int (e \cos (c+d x))^{5/2} \sqrt{a+i a \tan (c+d x)} \, dx","Int[(e*Cos[c + d*x])^(5/2)*Sqrt[a + I*a*Tan[c + d*x]],x]","-\frac{2 i \sqrt{a+i a \tan (c+d x)} (e \cos (c+d x))^{5/2}}{5 d}-\frac{16 i \sec ^2(c+d x) \sqrt{a+i a \tan (c+d x)} (e \cos (c+d x))^{5/2}}{15 d}+\frac{8 i a \sec ^2(c+d x) (e \cos (c+d x))^{5/2}}{15 d \sqrt{a+i a \tan (c+d x)}}","-\frac{2 i \sqrt{a+i a \tan (c+d x)} (e \cos (c+d x))^{5/2}}{5 d}-\frac{16 i \sec ^2(c+d x) \sqrt{a+i a \tan (c+d x)} (e \cos (c+d x))^{5/2}}{15 d}+\frac{8 i a \sec ^2(c+d x) (e \cos (c+d x))^{5/2}}{15 d \sqrt{a+i a \tan (c+d x)}}",1,"(((8*I)/15)*a*(e*Cos[c + d*x])^(5/2)*Sec[c + d*x]^2)/(d*Sqrt[a + I*a*Tan[c + d*x]]) - (((2*I)/5)*(e*Cos[c + d*x])^(5/2)*Sqrt[a + I*a*Tan[c + d*x]])/d - (((16*I)/15)*(e*Cos[c + d*x])^(5/2)*Sec[c + d*x]^2*Sqrt[a + I*a*Tan[c + d*x]])/d","A",4,4,30,0.1333,1,"{3515, 3497, 3502, 3488}"
675,1,86,0,0.2121662,"\int (e \cos (c+d x))^{3/2} \sqrt{a+i a \tan (c+d x)} \, dx","Int[(e*Cos[c + d*x])^(3/2)*Sqrt[a + I*a*Tan[c + d*x]],x]","\frac{4 i a \sec ^2(c+d x) (e \cos (c+d x))^{3/2}}{3 d \sqrt{a+i a \tan (c+d x)}}-\frac{2 i \sqrt{a+i a \tan (c+d x)} (e \cos (c+d x))^{3/2}}{3 d}","\frac{4 i a e \sec (c+d x) \sqrt{e \cos (c+d x)}}{3 d \sqrt{a+i a \tan (c+d x)}}-\frac{2 i \sqrt{a+i a \tan (c+d x)} (e \cos (c+d x))^{3/2}}{3 d}",1,"(((4*I)/3)*a*(e*Cos[c + d*x])^(3/2)*Sec[c + d*x]^2)/(d*Sqrt[a + I*a*Tan[c + d*x]]) - (((2*I)/3)*(e*Cos[c + d*x])^(3/2)*Sqrt[a + I*a*Tan[c + d*x]])/d","A",3,3,30,0.1000,1,"{3515, 3497, 3488}"
676,1,36,0,0.1293113,"\int \sqrt{e \cos (c+d x)} \sqrt{a+i a \tan (c+d x)} \, dx","Int[Sqrt[e*Cos[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]],x]","-\frac{2 i \sqrt{a+i a \tan (c+d x)} \sqrt{e \cos (c+d x)}}{d}","-\frac{2 i \sqrt{a+i a \tan (c+d x)} \sqrt{e \cos (c+d x)}}{d}",1,"((-2*I)*Sqrt[e*Cos[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]])/d","A",2,2,30,0.06667,1,"{3515, 3488}"
677,1,335,0,0.2140577,"\int \frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{e \cos (c+d x)}} \, dx","Int[Sqrt[a + I*a*Tan[c + d*x]]/Sqrt[e*Cos[c + d*x]],x]","\frac{i \sqrt{2} \sqrt{a} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{a+i a \tan (c+d x)} \sqrt{e \cos (c+d x)}}{\sqrt{a} \sqrt{e}}\right)}{d \sqrt{e}}-\frac{i \sqrt{2} \sqrt{a} \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt{a+i a \tan (c+d x)} \sqrt{e \cos (c+d x)}}{\sqrt{a} \sqrt{e}}\right)}{d \sqrt{e}}-\frac{i \sqrt{a} \log \left(-\sqrt{2} \sqrt{a} \sqrt{a+i a \tan (c+d x)} \sqrt{e \cos (c+d x)}+\sqrt{e} \cos (c+d x) (a+i a \tan (c+d x))+a \sqrt{e}\right)}{\sqrt{2} d \sqrt{e}}+\frac{i \sqrt{a} \log \left(\sqrt{2} \sqrt{a} \sqrt{a+i a \tan (c+d x)} \sqrt{e \cos (c+d x)}+\sqrt{e} \cos (c+d x) (a+i a \tan (c+d x))+a \sqrt{e}\right)}{\sqrt{2} d \sqrt{e}}","\frac{i \sqrt{2} \sqrt{a} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{a+i a \tan (c+d x)} \sqrt{e \cos (c+d x)}}{\sqrt{a} \sqrt{e}}\right)}{d \sqrt{e}}-\frac{i \sqrt{2} \sqrt{a} \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt{a+i a \tan (c+d x)} \sqrt{e \cos (c+d x)}}{\sqrt{a} \sqrt{e}}\right)}{d \sqrt{e}}-\frac{i \sqrt{a} \log \left(-\sqrt{2} \sqrt{a} \sqrt{a+i a \tan (c+d x)} \sqrt{e \cos (c+d x)}+\sqrt{e} \cos (c+d x) (a+i a \tan (c+d x))+a \sqrt{e}\right)}{\sqrt{2} d \sqrt{e}}+\frac{i \sqrt{a} \log \left(\sqrt{2} \sqrt{a} \sqrt{a+i a \tan (c+d x)} \sqrt{e \cos (c+d x)}+\sqrt{e} \cos (c+d x) (a+i a \tan (c+d x))+a \sqrt{e}\right)}{\sqrt{2} d \sqrt{e}}",1,"(I*Sqrt[2]*Sqrt[a]*ArcTan[1 - (Sqrt[2]*Sqrt[e*Cos[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]])/(Sqrt[a]*Sqrt[e])])/(d*Sqrt[e]) - (I*Sqrt[2]*Sqrt[a]*ArcTan[1 + (Sqrt[2]*Sqrt[e*Cos[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]])/(Sqrt[a]*Sqrt[e])])/(d*Sqrt[e]) - (I*Sqrt[a]*Log[a*Sqrt[e] - Sqrt[2]*Sqrt[a]*Sqrt[e*Cos[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]] + Sqrt[e]*Cos[c + d*x]*(a + I*a*Tan[c + d*x])])/(Sqrt[2]*d*Sqrt[e]) + (I*Sqrt[a]*Log[a*Sqrt[e] + Sqrt[2]*Sqrt[a]*Sqrt[e*Cos[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]] + Sqrt[e]*Cos[c + d*x]*(a + I*a*Tan[c + d*x])])/(Sqrt[2]*d*Sqrt[e])","A",10,7,30,0.2333,1,"{3513, 297, 1162, 617, 204, 1165, 628}"
678,1,620,0,0.590468,"\int \frac{\sqrt{a+i a \tan (c+d x)}}{(e \cos (c+d x))^{3/2}} \, dx","Int[Sqrt[a + I*a*Tan[c + d*x]]/(e*Cos[c + d*x])^(3/2),x]","-\frac{i a^{3/2} e^{3/2} \sec (c+d x) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{e} \sqrt{a-i a \tan (c+d x)}}{\sqrt{a} \sqrt{e \sec (c+d x)}}\right)}{\sqrt{2} d \sqrt{a-i a \tan (c+d x)} \sqrt{a+i a \tan (c+d x)} (e \cos (c+d x))^{3/2} (e \sec (c+d x))^{3/2}}+\frac{i a^{3/2} e^{3/2} \sec (c+d x) \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt{e} \sqrt{a-i a \tan (c+d x)}}{\sqrt{a} \sqrt{e \sec (c+d x)}}\right)}{\sqrt{2} d \sqrt{a-i a \tan (c+d x)} \sqrt{a+i a \tan (c+d x)} (e \cos (c+d x))^{3/2} (e \sec (c+d x))^{3/2}}+\frac{i a^{3/2} e^{3/2} \sec (c+d x) \log \left(-\frac{\sqrt{2} \sqrt{a} \sqrt{e} \sqrt{a-i a \tan (c+d x)}}{\sqrt{e \sec (c+d x)}}+\cos (c+d x) (a-i a \tan (c+d x))+a\right)}{2 \sqrt{2} d \sqrt{a-i a \tan (c+d x)} \sqrt{a+i a \tan (c+d x)} (e \cos (c+d x))^{3/2} (e \sec (c+d x))^{3/2}}-\frac{i a^{3/2} e^{3/2} \sec (c+d x) \log \left(\frac{\sqrt{2} \sqrt{a} \sqrt{e} \sqrt{a-i a \tan (c+d x)}}{\sqrt{e \sec (c+d x)}}+\cos (c+d x) (a-i a \tan (c+d x))+a\right)}{2 \sqrt{2} d \sqrt{a-i a \tan (c+d x)} \sqrt{a+i a \tan (c+d x)} (e \cos (c+d x))^{3/2} (e \sec (c+d x))^{3/2}}+\frac{i a}{d \sqrt{a+i a \tan (c+d x)} (e \cos (c+d x))^{3/2}}","-\frac{i a^{3/2} \sec (c+d x) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{a-i a \tan (c+d x)} \sqrt{e \cos (c+d x)}}{\sqrt{a} \sqrt{e}}\right)}{\sqrt{2} d e^{3/2} \sqrt{a-i a \tan (c+d x)} \sqrt{a+i a \tan (c+d x)}}+\frac{i a^{3/2} \sec (c+d x) \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt{a-i a \tan (c+d x)} \sqrt{e \cos (c+d x)}}{\sqrt{a} \sqrt{e}}\right)}{\sqrt{2} d e^{3/2} \sqrt{a-i a \tan (c+d x)} \sqrt{a+i a \tan (c+d x)}}+\frac{i a^{3/2} \sec (c+d x) \log \left(-\frac{\sqrt{2} \sqrt{a} \sqrt{a-i a \tan (c+d x)} \sqrt{e \cos (c+d x)}}{\sqrt{e}}+\cos (c+d x) (a-i a \tan (c+d x))+a\right)}{2 \sqrt{2} d e^{3/2} \sqrt{a-i a \tan (c+d x)} \sqrt{a+i a \tan (c+d x)}}-\frac{i a^{3/2} \sec (c+d x) \log \left(\frac{\sqrt{2} \sqrt{a} \sqrt{a-i a \tan (c+d x)} \sqrt{e \cos (c+d x)}}{\sqrt{e}}+\cos (c+d x) (a-i a \tan (c+d x))+a\right)}{2 \sqrt{2} d e^{3/2} \sqrt{a-i a \tan (c+d x)} \sqrt{a+i a \tan (c+d x)}}+\frac{i a}{d \sqrt{a+i a \tan (c+d x)} (e \cos (c+d x))^{3/2}}",1,"(I*a)/(d*(e*Cos[c + d*x])^(3/2)*Sqrt[a + I*a*Tan[c + d*x]]) - (I*a^(3/2)*e^(3/2)*ArcTan[1 - (Sqrt[2]*Sqrt[e]*Sqrt[a - I*a*Tan[c + d*x]])/(Sqrt[a]*Sqrt[e*Sec[c + d*x]])]*Sec[c + d*x])/(Sqrt[2]*d*(e*Cos[c + d*x])^(3/2)*(e*Sec[c + d*x])^(3/2)*Sqrt[a - I*a*Tan[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]]) + (I*a^(3/2)*e^(3/2)*ArcTan[1 + (Sqrt[2]*Sqrt[e]*Sqrt[a - I*a*Tan[c + d*x]])/(Sqrt[a]*Sqrt[e*Sec[c + d*x]])]*Sec[c + d*x])/(Sqrt[2]*d*(e*Cos[c + d*x])^(3/2)*(e*Sec[c + d*x])^(3/2)*Sqrt[a - I*a*Tan[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]]) + ((I/2)*a^(3/2)*e^(3/2)*Log[a - (Sqrt[2]*Sqrt[a]*Sqrt[e]*Sqrt[a - I*a*Tan[c + d*x]])/Sqrt[e*Sec[c + d*x]] + Cos[c + d*x]*(a - I*a*Tan[c + d*x])]*Sec[c + d*x])/(Sqrt[2]*d*(e*Cos[c + d*x])^(3/2)*(e*Sec[c + d*x])^(3/2)*Sqrt[a - I*a*Tan[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]]) - ((I/2)*a^(3/2)*e^(3/2)*Log[a + (Sqrt[2]*Sqrt[a]*Sqrt[e]*Sqrt[a - I*a*Tan[c + d*x]])/Sqrt[e*Sec[c + d*x]] + Cos[c + d*x]*(a - I*a*Tan[c + d*x])]*Sec[c + d*x])/(Sqrt[2]*d*(e*Cos[c + d*x])^(3/2)*(e*Sec[c + d*x])^(3/2)*Sqrt[a - I*a*Tan[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]])","A",13,10,30,0.3333,1,"{3515, 3498, 3499, 3495, 297, 1162, 617, 204, 1165, 628}"
679,1,512,0,0.564371,"\int \frac{\sqrt{a+i a \tan (c+d x)}}{(e \cos (c+d x))^{5/2}} \, dx","Int[Sqrt[a + I*a*Tan[c + d*x]]/(e*Cos[c + d*x])^(5/2),x]","\frac{3 i \sqrt{a} e^{5/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{e} \sqrt{a+i a \tan (c+d x)}}{\sqrt{a} \sqrt{e \sec (c+d x)}}\right)}{4 \sqrt{2} d (e \cos (c+d x))^{5/2} (e \sec (c+d x))^{5/2}}-\frac{3 i \sqrt{a} e^{5/2} \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt{e} \sqrt{a+i a \tan (c+d x)}}{\sqrt{a} \sqrt{e \sec (c+d x)}}\right)}{4 \sqrt{2} d (e \cos (c+d x))^{5/2} (e \sec (c+d x))^{5/2}}-\frac{3 i \sqrt{a} e^{5/2} \log \left(-\frac{\sqrt{2} \sqrt{a} \sqrt{e} \sqrt{a+i a \tan (c+d x)}}{\sqrt{e \sec (c+d x)}}+\cos (c+d x) (a+i a \tan (c+d x))+a\right)}{8 \sqrt{2} d (e \cos (c+d x))^{5/2} (e \sec (c+d x))^{5/2}}+\frac{3 i \sqrt{a} e^{5/2} \log \left(\frac{\sqrt{2} \sqrt{a} \sqrt{e} \sqrt{a+i a \tan (c+d x)}}{\sqrt{e \sec (c+d x)}}+\cos (c+d x) (a+i a \tan (c+d x))+a\right)}{8 \sqrt{2} d (e \cos (c+d x))^{5/2} (e \sec (c+d x))^{5/2}}-\frac{3 i \cos ^2(c+d x) \sqrt{a+i a \tan (c+d x)}}{4 d (e \cos (c+d x))^{5/2}}+\frac{i a}{2 d \sqrt{a+i a \tan (c+d x)} (e \cos (c+d x))^{5/2}}","\frac{3 i \sqrt{a} e^{5/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{e} \sqrt{a+i a \tan (c+d x)}}{\sqrt{a} \sqrt{e \sec (c+d x)}}\right)}{4 \sqrt{2} d (e \cos (c+d x))^{5/2} (e \sec (c+d x))^{5/2}}-\frac{3 i \sqrt{a} e^{5/2} \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt{e} \sqrt{a+i a \tan (c+d x)}}{\sqrt{a} \sqrt{e \sec (c+d x)}}\right)}{4 \sqrt{2} d (e \cos (c+d x))^{5/2} (e \sec (c+d x))^{5/2}}-\frac{3 i \sqrt{a} e^{5/2} \log \left(-\frac{\sqrt{2} \sqrt{a} \sqrt{e} \sqrt{a+i a \tan (c+d x)}}{\sqrt{e \sec (c+d x)}}+\cos (c+d x) (a+i a \tan (c+d x))+a\right)}{8 \sqrt{2} d (e \cos (c+d x))^{5/2} (e \sec (c+d x))^{5/2}}+\frac{3 i \sqrt{a} e^{5/2} \log \left(\frac{\sqrt{2} \sqrt{a} \sqrt{e} \sqrt{a+i a \tan (c+d x)}}{\sqrt{e \sec (c+d x)}}+\cos (c+d x) (a+i a \tan (c+d x))+a\right)}{8 \sqrt{2} d (e \cos (c+d x))^{5/2} (e \sec (c+d x))^{5/2}}-\frac{3 i \cos ^2(c+d x) \sqrt{a+i a \tan (c+d x)}}{4 d (e \cos (c+d x))^{5/2}}+\frac{i a}{2 d \sqrt{a+i a \tan (c+d x)} (e \cos (c+d x))^{5/2}}",1,"(((3*I)/4)*Sqrt[a]*e^(5/2)*ArcTan[1 - (Sqrt[2]*Sqrt[e]*Sqrt[a + I*a*Tan[c + d*x]])/(Sqrt[a]*Sqrt[e*Sec[c + d*x]])])/(Sqrt[2]*d*(e*Cos[c + d*x])^(5/2)*(e*Sec[c + d*x])^(5/2)) - (((3*I)/4)*Sqrt[a]*e^(5/2)*ArcTan[1 + (Sqrt[2]*Sqrt[e]*Sqrt[a + I*a*Tan[c + d*x]])/(Sqrt[a]*Sqrt[e*Sec[c + d*x]])])/(Sqrt[2]*d*(e*Cos[c + d*x])^(5/2)*(e*Sec[c + d*x])^(5/2)) - (((3*I)/8)*Sqrt[a]*e^(5/2)*Log[a - (Sqrt[2]*Sqrt[a]*Sqrt[e]*Sqrt[a + I*a*Tan[c + d*x]])/Sqrt[e*Sec[c + d*x]] + Cos[c + d*x]*(a + I*a*Tan[c + d*x])])/(Sqrt[2]*d*(e*Cos[c + d*x])^(5/2)*(e*Sec[c + d*x])^(5/2)) + (((3*I)/8)*Sqrt[a]*e^(5/2)*Log[a + (Sqrt[2]*Sqrt[a]*Sqrt[e]*Sqrt[a + I*a*Tan[c + d*x]])/Sqrt[e*Sec[c + d*x]] + Cos[c + d*x]*(a + I*a*Tan[c + d*x])])/(Sqrt[2]*d*(e*Cos[c + d*x])^(5/2)*(e*Sec[c + d*x])^(5/2)) + ((I/2)*a)/(d*(e*Cos[c + d*x])^(5/2)*Sqrt[a + I*a*Tan[c + d*x]]) - (((3*I)/4)*Cos[c + d*x]^2*Sqrt[a + I*a*Tan[c + d*x]])/(d*(e*Cos[c + d*x])^(5/2))","A",13,10,30,0.3333,1,"{3515, 3498, 3501, 3495, 297, 1162, 617, 204, 1165, 628}"
680,1,719,0,0.8598186,"\int \frac{\sqrt{a+i a \tan (c+d x)}}{(e \cos (c+d x))^{7/2}} \, dx","Int[Sqrt[a + I*a*Tan[c + d*x]]/(e*Cos[c + d*x])^(7/2),x]","-\frac{5 i a^{3/2} e^{7/2} \sec (c+d x) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{e} \sqrt{a-i a \tan (c+d x)}}{\sqrt{a} \sqrt{e \sec (c+d x)}}\right)}{8 \sqrt{2} d \sqrt{a-i a \tan (c+d x)} \sqrt{a+i a \tan (c+d x)} (e \cos (c+d x))^{7/2} (e \sec (c+d x))^{7/2}}+\frac{5 i a^{3/2} e^{7/2} \sec (c+d x) \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt{e} \sqrt{a-i a \tan (c+d x)}}{\sqrt{a} \sqrt{e \sec (c+d x)}}\right)}{8 \sqrt{2} d \sqrt{a-i a \tan (c+d x)} \sqrt{a+i a \tan (c+d x)} (e \cos (c+d x))^{7/2} (e \sec (c+d x))^{7/2}}+\frac{5 i a^{3/2} e^{7/2} \sec (c+d x) \log \left(-\frac{\sqrt{2} \sqrt{a} \sqrt{e} \sqrt{a-i a \tan (c+d x)}}{\sqrt{e \sec (c+d x)}}+\cos (c+d x) (a-i a \tan (c+d x))+a\right)}{16 \sqrt{2} d \sqrt{a-i a \tan (c+d x)} \sqrt{a+i a \tan (c+d x)} (e \cos (c+d x))^{7/2} (e \sec (c+d x))^{7/2}}-\frac{5 i a^{3/2} e^{7/2} \sec (c+d x) \log \left(\frac{\sqrt{2} \sqrt{a} \sqrt{e} \sqrt{a-i a \tan (c+d x)}}{\sqrt{e \sec (c+d x)}}+\cos (c+d x) (a-i a \tan (c+d x))+a\right)}{16 \sqrt{2} d \sqrt{a-i a \tan (c+d x)} \sqrt{a+i a \tan (c+d x)} (e \cos (c+d x))^{7/2} (e \sec (c+d x))^{7/2}}-\frac{5 i \cos ^2(c+d x) \sqrt{a+i a \tan (c+d x)}}{12 d (e \cos (c+d x))^{7/2}}+\frac{5 i a \cos ^2(c+d x)}{8 d \sqrt{a+i a \tan (c+d x)} (e \cos (c+d x))^{7/2}}+\frac{i a}{3 d \sqrt{a+i a \tan (c+d x)} (e \cos (c+d x))^{7/2}}","-\frac{5 i a^{3/2} e^{7/2} \sec (c+d x) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{e} \sqrt{a-i a \tan (c+d x)}}{\sqrt{a} \sqrt{e \sec (c+d x)}}\right)}{8 \sqrt{2} d \sqrt{a-i a \tan (c+d x)} \sqrt{a+i a \tan (c+d x)} (e \cos (c+d x))^{7/2} (e \sec (c+d x))^{7/2}}+\frac{5 i a^{3/2} e^{7/2} \sec (c+d x) \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt{e} \sqrt{a-i a \tan (c+d x)}}{\sqrt{a} \sqrt{e \sec (c+d x)}}\right)}{8 \sqrt{2} d \sqrt{a-i a \tan (c+d x)} \sqrt{a+i a \tan (c+d x)} (e \cos (c+d x))^{7/2} (e \sec (c+d x))^{7/2}}+\frac{5 i a^{3/2} e^{7/2} \sec (c+d x) \log \left(-\frac{\sqrt{2} \sqrt{a} \sqrt{e} \sqrt{a-i a \tan (c+d x)}}{\sqrt{e \sec (c+d x)}}+\cos (c+d x) (a-i a \tan (c+d x))+a\right)}{16 \sqrt{2} d \sqrt{a-i a \tan (c+d x)} \sqrt{a+i a \tan (c+d x)} (e \cos (c+d x))^{7/2} (e \sec (c+d x))^{7/2}}-\frac{5 i a^{3/2} e^{7/2} \sec (c+d x) \log \left(\frac{\sqrt{2} \sqrt{a} \sqrt{e} \sqrt{a-i a \tan (c+d x)}}{\sqrt{e \sec (c+d x)}}+\cos (c+d x) (a-i a \tan (c+d x))+a\right)}{16 \sqrt{2} d \sqrt{a-i a \tan (c+d x)} \sqrt{a+i a \tan (c+d x)} (e \cos (c+d x))^{7/2} (e \sec (c+d x))^{7/2}}-\frac{5 i \cos ^2(c+d x) \sqrt{a+i a \tan (c+d x)}}{12 d (e \cos (c+d x))^{7/2}}+\frac{5 i a \cos ^2(c+d x)}{8 d \sqrt{a+i a \tan (c+d x)} (e \cos (c+d x))^{7/2}}+\frac{i a}{3 d \sqrt{a+i a \tan (c+d x)} (e \cos (c+d x))^{7/2}}",1,"((I/3)*a)/(d*(e*Cos[c + d*x])^(7/2)*Sqrt[a + I*a*Tan[c + d*x]]) + (((5*I)/8)*a*Cos[c + d*x]^2)/(d*(e*Cos[c + d*x])^(7/2)*Sqrt[a + I*a*Tan[c + d*x]]) - (((5*I)/8)*a^(3/2)*e^(7/2)*ArcTan[1 - (Sqrt[2]*Sqrt[e]*Sqrt[a - I*a*Tan[c + d*x]])/(Sqrt[a]*Sqrt[e*Sec[c + d*x]])]*Sec[c + d*x])/(Sqrt[2]*d*(e*Cos[c + d*x])^(7/2)*(e*Sec[c + d*x])^(7/2)*Sqrt[a - I*a*Tan[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]]) + (((5*I)/8)*a^(3/2)*e^(7/2)*ArcTan[1 + (Sqrt[2]*Sqrt[e]*Sqrt[a - I*a*Tan[c + d*x]])/(Sqrt[a]*Sqrt[e*Sec[c + d*x]])]*Sec[c + d*x])/(Sqrt[2]*d*(e*Cos[c + d*x])^(7/2)*(e*Sec[c + d*x])^(7/2)*Sqrt[a - I*a*Tan[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]]) + (((5*I)/16)*a^(3/2)*e^(7/2)*Log[a - (Sqrt[2]*Sqrt[a]*Sqrt[e]*Sqrt[a - I*a*Tan[c + d*x]])/Sqrt[e*Sec[c + d*x]] + Cos[c + d*x]*(a - I*a*Tan[c + d*x])]*Sec[c + d*x])/(Sqrt[2]*d*(e*Cos[c + d*x])^(7/2)*(e*Sec[c + d*x])^(7/2)*Sqrt[a - I*a*Tan[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]]) - (((5*I)/16)*a^(3/2)*e^(7/2)*Log[a + (Sqrt[2]*Sqrt[a]*Sqrt[e]*Sqrt[a - I*a*Tan[c + d*x]])/Sqrt[e*Sec[c + d*x]] + Cos[c + d*x]*(a - I*a*Tan[c + d*x])]*Sec[c + d*x])/(Sqrt[2]*d*(e*Cos[c + d*x])^(7/2)*(e*Sec[c + d*x])^(7/2)*Sqrt[a - I*a*Tan[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]]) - (((5*I)/12)*Cos[c + d*x]^2*Sqrt[a + I*a*Tan[c + d*x]])/(d*(e*Cos[c + d*x])^(7/2))","A",15,11,30,0.3667,1,"{3515, 3498, 3501, 3499, 3495, 297, 1162, 617, 204, 1165, 628}"
681,1,175,0,0.3782852,"\int \frac{(e \cos (c+d x))^{5/2}}{\sqrt{a+i a \tan (c+d x)}} \, dx","Int[(e*Cos[c + d*x])^(5/2)/Sqrt[a + I*a*Tan[c + d*x]],x]","-\frac{12 i \sqrt{a+i a \tan (c+d x)} (e \cos (c+d x))^{5/2}}{35 a d}+\frac{2 i (e \cos (c+d x))^{5/2}}{7 d \sqrt{a+i a \tan (c+d x)}}-\frac{32 i \sec ^2(c+d x) \sqrt{a+i a \tan (c+d x)} (e \cos (c+d x))^{5/2}}{35 a d}+\frac{16 i \sec ^2(c+d x) (e \cos (c+d x))^{5/2}}{35 d \sqrt{a+i a \tan (c+d x)}}","-\frac{12 i \sqrt{a+i a \tan (c+d x)} (e \cos (c+d x))^{5/2}}{35 a d}+\frac{2 i (e \cos (c+d x))^{5/2}}{7 d \sqrt{a+i a \tan (c+d x)}}-\frac{32 i \sec ^2(c+d x) \sqrt{a+i a \tan (c+d x)} (e \cos (c+d x))^{5/2}}{35 a d}+\frac{16 i \sec ^2(c+d x) (e \cos (c+d x))^{5/2}}{35 d \sqrt{a+i a \tan (c+d x)}}",1,"(((2*I)/7)*(e*Cos[c + d*x])^(5/2))/(d*Sqrt[a + I*a*Tan[c + d*x]]) + (((16*I)/35)*(e*Cos[c + d*x])^(5/2)*Sec[c + d*x]^2)/(d*Sqrt[a + I*a*Tan[c + d*x]]) - (((12*I)/35)*(e*Cos[c + d*x])^(5/2)*Sqrt[a + I*a*Tan[c + d*x]])/(a*d) - (((32*I)/35)*(e*Cos[c + d*x])^(5/2)*Sec[c + d*x]^2*Sqrt[a + I*a*Tan[c + d*x]])/(a*d)","A",5,4,30,0.1333,1,"{3515, 3502, 3497, 3488}"
682,1,126,0,0.3129915,"\int \frac{(e \cos (c+d x))^{3/2}}{\sqrt{a+i a \tan (c+d x)}} \, dx","Int[(e*Cos[c + d*x])^(3/2)/Sqrt[a + I*a*Tan[c + d*x]],x]","-\frac{8 i \sqrt{a+i a \tan (c+d x)} (e \cos (c+d x))^{3/2}}{15 a d}+\frac{2 i (e \cos (c+d x))^{3/2}}{5 d \sqrt{a+i a \tan (c+d x)}}+\frac{16 i \sec ^2(c+d x) (e \cos (c+d x))^{3/2}}{15 d \sqrt{a+i a \tan (c+d x)}}","-\frac{8 i \sqrt{a+i a \tan (c+d x)} (e \cos (c+d x))^{3/2}}{15 a d}+\frac{2 i (e \cos (c+d x))^{3/2}}{5 d \sqrt{a+i a \tan (c+d x)}}+\frac{16 i \sec ^2(c+d x) (e \cos (c+d x))^{3/2}}{15 d \sqrt{a+i a \tan (c+d x)}}",1,"(((2*I)/5)*(e*Cos[c + d*x])^(3/2))/(d*Sqrt[a + I*a*Tan[c + d*x]]) + (((16*I)/15)*(e*Cos[c + d*x])^(3/2)*Sec[c + d*x]^2)/(d*Sqrt[a + I*a*Tan[c + d*x]]) - (((8*I)/15)*(e*Cos[c + d*x])^(3/2)*Sqrt[a + I*a*Tan[c + d*x]])/(a*d)","A",4,4,30,0.1333,1,"{3515, 3502, 3497, 3488}"
683,1,80,0,0.2087843,"\int \frac{\sqrt{e \cos (c+d x)}}{\sqrt{a+i a \tan (c+d x)}} \, dx","Int[Sqrt[e*Cos[c + d*x]]/Sqrt[a + I*a*Tan[c + d*x]],x]","\frac{2 i \sqrt{e \cos (c+d x)}}{3 d \sqrt{a+i a \tan (c+d x)}}-\frac{4 i \sqrt{a+i a \tan (c+d x)} \sqrt{e \cos (c+d x)}}{3 a d}","\frac{2 i \sqrt{e \cos (c+d x)}}{3 d \sqrt{a+i a \tan (c+d x)}}-\frac{4 i \sqrt{a+i a \tan (c+d x)} \sqrt{e \cos (c+d x)}}{3 a d}",1,"(((2*I)/3)*Sqrt[e*Cos[c + d*x]])/(d*Sqrt[a + I*a*Tan[c + d*x]]) - (((4*I)/3)*Sqrt[e*Cos[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]])/(a*d)","A",3,3,30,0.1000,1,"{3515, 3502, 3488}"
684,1,36,0,0.1394536,"\int \frac{1}{\sqrt{e \cos (c+d x)} \sqrt{a+i a \tan (c+d x)}} \, dx","Int[1/(Sqrt[e*Cos[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]]),x]","\frac{2 i}{d \sqrt{a+i a \tan (c+d x)} \sqrt{e \cos (c+d x)}}","\frac{2 i}{d \sqrt{a+i a \tan (c+d x)} \sqrt{e \cos (c+d x)}}",1,"(2*I)/(d*Sqrt[e*Cos[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]])","A",2,2,30,0.06667,1,"{3515, 3488}"
685,1,495,0,0.3321866,"\int \frac{1}{(e \cos (c+d x))^{3/2} \sqrt{a+i a \tan (c+d x)}} \, dx","Int[1/((e*Cos[c + d*x])^(3/2)*Sqrt[a + I*a*Tan[c + d*x]]),x]","-\frac{i \sqrt{2} \sqrt{a} \sec (c+d x) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{a-i a \tan (c+d x)} \sqrt{e \cos (c+d x)}}{\sqrt{a} \sqrt{e}}\right)}{d e^{3/2} \sqrt{a-i a \tan (c+d x)} \sqrt{a+i a \tan (c+d x)}}+\frac{i \sqrt{2} \sqrt{a} \sec (c+d x) \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt{a-i a \tan (c+d x)} \sqrt{e \cos (c+d x)}}{\sqrt{a} \sqrt{e}}\right)}{d e^{3/2} \sqrt{a-i a \tan (c+d x)} \sqrt{a+i a \tan (c+d x)}}+\frac{i \sqrt{a} \sec (c+d x) \log \left(-\sqrt{2} \sqrt{a} \sqrt{a-i a \tan (c+d x)} \sqrt{e \cos (c+d x)}+\sqrt{e} \cos (c+d x) (a-i a \tan (c+d x))+a \sqrt{e}\right)}{\sqrt{2} d e^{3/2} \sqrt{a-i a \tan (c+d x)} \sqrt{a+i a \tan (c+d x)}}-\frac{i \sqrt{a} \sec (c+d x) \log \left(\sqrt{2} \sqrt{a} \sqrt{a-i a \tan (c+d x)} \sqrt{e \cos (c+d x)}+\sqrt{e} \cos (c+d x) (a-i a \tan (c+d x))+a \sqrt{e}\right)}{\sqrt{2} d e^{3/2} \sqrt{a-i a \tan (c+d x)} \sqrt{a+i a \tan (c+d x)}}","-\frac{i \sqrt{2} \sqrt{a} \sec (c+d x) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{a-i a \tan (c+d x)} \sqrt{e \cos (c+d x)}}{\sqrt{a} \sqrt{e}}\right)}{d e^{3/2} \sqrt{a-i a \tan (c+d x)} \sqrt{a+i a \tan (c+d x)}}+\frac{i \sqrt{2} \sqrt{a} \sec (c+d x) \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt{a-i a \tan (c+d x)} \sqrt{e \cos (c+d x)}}{\sqrt{a} \sqrt{e}}\right)}{d e^{3/2} \sqrt{a-i a \tan (c+d x)} \sqrt{a+i a \tan (c+d x)}}+\frac{i \sqrt{a} \sec (c+d x) \log \left(-\sqrt{2} \sqrt{a} \sqrt{a-i a \tan (c+d x)} \sqrt{e \cos (c+d x)}+\sqrt{e} \cos (c+d x) (a-i a \tan (c+d x))+a \sqrt{e}\right)}{\sqrt{2} d e^{3/2} \sqrt{a-i a \tan (c+d x)} \sqrt{a+i a \tan (c+d x)}}-\frac{i \sqrt{a} \sec (c+d x) \log \left(\sqrt{2} \sqrt{a} \sqrt{a-i a \tan (c+d x)} \sqrt{e \cos (c+d x)}+\sqrt{e} \cos (c+d x) (a-i a \tan (c+d x))+a \sqrt{e}\right)}{\sqrt{2} d e^{3/2} \sqrt{a-i a \tan (c+d x)} \sqrt{a+i a \tan (c+d x)}}",1,"((-I)*Sqrt[2]*Sqrt[a]*ArcTan[1 - (Sqrt[2]*Sqrt[e*Cos[c + d*x]]*Sqrt[a - I*a*Tan[c + d*x]])/(Sqrt[a]*Sqrt[e])]*Sec[c + d*x])/(d*e^(3/2)*Sqrt[a - I*a*Tan[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]]) + (I*Sqrt[2]*Sqrt[a]*ArcTan[1 + (Sqrt[2]*Sqrt[e*Cos[c + d*x]]*Sqrt[a - I*a*Tan[c + d*x]])/(Sqrt[a]*Sqrt[e])]*Sec[c + d*x])/(d*e^(3/2)*Sqrt[a - I*a*Tan[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]]) + (I*Sqrt[a]*Log[a*Sqrt[e] - Sqrt[2]*Sqrt[a]*Sqrt[e*Cos[c + d*x]]*Sqrt[a - I*a*Tan[c + d*x]] + Sqrt[e]*Cos[c + d*x]*(a - I*a*Tan[c + d*x])]*Sec[c + d*x])/(Sqrt[2]*d*e^(3/2)*Sqrt[a - I*a*Tan[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]]) - (I*Sqrt[a]*Log[a*Sqrt[e] + Sqrt[2]*Sqrt[a]*Sqrt[e*Cos[c + d*x]]*Sqrt[a - I*a*Tan[c + d*x]] + Sqrt[e]*Cos[c + d*x]*(a - I*a*Tan[c + d*x])]*Sec[c + d*x])/(Sqrt[2]*d*e^(3/2)*Sqrt[a - I*a*Tan[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]])","A",11,8,30,0.2667,1,"{3514, 3513, 297, 1162, 617, 204, 1165, 628}"
686,1,470,0,0.4407145,"\int \frac{1}{(e \cos (c+d x))^{5/2} \sqrt{a+i a \tan (c+d x)}} \, dx","Int[1/((e*Cos[c + d*x])^(5/2)*Sqrt[a + I*a*Tan[c + d*x]]),x]","\frac{i e^{5/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{e} \sqrt{a+i a \tan (c+d x)}}{\sqrt{a} \sqrt{e \sec (c+d x)}}\right)}{\sqrt{2} \sqrt{a} d (e \cos (c+d x))^{5/2} (e \sec (c+d x))^{5/2}}-\frac{i e^{5/2} \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt{e} \sqrt{a+i a \tan (c+d x)}}{\sqrt{a} \sqrt{e \sec (c+d x)}}\right)}{\sqrt{2} \sqrt{a} d (e \cos (c+d x))^{5/2} (e \sec (c+d x))^{5/2}}-\frac{i e^{5/2} \log \left(-\frac{\sqrt{2} \sqrt{a} \sqrt{e} \sqrt{a+i a \tan (c+d x)}}{\sqrt{e \sec (c+d x)}}+\cos (c+d x) (a+i a \tan (c+d x))+a\right)}{2 \sqrt{2} \sqrt{a} d (e \cos (c+d x))^{5/2} (e \sec (c+d x))^{5/2}}+\frac{i e^{5/2} \log \left(\frac{\sqrt{2} \sqrt{a} \sqrt{e} \sqrt{a+i a \tan (c+d x)}}{\sqrt{e \sec (c+d x)}}+\cos (c+d x) (a+i a \tan (c+d x))+a\right)}{2 \sqrt{2} \sqrt{a} d (e \cos (c+d x))^{5/2} (e \sec (c+d x))^{5/2}}-\frac{i \cos ^2(c+d x) \sqrt{a+i a \tan (c+d x)}}{a d (e \cos (c+d x))^{5/2}}","\frac{i e^{5/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{e} \sqrt{a+i a \tan (c+d x)}}{\sqrt{a} \sqrt{e \sec (c+d x)}}\right)}{\sqrt{2} \sqrt{a} d (e \cos (c+d x))^{5/2} (e \sec (c+d x))^{5/2}}-\frac{i e^{5/2} \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt{e} \sqrt{a+i a \tan (c+d x)}}{\sqrt{a} \sqrt{e \sec (c+d x)}}\right)}{\sqrt{2} \sqrt{a} d (e \cos (c+d x))^{5/2} (e \sec (c+d x))^{5/2}}-\frac{i e^{5/2} \log \left(-\frac{\sqrt{2} \sqrt{a} \sqrt{e} \sqrt{a+i a \tan (c+d x)}}{\sqrt{e \sec (c+d x)}}+\cos (c+d x) (a+i a \tan (c+d x))+a\right)}{2 \sqrt{2} \sqrt{a} d (e \cos (c+d x))^{5/2} (e \sec (c+d x))^{5/2}}+\frac{i e^{5/2} \log \left(\frac{\sqrt{2} \sqrt{a} \sqrt{e} \sqrt{a+i a \tan (c+d x)}}{\sqrt{e \sec (c+d x)}}+\cos (c+d x) (a+i a \tan (c+d x))+a\right)}{2 \sqrt{2} \sqrt{a} d (e \cos (c+d x))^{5/2} (e \sec (c+d x))^{5/2}}-\frac{i \cos ^2(c+d x) \sqrt{a+i a \tan (c+d x)}}{a d (e \cos (c+d x))^{5/2}}",1,"(I*e^(5/2)*ArcTan[1 - (Sqrt[2]*Sqrt[e]*Sqrt[a + I*a*Tan[c + d*x]])/(Sqrt[a]*Sqrt[e*Sec[c + d*x]])])/(Sqrt[2]*Sqrt[a]*d*(e*Cos[c + d*x])^(5/2)*(e*Sec[c + d*x])^(5/2)) - (I*e^(5/2)*ArcTan[1 + (Sqrt[2]*Sqrt[e]*Sqrt[a + I*a*Tan[c + d*x]])/(Sqrt[a]*Sqrt[e*Sec[c + d*x]])])/(Sqrt[2]*Sqrt[a]*d*(e*Cos[c + d*x])^(5/2)*(e*Sec[c + d*x])^(5/2)) - ((I/2)*e^(5/2)*Log[a - (Sqrt[2]*Sqrt[a]*Sqrt[e]*Sqrt[a + I*a*Tan[c + d*x]])/Sqrt[e*Sec[c + d*x]] + Cos[c + d*x]*(a + I*a*Tan[c + d*x])])/(Sqrt[2]*Sqrt[a]*d*(e*Cos[c + d*x])^(5/2)*(e*Sec[c + d*x])^(5/2)) + ((I/2)*e^(5/2)*Log[a + (Sqrt[2]*Sqrt[a]*Sqrt[e]*Sqrt[a + I*a*Tan[c + d*x]])/Sqrt[e*Sec[c + d*x]] + Cos[c + d*x]*(a + I*a*Tan[c + d*x])])/(Sqrt[2]*Sqrt[a]*d*(e*Cos[c + d*x])^(5/2)*(e*Sec[c + d*x])^(5/2)) - (I*Cos[c + d*x]^2*Sqrt[a + I*a*Tan[c + d*x]])/(a*d*(e*Cos[c + d*x])^(5/2))","A",12,9,30,0.3000,1,"{3515, 3501, 3495, 297, 1162, 617, 204, 1165, 628}"
687,1,682,0,0.7781342,"\int \frac{1}{(e \cos (c+d x))^{7/2} \sqrt{a+i a \tan (c+d x)}} \, dx","Int[1/((e*Cos[c + d*x])^(7/2)*Sqrt[a + I*a*Tan[c + d*x]]),x]","-\frac{3 i \sqrt{a} e^{7/2} \sec (c+d x) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{e} \sqrt{a-i a \tan (c+d x)}}{\sqrt{a} \sqrt{e \sec (c+d x)}}\right)}{4 \sqrt{2} d \sqrt{a-i a \tan (c+d x)} \sqrt{a+i a \tan (c+d x)} (e \cos (c+d x))^{7/2} (e \sec (c+d x))^{7/2}}+\frac{3 i \sqrt{a} e^{7/2} \sec (c+d x) \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt{e} \sqrt{a-i a \tan (c+d x)}}{\sqrt{a} \sqrt{e \sec (c+d x)}}\right)}{4 \sqrt{2} d \sqrt{a-i a \tan (c+d x)} \sqrt{a+i a \tan (c+d x)} (e \cos (c+d x))^{7/2} (e \sec (c+d x))^{7/2}}+\frac{3 i \sqrt{a} e^{7/2} \sec (c+d x) \log \left(-\frac{\sqrt{2} \sqrt{a} \sqrt{e} \sqrt{a-i a \tan (c+d x)}}{\sqrt{e \sec (c+d x)}}+\cos (c+d x) (a-i a \tan (c+d x))+a\right)}{8 \sqrt{2} d \sqrt{a-i a \tan (c+d x)} \sqrt{a+i a \tan (c+d x)} (e \cos (c+d x))^{7/2} (e \sec (c+d x))^{7/2}}-\frac{3 i \sqrt{a} e^{7/2} \sec (c+d x) \log \left(\frac{\sqrt{2} \sqrt{a} \sqrt{e} \sqrt{a-i a \tan (c+d x)}}{\sqrt{e \sec (c+d x)}}+\cos (c+d x) (a-i a \tan (c+d x))+a\right)}{8 \sqrt{2} d \sqrt{a-i a \tan (c+d x)} \sqrt{a+i a \tan (c+d x)} (e \cos (c+d x))^{7/2} (e \sec (c+d x))^{7/2}}-\frac{i \cos ^2(c+d x) \sqrt{a+i a \tan (c+d x)}}{2 a d (e \cos (c+d x))^{7/2}}+\frac{3 i \cos ^2(c+d x)}{4 d \sqrt{a+i a \tan (c+d x)} (e \cos (c+d x))^{7/2}}","-\frac{3 i \sqrt{a} e^{7/2} \sec (c+d x) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{e} \sqrt{a-i a \tan (c+d x)}}{\sqrt{a} \sqrt{e \sec (c+d x)}}\right)}{4 \sqrt{2} d \sqrt{a-i a \tan (c+d x)} \sqrt{a+i a \tan (c+d x)} (e \cos (c+d x))^{7/2} (e \sec (c+d x))^{7/2}}+\frac{3 i \sqrt{a} e^{7/2} \sec (c+d x) \tan ^{-1}\left(1+\frac{\sqrt{2} \sqrt{e} \sqrt{a-i a \tan (c+d x)}}{\sqrt{a} \sqrt{e \sec (c+d x)}}\right)}{4 \sqrt{2} d \sqrt{a-i a \tan (c+d x)} \sqrt{a+i a \tan (c+d x)} (e \cos (c+d x))^{7/2} (e \sec (c+d x))^{7/2}}+\frac{3 i \sqrt{a} e^{7/2} \sec (c+d x) \log \left(-\frac{\sqrt{2} \sqrt{a} \sqrt{e} \sqrt{a-i a \tan (c+d x)}}{\sqrt{e \sec (c+d x)}}+\cos (c+d x) (a-i a \tan (c+d x))+a\right)}{8 \sqrt{2} d \sqrt{a-i a \tan (c+d x)} \sqrt{a+i a \tan (c+d x)} (e \cos (c+d x))^{7/2} (e \sec (c+d x))^{7/2}}-\frac{3 i \sqrt{a} e^{7/2} \sec (c+d x) \log \left(\frac{\sqrt{2} \sqrt{a} \sqrt{e} \sqrt{a-i a \tan (c+d x)}}{\sqrt{e \sec (c+d x)}}+\cos (c+d x) (a-i a \tan (c+d x))+a\right)}{8 \sqrt{2} d \sqrt{a-i a \tan (c+d x)} \sqrt{a+i a \tan (c+d x)} (e \cos (c+d x))^{7/2} (e \sec (c+d x))^{7/2}}-\frac{i \cos ^2(c+d x) \sqrt{a+i a \tan (c+d x)}}{2 a d (e \cos (c+d x))^{7/2}}+\frac{3 i \cos ^2(c+d x)}{4 d \sqrt{a+i a \tan (c+d x)} (e \cos (c+d x))^{7/2}}",1,"(((3*I)/4)*Cos[c + d*x]^2)/(d*(e*Cos[c + d*x])^(7/2)*Sqrt[a + I*a*Tan[c + d*x]]) - (((3*I)/4)*Sqrt[a]*e^(7/2)*ArcTan[1 - (Sqrt[2]*Sqrt[e]*Sqrt[a - I*a*Tan[c + d*x]])/(Sqrt[a]*Sqrt[e*Sec[c + d*x]])]*Sec[c + d*x])/(Sqrt[2]*d*(e*Cos[c + d*x])^(7/2)*(e*Sec[c + d*x])^(7/2)*Sqrt[a - I*a*Tan[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]]) + (((3*I)/4)*Sqrt[a]*e^(7/2)*ArcTan[1 + (Sqrt[2]*Sqrt[e]*Sqrt[a - I*a*Tan[c + d*x]])/(Sqrt[a]*Sqrt[e*Sec[c + d*x]])]*Sec[c + d*x])/(Sqrt[2]*d*(e*Cos[c + d*x])^(7/2)*(e*Sec[c + d*x])^(7/2)*Sqrt[a - I*a*Tan[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]]) + (((3*I)/8)*Sqrt[a]*e^(7/2)*Log[a - (Sqrt[2]*Sqrt[a]*Sqrt[e]*Sqrt[a - I*a*Tan[c + d*x]])/Sqrt[e*Sec[c + d*x]] + Cos[c + d*x]*(a - I*a*Tan[c + d*x])]*Sec[c + d*x])/(Sqrt[2]*d*(e*Cos[c + d*x])^(7/2)*(e*Sec[c + d*x])^(7/2)*Sqrt[a - I*a*Tan[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]]) - (((3*I)/8)*Sqrt[a]*e^(7/2)*Log[a + (Sqrt[2]*Sqrt[a]*Sqrt[e]*Sqrt[a - I*a*Tan[c + d*x]])/Sqrt[e*Sec[c + d*x]] + Cos[c + d*x]*(a - I*a*Tan[c + d*x])]*Sec[c + d*x])/(Sqrt[2]*d*(e*Cos[c + d*x])^(7/2)*(e*Sec[c + d*x])^(7/2)*Sqrt[a - I*a*Tan[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]]) - ((I/2)*Cos[c + d*x]^2*Sqrt[a + I*a*Tan[c + d*x]])/(a*d*(e*Cos[c + d*x])^(7/2))","A",14,11,30,0.3667,1,"{3515, 3501, 3498, 3499, 3495, 297, 1162, 617, 204, 1165, 628}"
688,1,105,0,0.2307181,"\int (e \cos (c+d x))^m (a+i a \tan (c+d x))^n \, dx","Int[(e*Cos[c + d*x])^m*(a + I*a*Tan[c + d*x])^n,x]","-\frac{i 2^{n-\frac{m}{2}} (a+i a \tan (c+d x))^n (e \cos (c+d x))^m (1+i \tan (c+d x))^{\frac{1}{2} (m-2 n)} \, _2F_1\left(-\frac{m}{2},\frac{1}{2} (m-2 n+2);1-\frac{m}{2};\frac{1}{2} (1-i \tan (c+d x))\right)}{d m}","-\frac{i 2^{n-\frac{m}{2}} (a+i a \tan (c+d x))^n (e \cos (c+d x))^m (1+i \tan (c+d x))^{\frac{1}{2} (m-2 n)} \, _2F_1\left(-\frac{m}{2},\frac{1}{2} (m-2 n+2);1-\frac{m}{2};\frac{1}{2} (1-i \tan (c+d x))\right)}{d m}",1,"((-I)*2^(-m/2 + n)*(e*Cos[c + d*x])^m*Hypergeometric2F1[-m/2, (2 + m - 2*n)/2, 1 - m/2, (1 - I*Tan[c + d*x])/2]*(1 + I*Tan[c + d*x])^((m - 2*n)/2)*(a + I*a*Tan[c + d*x])^n)/(d*m)","A",5,5,26,0.1923,1,"{3515, 3505, 3523, 70, 69}"
689,1,86,0,0.2190135,"\int (e \cos (c+d x))^m (a+i a \tan (c+d x))^2 \, dx","Int[(e*Cos[c + d*x])^m*(a + I*a*Tan[c + d*x])^2,x]","-\frac{i a^2 2^{2-\frac{m}{2}} (1+i \tan (c+d x))^{m/2} (e \cos (c+d x))^m \, _2F_1\left(\frac{m-2}{2},-\frac{m}{2};1-\frac{m}{2};\frac{1}{2} (1-i \tan (c+d x))\right)}{d m}","-\frac{i a^2 2^{2-\frac{m}{2}} (1+i \tan (c+d x))^{m/2} (e \cos (c+d x))^m \, _2F_1\left(\frac{m-2}{2},-\frac{m}{2};1-\frac{m}{2};\frac{1}{2} (1-i \tan (c+d x))\right)}{d m}",1,"((-I)*2^(2 - m/2)*a^2*(e*Cos[c + d*x])^m*Hypergeometric2F1[(-2 + m)/2, -m/2, 1 - m/2, (1 - I*Tan[c + d*x])/2]*(1 + I*Tan[c + d*x])^(m/2))/(d*m)","A",5,5,26,0.1923,1,"{3515, 3505, 3523, 70, 69}"
690,1,82,0,0.1749692,"\int (e \cos (c+d x))^m (a+i a \tan (c+d x)) \, dx","Int[(e*Cos[c + d*x])^m*(a + I*a*Tan[c + d*x]),x]","-\frac{i a 2^{1-\frac{m}{2}} (1+i \tan (c+d x))^{m/2} (e \cos (c+d x))^m \, _2F_1\left(-\frac{m}{2},\frac{m}{2};1-\frac{m}{2};\frac{1}{2} (1-i \tan (c+d x))\right)}{d m}","-\frac{i a 2^{1-\frac{m}{2}} (1+i \tan (c+d x))^{m/2} (e \cos (c+d x))^m \, _2F_1\left(-\frac{m}{2},\frac{m}{2};1-\frac{m}{2};\frac{1}{2} (1-i \tan (c+d x))\right)}{d m}",1,"((-I)*2^(1 - m/2)*a*(e*Cos[c + d*x])^m*Hypergeometric2F1[-m/2, m/2, 1 - m/2, (1 - I*Tan[c + d*x])/2]*(1 + I*Tan[c + d*x])^(m/2))/(d*m)","A",5,5,24,0.2083,1,"{3515, 3505, 3523, 70, 69}"
691,1,86,0,0.2380429,"\int \frac{(e \cos (c+d x))^m}{a+i a \tan (c+d x)} \, dx","Int[(e*Cos[c + d*x])^m/(a + I*a*Tan[c + d*x]),x]","-\frac{i 2^{-\frac{m}{2}-1} (1+i \tan (c+d x))^{m/2} (e \cos (c+d x))^m \, _2F_1\left(-\frac{m}{2},\frac{m+4}{2};1-\frac{m}{2};\frac{1}{2} (1-i \tan (c+d x))\right)}{a d m}","-\frac{i 2^{-\frac{m}{2}-1} (1+i \tan (c+d x))^{m/2} (e \cos (c+d x))^m \, _2F_1\left(-\frac{m}{2},\frac{m+4}{2};1-\frac{m}{2};\frac{1}{2} (1-i \tan (c+d x))\right)}{a d m}",1,"((-I)*2^(-1 - m/2)*(e*Cos[c + d*x])^m*Hypergeometric2F1[-m/2, (4 + m)/2, 1 - m/2, (1 - I*Tan[c + d*x])/2]*(1 + I*Tan[c + d*x])^(m/2))/(a*d*m)","A",5,5,26,0.1923,1,"{3515, 3505, 3523, 70, 69}"
692,1,86,0,0.2367807,"\int \frac{(e \cos (c+d x))^m}{(a+i a \tan (c+d x))^2} \, dx","Int[(e*Cos[c + d*x])^m/(a + I*a*Tan[c + d*x])^2,x]","-\frac{i 2^{-\frac{m}{2}-2} (1+i \tan (c+d x))^{m/2} (e \cos (c+d x))^m \, _2F_1\left(-\frac{m}{2},\frac{m+6}{2};1-\frac{m}{2};\frac{1}{2} (1-i \tan (c+d x))\right)}{a^2 d m}","-\frac{i 2^{-\frac{m}{2}-2} (1+i \tan (c+d x))^{m/2} (e \cos (c+d x))^m \, _2F_1\left(-\frac{m}{2},\frac{m+6}{2};1-\frac{m}{2};\frac{1}{2} (1-i \tan (c+d x))\right)}{a^2 d m}",1,"((-I)*2^(-2 - m/2)*(e*Cos[c + d*x])^m*Hypergeometric2F1[-m/2, (6 + m)/2, 1 - m/2, (1 - I*Tan[c + d*x])/2]*(1 + I*Tan[c + d*x])^(m/2))/(a^2*d*m)","A",5,5,26,0.1923,1,"{3515, 3505, 3523, 70, 69}"
693,1,105,0,0.2863861,"\int (e \cos (c+d x))^m \sqrt{a+i a \tan (c+d x)} \, dx","Int[(e*Cos[c + d*x])^m*Sqrt[a + I*a*Tan[c + d*x]],x]","-\frac{i a 2^{\frac{1}{2}-\frac{m}{2}} (1+i \tan (c+d x))^{\frac{m+1}{2}} (e \cos (c+d x))^m \, _2F_1\left(-\frac{m}{2},\frac{m+1}{2};1-\frac{m}{2};\frac{1}{2} (1-i \tan (c+d x))\right)}{d m \sqrt{a+i a \tan (c+d x)}}","-\frac{i a 2^{\frac{1}{2}-\frac{m}{2}} (1+i \tan (c+d x))^{\frac{m+1}{2}} (e \cos (c+d x))^m \, _2F_1\left(-\frac{m}{2},\frac{m+1}{2};1-\frac{m}{2};\frac{1}{2} (1-i \tan (c+d x))\right)}{d m \sqrt{a+i a \tan (c+d x)}}",1,"((-I)*2^(1/2 - m/2)*a*(e*Cos[c + d*x])^m*Hypergeometric2F1[-m/2, (1 + m)/2, 1 - m/2, (1 - I*Tan[c + d*x])/2]*(1 + I*Tan[c + d*x])^((1 + m)/2))/(d*m*Sqrt[a + I*a*Tan[c + d*x]])","A",5,5,28,0.1786,1,"{3515, 3505, 3523, 70, 69}"
694,1,104,0,0.2901819,"\int \frac{(e \cos (c+d x))^m}{\sqrt{a+i a \tan (c+d x)}} \, dx","Int[(e*Cos[c + d*x])^m/Sqrt[a + I*a*Tan[c + d*x]],x]","-\frac{i 2^{-\frac{m}{2}-\frac{1}{2}} (1+i \tan (c+d x))^{\frac{m+1}{2}} (e \cos (c+d x))^m \, _2F_1\left(-\frac{m}{2},\frac{m+3}{2};1-\frac{m}{2};\frac{1}{2} (1-i \tan (c+d x))\right)}{d m \sqrt{a+i a \tan (c+d x)}}","-\frac{i 2^{-\frac{m}{2}-\frac{1}{2}} (1+i \tan (c+d x))^{\frac{m+1}{2}} (e \cos (c+d x))^m \, _2F_1\left(-\frac{m}{2},\frac{m+3}{2};1-\frac{m}{2};\frac{1}{2} (1-i \tan (c+d x))\right)}{d m \sqrt{a+i a \tan (c+d x)}}",1,"((-I)*2^(-1/2 - m/2)*(e*Cos[c + d*x])^m*Hypergeometric2F1[-m/2, (3 + m)/2, 1 - m/2, (1 - I*Tan[c + d*x])/2]*(1 + I*Tan[c + d*x])^((1 + m)/2))/(d*m*Sqrt[a + I*a*Tan[c + d*x]])","A",5,5,28,0.1786,1,"{3515, 3505, 3523, 70, 69}"
695,1,175,0,0.2850214,"\int (d \cos (e+f x))^m (a+b \tan (e+f x))^3 \, dx","Int[(d*Cos[e + f*x])^m*(a + b*Tan[e + f*x])^3,x]","\frac{a \left(a^2-\frac{3 b^2}{1-m}\right) \tan (e+f x) \sec ^2(e+f x)^{m/2} (d \cos (e+f x))^m \, _2F_1\left(\frac{1}{2},\frac{m+2}{2};\frac{3}{2};-\tan ^2(e+f x)\right)}{f}+\frac{b (d \cos (e+f x))^m \left(2 (1-m) \left(b^2-a^2 (3-m)\right)+a b (4-m) m \tan (e+f x)\right)}{f m \left(m^2-3 m+2\right)}+\frac{b (a+b \tan (e+f x))^2 (d \cos (e+f x))^m}{f (2-m)}","-\frac{a \left(3 b^2-a^2 (1-m)\right) \tan (e+f x) \sec ^2(e+f x)^{m/2} (d \cos (e+f x))^m \, _2F_1\left(\frac{1}{2},\frac{m+2}{2};\frac{3}{2};-\tan ^2(e+f x)\right)}{f (1-m)}+\frac{b (d \cos (e+f x))^m \left(2 (1-m) \left(b^2-a^2 (3-m)\right)+a b (4-m) m \tan (e+f x)\right)}{f m \left(m^2-3 m+2\right)}+\frac{b (a+b \tan (e+f x))^2 (d \cos (e+f x))^m}{f (2-m)}",1,"(a*(a^2 - (3*b^2)/(1 - m))*(d*Cos[e + f*x])^m*Hypergeometric2F1[1/2, (2 + m)/2, 3/2, -Tan[e + f*x]^2]*(Sec[e + f*x]^2)^(m/2)*Tan[e + f*x])/f + (b*(d*Cos[e + f*x])^m*(a + b*Tan[e + f*x])^2)/(f*(2 - m)) + (b*(d*Cos[e + f*x])^m*(2*(b^2 - a^2*(3 - m))*(1 - m) + a*b*(4 - m)*m*Tan[e + f*x]))/(f*m*(2 - 3*m + m^2))","A",5,5,23,0.2174,1,"{3515, 3512, 743, 780, 245}"
696,1,155,0,0.2384883,"\int (d \cos (e+f x))^m (a+b \tan (e+f x))^2 \, dx","Int[(d*Cos[e + f*x])^m*(a + b*Tan[e + f*x])^2,x]","\frac{\left(b^2-a^2 (1-m)\right) \sin (e+f x) \cos (e+f x) (d \cos (e+f x))^m \, _2F_1\left(\frac{1}{2},\frac{m+1}{2};\frac{m+3}{2};\cos ^2(e+f x)\right)}{f (1-m) (m+1) \sqrt{\sin ^2(e+f x)}}-\frac{a b (2-m) (d \cos (e+f x))^m}{f (1-m) m}+\frac{b (a+b \tan (e+f x)) (d \cos (e+f x))^m}{f (1-m)}","\frac{\left(b^2-a^2 (1-m)\right) \sin (e+f x) \cos (e+f x) (d \cos (e+f x))^m \, _2F_1\left(\frac{1}{2},\frac{m+1}{2};\frac{m+3}{2};\cos ^2(e+f x)\right)}{f (1-m) (m+1) \sqrt{\sin ^2(e+f x)}}-\frac{a b (2-m) (d \cos (e+f x))^m}{f (1-m) m}+\frac{b (a+b \tan (e+f x)) (d \cos (e+f x))^m}{f (1-m)}",1,"-((a*b*(2 - m)*(d*Cos[e + f*x])^m)/(f*(1 - m)*m)) + ((b^2 - a^2*(1 - m))*Cos[e + f*x]*(d*Cos[e + f*x])^m*Hypergeometric2F1[1/2, (1 + m)/2, (3 + m)/2, Cos[e + f*x]^2]*Sin[e + f*x])/(f*(1 - m)*(1 + m)*Sqrt[Sin[e + f*x]^2]) + (b*(d*Cos[e + f*x])^m*(a + b*Tan[e + f*x]))/(f*(1 - m))","A",5,5,23,0.2174,1,"{3515, 3508, 3486, 3772, 2643}"
697,1,91,0,0.0999522,"\int (d \cos (e+f x))^m (a+b \tan (e+f x)) \, dx","Int[(d*Cos[e + f*x])^m*(a + b*Tan[e + f*x]),x]","-\frac{a \sin (e+f x) \cos (e+f x) (d \cos (e+f x))^m \, _2F_1\left(\frac{1}{2},\frac{m+1}{2};\frac{m+3}{2};\cos ^2(e+f x)\right)}{f (m+1) \sqrt{\sin ^2(e+f x)}}-\frac{b (d \cos (e+f x))^m}{f m}","-\frac{a \sin (e+f x) (d \cos (e+f x))^{m+1} \, _2F_1\left(\frac{1}{2},\frac{m+1}{2};\frac{m+3}{2};\cos ^2(e+f x)\right)}{d f (m+1) \sqrt{\sin ^2(e+f x)}}-\frac{b (d \cos (e+f x))^m}{f m}",1,"-((b*(d*Cos[e + f*x])^m)/(f*m)) - (a*Cos[e + f*x]*(d*Cos[e + f*x])^m*Hypergeometric2F1[1/2, (1 + m)/2, (3 + m)/2, Cos[e + f*x]^2]*Sin[e + f*x])/(f*(1 + m)*Sqrt[Sin[e + f*x]^2])","A",4,4,21,0.1905,1,"{3515, 3486, 3772, 2643}"
698,1,140,0,0.210547,"\int \frac{(d \cos (e+f x))^m}{a+b \tan (e+f x)} \, dx","Int[(d*Cos[e + f*x])^m/(a + b*Tan[e + f*x]),x]","\frac{\tan (e+f x) \sec ^2(e+f x)^{m/2} (d \cos (e+f x))^m F_1\left(\frac{1}{2};1,\frac{m+2}{2};\frac{3}{2};\frac{b^2 \tan ^2(e+f x)}{a^2},-\tan ^2(e+f x)\right)}{a f}+\frac{b (d \cos (e+f x))^m \, _2F_1\left(1,-\frac{m}{2};1-\frac{m}{2};\frac{b^2 \sec ^2(e+f x)}{a^2+b^2}\right)}{f m \left(a^2+b^2\right)}","\frac{\tan (e+f x) \sec ^2(e+f x)^{m/2} (d \cos (e+f x))^m F_1\left(\frac{1}{2};1,\frac{m+2}{2};\frac{3}{2};\frac{b^2 \tan ^2(e+f x)}{a^2},-\tan ^2(e+f x)\right)}{a f}+\frac{b (d \cos (e+f x))^m \, _2F_1\left(1,-\frac{m}{2};1-\frac{m}{2};\frac{b^2 \sec ^2(e+f x)}{a^2+b^2}\right)}{f m \left(a^2+b^2\right)}",1,"(b*(d*Cos[e + f*x])^m*Hypergeometric2F1[1, -m/2, 1 - m/2, (b^2*Sec[e + f*x]^2)/(a^2 + b^2)])/((a^2 + b^2)*f*m) + (AppellF1[1/2, 1, (2 + m)/2, 3/2, (b^2*Tan[e + f*x]^2)/a^2, -Tan[e + f*x]^2]*(d*Cos[e + f*x])^m*(Sec[e + f*x]^2)^(m/2)*Tan[e + f*x])/(a*f)","A",7,6,23,0.2609,1,"{3515, 3512, 757, 429, 444, 68}"
699,1,227,0,0.2766325,"\int \frac{(d \cos (e+f x))^m}{(a+b \tan (e+f x))^2} \, dx","Int[(d*Cos[e + f*x])^m/(a + b*Tan[e + f*x])^2,x]","\frac{b^2 \tan ^3(e+f x) \sec ^2(e+f x)^{m/2} (d \cos (e+f x))^m F_1\left(\frac{3}{2};2,\frac{m+2}{2};\frac{5}{2};\frac{b^2 \tan ^2(e+f x)}{a^2},-\tan ^2(e+f x)\right)}{3 a^4 f}+\frac{\tan (e+f x) \sec ^2(e+f x)^{m/2} (d \cos (e+f x))^m F_1\left(\frac{1}{2};2,\frac{m+2}{2};\frac{3}{2};\frac{b^2 \tan ^2(e+f x)}{a^2},-\tan ^2(e+f x)\right)}{a^2 f}+\frac{2 a b (d \cos (e+f x))^m \, _2F_1\left(2,-\frac{m}{2};1-\frac{m}{2};\frac{b^2 \sec ^2(e+f x)}{a^2+b^2}\right)}{f m \left(a^2+b^2\right)^2}","\frac{b^2 \tan ^3(e+f x) \sec ^2(e+f x)^{m/2} (d \cos (e+f x))^m F_1\left(\frac{3}{2};2,\frac{m+2}{2};\frac{5}{2};\frac{b^2 \tan ^2(e+f x)}{a^2},-\tan ^2(e+f x)\right)}{3 a^4 f}+\frac{\tan (e+f x) \sec ^2(e+f x)^{m/2} (d \cos (e+f x))^m F_1\left(\frac{1}{2};2,\frac{m+2}{2};\frac{3}{2};\frac{b^2 \tan ^2(e+f x)}{a^2},-\tan ^2(e+f x)\right)}{a^2 f}+\frac{2 a b (d \cos (e+f x))^m \, _2F_1\left(2,-\frac{m}{2};1-\frac{m}{2};\frac{b^2 \sec ^2(e+f x)}{a^2+b^2}\right)}{f m \left(a^2+b^2\right)^2}",1,"(2*a*b*(d*Cos[e + f*x])^m*Hypergeometric2F1[2, -m/2, 1 - m/2, (b^2*Sec[e + f*x]^2)/(a^2 + b^2)])/((a^2 + b^2)^2*f*m) + (AppellF1[1/2, 2, (2 + m)/2, 3/2, (b^2*Tan[e + f*x]^2)/a^2, -Tan[e + f*x]^2]*(d*Cos[e + f*x])^m*(Sec[e + f*x]^2)^(m/2)*Tan[e + f*x])/(a^2*f) + (b^2*AppellF1[3/2, 2, (2 + m)/2, 5/2, (b^2*Tan[e + f*x]^2)/a^2, -Tan[e + f*x]^2]*(d*Cos[e + f*x])^m*(Sec[e + f*x]^2)^(m/2)*Tan[e + f*x]^3)/(3*a^4*f)","A",8,7,23,0.3043,1,"{3515, 3512, 757, 429, 444, 68, 510}"
700,1,187,0,0.2028842,"\int (d \cos (e+f x))^m (a+b \tan (e+f x))^n \, dx","Int[(d*Cos[e + f*x])^m*(a + b*Tan[e + f*x])^n,x]","\frac{\cos ^2(e+f x) (d \cos (e+f x))^m \left(1-\frac{a+b \tan (e+f x)}{a-\sqrt{-b^2}}\right)^{\frac{m+2}{2}} \left(1-\frac{a+b \tan (e+f x)}{a+\sqrt{-b^2}}\right)^{\frac{m+2}{2}} (a+b \tan (e+f x))^{n+1} F_1\left(n+1;\frac{m+2}{2},\frac{m+2}{2};n+2;\frac{a+b \tan (e+f x)}{a-\sqrt{-b^2}},\frac{a+b \tan (e+f x)}{a+\sqrt{-b^2}}\right)}{b f (n+1)}","\frac{\cos ^2(e+f x) (d \cos (e+f x))^m \left(1-\frac{a+b \tan (e+f x)}{a-\sqrt{-b^2}}\right)^{\frac{m+2}{2}} \left(1-\frac{a+b \tan (e+f x)}{a+\sqrt{-b^2}}\right)^{\frac{m+2}{2}} (a+b \tan (e+f x))^{n+1} F_1\left(n+1;\frac{m+2}{2},\frac{m+2}{2};n+2;\frac{a+b \tan (e+f x)}{a-\sqrt{-b^2}},\frac{a+b \tan (e+f x)}{a+\sqrt{-b^2}}\right)}{b f (n+1)}",1,"(AppellF1[1 + n, (2 + m)/2, (2 + m)/2, 2 + n, (a + b*Tan[e + f*x])/(a - Sqrt[-b^2]), (a + b*Tan[e + f*x])/(a + Sqrt[-b^2])]*Cos[e + f*x]^2*(d*Cos[e + f*x])^m*(a + b*Tan[e + f*x])^(1 + n)*(1 - (a + b*Tan[e + f*x])/(a - Sqrt[-b^2]))^((2 + m)/2)*(1 - (a + b*Tan[e + f*x])/(a + Sqrt[-b^2]))^((2 + m)/2))/(b*f*(1 + n))","A",4,4,23,0.1739,1,"{3515, 3512, 760, 133}"