1,1,61,0,0.0574345,"\int \sin (a+b x) \sin ^7(2 a+2 b x) \, dx","Int[Sin[a + b*x]*Sin[2*a + 2*b*x]^7,x]","-\frac{128 \sin ^{15}(a+b x)}{15 b}+\frac{384 \sin ^{13}(a+b x)}{13 b}-\frac{384 \sin ^{11}(a+b x)}{11 b}+\frac{128 \sin ^9(a+b x)}{9 b}","-\frac{128 \sin ^{15}(a+b x)}{15 b}+\frac{384 \sin ^{13}(a+b x)}{13 b}-\frac{384 \sin ^{11}(a+b x)}{11 b}+\frac{128 \sin ^9(a+b x)}{9 b}",1,"(128*Sin[a + b*x]^9)/(9*b) - (384*Sin[a + b*x]^11)/(11*b) + (384*Sin[a + b*x]^13)/(13*b) - (128*Sin[a + b*x]^15)/(15*b)","A",4,3,18,0.1667,1,"{4288, 2564, 270}"
2,1,61,0,0.0580589,"\int \sin (a+b x) \sin ^6(2 a+2 b x) \, dx","Int[Sin[a + b*x]*Sin[2*a + 2*b*x]^6,x]","\frac{64 \cos ^{13}(a+b x)}{13 b}-\frac{192 \cos ^{11}(a+b x)}{11 b}+\frac{64 \cos ^9(a+b x)}{3 b}-\frac{64 \cos ^7(a+b x)}{7 b}","\frac{64 \cos ^{13}(a+b x)}{13 b}-\frac{192 \cos ^{11}(a+b x)}{11 b}+\frac{64 \cos ^9(a+b x)}{3 b}-\frac{64 \cos ^7(a+b x)}{7 b}",1,"(-64*Cos[a + b*x]^7)/(7*b) + (64*Cos[a + b*x]^9)/(3*b) - (192*Cos[a + b*x]^11)/(11*b) + (64*Cos[a + b*x]^13)/(13*b)","A",4,3,18,0.1667,1,"{4288, 2565, 270}"
3,1,46,0,0.0546081,"\int \sin (a+b x) \sin ^5(2 a+2 b x) \, dx","Int[Sin[a + b*x]*Sin[2*a + 2*b*x]^5,x]","\frac{32 \sin ^{11}(a+b x)}{11 b}-\frac{64 \sin ^9(a+b x)}{9 b}+\frac{32 \sin ^7(a+b x)}{7 b}","\frac{32 \sin ^{11}(a+b x)}{11 b}-\frac{64 \sin ^9(a+b x)}{9 b}+\frac{32 \sin ^7(a+b x)}{7 b}",1,"(32*Sin[a + b*x]^7)/(7*b) - (64*Sin[a + b*x]^9)/(9*b) + (32*Sin[a + b*x]^11)/(11*b)","A",4,3,18,0.1667,1,"{4288, 2564, 270}"
4,1,46,0,0.055045,"\int \sin (a+b x) \sin ^4(2 a+2 b x) \, dx","Int[Sin[a + b*x]*Sin[2*a + 2*b*x]^4,x]","-\frac{16 \cos ^9(a+b x)}{9 b}+\frac{32 \cos ^7(a+b x)}{7 b}-\frac{16 \cos ^5(a+b x)}{5 b}","-\frac{16 \cos ^9(a+b x)}{9 b}+\frac{32 \cos ^7(a+b x)}{7 b}-\frac{16 \cos ^5(a+b x)}{5 b}",1,"(-16*Cos[a + b*x]^5)/(5*b) + (32*Cos[a + b*x]^7)/(7*b) - (16*Cos[a + b*x]^9)/(9*b)","A",4,3,18,0.1667,1,"{4288, 2565, 270}"
5,1,31,0,0.0496947,"\int \sin (a+b x) \sin ^3(2 a+2 b x) \, dx","Int[Sin[a + b*x]*Sin[2*a + 2*b*x]^3,x]","\frac{8 \sin ^5(a+b x)}{5 b}-\frac{8 \sin ^7(a+b x)}{7 b}","\frac{8 \sin ^5(a+b x)}{5 b}-\frac{8 \sin ^7(a+b x)}{7 b}",1,"(8*Sin[a + b*x]^5)/(5*b) - (8*Sin[a + b*x]^7)/(7*b)","A",4,3,18,0.1667,1,"{4288, 2564, 14}"
6,1,31,0,0.0496542,"\int \sin (a+b x) \sin ^2(2 a+2 b x) \, dx","Int[Sin[a + b*x]*Sin[2*a + 2*b*x]^2,x]","\frac{4 \cos ^5(a+b x)}{5 b}-\frac{4 \cos ^3(a+b x)}{3 b}","\frac{4 \cos ^5(a+b x)}{5 b}-\frac{4 \cos ^3(a+b x)}{3 b}",1,"(-4*Cos[a + b*x]^3)/(3*b) + (4*Cos[a + b*x]^5)/(5*b)","A",4,3,18,0.1667,1,"{4288, 2565, 14}"
7,1,30,0,0.011129,"\int \sin (a+b x) \sin (2 a+2 b x) \, dx","Int[Sin[a + b*x]*Sin[2*a + 2*b*x],x]","\frac{\sin (a+b x)}{2 b}-\frac{\sin (3 a+3 b x)}{6 b}","\frac{\sin (a+b x)}{2 b}-\frac{\sin (3 a+3 b x)}{6 b}",1,"Sin[a + b*x]/(2*b) - Sin[3*a + 3*b*x]/(6*b)","A",1,1,16,0.06250,1,"{4282}"
8,1,14,0,0.0169135,"\int \csc (2 a+2 b x) \sin (a+b x) \, dx","Int[Csc[2*a + 2*b*x]*Sin[a + b*x],x]","\frac{\tanh ^{-1}(\sin (a+b x))}{2 b}","\frac{\tanh ^{-1}(\sin (a+b x))}{2 b}",1,"ArcTanh[Sin[a + b*x]]/(2*b)","A",2,2,16,0.1250,1,"{4288, 3770}"
9,1,28,0,0.0382959,"\int \csc ^2(2 a+2 b x) \sin (a+b x) \, dx","Int[Csc[2*a + 2*b*x]^2*Sin[a + b*x],x]","\frac{\sec (a+b x)}{4 b}-\frac{\tanh ^{-1}(\cos (a+b x))}{4 b}","\frac{\sec (a+b x)}{4 b}-\frac{\tanh ^{-1}(\cos (a+b x))}{4 b}",1,"-ArcTanh[Cos[a + b*x]]/(4*b) + Sec[a + b*x]/(4*b)","A",4,4,18,0.2222,1,"{4288, 2622, 321, 207}"
10,1,49,0,0.062518,"\int \csc ^3(2 a+2 b x) \sin (a+b x) \, dx","Int[Csc[2*a + 2*b*x]^3*Sin[a + b*x],x]","-\frac{3 \csc (a+b x)}{16 b}+\frac{3 \tanh ^{-1}(\sin (a+b x))}{16 b}+\frac{\csc (a+b x) \sec ^2(a+b x)}{16 b}","-\frac{3 \csc (a+b x)}{16 b}+\frac{3 \tanh ^{-1}(\sin (a+b x))}{16 b}+\frac{\csc (a+b x) \sec ^2(a+b x)}{16 b}",1,"(3*ArcTanh[Sin[a + b*x]])/(16*b) - (3*Csc[a + b*x])/(16*b) + (Csc[a + b*x]*Sec[a + b*x]^2)/(16*b)","A",5,5,18,0.2778,1,"{4288, 2621, 288, 321, 207}"
11,1,66,0,0.0674468,"\int \csc ^4(2 a+2 b x) \sin (a+b x) \, dx","Int[Csc[2*a + 2*b*x]^4*Sin[a + b*x],x]","\frac{5 \sec ^3(a+b x)}{96 b}+\frac{5 \sec (a+b x)}{32 b}-\frac{5 \tanh ^{-1}(\cos (a+b x))}{32 b}-\frac{\csc ^2(a+b x) \sec ^3(a+b x)}{32 b}","\frac{5 \sec ^3(a+b x)}{96 b}+\frac{5 \sec (a+b x)}{32 b}-\frac{5 \tanh ^{-1}(\cos (a+b x))}{32 b}-\frac{\csc ^2(a+b x) \sec ^3(a+b x)}{32 b}",1,"(-5*ArcTanh[Cos[a + b*x]])/(32*b) + (5*Sec[a + b*x])/(32*b) + (5*Sec[a + b*x]^3)/(96*b) - (Csc[a + b*x]^2*Sec[a + b*x]^3)/(32*b)","A",6,5,18,0.2778,1,"{4288, 2622, 288, 302, 207}"
12,1,89,0,0.0694721,"\int \csc ^5(2 a+2 b x) \sin (a+b x) \, dx","Int[Csc[2*a + 2*b*x]^5*Sin[a + b*x],x]","-\frac{35 \csc ^3(a+b x)}{768 b}-\frac{35 \csc (a+b x)}{256 b}+\frac{35 \tanh ^{-1}(\sin (a+b x))}{256 b}+\frac{\csc ^3(a+b x) \sec ^4(a+b x)}{128 b}+\frac{7 \csc ^3(a+b x) \sec ^2(a+b x)}{256 b}","-\frac{35 \csc ^3(a+b x)}{768 b}-\frac{35 \csc (a+b x)}{256 b}+\frac{35 \tanh ^{-1}(\sin (a+b x))}{256 b}+\frac{\csc ^3(a+b x) \sec ^4(a+b x)}{128 b}+\frac{7 \csc ^3(a+b x) \sec ^2(a+b x)}{256 b}",1,"(35*ArcTanh[Sin[a + b*x]])/(256*b) - (35*Csc[a + b*x])/(256*b) - (35*Csc[a + b*x]^3)/(768*b) + (7*Csc[a + b*x]^3*Sec[a + b*x]^2)/(256*b) + (Csc[a + b*x]^3*Sec[a + b*x]^4)/(128*b)","A",7,5,18,0.2778,1,"{4288, 2621, 288, 302, 207}"
13,1,44,0,0.0687566,"\int \sin ^2(a+b x) \sin ^5(2 a+2 b x) \, dx","Int[Sin[a + b*x]^2*Sin[2*a + 2*b*x]^5,x]","\frac{8 \sin ^{12}(a+b x)}{3 b}-\frac{32 \sin ^{10}(a+b x)}{5 b}+\frac{4 \sin ^8(a+b x)}{b}","\frac{8 \sin ^{12}(a+b x)}{3 b}-\frac{32 \sin ^{10}(a+b x)}{5 b}+\frac{4 \sin ^8(a+b x)}{b}",1,"(4*Sin[a + b*x]^8)/b - (32*Sin[a + b*x]^10)/(5*b) + (8*Sin[a + b*x]^12)/(3*b)","A",5,4,20,0.2000,1,"{4288, 2564, 266, 43}"
14,1,76,0,0.0676803,"\int \sin ^2(a+b x) \sin ^4(2 a+2 b x) \, dx","Int[Sin[a + b*x]^2*Sin[2*a + 2*b*x]^4,x]","-\frac{\sin ^5(2 a+2 b x)}{20 b}-\frac{\sin ^3(2 a+2 b x) \cos (2 a+2 b x)}{16 b}-\frac{3 \sin (2 a+2 b x) \cos (2 a+2 b x)}{32 b}+\frac{3 x}{16}","-\frac{\sin ^5(2 a+2 b x)}{20 b}-\frac{\sin ^3(2 a+2 b x) \cos (2 a+2 b x)}{16 b}-\frac{3 \sin (2 a+2 b x) \cos (2 a+2 b x)}{32 b}+\frac{3 x}{16}",1,"(3*x)/16 - (3*Cos[2*a + 2*b*x]*Sin[2*a + 2*b*x])/(32*b) - (Cos[2*a + 2*b*x]*Sin[2*a + 2*b*x]^3)/(16*b) - Sin[2*a + 2*b*x]^5/(20*b)","A",6,5,20,0.2500,1,"{4286, 2635, 8, 2564, 30}"
15,1,29,0,0.0591716,"\int \sin ^2(a+b x) \sin ^3(2 a+2 b x) \, dx","Int[Sin[a + b*x]^2*Sin[2*a + 2*b*x]^3,x]","\frac{4 \sin ^6(a+b x)}{3 b}-\frac{\sin ^8(a+b x)}{b}","\frac{4 \sin ^6(a+b x)}{3 b}-\frac{\sin ^8(a+b x)}{b}",1,"(4*Sin[a + b*x]^6)/(3*b) - Sin[a + b*x]^8/b","A",4,3,20,0.1500,1,"{4288, 2564, 14}"
16,1,49,0,0.0560334,"\int \sin ^2(a+b x) \sin ^2(2 a+2 b x) \, dx","Int[Sin[a + b*x]^2*Sin[2*a + 2*b*x]^2,x]","-\frac{\sin ^3(2 a+2 b x)}{12 b}-\frac{\sin (2 a+2 b x) \cos (2 a+2 b x)}{8 b}+\frac{x}{4}","-\frac{\sin ^3(2 a+2 b x)}{12 b}-\frac{\sin (2 a+2 b x) \cos (2 a+2 b x)}{8 b}+\frac{x}{4}",1,"x/4 - (Cos[2*a + 2*b*x]*Sin[2*a + 2*b*x])/(8*b) - Sin[2*a + 2*b*x]^3/(12*b)","A",5,5,20,0.2500,1,"{4286, 2635, 8, 2564, 30}"
17,1,15,0,0.0332715,"\int \sin ^2(a+b x) \sin (2 a+2 b x) \, dx","Int[Sin[a + b*x]^2*Sin[2*a + 2*b*x],x]","\frac{\sin ^4(a+b x)}{2 b}","\frac{\sin ^4(a+b x)}{2 b}",1,"Sin[a + b*x]^4/(2*b)","A",3,3,18,0.1667,1,"{4288, 2564, 30}"
18,1,14,0,0.026394,"\int \csc (2 a+2 b x) \sin ^2(a+b x) \, dx","Int[Csc[2*a + 2*b*x]*Sin[a + b*x]^2,x]","-\frac{\log (\cos (a+b x))}{2 b}","-\frac{\log (\cos (a+b x))}{2 b}",1,"-Log[Cos[a + b*x]]/(2*b)","A",2,2,18,0.1111,1,"{4288, 3475}"
19,1,13,0,0.034776,"\int \csc ^2(2 a+2 b x) \sin ^2(a+b x) \, dx","Int[Csc[2*a + 2*b*x]^2*Sin[a + b*x]^2,x]","\frac{\tan (a+b x)}{4 b}","\frac{\tan (a+b x)}{4 b}",1,"Tan[a + b*x]/(4*b)","A",3,3,20,0.1500,1,"{4288, 3767, 8}"
20,1,30,0,0.0478498,"\int \csc ^3(2 a+2 b x) \sin ^2(a+b x) \, dx","Int[Csc[2*a + 2*b*x]^3*Sin[a + b*x]^2,x]","\frac{\tan ^2(a+b x)}{16 b}+\frac{\log (\tan (a+b x))}{8 b}","\frac{\tan ^2(a+b x)}{16 b}+\frac{\log (\tan (a+b x))}{8 b}",1,"Log[Tan[a + b*x]]/(8*b) + Tan[a + b*x]^2/(16*b)","A",4,3,20,0.1500,1,"{4288, 2620, 14}"
21,1,42,0,0.062722,"\int \csc ^4(2 a+2 b x) \sin ^2(a+b x) \, dx","Int[Csc[2*a + 2*b*x]^4*Sin[a + b*x]^2,x]","\frac{\tan ^3(a+b x)}{48 b}+\frac{\tan (a+b x)}{8 b}-\frac{\cot (a+b x)}{16 b}","\frac{\tan ^3(a+b x)}{48 b}+\frac{\tan (a+b x)}{8 b}-\frac{\cot (a+b x)}{16 b}",1,"-Cot[a + b*x]/(16*b) + Tan[a + b*x]/(8*b) + Tan[a + b*x]^3/(48*b)","A",4,3,20,0.1500,1,"{4288, 2620, 270}"
22,1,60,0,0.0713194,"\int \csc ^5(2 a+2 b x) \sin ^2(a+b x) \, dx","Int[Csc[2*a + 2*b*x]^5*Sin[a + b*x]^2,x]","\frac{\tan ^4(a+b x)}{128 b}+\frac{3 \tan ^2(a+b x)}{64 b}-\frac{\cot ^2(a+b x)}{64 b}+\frac{3 \log (\tan (a+b x))}{32 b}","\frac{\tan ^4(a+b x)}{128 b}+\frac{3 \tan ^2(a+b x)}{64 b}-\frac{\cot ^2(a+b x)}{64 b}+\frac{3 \log (\tan (a+b x))}{32 b}",1,"-Cot[a + b*x]^2/(64*b) + (3*Log[Tan[a + b*x]])/(32*b) + (3*Tan[a + b*x]^2)/(64*b) + Tan[a + b*x]^4/(128*b)","A",5,4,20,0.2000,1,"{4288, 2620, 266, 43}"
23,1,46,0,0.0631673,"\int \sin ^3(a+b x) \sin ^5(2 a+2 b x) \, dx","Int[Sin[a + b*x]^3*Sin[2*a + 2*b*x]^5,x]","\frac{32 \sin ^{13}(a+b x)}{13 b}-\frac{64 \sin ^{11}(a+b x)}{11 b}+\frac{32 \sin ^9(a+b x)}{9 b}","\frac{32 \sin ^{13}(a+b x)}{13 b}-\frac{64 \sin ^{11}(a+b x)}{11 b}+\frac{32 \sin ^9(a+b x)}{9 b}",1,"(32*Sin[a + b*x]^9)/(9*b) - (64*Sin[a + b*x]^11)/(11*b) + (32*Sin[a + b*x]^13)/(13*b)","A",4,3,20,0.1500,1,"{4288, 2564, 270}"
24,1,61,0,0.0685345,"\int \sin ^3(a+b x) \sin ^4(2 a+2 b x) \, dx","Int[Sin[a + b*x]^3*Sin[2*a + 2*b*x]^4,x]","\frac{16 \cos ^{11}(a+b x)}{11 b}-\frac{16 \cos ^9(a+b x)}{3 b}+\frac{48 \cos ^7(a+b x)}{7 b}-\frac{16 \cos ^5(a+b x)}{5 b}","\frac{16 \cos ^{11}(a+b x)}{11 b}-\frac{16 \cos ^9(a+b x)}{3 b}+\frac{48 \cos ^7(a+b x)}{7 b}-\frac{16 \cos ^5(a+b x)}{5 b}",1,"(-16*Cos[a + b*x]^5)/(5*b) + (48*Cos[a + b*x]^7)/(7*b) - (16*Cos[a + b*x]^9)/(3*b) + (16*Cos[a + b*x]^11)/(11*b)","A",4,3,20,0.1500,1,"{4288, 2565, 270}"
25,1,31,0,0.059593,"\int \sin ^3(a+b x) \sin ^3(2 a+2 b x) \, dx","Int[Sin[a + b*x]^3*Sin[2*a + 2*b*x]^3,x]","\frac{8 \sin ^7(a+b x)}{7 b}-\frac{8 \sin ^9(a+b x)}{9 b}","\frac{8 \sin ^7(a+b x)}{7 b}-\frac{8 \sin ^9(a+b x)}{9 b}",1,"(8*Sin[a + b*x]^7)/(7*b) - (8*Sin[a + b*x]^9)/(9*b)","A",4,3,20,0.1500,1,"{4288, 2564, 14}"
26,1,46,0,0.0635506,"\int \sin ^3(a+b x) \sin ^2(2 a+2 b x) \, dx","Int[Sin[a + b*x]^3*Sin[2*a + 2*b*x]^2,x]","-\frac{4 \cos ^7(a+b x)}{7 b}+\frac{8 \cos ^5(a+b x)}{5 b}-\frac{4 \cos ^3(a+b x)}{3 b}","-\frac{4 \cos ^7(a+b x)}{7 b}+\frac{8 \cos ^5(a+b x)}{5 b}-\frac{4 \cos ^3(a+b x)}{3 b}",1,"(-4*Cos[a + b*x]^3)/(3*b) + (8*Cos[a + b*x]^5)/(5*b) - (4*Cos[a + b*x]^7)/(7*b)","A",4,3,20,0.1500,1,"{4288, 2565, 270}"
27,1,15,0,0.0330478,"\int \sin ^3(a+b x) \sin (2 a+2 b x) \, dx","Int[Sin[a + b*x]^3*Sin[2*a + 2*b*x],x]","\frac{2 \sin ^5(a+b x)}{5 b}","\frac{2 \sin ^5(a+b x)}{5 b}",1,"(2*Sin[a + b*x]^5)/(5*b)","A",3,3,18,0.1667,1,"{4288, 2564, 30}"
28,1,28,0,0.0372884,"\int \csc (2 a+2 b x) \sin ^3(a+b x) \, dx","Int[Csc[2*a + 2*b*x]*Sin[a + b*x]^3,x]","\frac{\tanh ^{-1}(\sin (a+b x))}{2 b}-\frac{\sin (a+b x)}{2 b}","\frac{\tanh ^{-1}(\sin (a+b x))}{2 b}-\frac{\sin (a+b x)}{2 b}",1,"ArcTanh[Sin[a + b*x]]/(2*b) - Sin[a + b*x]/(2*b)","A",4,4,18,0.2222,1,"{4288, 2592, 321, 206}"
29,1,13,0,0.0353868,"\int \csc ^2(2 a+2 b x) \sin ^3(a+b x) \, dx","Int[Csc[2*a + 2*b*x]^2*Sin[a + b*x]^3,x]","\frac{\sec (a+b x)}{4 b}","\frac{\sec (a+b x)}{4 b}",1,"Sec[a + b*x]/(4*b)","A",3,3,20,0.1500,1,"{4288, 2606, 8}"
30,1,34,0,0.0413876,"\int \csc ^3(2 a+2 b x) \sin ^3(a+b x) \, dx","Int[Csc[2*a + 2*b*x]^3*Sin[a + b*x]^3,x]","\frac{\tanh ^{-1}(\sin (a+b x))}{16 b}+\frac{\tan (a+b x) \sec (a+b x)}{16 b}","\frac{\tanh ^{-1}(\sin (a+b x))}{16 b}+\frac{\tan (a+b x) \sec (a+b x)}{16 b}",1,"ArcTanh[Sin[a + b*x]]/(16*b) + (Sec[a + b*x]*Tan[a + b*x])/(16*b)","A",3,3,20,0.1500,1,"{4288, 3768, 3770}"
31,1,43,0,0.0529464,"\int \csc ^4(2 a+2 b x) \sin ^3(a+b x) \, dx","Int[Csc[2*a + 2*b*x]^4*Sin[a + b*x]^3,x]","\frac{\sec ^3(a+b x)}{48 b}+\frac{\sec (a+b x)}{16 b}-\frac{\tanh ^{-1}(\cos (a+b x))}{16 b}","\frac{\sec ^3(a+b x)}{48 b}+\frac{\sec (a+b x)}{16 b}-\frac{\tanh ^{-1}(\cos (a+b x))}{16 b}",1,"-ArcTanh[Cos[a + b*x]]/(16*b) + Sec[a + b*x]/(16*b) + Sec[a + b*x]^3/(48*b)","A",5,4,20,0.2000,1,"{4288, 2622, 302, 207}"
32,1,70,0,0.0721454,"\int \csc ^5(2 a+2 b x) \sin ^3(a+b x) \, dx","Int[Csc[2*a + 2*b*x]^5*Sin[a + b*x]^3,x]","-\frac{15 \csc (a+b x)}{256 b}+\frac{15 \tanh ^{-1}(\sin (a+b x))}{256 b}+\frac{\csc (a+b x) \sec ^4(a+b x)}{128 b}+\frac{5 \csc (a+b x) \sec ^2(a+b x)}{256 b}","-\frac{15 \csc (a+b x)}{256 b}+\frac{15 \tanh ^{-1}(\sin (a+b x))}{256 b}+\frac{\csc (a+b x) \sec ^4(a+b x)}{128 b}+\frac{5 \csc (a+b x) \sec ^2(a+b x)}{256 b}",1,"(15*ArcTanh[Sin[a + b*x]])/(256*b) - (15*Csc[a + b*x])/(256*b) + (5*Csc[a + b*x]*Sec[a + b*x]^2)/(256*b) + (Csc[a + b*x]*Sec[a + b*x]^4)/(128*b)","A",6,5,20,0.2500,1,"{4288, 2621, 288, 321, 207}"
33,1,61,0,0.0613116,"\int \csc (a+b x) \sin ^8(2 a+2 b x) \, dx","Int[Csc[a + b*x]*Sin[2*a + 2*b*x]^8,x]","\frac{256 \cos ^{15}(a+b x)}{15 b}-\frac{768 \cos ^{13}(a+b x)}{13 b}+\frac{768 \cos ^{11}(a+b x)}{11 b}-\frac{256 \cos ^9(a+b x)}{9 b}","\frac{256 \cos ^{15}(a+b x)}{15 b}-\frac{768 \cos ^{13}(a+b x)}{13 b}+\frac{768 \cos ^{11}(a+b x)}{11 b}-\frac{256 \cos ^9(a+b x)}{9 b}",1,"(-256*Cos[a + b*x]^9)/(9*b) + (768*Cos[a + b*x]^11)/(11*b) - (768*Cos[a + b*x]^13)/(13*b) + (256*Cos[a + b*x]^15)/(15*b)","A",4,3,18,0.1667,1,"{4288, 2565, 270}"
34,1,61,0,0.0606673,"\int \csc (a+b x) \sin ^7(2 a+2 b x) \, dx","Int[Csc[a + b*x]*Sin[2*a + 2*b*x]^7,x]","-\frac{128 \sin ^{13}(a+b x)}{13 b}+\frac{384 \sin ^{11}(a+b x)}{11 b}-\frac{128 \sin ^9(a+b x)}{3 b}+\frac{128 \sin ^7(a+b x)}{7 b}","-\frac{128 \sin ^{13}(a+b x)}{13 b}+\frac{384 \sin ^{11}(a+b x)}{11 b}-\frac{128 \sin ^9(a+b x)}{3 b}+\frac{128 \sin ^7(a+b x)}{7 b}",1,"(128*Sin[a + b*x]^7)/(7*b) - (128*Sin[a + b*x]^9)/(3*b) + (384*Sin[a + b*x]^11)/(11*b) - (128*Sin[a + b*x]^13)/(13*b)","A",4,3,18,0.1667,1,"{4288, 2564, 270}"
35,1,46,0,0.0559452,"\int \csc (a+b x) \sin ^6(2 a+2 b x) \, dx","Int[Csc[a + b*x]*Sin[2*a + 2*b*x]^6,x]","-\frac{64 \cos ^{11}(a+b x)}{11 b}+\frac{128 \cos ^9(a+b x)}{9 b}-\frac{64 \cos ^7(a+b x)}{7 b}","-\frac{64 \cos ^{11}(a+b x)}{11 b}+\frac{128 \cos ^9(a+b x)}{9 b}-\frac{64 \cos ^7(a+b x)}{7 b}",1,"(-64*Cos[a + b*x]^7)/(7*b) + (128*Cos[a + b*x]^9)/(9*b) - (64*Cos[a + b*x]^11)/(11*b)","A",4,3,18,0.1667,1,"{4288, 2565, 270}"
36,1,46,0,0.0565101,"\int \csc (a+b x) \sin ^5(2 a+2 b x) \, dx","Int[Csc[a + b*x]*Sin[2*a + 2*b*x]^5,x]","\frac{32 \sin ^9(a+b x)}{9 b}-\frac{64 \sin ^7(a+b x)}{7 b}+\frac{32 \sin ^5(a+b x)}{5 b}","\frac{32 \sin ^9(a+b x)}{9 b}-\frac{64 \sin ^7(a+b x)}{7 b}+\frac{32 \sin ^5(a+b x)}{5 b}",1,"(32*Sin[a + b*x]^5)/(5*b) - (64*Sin[a + b*x]^7)/(7*b) + (32*Sin[a + b*x]^9)/(9*b)","A",4,3,18,0.1667,1,"{4288, 2564, 270}"
37,1,31,0,0.0519787,"\int \csc (a+b x) \sin ^4(2 a+2 b x) \, dx","Int[Csc[a + b*x]*Sin[2*a + 2*b*x]^4,x]","\frac{16 \cos ^7(a+b x)}{7 b}-\frac{16 \cos ^5(a+b x)}{5 b}","\frac{16 \cos ^7(a+b x)}{7 b}-\frac{16 \cos ^5(a+b x)}{5 b}",1,"(-16*Cos[a + b*x]^5)/(5*b) + (16*Cos[a + b*x]^7)/(7*b)","A",4,3,18,0.1667,1,"{4288, 2565, 14}"
38,1,31,0,0.0513627,"\int \csc (a+b x) \sin ^3(2 a+2 b x) \, dx","Int[Csc[a + b*x]*Sin[2*a + 2*b*x]^3,x]","\frac{8 \sin ^3(a+b x)}{3 b}-\frac{8 \sin ^5(a+b x)}{5 b}","\frac{8 \sin ^3(a+b x)}{3 b}-\frac{8 \sin ^5(a+b x)}{5 b}",1,"(8*Sin[a + b*x]^3)/(3*b) - (8*Sin[a + b*x]^5)/(5*b)","A",4,3,18,0.1667,1,"{4288, 2564, 14}"
39,1,15,0,0.0372745,"\int \csc (a+b x) \sin ^2(2 a+2 b x) \, dx","Int[Csc[a + b*x]*Sin[2*a + 2*b*x]^2,x]","-\frac{4 \cos ^3(a+b x)}{3 b}","-\frac{4 \cos ^3(a+b x)}{3 b}",1,"(-4*Cos[a + b*x]^3)/(3*b)","A",3,3,18,0.1667,1,"{4288, 2565, 30}"
40,1,11,0,0.0165524,"\int \csc (a+b x) \sin (2 a+2 b x) \, dx","Int[Csc[a + b*x]*Sin[2*a + 2*b*x],x]","\frac{2 \sin (a+b x)}{b}","\frac{2 \sin (a+b x)}{b}",1,"(2*Sin[a + b*x])/b","A",2,2,16,0.1250,1,"{4288, 2637}"
41,1,28,0,0.0413485,"\int \csc (a+b x) \csc (2 a+2 b x) \, dx","Int[Csc[a + b*x]*Csc[2*a + 2*b*x],x]","\frac{\tanh ^{-1}(\sin (a+b x))}{2 b}-\frac{\csc (a+b x)}{2 b}","\frac{\tanh ^{-1}(\sin (a+b x))}{2 b}-\frac{\csc (a+b x)}{2 b}",1,"ArcTanh[Sin[a + b*x]]/(2*b) - Csc[a + b*x]/(2*b)","A",4,4,16,0.2500,1,"{4288, 2621, 321, 207}"
42,1,49,0,0.058755,"\int \csc (a+b x) \csc ^2(2 a+2 b x) \, dx","Int[Csc[a + b*x]*Csc[2*a + 2*b*x]^2,x]","\frac{3 \sec (a+b x)}{8 b}-\frac{3 \tanh ^{-1}(\cos (a+b x))}{8 b}-\frac{\csc ^2(a+b x) \sec (a+b x)}{8 b}","\frac{3 \sec (a+b x)}{8 b}-\frac{3 \tanh ^{-1}(\cos (a+b x))}{8 b}-\frac{\csc ^2(a+b x) \sec (a+b x)}{8 b}",1,"(-3*ArcTanh[Cos[a + b*x]])/(8*b) + (3*Sec[a + b*x])/(8*b) - (Csc[a + b*x]^2*Sec[a + b*x])/(8*b)","A",5,5,18,0.2778,1,"{4288, 2622, 288, 321, 207}"
43,1,66,0,0.0627575,"\int \csc (a+b x) \csc ^3(2 a+2 b x) \, dx","Int[Csc[a + b*x]*Csc[2*a + 2*b*x]^3,x]","-\frac{5 \csc ^3(a+b x)}{48 b}-\frac{5 \csc (a+b x)}{16 b}+\frac{5 \tanh ^{-1}(\sin (a+b x))}{16 b}+\frac{\csc ^3(a+b x) \sec ^2(a+b x)}{16 b}","-\frac{5 \csc ^3(a+b x)}{48 b}-\frac{5 \csc (a+b x)}{16 b}+\frac{5 \tanh ^{-1}(\sin (a+b x))}{16 b}+\frac{\csc ^3(a+b x) \sec ^2(a+b x)}{16 b}",1,"(5*ArcTanh[Sin[a + b*x]])/(16*b) - (5*Csc[a + b*x])/(16*b) - (5*Csc[a + b*x]^3)/(48*b) + (Csc[a + b*x]^3*Sec[a + b*x]^2)/(16*b)","A",6,5,18,0.2778,1,"{4288, 2621, 288, 302, 207}"
44,1,89,0,0.07168,"\int \csc (a+b x) \csc ^4(2 a+2 b x) \, dx","Int[Csc[a + b*x]*Csc[2*a + 2*b*x]^4,x]","\frac{35 \sec ^3(a+b x)}{384 b}+\frac{35 \sec (a+b x)}{128 b}-\frac{35 \tanh ^{-1}(\cos (a+b x))}{128 b}-\frac{\csc ^4(a+b x) \sec ^3(a+b x)}{64 b}-\frac{7 \csc ^2(a+b x) \sec ^3(a+b x)}{128 b}","\frac{35 \sec ^3(a+b x)}{384 b}+\frac{35 \sec (a+b x)}{128 b}-\frac{35 \tanh ^{-1}(\cos (a+b x))}{128 b}-\frac{\csc ^4(a+b x) \sec ^3(a+b x)}{64 b}-\frac{7 \csc ^2(a+b x) \sec ^3(a+b x)}{128 b}",1,"(-35*ArcTanh[Cos[a + b*x]])/(128*b) + (35*Sec[a + b*x])/(128*b) + (35*Sec[a + b*x]^3)/(384*b) - (7*Csc[a + b*x]^2*Sec[a + b*x]^3)/(128*b) - (Csc[a + b*x]^4*Sec[a + b*x]^3)/(64*b)","A",7,5,18,0.2778,1,"{4288, 2622, 288, 302, 207}"
45,1,155,0,0.1714429,"\int \csc ^2(a+b x) \sin ^8(2 a+2 b x) \, dx","Int[Csc[a + b*x]^2*Sin[2*a + 2*b*x]^8,x]","-\frac{128 \sin ^5(a+b x) \cos ^9(a+b x)}{7 b}-\frac{160 \sin ^3(a+b x) \cos ^9(a+b x)}{21 b}-\frac{16 \sin (a+b x) \cos ^9(a+b x)}{7 b}+\frac{2 \sin (a+b x) \cos ^7(a+b x)}{7 b}+\frac{\sin (a+b x) \cos ^5(a+b x)}{3 b}+\frac{5 \sin (a+b x) \cos ^3(a+b x)}{12 b}+\frac{5 \sin (a+b x) \cos (a+b x)}{8 b}+\frac{5 x}{8}","-\frac{128 \sin ^5(a+b x) \cos ^9(a+b x)}{7 b}-\frac{160 \sin ^3(a+b x) \cos ^9(a+b x)}{21 b}-\frac{16 \sin (a+b x) \cos ^9(a+b x)}{7 b}+\frac{2 \sin (a+b x) \cos ^7(a+b x)}{7 b}+\frac{\sin (a+b x) \cos ^5(a+b x)}{3 b}+\frac{5 \sin (a+b x) \cos ^3(a+b x)}{12 b}+\frac{5 \sin (a+b x) \cos (a+b x)}{8 b}+\frac{5 x}{8}",1,"(5*x)/8 + (5*Cos[a + b*x]*Sin[a + b*x])/(8*b) + (5*Cos[a + b*x]^3*Sin[a + b*x])/(12*b) + (Cos[a + b*x]^5*Sin[a + b*x])/(3*b) + (2*Cos[a + b*x]^7*Sin[a + b*x])/(7*b) - (16*Cos[a + b*x]^9*Sin[a + b*x])/(7*b) - (160*Cos[a + b*x]^9*Sin[a + b*x]^3)/(21*b) - (128*Cos[a + b*x]^9*Sin[a + b*x]^5)/(7*b)","A",9,4,20,0.2000,1,"{4288, 2568, 2635, 8}"
46,1,44,0,0.0653625,"\int \csc ^2(a+b x) \sin ^7(2 a+2 b x) \, dx","Int[Csc[a + b*x]^2*Sin[2*a + 2*b*x]^7,x]","-\frac{32 \cos ^{12}(a+b x)}{3 b}+\frac{128 \cos ^{10}(a+b x)}{5 b}-\frac{16 \cos ^8(a+b x)}{b}","-\frac{32 \cos ^{12}(a+b x)}{3 b}+\frac{128 \cos ^{10}(a+b x)}{5 b}-\frac{16 \cos ^8(a+b x)}{b}",1,"(-16*Cos[a + b*x]^8)/b + (128*Cos[a + b*x]^10)/(5*b) - (32*Cos[a + b*x]^12)/(3*b)","A",5,4,20,0.2000,1,"{4288, 2565, 266, 43}"
47,1,111,0,0.1200237,"\int \csc ^2(a+b x) \sin ^6(2 a+2 b x) \, dx","Int[Csc[a + b*x]^2*Sin[2*a + 2*b*x]^6,x]","-\frac{32 \sin ^3(a+b x) \cos ^7(a+b x)}{5 b}-\frac{12 \sin (a+b x) \cos ^7(a+b x)}{5 b}+\frac{2 \sin (a+b x) \cos ^5(a+b x)}{5 b}+\frac{\sin (a+b x) \cos ^3(a+b x)}{2 b}+\frac{3 \sin (a+b x) \cos (a+b x)}{4 b}+\frac{3 x}{4}","-\frac{32 \sin ^3(a+b x) \cos ^7(a+b x)}{5 b}-\frac{12 \sin (a+b x) \cos ^7(a+b x)}{5 b}+\frac{2 \sin (a+b x) \cos ^5(a+b x)}{5 b}+\frac{\sin (a+b x) \cos ^3(a+b x)}{2 b}+\frac{3 \sin (a+b x) \cos (a+b x)}{4 b}+\frac{3 x}{4}",1,"(3*x)/4 + (3*Cos[a + b*x]*Sin[a + b*x])/(4*b) + (Cos[a + b*x]^3*Sin[a + b*x])/(2*b) + (2*Cos[a + b*x]^5*Sin[a + b*x])/(5*b) - (12*Cos[a + b*x]^7*Sin[a + b*x])/(5*b) - (32*Cos[a + b*x]^7*Sin[a + b*x]^3)/(5*b)","A",7,4,20,0.2000,1,"{4288, 2568, 2635, 8}"
48,1,29,0,0.0567422,"\int \csc ^2(a+b x) \sin ^5(2 a+2 b x) \, dx","Int[Csc[a + b*x]^2*Sin[2*a + 2*b*x]^5,x]","\frac{4 \cos ^8(a+b x)}{b}-\frac{16 \cos ^6(a+b x)}{3 b}","\frac{4 \cos ^8(a+b x)}{b}-\frac{16 \cos ^6(a+b x)}{3 b}",1,"(-16*Cos[a + b*x]^6)/(3*b) + (4*Cos[a + b*x]^8)/b","A",4,3,20,0.1500,1,"{4288, 2565, 14}"
49,1,60,0,0.0743127,"\int \csc ^2(a+b x) \sin ^4(2 a+2 b x) \, dx","Int[Csc[a + b*x]^2*Sin[2*a + 2*b*x]^4,x]","-\frac{8 \sin (a+b x) \cos ^5(a+b x)}{3 b}+\frac{2 \sin (a+b x) \cos ^3(a+b x)}{3 b}+\frac{\sin (a+b x) \cos (a+b x)}{b}+x","-\frac{8 \sin (a+b x) \cos ^5(a+b x)}{3 b}+\frac{2 \sin (a+b x) \cos ^3(a+b x)}{3 b}+\frac{\sin (a+b x) \cos (a+b x)}{b}+x",1,"x + (Cos[a + b*x]*Sin[a + b*x])/b + (2*Cos[a + b*x]^3*Sin[a + b*x])/(3*b) - (8*Cos[a + b*x]^5*Sin[a + b*x])/(3*b)","A",5,4,20,0.2000,1,"{4288, 2568, 2635, 8}"
50,1,13,0,0.0414177,"\int \csc ^2(a+b x) \sin ^3(2 a+2 b x) \, dx","Int[Csc[a + b*x]^2*Sin[2*a + 2*b*x]^3,x]","-\frac{2 \cos ^4(a+b x)}{b}","-\frac{2 \cos ^4(a+b x)}{b}",1,"(-2*Cos[a + b*x]^4)/b","A",3,3,20,0.1500,1,"{4288, 2565, 30}"
51,1,21,0,0.0343239,"\int \csc ^2(a+b x) \sin ^2(2 a+2 b x) \, dx","Int[Csc[a + b*x]^2*Sin[2*a + 2*b*x]^2,x]","\frac{2 \sin (a+b x) \cos (a+b x)}{b}+2 x","\frac{2 \sin (a+b x) \cos (a+b x)}{b}+2 x",1,"2*x + (2*Cos[a + b*x]*Sin[a + b*x])/b","A",3,3,20,0.1500,1,"{4288, 2635, 8}"
52,1,12,0,0.0201196,"\int \csc ^2(a+b x) \sin (2 a+2 b x) \, dx","Int[Csc[a + b*x]^2*Sin[2*a + 2*b*x],x]","\frac{2 \log (\sin (a+b x))}{b}","\frac{2 \log (\sin (a+b x))}{b}",1,"(2*Log[Sin[a + b*x]])/b","A",2,2,18,0.1111,1,"{4288, 3475}"
53,1,30,0,0.0420328,"\int \csc ^2(a+b x) \csc (2 a+2 b x) \, dx","Int[Csc[a + b*x]^2*Csc[2*a + 2*b*x],x]","\frac{\log (\tan (a+b x))}{2 b}-\frac{\cot ^2(a+b x)}{4 b}","\frac{\log (\tan (a+b x))}{2 b}-\frac{\cot ^2(a+b x)}{4 b}",1,"-Cot[a + b*x]^2/(4*b) + Log[Tan[a + b*x]]/(2*b)","A",4,3,18,0.1667,1,"{4288, 2620, 14}"
54,1,42,0,0.0590592,"\int \csc ^2(a+b x) \csc ^2(2 a+2 b x) \, dx","Int[Csc[a + b*x]^2*Csc[2*a + 2*b*x]^2,x]","\frac{\tan (a+b x)}{4 b}-\frac{\cot ^3(a+b x)}{12 b}-\frac{\cot (a+b x)}{2 b}","\frac{\tan (a+b x)}{4 b}-\frac{\cot ^3(a+b x)}{12 b}-\frac{\cot (a+b x)}{2 b}",1,"-Cot[a + b*x]/(2*b) - Cot[a + b*x]^3/(12*b) + Tan[a + b*x]/(4*b)","A",4,3,20,0.1500,1,"{4288, 2620, 270}"
55,1,60,0,0.0671915,"\int \csc ^2(a+b x) \csc ^3(2 a+2 b x) \, dx","Int[Csc[a + b*x]^2*Csc[2*a + 2*b*x]^3,x]","\frac{\tan ^2(a+b x)}{16 b}-\frac{\cot ^4(a+b x)}{32 b}-\frac{3 \cot ^2(a+b x)}{16 b}+\frac{3 \log (\tan (a+b x))}{8 b}","\frac{\tan ^2(a+b x)}{16 b}-\frac{\cot ^4(a+b x)}{32 b}-\frac{3 \cot ^2(a+b x)}{16 b}+\frac{3 \log (\tan (a+b x))}{8 b}",1,"(-3*Cot[a + b*x]^2)/(16*b) - Cot[a + b*x]^4/(32*b) + (3*Log[Tan[a + b*x]])/(8*b) + Tan[a + b*x]^2/(16*b)","A",5,4,20,0.2000,1,"{4288, 2620, 266, 43}"
56,1,72,0,0.070376,"\int \csc ^2(a+b x) \csc ^4(2 a+2 b x) \, dx","Int[Csc[a + b*x]^2*Csc[2*a + 2*b*x]^4,x]","\frac{\tan ^3(a+b x)}{48 b}+\frac{\tan (a+b x)}{4 b}-\frac{\cot ^5(a+b x)}{80 b}-\frac{\cot ^3(a+b x)}{12 b}-\frac{3 \cot (a+b x)}{8 b}","\frac{\tan ^3(a+b x)}{48 b}+\frac{\tan (a+b x)}{4 b}-\frac{\cot ^5(a+b x)}{80 b}-\frac{\cot ^3(a+b x)}{12 b}-\frac{3 \cot (a+b x)}{8 b}",1,"(-3*Cot[a + b*x])/(8*b) - Cot[a + b*x]^3/(12*b) - Cot[a + b*x]^5/(80*b) + Tan[a + b*x]/(4*b) + Tan[a + b*x]^3/(48*b)","A",4,3,20,0.1500,1,"{4288, 2620, 270}"
57,1,90,0,0.0817974,"\int \csc ^2(a+b x) \csc ^5(2 a+2 b x) \, dx","Int[Csc[a + b*x]^2*Csc[2*a + 2*b*x]^5,x]","\frac{\tan ^4(a+b x)}{128 b}+\frac{5 \tan ^2(a+b x)}{64 b}-\frac{\cot ^6(a+b x)}{192 b}-\frac{5 \cot ^4(a+b x)}{128 b}-\frac{5 \cot ^2(a+b x)}{32 b}+\frac{5 \log (\tan (a+b x))}{16 b}","\frac{\tan ^4(a+b x)}{128 b}+\frac{5 \tan ^2(a+b x)}{64 b}-\frac{\cot ^6(a+b x)}{192 b}-\frac{5 \cot ^4(a+b x)}{128 b}-\frac{5 \cot ^2(a+b x)}{32 b}+\frac{5 \log (\tan (a+b x))}{16 b}",1,"(-5*Cot[a + b*x]^2)/(32*b) - (5*Cot[a + b*x]^4)/(128*b) - Cot[a + b*x]^6/(192*b) + (5*Log[Tan[a + b*x]])/(16*b) + (5*Tan[a + b*x]^2)/(64*b) + Tan[a + b*x]^4/(128*b)","A",5,4,20,0.2000,1,"{4288, 2620, 266, 43}"
58,1,102,0,0.0843532,"\int \csc ^2(a+b x) \csc ^6(2 a+2 b x) \, dx","Int[Csc[a + b*x]^2*Csc[2*a + 2*b*x]^6,x]","\frac{\tan ^5(a+b x)}{320 b}+\frac{\tan ^3(a+b x)}{32 b}+\frac{15 \tan (a+b x)}{64 b}-\frac{\cot ^7(a+b x)}{448 b}-\frac{3 \cot ^5(a+b x)}{160 b}-\frac{5 \cot ^3(a+b x)}{64 b}-\frac{5 \cot (a+b x)}{16 b}","\frac{\tan ^5(a+b x)}{320 b}+\frac{\tan ^3(a+b x)}{32 b}+\frac{15 \tan (a+b x)}{64 b}-\frac{\cot ^7(a+b x)}{448 b}-\frac{3 \cot ^5(a+b x)}{160 b}-\frac{5 \cot ^3(a+b x)}{64 b}-\frac{5 \cot (a+b x)}{16 b}",1,"(-5*Cot[a + b*x])/(16*b) - (5*Cot[a + b*x]^3)/(64*b) - (3*Cot[a + b*x]^5)/(160*b) - Cot[a + b*x]^7/(448*b) + (15*Tan[a + b*x])/(64*b) + Tan[a + b*x]^3/(32*b) + Tan[a + b*x]^5/(320*b)","A",4,3,20,0.1500,1,"{4288, 2620, 270}"
59,1,61,0,0.0722782,"\int \csc ^3(a+b x) \sin ^{10}(2 a+2 b x) \, dx","Int[Csc[a + b*x]^3*Sin[2*a + 2*b*x]^10,x]","\frac{1024 \cos ^{17}(a+b x)}{17 b}-\frac{1024 \cos ^{15}(a+b x)}{5 b}+\frac{3072 \cos ^{13}(a+b x)}{13 b}-\frac{1024 \cos ^{11}(a+b x)}{11 b}","\frac{1024 \cos ^{17}(a+b x)}{17 b}-\frac{1024 \cos ^{15}(a+b x)}{5 b}+\frac{3072 \cos ^{13}(a+b x)}{13 b}-\frac{1024 \cos ^{11}(a+b x)}{11 b}",1,"(-1024*Cos[a + b*x]^11)/(11*b) + (3072*Cos[a + b*x]^13)/(13*b) - (1024*Cos[a + b*x]^15)/(5*b) + (1024*Cos[a + b*x]^17)/(17*b)","A",4,3,20,0.1500,1,"{4288, 2565, 270}"
60,1,76,0,0.0773139,"\int \csc ^3(a+b x) \sin ^9(2 a+2 b x) \, dx","Int[Csc[a + b*x]^3*Sin[2*a + 2*b*x]^9,x]","\frac{512 \sin ^{15}(a+b x)}{15 b}-\frac{2048 \sin ^{13}(a+b x)}{13 b}+\frac{3072 \sin ^{11}(a+b x)}{11 b}-\frac{2048 \sin ^9(a+b x)}{9 b}+\frac{512 \sin ^7(a+b x)}{7 b}","\frac{512 \sin ^{15}(a+b x)}{15 b}-\frac{2048 \sin ^{13}(a+b x)}{13 b}+\frac{3072 \sin ^{11}(a+b x)}{11 b}-\frac{2048 \sin ^9(a+b x)}{9 b}+\frac{512 \sin ^7(a+b x)}{7 b}",1,"(512*Sin[a + b*x]^7)/(7*b) - (2048*Sin[a + b*x]^9)/(9*b) + (3072*Sin[a + b*x]^11)/(11*b) - (2048*Sin[a + b*x]^13)/(13*b) + (512*Sin[a + b*x]^15)/(15*b)","A",4,3,20,0.1500,1,"{4288, 2564, 270}"
61,1,46,0,0.0672123,"\int \csc ^3(a+b x) \sin ^8(2 a+2 b x) \, dx","Int[Csc[a + b*x]^3*Sin[2*a + 2*b*x]^8,x]","-\frac{256 \cos ^{13}(a+b x)}{13 b}+\frac{512 \cos ^{11}(a+b x)}{11 b}-\frac{256 \cos ^9(a+b x)}{9 b}","-\frac{256 \cos ^{13}(a+b x)}{13 b}+\frac{512 \cos ^{11}(a+b x)}{11 b}-\frac{256 \cos ^9(a+b x)}{9 b}",1,"(-256*Cos[a + b*x]^9)/(9*b) + (512*Cos[a + b*x]^11)/(11*b) - (256*Cos[a + b*x]^13)/(13*b)","A",4,3,20,0.1500,1,"{4288, 2565, 270}"
62,1,61,0,0.0712247,"\int \csc ^3(a+b x) \sin ^7(2 a+2 b x) \, dx","Int[Csc[a + b*x]^3*Sin[2*a + 2*b*x]^7,x]","-\frac{128 \sin ^{11}(a+b x)}{11 b}+\frac{128 \sin ^9(a+b x)}{3 b}-\frac{384 \sin ^7(a+b x)}{7 b}+\frac{128 \sin ^5(a+b x)}{5 b}","-\frac{128 \sin ^{11}(a+b x)}{11 b}+\frac{128 \sin ^9(a+b x)}{3 b}-\frac{384 \sin ^7(a+b x)}{7 b}+\frac{128 \sin ^5(a+b x)}{5 b}",1,"(128*Sin[a + b*x]^5)/(5*b) - (384*Sin[a + b*x]^7)/(7*b) + (128*Sin[a + b*x]^9)/(3*b) - (128*Sin[a + b*x]^11)/(11*b)","A",4,3,20,0.1500,1,"{4288, 2564, 270}"
63,1,31,0,0.0607875,"\int \csc ^3(a+b x) \sin ^6(2 a+2 b x) \, dx","Int[Csc[a + b*x]^3*Sin[2*a + 2*b*x]^6,x]","\frac{64 \cos ^9(a+b x)}{9 b}-\frac{64 \cos ^7(a+b x)}{7 b}","\frac{64 \cos ^9(a+b x)}{9 b}-\frac{64 \cos ^7(a+b x)}{7 b}",1,"(-64*Cos[a + b*x]^7)/(7*b) + (64*Cos[a + b*x]^9)/(9*b)","A",4,3,20,0.1500,1,"{4288, 2565, 14}"
64,1,46,0,0.0656032,"\int \csc ^3(a+b x) \sin ^5(2 a+2 b x) \, dx","Int[Csc[a + b*x]^3*Sin[2*a + 2*b*x]^5,x]","\frac{32 \sin ^7(a+b x)}{7 b}-\frac{64 \sin ^5(a+b x)}{5 b}+\frac{32 \sin ^3(a+b x)}{3 b}","\frac{32 \sin ^7(a+b x)}{7 b}-\frac{64 \sin ^5(a+b x)}{5 b}+\frac{32 \sin ^3(a+b x)}{3 b}",1,"(32*Sin[a + b*x]^3)/(3*b) - (64*Sin[a + b*x]^5)/(5*b) + (32*Sin[a + b*x]^7)/(7*b)","A",4,3,20,0.1500,1,"{4288, 2564, 270}"
65,1,15,0,0.0444241,"\int \csc ^3(a+b x) \sin ^4(2 a+2 b x) \, dx","Int[Csc[a + b*x]^3*Sin[2*a + 2*b*x]^4,x]","-\frac{16 \cos ^5(a+b x)}{5 b}","-\frac{16 \cos ^5(a+b x)}{5 b}",1,"(-16*Cos[a + b*x]^5)/(5*b)","A",3,3,20,0.1500,1,"{4288, 2565, 30}"
66,1,27,0,0.0389608,"\int \csc ^3(a+b x) \sin ^3(2 a+2 b x) \, dx","Int[Csc[a + b*x]^3*Sin[2*a + 2*b*x]^3,x]","\frac{8 \sin (a+b x)}{b}-\frac{8 \sin ^3(a+b x)}{3 b}","\frac{8 \sin (a+b x)}{b}-\frac{8 \sin ^3(a+b x)}{3 b}",1,"(8*Sin[a + b*x])/b - (8*Sin[a + b*x]^3)/(3*b)","A",3,2,20,0.1000,1,"{4288, 2633}"
67,1,24,0,0.0430228,"\int \csc ^3(a+b x) \sin ^2(2 a+2 b x) \, dx","Int[Csc[a + b*x]^3*Sin[2*a + 2*b*x]^2,x]","\frac{4 \cos (a+b x)}{b}-\frac{4 \tanh ^{-1}(\cos (a+b x))}{b}","\frac{4 \cos (a+b x)}{b}-\frac{4 \tanh ^{-1}(\cos (a+b x))}{b}",1,"(-4*ArcTanh[Cos[a + b*x]])/b + (4*Cos[a + b*x])/b","A",4,4,20,0.2000,1,"{4288, 2592, 321, 206}"
68,1,11,0,0.0255341,"\int \csc ^3(a+b x) \sin (2 a+2 b x) \, dx","Int[Csc[a + b*x]^3*Sin[2*a + 2*b*x],x]","-\frac{2 \csc (a+b x)}{b}","-\frac{2 \csc (a+b x)}{b}",1,"(-2*Csc[a + b*x])/b","A",3,3,18,0.1667,1,"{4288, 2606, 8}"
69,1,43,0,0.049419,"\int \csc ^3(a+b x) \csc (2 a+2 b x) \, dx","Int[Csc[a + b*x]^3*Csc[2*a + 2*b*x],x]","-\frac{\csc ^3(a+b x)}{6 b}-\frac{\csc (a+b x)}{2 b}+\frac{\tanh ^{-1}(\sin (a+b x))}{2 b}","-\frac{\csc ^3(a+b x)}{6 b}-\frac{\csc (a+b x)}{2 b}+\frac{\tanh ^{-1}(\sin (a+b x))}{2 b}",1,"ArcTanh[Sin[a + b*x]]/(2*b) - Csc[a + b*x]/(2*b) - Csc[a + b*x]^3/(6*b)","A",5,4,18,0.2222,1,"{4288, 2621, 302, 207}"
70,1,70,0,0.0726865,"\int \csc ^3(a+b x) \csc ^2(2 a+2 b x) \, dx","Int[Csc[a + b*x]^3*Csc[2*a + 2*b*x]^2,x]","\frac{15 \sec (a+b x)}{32 b}-\frac{15 \tanh ^{-1}(\cos (a+b x))}{32 b}-\frac{\csc ^4(a+b x) \sec (a+b x)}{16 b}-\frac{5 \csc ^2(a+b x) \sec (a+b x)}{32 b}","\frac{15 \sec (a+b x)}{32 b}-\frac{15 \tanh ^{-1}(\cos (a+b x))}{32 b}-\frac{\csc ^4(a+b x) \sec (a+b x)}{16 b}-\frac{5 \csc ^2(a+b x) \sec (a+b x)}{32 b}",1,"(-15*ArcTanh[Cos[a + b*x]])/(32*b) + (15*Sec[a + b*x])/(32*b) - (5*Csc[a + b*x]^2*Sec[a + b*x])/(32*b) - (Csc[a + b*x]^4*Sec[a + b*x])/(16*b)","A",6,5,20,0.2500,1,"{4288, 2622, 288, 321, 207}"
71,1,81,0,0.0731432,"\int \csc ^3(a+b x) \csc ^3(2 a+2 b x) \, dx","Int[Csc[a + b*x]^3*Csc[2*a + 2*b*x]^3,x]","-\frac{7 \csc ^5(a+b x)}{80 b}-\frac{7 \csc ^3(a+b x)}{48 b}-\frac{7 \csc (a+b x)}{16 b}+\frac{7 \tanh ^{-1}(\sin (a+b x))}{16 b}+\frac{\csc ^5(a+b x) \sec ^2(a+b x)}{16 b}","-\frac{7 \csc ^5(a+b x)}{80 b}-\frac{7 \csc ^3(a+b x)}{48 b}-\frac{7 \csc (a+b x)}{16 b}+\frac{7 \tanh ^{-1}(\sin (a+b x))}{16 b}+\frac{\csc ^5(a+b x) \sec ^2(a+b x)}{16 b}",1,"(7*ArcTanh[Sin[a + b*x]])/(16*b) - (7*Csc[a + b*x])/(16*b) - (7*Csc[a + b*x]^3)/(48*b) - (7*Csc[a + b*x]^5)/(80*b) + (Csc[a + b*x]^5*Sec[a + b*x]^2)/(16*b)","A",6,5,20,0.2500,1,"{4288, 2621, 288, 302, 207}"
72,1,112,0,0.0870985,"\int \csc ^3(a+b x) \csc ^4(2 a+2 b x) \, dx","Int[Csc[a + b*x]^3*Csc[2*a + 2*b*x]^4,x]","\frac{35 \sec ^3(a+b x)}{256 b}+\frac{105 \sec (a+b x)}{256 b}-\frac{105 \tanh ^{-1}(\cos (a+b x))}{256 b}-\frac{\csc ^6(a+b x) \sec ^3(a+b x)}{96 b}-\frac{3 \csc ^4(a+b x) \sec ^3(a+b x)}{128 b}-\frac{21 \csc ^2(a+b x) \sec ^3(a+b x)}{256 b}","\frac{35 \sec ^3(a+b x)}{256 b}+\frac{105 \sec (a+b x)}{256 b}-\frac{105 \tanh ^{-1}(\cos (a+b x))}{256 b}-\frac{\csc ^6(a+b x) \sec ^3(a+b x)}{96 b}-\frac{3 \csc ^4(a+b x) \sec ^3(a+b x)}{128 b}-\frac{21 \csc ^2(a+b x) \sec ^3(a+b x)}{256 b}",1,"(-105*ArcTanh[Cos[a + b*x]])/(256*b) + (105*Sec[a + b*x])/(256*b) + (35*Sec[a + b*x]^3)/(256*b) - (21*Csc[a + b*x]^2*Sec[a + b*x]^3)/(256*b) - (3*Csc[a + b*x]^4*Sec[a + b*x]^3)/(128*b) - (Csc[a + b*x]^6*Sec[a + b*x]^3)/(96*b)","A",8,5,20,0.2500,1,"{4288, 2622, 288, 302, 207}"
73,1,136,0,0.0943819,"\int \sin (a+b x) \sin ^{\frac{5}{2}}(2 a+2 b x) \, dx","Int[Sin[a + b*x]*Sin[2*a + 2*b*x]^(5/2),x]","\frac{5 \sin (a+b x) \sin ^{\frac{3}{2}}(2 a+2 b x)}{24 b}-\frac{\sin ^{\frac{5}{2}}(2 a+2 b x) \cos (a+b x)}{6 b}-\frac{5 \sin ^{-1}(\cos (a+b x)-\sin (a+b x))}{32 b}-\frac{5 \sqrt{\sin (2 a+2 b x)} \cos (a+b x)}{16 b}+\frac{5 \log \left(\sin (a+b x)+\sqrt{\sin (2 a+2 b x)}+\cos (a+b x)\right)}{32 b}","\frac{5 \sin (a+b x) \sin ^{\frac{3}{2}}(2 a+2 b x)}{24 b}-\frac{\sin ^{\frac{5}{2}}(2 a+2 b x) \cos (a+b x)}{6 b}-\frac{5 \sin ^{-1}(\cos (a+b x)-\sin (a+b x))}{32 b}-\frac{5 \sqrt{\sin (2 a+2 b x)} \cos (a+b x)}{16 b}+\frac{5 \log \left(\sin (a+b x)+\sqrt{\sin (2 a+2 b x)}+\cos (a+b x)\right)}{32 b}",1,"(-5*ArcSin[Cos[a + b*x] - Sin[a + b*x]])/(32*b) + (5*Log[Cos[a + b*x] + Sin[a + b*x] + Sqrt[Sin[2*a + 2*b*x]]])/(32*b) - (5*Cos[a + b*x]*Sqrt[Sin[2*a + 2*b*x]])/(16*b) + (5*Sin[a + b*x]*Sin[2*a + 2*b*x]^(3/2))/(24*b) - (Cos[a + b*x]*Sin[2*a + 2*b*x]^(5/2))/(6*b)","A",4,3,20,0.1500,1,"{4302, 4301, 4305}"
74,1,110,0,0.0675042,"\int \sin (a+b x) \sin ^{\frac{3}{2}}(2 a+2 b x) \, dx","Int[Sin[a + b*x]*Sin[2*a + 2*b*x]^(3/2),x]","\frac{3 \sin (a+b x) \sqrt{\sin (2 a+2 b x)}}{8 b}-\frac{\sin ^{\frac{3}{2}}(2 a+2 b x) \cos (a+b x)}{4 b}-\frac{3 \sin ^{-1}(\cos (a+b x)-\sin (a+b x))}{16 b}-\frac{3 \log \left(\sin (a+b x)+\sqrt{\sin (2 a+2 b x)}+\cos (a+b x)\right)}{16 b}","\frac{3 \sin (a+b x) \sqrt{\sin (2 a+2 b x)}}{8 b}-\frac{\sin ^{\frac{3}{2}}(2 a+2 b x) \cos (a+b x)}{4 b}-\frac{3 \sin ^{-1}(\cos (a+b x)-\sin (a+b x))}{16 b}-\frac{3 \log \left(\sin (a+b x)+\sqrt{\sin (2 a+2 b x)}+\cos (a+b x)\right)}{16 b}",1,"(-3*ArcSin[Cos[a + b*x] - Sin[a + b*x]])/(16*b) - (3*Log[Cos[a + b*x] + Sin[a + b*x] + Sqrt[Sin[2*a + 2*b*x]]])/(16*b) + (3*Sin[a + b*x]*Sqrt[Sin[2*a + 2*b*x]])/(8*b) - (Cos[a + b*x]*Sin[2*a + 2*b*x]^(3/2))/(4*b)","A",3,3,20,0.1500,1,"{4302, 4301, 4306}"
75,1,84,0,0.0431275,"\int \sin (a+b x) \sqrt{\sin (2 a+2 b x)} \, dx","Int[Sin[a + b*x]*Sqrt[Sin[2*a + 2*b*x]],x]","-\frac{\sin ^{-1}(\cos (a+b x)-\sin (a+b x))}{4 b}-\frac{\sqrt{\sin (2 a+2 b x)} \cos (a+b x)}{2 b}+\frac{\log \left(\sin (a+b x)+\sqrt{\sin (2 a+2 b x)}+\cos (a+b x)\right)}{4 b}","-\frac{\sin ^{-1}(\cos (a+b x)-\sin (a+b x))}{4 b}-\frac{\sqrt{\sin (2 a+2 b x)} \cos (a+b x)}{2 b}+\frac{\log \left(\sin (a+b x)+\sqrt{\sin (2 a+2 b x)}+\cos (a+b x)\right)}{4 b}",1,"-ArcSin[Cos[a + b*x] - Sin[a + b*x]]/(4*b) + Log[Cos[a + b*x] + Sin[a + b*x] + Sqrt[Sin[2*a + 2*b*x]]]/(4*b) - (Cos[a + b*x]*Sqrt[Sin[2*a + 2*b*x]])/(2*b)","A",2,2,20,0.1000,1,"{4302, 4305}"
76,1,58,0,0.021149,"\int \frac{\sin (a+b x)}{\sqrt{\sin (2 a+2 b x)}} \, dx","Int[Sin[a + b*x]/Sqrt[Sin[2*a + 2*b*x]],x]","-\frac{\sin ^{-1}(\cos (a+b x)-\sin (a+b x))}{2 b}-\frac{\log \left(\sin (a+b x)+\sqrt{\sin (2 a+2 b x)}+\cos (a+b x)\right)}{2 b}","-\frac{\sin ^{-1}(\cos (a+b x)-\sin (a+b x))}{2 b}-\frac{\log \left(\sin (a+b x)+\sqrt{\sin (2 a+2 b x)}+\cos (a+b x)\right)}{2 b}",1,"-ArcSin[Cos[a + b*x] - Sin[a + b*x]]/(2*b) - Log[Cos[a + b*x] + Sin[a + b*x] + Sqrt[Sin[2*a + 2*b*x]]]/(2*b)","A",1,1,20,0.05000,1,"{4306}"
77,1,23,0,0.0176177,"\int \frac{\sin (a+b x)}{\sin ^{\frac{3}{2}}(2 a+2 b x)} \, dx","Int[Sin[a + b*x]/Sin[2*a + 2*b*x]^(3/2),x]","\frac{\sin (a+b x)}{b \sqrt{\sin (2 a+2 b x)}}","\frac{\sin (a+b x)}{b \sqrt{\sin (2 a+2 b x)}}",1,"Sin[a + b*x]/(b*Sqrt[Sin[2*a + 2*b*x]])","A",1,1,20,0.05000,1,"{4292}"
78,1,53,0,0.0395403,"\int \frac{\sin (a+b x)}{\sin ^{\frac{5}{2}}(2 a+2 b x)} \, dx","Int[Sin[a + b*x]/Sin[2*a + 2*b*x]^(5/2),x]","\frac{\sin (a+b x)}{3 b \sin ^{\frac{3}{2}}(2 a+2 b x)}-\frac{2 \cos (a+b x)}{3 b \sqrt{\sin (2 a+2 b x)}}","\frac{\sin (a+b x)}{3 b \sin ^{\frac{3}{2}}(2 a+2 b x)}-\frac{2 \cos (a+b x)}{3 b \sqrt{\sin (2 a+2 b x)}}",1,"Sin[a + b*x]/(3*b*Sin[2*a + 2*b*x]^(3/2)) - (2*Cos[a + b*x])/(3*b*Sqrt[Sin[2*a + 2*b*x]])","A",2,2,20,0.1000,1,"{4304, 4291}"
79,1,79,0,0.0586601,"\int \frac{\sin (a+b x)}{\sin ^{\frac{7}{2}}(2 a+2 b x)} \, dx","Int[Sin[a + b*x]/Sin[2*a + 2*b*x]^(7/2),x]","\frac{\sin (a+b x)}{5 b \sin ^{\frac{5}{2}}(2 a+2 b x)}+\frac{8 \sin (a+b x)}{15 b \sqrt{\sin (2 a+2 b x)}}-\frac{4 \cos (a+b x)}{15 b \sin ^{\frac{3}{2}}(2 a+2 b x)}","\frac{\sin (a+b x)}{5 b \sin ^{\frac{5}{2}}(2 a+2 b x)}+\frac{8 \sin (a+b x)}{15 b \sqrt{\sin (2 a+2 b x)}}-\frac{4 \cos (a+b x)}{15 b \sin ^{\frac{3}{2}}(2 a+2 b x)}",1,"Sin[a + b*x]/(5*b*Sin[2*a + 2*b*x]^(5/2)) - (4*Cos[a + b*x])/(15*b*Sin[2*a + 2*b*x]^(3/2)) + (8*Sin[a + b*x])/(15*b*Sqrt[Sin[2*a + 2*b*x]])","A",3,3,20,0.1500,1,"{4304, 4303, 4292}"
80,1,105,0,0.0833013,"\int \frac{\sin (a+b x)}{\sin ^{\frac{9}{2}}(2 a+2 b x)} \, dx","Int[Sin[a + b*x]/Sin[2*a + 2*b*x]^(9/2),x]","\frac{8 \sin (a+b x)}{35 b \sin ^{\frac{3}{2}}(2 a+2 b x)}+\frac{\sin (a+b x)}{7 b \sin ^{\frac{7}{2}}(2 a+2 b x)}-\frac{6 \cos (a+b x)}{35 b \sin ^{\frac{5}{2}}(2 a+2 b x)}-\frac{16 \cos (a+b x)}{35 b \sqrt{\sin (2 a+2 b x)}}","\frac{8 \sin (a+b x)}{35 b \sin ^{\frac{3}{2}}(2 a+2 b x)}+\frac{\sin (a+b x)}{7 b \sin ^{\frac{7}{2}}(2 a+2 b x)}-\frac{6 \cos (a+b x)}{35 b \sin ^{\frac{5}{2}}(2 a+2 b x)}-\frac{16 \cos (a+b x)}{35 b \sqrt{\sin (2 a+2 b x)}}",1,"Sin[a + b*x]/(7*b*Sin[2*a + 2*b*x]^(7/2)) - (6*Cos[a + b*x])/(35*b*Sin[2*a + 2*b*x]^(5/2)) + (8*Sin[a + b*x])/(35*b*Sin[2*a + 2*b*x]^(3/2)) - (16*Cos[a + b*x])/(35*b*Sqrt[Sin[2*a + 2*b*x]])","A",4,3,20,0.1500,1,"{4304, 4303, 4291}"
81,1,98,0,0.0595323,"\int \sin ^2(a+b x) \sin ^{\frac{7}{2}}(2 a+2 b x) \, dx","Int[Sin[a + b*x]^2*Sin[2*a + 2*b*x]^(7/2),x]","-\frac{\sin ^{\frac{9}{2}}(2 a+2 b x)}{18 b}+\frac{5 F\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{42 b}-\frac{\sin ^{\frac{5}{2}}(2 a+2 b x) \cos (2 a+2 b x)}{14 b}-\frac{5 \sqrt{\sin (2 a+2 b x)} \cos (2 a+2 b x)}{42 b}","-\frac{\sin ^{\frac{9}{2}}(2 a+2 b x)}{18 b}+\frac{5 F\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{42 b}-\frac{\sin ^{\frac{5}{2}}(2 a+2 b x) \cos (2 a+2 b x)}{14 b}-\frac{5 \sqrt{\sin (2 a+2 b x)} \cos (2 a+2 b x)}{42 b}",1,"(5*EllipticF[a - Pi/4 + b*x, 2])/(42*b) - (5*Cos[2*a + 2*b*x]*Sqrt[Sin[2*a + 2*b*x]])/(42*b) - (Cos[2*a + 2*b*x]*Sin[2*a + 2*b*x]^(5/2))/(14*b) - Sin[2*a + 2*b*x]^(9/2)/(18*b)","A",4,3,22,0.1364,1,"{4298, 2635, 2641}"
82,1,69,0,0.0474207,"\int \sin ^2(a+b x) \sin ^{\frac{5}{2}}(2 a+2 b x) \, dx","Int[Sin[a + b*x]^2*Sin[2*a + 2*b*x]^(5/2),x]","-\frac{\sin ^{\frac{7}{2}}(2 a+2 b x)}{14 b}+\frac{3 E\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{10 b}-\frac{\sin ^{\frac{3}{2}}(2 a+2 b x) \cos (2 a+2 b x)}{10 b}","-\frac{\sin ^{\frac{7}{2}}(2 a+2 b x)}{14 b}+\frac{3 E\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{10 b}-\frac{\sin ^{\frac{3}{2}}(2 a+2 b x) \cos (2 a+2 b x)}{10 b}",1,"(3*EllipticE[a - Pi/4 + b*x, 2])/(10*b) - (Cos[2*a + 2*b*x]*Sin[2*a + 2*b*x]^(3/2))/(10*b) - Sin[2*a + 2*b*x]^(7/2)/(14*b)","A",3,3,22,0.1364,1,"{4298, 2635, 2639}"
83,1,69,0,0.0474437,"\int \sin ^2(a+b x) \sin ^{\frac{3}{2}}(2 a+2 b x) \, dx","Int[Sin[a + b*x]^2*Sin[2*a + 2*b*x]^(3/2),x]","-\frac{\sin ^{\frac{5}{2}}(2 a+2 b x)}{10 b}+\frac{F\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{6 b}-\frac{\sqrt{\sin (2 a+2 b x)} \cos (2 a+2 b x)}{6 b}","-\frac{\sin ^{\frac{5}{2}}(2 a+2 b x)}{10 b}+\frac{F\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{6 b}-\frac{\sqrt{\sin (2 a+2 b x)} \cos (2 a+2 b x)}{6 b}",1,"EllipticF[a - Pi/4 + b*x, 2]/(6*b) - (Cos[2*a + 2*b*x]*Sqrt[Sin[2*a + 2*b*x]])/(6*b) - Sin[2*a + 2*b*x]^(5/2)/(10*b)","A",3,3,22,0.1364,1,"{4298, 2635, 2641}"
84,1,40,0,0.0357468,"\int \sin ^2(a+b x) \sqrt{\sin (2 a+2 b x)} \, dx","Int[Sin[a + b*x]^2*Sqrt[Sin[2*a + 2*b*x]],x]","\frac{E\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{2 b}-\frac{\sin ^{\frac{3}{2}}(2 a+2 b x)}{6 b}","\frac{E\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{2 b}-\frac{\sin ^{\frac{3}{2}}(2 a+2 b x)}{6 b}",1,"EllipticE[a - Pi/4 + b*x, 2]/(2*b) - Sin[2*a + 2*b*x]^(3/2)/(6*b)","A",2,2,22,0.09091,1,"{4298, 2639}"
85,1,40,0,0.0369828,"\int \frac{\sin ^2(a+b x)}{\sqrt{\sin (2 a+2 b x)}} \, dx","Int[Sin[a + b*x]^2/Sqrt[Sin[2*a + 2*b*x]],x]","\frac{F\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{2 b}-\frac{\sqrt{\sin (2 a+2 b x)}}{2 b}","\frac{F\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{2 b}-\frac{\sqrt{\sin (2 a+2 b x)}}{2 b}",1,"EllipticF[a - Pi/4 + b*x, 2]/(2*b) - Sqrt[Sin[2*a + 2*b*x]]/(2*b)","A",2,2,22,0.09091,1,"{4298, 2641}"
86,1,45,0,0.0373112,"\int \frac{\sin ^2(a+b x)}{\sin ^{\frac{3}{2}}(2 a+2 b x)} \, dx","Int[Sin[a + b*x]^2/Sin[2*a + 2*b*x]^(3/2),x]","\frac{\sin ^2(a+b x)}{b \sqrt{\sin (2 a+2 b x)}}-\frac{E\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{2 b}","\frac{\sin ^2(a+b x)}{b \sqrt{\sin (2 a+2 b x)}}-\frac{E\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{2 b}",1,"-EllipticE[a - Pi/4 + b*x, 2]/(2*b) + Sin[a + b*x]^2/(b*Sqrt[Sin[2*a + 2*b*x]])","A",2,2,22,0.09091,1,"{4296, 2639}"
87,1,48,0,0.0376517,"\int \frac{\sin ^2(a+b x)}{\sin ^{\frac{5}{2}}(2 a+2 b x)} \, dx","Int[Sin[a + b*x]^2/Sin[2*a + 2*b*x]^(5/2),x]","\frac{\sin ^2(a+b x)}{3 b \sin ^{\frac{3}{2}}(2 a+2 b x)}+\frac{F\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{6 b}","\frac{\sin ^2(a+b x)}{3 b \sin ^{\frac{3}{2}}(2 a+2 b x)}+\frac{F\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{6 b}",1,"EllipticF[a - Pi/4 + b*x, 2]/(6*b) + Sin[a + b*x]^2/(3*b*Sin[2*a + 2*b*x]^(3/2))","A",2,2,22,0.09091,1,"{4296, 2641}"
88,1,77,0,0.0464883,"\int \frac{\sin ^2(a+b x)}{\sin ^{\frac{7}{2}}(2 a+2 b x)} \, dx","Int[Sin[a + b*x]^2/Sin[2*a + 2*b*x]^(7/2),x]","\frac{\sin ^2(a+b x)}{5 b \sin ^{\frac{5}{2}}(2 a+2 b x)}-\frac{3 E\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{10 b}-\frac{3 \cos (2 a+2 b x)}{10 b \sqrt{\sin (2 a+2 b x)}}","\frac{\sin ^2(a+b x)}{5 b \sin ^{\frac{5}{2}}(2 a+2 b x)}-\frac{3 E\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{10 b}-\frac{3 \cos (2 a+2 b x)}{10 b \sqrt{\sin (2 a+2 b x)}}",1,"(-3*EllipticE[a - Pi/4 + b*x, 2])/(10*b) + Sin[a + b*x]^2/(5*b*Sin[2*a + 2*b*x]^(5/2)) - (3*Cos[2*a + 2*b*x])/(10*b*Sqrt[Sin[2*a + 2*b*x]])","A",3,3,22,0.1364,1,"{4296, 2636, 2639}"
89,1,136,0,0.1014291,"\int \sin ^3(a+b x) \sin ^{\frac{3}{2}}(2 a+2 b x) \, dx","Int[Sin[a + b*x]^3*Sin[2*a + 2*b*x]^(3/2),x]","-\frac{\sin (a+b x) \sin ^{\frac{5}{2}}(2 a+2 b x)}{12 b}+\frac{7 \sin (a+b x) \sqrt{\sin (2 a+2 b x)}}{32 b}-\frac{7 \sin ^{\frac{3}{2}}(2 a+2 b x) \cos (a+b x)}{48 b}-\frac{7 \sin ^{-1}(\cos (a+b x)-\sin (a+b x))}{64 b}-\frac{7 \log \left(\sin (a+b x)+\sqrt{\sin (2 a+2 b x)}+\cos (a+b x)\right)}{64 b}","-\frac{\sin (a+b x) \sin ^{\frac{5}{2}}(2 a+2 b x)}{12 b}+\frac{7 \sin (a+b x) \sqrt{\sin (2 a+2 b x)}}{32 b}-\frac{7 \sin ^{\frac{3}{2}}(2 a+2 b x) \cos (a+b x)}{48 b}-\frac{7 \sin ^{-1}(\cos (a+b x)-\sin (a+b x))}{64 b}-\frac{7 \log \left(\sin (a+b x)+\sqrt{\sin (2 a+2 b x)}+\cos (a+b x)\right)}{64 b}",1,"(-7*ArcSin[Cos[a + b*x] - Sin[a + b*x]])/(64*b) - (7*Log[Cos[a + b*x] + Sin[a + b*x] + Sqrt[Sin[2*a + 2*b*x]]])/(64*b) + (7*Sin[a + b*x]*Sqrt[Sin[2*a + 2*b*x]])/(32*b) - (7*Cos[a + b*x]*Sin[2*a + 2*b*x]^(3/2))/(48*b) - (Sin[a + b*x]*Sin[2*a + 2*b*x]^(5/2))/(12*b)","A",4,4,22,0.1818,1,"{4298, 4302, 4301, 4306}"
90,1,110,0,0.0782088,"\int \sin ^3(a+b x) \sqrt{\sin (2 a+2 b x)} \, dx","Int[Sin[a + b*x]^3*Sqrt[Sin[2*a + 2*b*x]],x]","-\frac{\sin (a+b x) \sin ^{\frac{3}{2}}(2 a+2 b x)}{8 b}-\frac{5 \sin ^{-1}(\cos (a+b x)-\sin (a+b x))}{32 b}-\frac{5 \sqrt{\sin (2 a+2 b x)} \cos (a+b x)}{16 b}+\frac{5 \log \left(\sin (a+b x)+\sqrt{\sin (2 a+2 b x)}+\cos (a+b x)\right)}{32 b}","-\frac{\sin (a+b x) \sin ^{\frac{3}{2}}(2 a+2 b x)}{8 b}-\frac{5 \sin ^{-1}(\cos (a+b x)-\sin (a+b x))}{32 b}-\frac{5 \sqrt{\sin (2 a+2 b x)} \cos (a+b x)}{16 b}+\frac{5 \log \left(\sin (a+b x)+\sqrt{\sin (2 a+2 b x)}+\cos (a+b x)\right)}{32 b}",1,"(-5*ArcSin[Cos[a + b*x] - Sin[a + b*x]])/(32*b) + (5*Log[Cos[a + b*x] + Sin[a + b*x] + Sqrt[Sin[2*a + 2*b*x]]])/(32*b) - (5*Cos[a + b*x]*Sqrt[Sin[2*a + 2*b*x]])/(16*b) - (Sin[a + b*x]*Sin[2*a + 2*b*x]^(3/2))/(8*b)","A",3,3,22,0.1364,1,"{4298, 4302, 4305}"
91,1,84,0,0.0541423,"\int \frac{\sin ^3(a+b x)}{\sqrt{\sin (2 a+2 b x)}} \, dx","Int[Sin[a + b*x]^3/Sqrt[Sin[2*a + 2*b*x]],x]","-\frac{\sin (a+b x) \sqrt{\sin (2 a+2 b x)}}{4 b}-\frac{3 \sin ^{-1}(\cos (a+b x)-\sin (a+b x))}{8 b}-\frac{3 \log \left(\sin (a+b x)+\sqrt{\sin (2 a+2 b x)}+\cos (a+b x)\right)}{8 b}","-\frac{\sin (a+b x) \sqrt{\sin (2 a+2 b x)}}{4 b}-\frac{3 \sin ^{-1}(\cos (a+b x)-\sin (a+b x))}{8 b}-\frac{3 \log \left(\sin (a+b x)+\sqrt{\sin (2 a+2 b x)}+\cos (a+b x)\right)}{8 b}",1,"(-3*ArcSin[Cos[a + b*x] - Sin[a + b*x]])/(8*b) - (3*Log[Cos[a + b*x] + Sin[a + b*x] + Sqrt[Sin[2*a + 2*b*x]]])/(8*b) - (Sin[a + b*x]*Sqrt[Sin[2*a + 2*b*x]])/(4*b)","A",2,2,22,0.09091,1,"{4298, 4306}"
92,1,81,0,0.0778138,"\int \frac{\sin ^3(a+b x)}{\sin ^{\frac{3}{2}}(2 a+2 b x)} \, dx","Int[Sin[a + b*x]^3/Sin[2*a + 2*b*x]^(3/2),x]","\frac{\sin (a+b x)}{b \sqrt{\sin (2 a+2 b x)}}+\frac{\sin ^{-1}(\cos (a+b x)-\sin (a+b x))}{4 b}-\frac{\log \left(\sin (a+b x)+\sqrt{\sin (2 a+2 b x)}+\cos (a+b x)\right)}{4 b}","\frac{\sin (a+b x)}{b \sqrt{\sin (2 a+2 b x)}}+\frac{\sin ^{-1}(\cos (a+b x)-\sin (a+b x))}{4 b}-\frac{\log \left(\sin (a+b x)+\sqrt{\sin (2 a+2 b x)}+\cos (a+b x)\right)}{4 b}",1,"ArcSin[Cos[a + b*x] - Sin[a + b*x]]/(4*b) - Log[Cos[a + b*x] + Sin[a + b*x] + Sqrt[Sin[2*a + 2*b*x]]]/(4*b) + Sin[a + b*x]/(b*Sqrt[Sin[2*a + 2*b*x]])","A",3,3,22,0.1364,1,"{4294, 4308, 4305}"
93,1,28,0,0.0280523,"\int \frac{\sin ^3(a+b x)}{\sin ^{\frac{5}{2}}(2 a+2 b x)} \, dx","Int[Sin[a + b*x]^3/Sin[2*a + 2*b*x]^(5/2),x]","\frac{\sin ^3(a+b x)}{3 b \sin ^{\frac{3}{2}}(2 a+2 b x)}","\frac{\sin ^3(a+b x)}{3 b \sin ^{\frac{3}{2}}(2 a+2 b x)}",1,"Sin[a + b*x]^3/(3*b*Sin[2*a + 2*b*x]^(3/2))","A",1,1,22,0.04545,1,"{4292}"
94,1,55,0,0.0486463,"\int \frac{\sin ^3(a+b x)}{\sin ^{\frac{7}{2}}(2 a+2 b x)} \, dx","Int[Sin[a + b*x]^3/Sin[2*a + 2*b*x]^(7/2),x]","\frac{\sin ^3(a+b x)}{5 b \sin ^{\frac{5}{2}}(2 a+2 b x)}+\frac{\sin (a+b x)}{5 b \sqrt{\sin (2 a+2 b x)}}","\frac{\sin ^3(a+b x)}{5 b \sin ^{\frac{5}{2}}(2 a+2 b x)}+\frac{\sin (a+b x)}{5 b \sqrt{\sin (2 a+2 b x)}}",1,"Sin[a + b*x]^3/(5*b*Sin[2*a + 2*b*x]^(5/2)) + Sin[a + b*x]/(5*b*Sqrt[Sin[2*a + 2*b*x]])","A",2,2,22,0.09091,1,"{4296, 4292}"
95,1,81,0,0.0691508,"\int \frac{\sin ^3(a+b x)}{\sin ^{\frac{9}{2}}(2 a+2 b x)} \, dx","Int[Sin[a + b*x]^3/Sin[2*a + 2*b*x]^(9/2),x]","\frac{\sin ^3(a+b x)}{7 b \sin ^{\frac{7}{2}}(2 a+2 b x)}+\frac{2 \sin (a+b x)}{21 b \sin ^{\frac{3}{2}}(2 a+2 b x)}-\frac{4 \cos (a+b x)}{21 b \sqrt{\sin (2 a+2 b x)}}","\frac{\sin ^3(a+b x)}{7 b \sin ^{\frac{7}{2}}(2 a+2 b x)}+\frac{2 \sin (a+b x)}{21 b \sin ^{\frac{3}{2}}(2 a+2 b x)}-\frac{4 \cos (a+b x)}{21 b \sqrt{\sin (2 a+2 b x)}}",1,"Sin[a + b*x]^3/(7*b*Sin[2*a + 2*b*x]^(7/2)) + (2*Sin[a + b*x])/(21*b*Sin[2*a + 2*b*x]^(3/2)) - (4*Cos[a + b*x])/(21*b*Sqrt[Sin[2*a + 2*b*x]])","A",3,3,22,0.1364,1,"{4296, 4304, 4291}"
96,1,107,0,0.0924541,"\int \frac{\sin ^3(a+b x)}{\sin ^{\frac{11}{2}}(2 a+2 b x)} \, dx","Int[Sin[a + b*x]^3/Sin[2*a + 2*b*x]^(11/2),x]","\frac{\sin ^3(a+b x)}{9 b \sin ^{\frac{9}{2}}(2 a+2 b x)}+\frac{\sin (a+b x)}{15 b \sin ^{\frac{5}{2}}(2 a+2 b x)}+\frac{8 \sin (a+b x)}{45 b \sqrt{\sin (2 a+2 b x)}}-\frac{4 \cos (a+b x)}{45 b \sin ^{\frac{3}{2}}(2 a+2 b x)}","\frac{\sin ^3(a+b x)}{9 b \sin ^{\frac{9}{2}}(2 a+2 b x)}+\frac{\sin (a+b x)}{15 b \sin ^{\frac{5}{2}}(2 a+2 b x)}+\frac{8 \sin (a+b x)}{45 b \sqrt{\sin (2 a+2 b x)}}-\frac{4 \cos (a+b x)}{45 b \sin ^{\frac{3}{2}}(2 a+2 b x)}",1,"Sin[a + b*x]^3/(9*b*Sin[2*a + 2*b*x]^(9/2)) + Sin[a + b*x]/(15*b*Sin[2*a + 2*b*x]^(5/2)) - (4*Cos[a + b*x])/(45*b*Sin[2*a + 2*b*x]^(3/2)) + (8*Sin[a + b*x])/(45*b*Sqrt[Sin[2*a + 2*b*x]])","A",4,4,22,0.1818,1,"{4296, 4304, 4303, 4292}"
97,1,136,0,0.1229511,"\int \csc (a+b x) \sin ^{\frac{7}{2}}(2 a+2 b x) \, dx","Int[Csc[a + b*x]*Sin[2*a + 2*b*x]^(7/2),x]","\frac{\sin (a+b x) \sin ^{\frac{5}{2}}(2 a+2 b x)}{3 b}+\frac{5 \sin (a+b x) \sqrt{\sin (2 a+2 b x)}}{8 b}-\frac{5 \sin ^{\frac{3}{2}}(2 a+2 b x) \cos (a+b x)}{12 b}-\frac{5 \sin ^{-1}(\cos (a+b x)-\sin (a+b x))}{16 b}-\frac{5 \log \left(\sin (a+b x)+\sqrt{\sin (2 a+2 b x)}+\cos (a+b x)\right)}{16 b}","\frac{\sin (a+b x) \sin ^{\frac{5}{2}}(2 a+2 b x)}{3 b}+\frac{5 \sin (a+b x) \sqrt{\sin (2 a+2 b x)}}{8 b}-\frac{5 \sin ^{\frac{3}{2}}(2 a+2 b x) \cos (a+b x)}{12 b}-\frac{5 \sin ^{-1}(\cos (a+b x)-\sin (a+b x))}{16 b}-\frac{5 \log \left(\sin (a+b x)+\sqrt{\sin (2 a+2 b x)}+\cos (a+b x)\right)}{16 b}",1,"(-5*ArcSin[Cos[a + b*x] - Sin[a + b*x]])/(16*b) - (5*Log[Cos[a + b*x] + Sin[a + b*x] + Sqrt[Sin[2*a + 2*b*x]]])/(16*b) + (5*Sin[a + b*x]*Sqrt[Sin[2*a + 2*b*x]])/(8*b) - (5*Cos[a + b*x]*Sin[2*a + 2*b*x]^(3/2))/(12*b) + (Sin[a + b*x]*Sin[2*a + 2*b*x]^(5/2))/(3*b)","A",5,4,20,0.2000,1,"{4308, 4301, 4302, 4306}"
98,1,110,0,0.095278,"\int \csc (a+b x) \sin ^{\frac{5}{2}}(2 a+2 b x) \, dx","Int[Csc[a + b*x]*Sin[2*a + 2*b*x]^(5/2),x]","\frac{\sin (a+b x) \sin ^{\frac{3}{2}}(2 a+2 b x)}{2 b}-\frac{3 \sin ^{-1}(\cos (a+b x)-\sin (a+b x))}{8 b}-\frac{3 \sqrt{\sin (2 a+2 b x)} \cos (a+b x)}{4 b}+\frac{3 \log \left(\sin (a+b x)+\sqrt{\sin (2 a+2 b x)}+\cos (a+b x)\right)}{8 b}","\frac{\sin (a+b x) \sin ^{\frac{3}{2}}(2 a+2 b x)}{2 b}-\frac{3 \sin ^{-1}(\cos (a+b x)-\sin (a+b x))}{8 b}-\frac{3 \sqrt{\sin (2 a+2 b x)} \cos (a+b x)}{4 b}+\frac{3 \log \left(\sin (a+b x)+\sqrt{\sin (2 a+2 b x)}+\cos (a+b x)\right)}{8 b}",1,"(-3*ArcSin[Cos[a + b*x] - Sin[a + b*x]])/(8*b) + (3*Log[Cos[a + b*x] + Sin[a + b*x] + Sqrt[Sin[2*a + 2*b*x]]])/(8*b) - (3*Cos[a + b*x]*Sqrt[Sin[2*a + 2*b*x]])/(4*b) + (Sin[a + b*x]*Sin[2*a + 2*b*x]^(3/2))/(2*b)","A",4,4,20,0.2000,1,"{4308, 4301, 4302, 4305}"
99,1,81,0,0.0722475,"\int \csc (a+b x) \sin ^{\frac{3}{2}}(2 a+2 b x) \, dx","Int[Csc[a + b*x]*Sin[2*a + 2*b*x]^(3/2),x]","\frac{\sin (a+b x) \sqrt{\sin (2 a+2 b x)}}{b}-\frac{\sin ^{-1}(\cos (a+b x)-\sin (a+b x))}{2 b}-\frac{\log \left(\sin (a+b x)+\sqrt{\sin (2 a+2 b x)}+\cos (a+b x)\right)}{2 b}","\frac{\sin (a+b x) \sqrt{\sin (2 a+2 b x)}}{b}-\frac{\sin ^{-1}(\cos (a+b x)-\sin (a+b x))}{2 b}-\frac{\log \left(\sin (a+b x)+\sqrt{\sin (2 a+2 b x)}+\cos (a+b x)\right)}{2 b}",1,"-ArcSin[Cos[a + b*x] - Sin[a + b*x]]/(2*b) - Log[Cos[a + b*x] + Sin[a + b*x] + Sqrt[Sin[2*a + 2*b*x]]]/(2*b) + (Sin[a + b*x]*Sqrt[Sin[2*a + 2*b*x]])/b","A",3,3,20,0.1500,1,"{4308, 4301, 4306}"
100,1,53,0,0.0472142,"\int \csc (a+b x) \sqrt{\sin (2 a+2 b x)} \, dx","Int[Csc[a + b*x]*Sqrt[Sin[2*a + 2*b*x]],x]","\frac{\log \left(\sin (a+b x)+\sqrt{\sin (2 a+2 b x)}+\cos (a+b x)\right)}{b}-\frac{\sin ^{-1}(\cos (a+b x)-\sin (a+b x))}{b}","\frac{\log \left(\sin (a+b x)+\sqrt{\sin (2 a+2 b x)}+\cos (a+b x)\right)}{b}-\frac{\sin ^{-1}(\cos (a+b x)-\sin (a+b x))}{b}",1,"-(ArcSin[Cos[a + b*x] - Sin[a + b*x]]/b) + Log[Cos[a + b*x] + Sin[a + b*x] + Sqrt[Sin[2*a + 2*b*x]]]/b","A",2,2,20,0.1000,1,"{4308, 4305}"
101,1,24,0,0.0238121,"\int \frac{\csc (a+b x)}{\sqrt{\sin (2 a+2 b x)}} \, dx","Int[Csc[a + b*x]/Sqrt[Sin[2*a + 2*b*x]],x]","-\frac{\sqrt{\sin (2 a+2 b x)} \csc (a+b x)}{b}","-\frac{\sqrt{\sin (2 a+2 b x)} \csc (a+b x)}{b}",1,"-((Csc[a + b*x]*Sqrt[Sin[2*a + 2*b*x]])/b)","A",1,1,20,0.05000,1,"{4292}"
102,1,53,0,0.0642377,"\int \frac{\csc (a+b x)}{\sin ^{\frac{3}{2}}(2 a+2 b x)} \, dx","Int[Csc[a + b*x]/Sin[2*a + 2*b*x]^(3/2),x]","\frac{4 \sin (a+b x)}{3 b \sqrt{\sin (2 a+2 b x)}}-\frac{2 \cos (a+b x)}{3 b \sin ^{\frac{3}{2}}(2 a+2 b x)}","\frac{4 \sin (a+b x)}{3 b \sqrt{\sin (2 a+2 b x)}}-\frac{2 \cos (a+b x)}{3 b \sin ^{\frac{3}{2}}(2 a+2 b x)}",1,"(-2*Cos[a + b*x])/(3*b*Sin[2*a + 2*b*x]^(3/2)) + (4*Sin[a + b*x])/(3*b*Sqrt[Sin[2*a + 2*b*x]])","A",3,3,20,0.1500,1,"{4308, 4303, 4292}"
103,1,79,0,0.0860161,"\int \frac{\csc (a+b x)}{\sin ^{\frac{5}{2}}(2 a+2 b x)} \, dx","Int[Csc[a + b*x]/Sin[2*a + 2*b*x]^(5/2),x]","\frac{8 \sin (a+b x)}{15 b \sin ^{\frac{3}{2}}(2 a+2 b x)}-\frac{2 \cos (a+b x)}{5 b \sin ^{\frac{5}{2}}(2 a+2 b x)}-\frac{16 \cos (a+b x)}{15 b \sqrt{\sin (2 a+2 b x)}}","\frac{8 \sin (a+b x)}{15 b \sin ^{\frac{3}{2}}(2 a+2 b x)}-\frac{2 \cos (a+b x)}{5 b \sin ^{\frac{5}{2}}(2 a+2 b x)}-\frac{16 \cos (a+b x)}{15 b \sqrt{\sin (2 a+2 b x)}}",1,"(-2*Cos[a + b*x])/(5*b*Sin[2*a + 2*b*x]^(5/2)) + (8*Sin[a + b*x])/(15*b*Sin[2*a + 2*b*x]^(3/2)) - (16*Cos[a + b*x])/(15*b*Sqrt[Sin[2*a + 2*b*x]])","A",4,4,20,0.2000,1,"{4308, 4303, 4304, 4291}"
104,1,105,0,0.1078932,"\int \frac{\csc (a+b x)}{\sin ^{\frac{7}{2}}(2 a+2 b x)} \, dx","Int[Csc[a + b*x]/Sin[2*a + 2*b*x]^(7/2),x]","\frac{12 \sin (a+b x)}{35 b \sin ^{\frac{5}{2}}(2 a+2 b x)}+\frac{32 \sin (a+b x)}{35 b \sqrt{\sin (2 a+2 b x)}}-\frac{16 \cos (a+b x)}{35 b \sin ^{\frac{3}{2}}(2 a+2 b x)}-\frac{2 \cos (a+b x)}{7 b \sin ^{\frac{7}{2}}(2 a+2 b x)}","\frac{12 \sin (a+b x)}{35 b \sin ^{\frac{5}{2}}(2 a+2 b x)}+\frac{32 \sin (a+b x)}{35 b \sqrt{\sin (2 a+2 b x)}}-\frac{16 \cos (a+b x)}{35 b \sin ^{\frac{3}{2}}(2 a+2 b x)}-\frac{2 \cos (a+b x)}{7 b \sin ^{\frac{7}{2}}(2 a+2 b x)}",1,"(-2*Cos[a + b*x])/(7*b*Sin[2*a + 2*b*x]^(7/2)) + (12*Sin[a + b*x])/(35*b*Sin[2*a + 2*b*x]^(5/2)) - (16*Cos[a + b*x])/(35*b*Sin[2*a + 2*b*x]^(3/2)) + (32*Sin[a + b*x])/(35*b*Sqrt[Sin[2*a + 2*b*x]])","A",5,4,20,0.2000,1,"{4308, 4303, 4304, 4292}"
105,1,106,0,0.0584837,"\int \csc ^2(a+b x) \sin ^{\frac{9}{2}}(2 a+2 b x) \, dx","Int[Csc[a + b*x]^2*Sin[2*a + 2*b*x]^(9/2),x]","\frac{6 E\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{5 b}-\frac{2 \sin ^{\frac{7}{2}}(2 a+2 b x) \cos (2 a+2 b x)}{7 b}-\frac{2 \sin ^{\frac{3}{2}}(2 a+2 b x) \cos (2 a+2 b x)}{5 b}+\frac{\sin ^{\frac{11}{2}}(2 a+2 b x) \csc ^2(a+b x)}{7 b}","\frac{6 E\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{5 b}-\frac{2 \sin ^{\frac{7}{2}}(2 a+2 b x) \cos (2 a+2 b x)}{7 b}-\frac{2 \sin ^{\frac{3}{2}}(2 a+2 b x) \cos (2 a+2 b x)}{5 b}+\frac{\sin ^{\frac{11}{2}}(2 a+2 b x) \csc ^2(a+b x)}{7 b}",1,"(6*EllipticE[a - Pi/4 + b*x, 2])/(5*b) - (2*Cos[2*a + 2*b*x]*Sin[2*a + 2*b*x]^(3/2))/(5*b) - (2*Cos[2*a + 2*b*x]*Sin[2*a + 2*b*x]^(7/2))/(7*b) + (Csc[a + b*x]^2*Sin[2*a + 2*b*x]^(11/2))/(7*b)","A",4,3,22,0.1364,1,"{4300, 2635, 2639}"
106,1,106,0,0.059291,"\int \csc ^2(a+b x) \sin ^{\frac{7}{2}}(2 a+2 b x) \, dx","Int[Csc[a + b*x]^2*Sin[2*a + 2*b*x]^(7/2),x]","\frac{2 F\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{3 b}-\frac{2 \sin ^{\frac{5}{2}}(2 a+2 b x) \cos (2 a+2 b x)}{5 b}-\frac{2 \sqrt{\sin (2 a+2 b x)} \cos (2 a+2 b x)}{3 b}+\frac{\sin ^{\frac{9}{2}}(2 a+2 b x) \csc ^2(a+b x)}{5 b}","\frac{2 F\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{3 b}-\frac{2 \sin ^{\frac{5}{2}}(2 a+2 b x) \cos (2 a+2 b x)}{5 b}-\frac{2 \sqrt{\sin (2 a+2 b x)} \cos (2 a+2 b x)}{3 b}+\frac{\sin ^{\frac{9}{2}}(2 a+2 b x) \csc ^2(a+b x)}{5 b}",1,"(2*EllipticF[a - Pi/4 + b*x, 2])/(3*b) - (2*Cos[2*a + 2*b*x]*Sqrt[Sin[2*a + 2*b*x]])/(3*b) - (2*Cos[2*a + 2*b*x]*Sin[2*a + 2*b*x]^(5/2))/(5*b) + (Csc[a + b*x]^2*Sin[2*a + 2*b*x]^(9/2))/(5*b)","A",4,3,22,0.1364,1,"{4300, 2635, 2641}"
107,1,75,0,0.0469874,"\int \csc ^2(a+b x) \sin ^{\frac{5}{2}}(2 a+2 b x) \, dx","Int[Csc[a + b*x]^2*Sin[2*a + 2*b*x]^(5/2),x]","\frac{2 E\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{b}-\frac{2 \sin ^{\frac{3}{2}}(2 a+2 b x) \cos (2 a+2 b x)}{3 b}+\frac{\sin ^{\frac{7}{2}}(2 a+2 b x) \csc ^2(a+b x)}{3 b}","\frac{2 E\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{b}-\frac{2 \sin ^{\frac{3}{2}}(2 a+2 b x) \cos (2 a+2 b x)}{3 b}+\frac{\sin ^{\frac{7}{2}}(2 a+2 b x) \csc ^2(a+b x)}{3 b}",1,"(2*EllipticE[a - Pi/4 + b*x, 2])/b - (2*Cos[2*a + 2*b*x]*Sin[2*a + 2*b*x]^(3/2))/(3*b) + (Csc[a + b*x]^2*Sin[2*a + 2*b*x]^(7/2))/(3*b)","A",3,3,22,0.1364,1,"{4300, 2635, 2639}"
108,1,70,0,0.0482702,"\int \csc ^2(a+b x) \sin ^{\frac{3}{2}}(2 a+2 b x) \, dx","Int[Csc[a + b*x]^2*Sin[2*a + 2*b*x]^(3/2),x]","\frac{2 F\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{b}-\frac{2 \sqrt{\sin (2 a+2 b x)} \cos (2 a+2 b x)}{b}+\frac{\sin ^{\frac{5}{2}}(2 a+2 b x) \csc ^2(a+b x)}{b}","\frac{2 F\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{b}-\frac{2 \sqrt{\sin (2 a+2 b x)} \cos (2 a+2 b x)}{b}+\frac{\sin ^{\frac{5}{2}}(2 a+2 b x) \csc ^2(a+b x)}{b}",1,"(2*EllipticF[a - Pi/4 + b*x, 2])/b - (2*Cos[2*a + 2*b*x]*Sqrt[Sin[2*a + 2*b*x]])/b + (Csc[a + b*x]^2*Sin[2*a + 2*b*x]^(5/2))/b","A",3,3,22,0.1364,1,"{4300, 2635, 2641}"
109,1,44,0,0.0361731,"\int \csc ^2(a+b x) \sqrt{\sin (2 a+2 b x)} \, dx","Int[Csc[a + b*x]^2*Sqrt[Sin[2*a + 2*b*x]],x]","-\frac{2 E\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{b}-\frac{\sin ^{\frac{3}{2}}(2 a+2 b x) \csc ^2(a+b x)}{b}","-\frac{2 E\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{b}-\frac{\sin ^{\frac{3}{2}}(2 a+2 b x) \csc ^2(a+b x)}{b}",1,"(-2*EllipticE[a - Pi/4 + b*x, 2])/b - (Csc[a + b*x]^2*Sin[2*a + 2*b*x]^(3/2))/b","A",2,2,22,0.09091,1,"{4300, 2639}"
110,1,48,0,0.0367026,"\int \frac{\csc ^2(a+b x)}{\sqrt{\sin (2 a+2 b x)}} \, dx","Int[Csc[a + b*x]^2/Sqrt[Sin[2*a + 2*b*x]],x]","\frac{2 F\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{3 b}-\frac{\sqrt{\sin (2 a+2 b x)} \csc ^2(a+b x)}{3 b}","\frac{2 F\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{3 b}-\frac{\sqrt{\sin (2 a+2 b x)} \csc ^2(a+b x)}{3 b}",1,"(2*EllipticF[a - Pi/4 + b*x, 2])/(3*b) - (Csc[a + b*x]^2*Sqrt[Sin[2*a + 2*b*x]])/(3*b)","A",2,2,22,0.09091,1,"{4300, 2641}"
111,1,77,0,0.0466341,"\int \frac{\csc ^2(a+b x)}{\sin ^{\frac{3}{2}}(2 a+2 b x)} \, dx","Int[Csc[a + b*x]^2/Sin[2*a + 2*b*x]^(3/2),x]","-\frac{6 E\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{5 b}-\frac{6 \cos (2 a+2 b x)}{5 b \sqrt{\sin (2 a+2 b x)}}-\frac{\csc ^2(a+b x)}{5 b \sqrt{\sin (2 a+2 b x)}}","-\frac{6 E\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{5 b}-\frac{6 \cos (2 a+2 b x)}{5 b \sqrt{\sin (2 a+2 b x)}}-\frac{\csc ^2(a+b x)}{5 b \sqrt{\sin (2 a+2 b x)}}",1,"(-6*EllipticE[a - Pi/4 + b*x, 2])/(5*b) - (6*Cos[2*a + 2*b*x])/(5*b*Sqrt[Sin[2*a + 2*b*x]]) - Csc[a + b*x]^2/(5*b*Sqrt[Sin[2*a + 2*b*x]])","A",3,3,22,0.1364,1,"{4300, 2636, 2639}"
112,1,77,0,0.0478643,"\int \frac{\csc ^2(a+b x)}{\sin ^{\frac{5}{2}}(2 a+2 b x)} \, dx","Int[Csc[a + b*x]^2/Sin[2*a + 2*b*x]^(5/2),x]","\frac{10 F\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{21 b}-\frac{10 \cos (2 a+2 b x)}{21 b \sin ^{\frac{3}{2}}(2 a+2 b x)}-\frac{\csc ^2(a+b x)}{7 b \sin ^{\frac{3}{2}}(2 a+2 b x)}","\frac{10 F\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{21 b}-\frac{10 \cos (2 a+2 b x)}{21 b \sin ^{\frac{3}{2}}(2 a+2 b x)}-\frac{\csc ^2(a+b x)}{7 b \sin ^{\frac{3}{2}}(2 a+2 b x)}",1,"(10*EllipticF[a - Pi/4 + b*x, 2])/(21*b) - (10*Cos[2*a + 2*b*x])/(21*b*Sin[2*a + 2*b*x]^(3/2)) - Csc[a + b*x]^2/(7*b*Sin[2*a + 2*b*x]^(3/2))","A",3,3,22,0.1364,1,"{4300, 2636, 2641}"
113,1,106,0,0.0580496,"\int \frac{\csc ^2(a+b x)}{\sin ^{\frac{7}{2}}(2 a+2 b x)} \, dx","Int[Csc[a + b*x]^2/Sin[2*a + 2*b*x]^(7/2),x]","-\frac{14 E\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{15 b}-\frac{14 \cos (2 a+2 b x)}{45 b \sin ^{\frac{5}{2}}(2 a+2 b x)}-\frac{14 \cos (2 a+2 b x)}{15 b \sqrt{\sin (2 a+2 b x)}}-\frac{\csc ^2(a+b x)}{9 b \sin ^{\frac{5}{2}}(2 a+2 b x)}","-\frac{14 E\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{15 b}-\frac{14 \cos (2 a+2 b x)}{45 b \sin ^{\frac{5}{2}}(2 a+2 b x)}-\frac{14 \cos (2 a+2 b x)}{15 b \sqrt{\sin (2 a+2 b x)}}-\frac{\csc ^2(a+b x)}{9 b \sin ^{\frac{5}{2}}(2 a+2 b x)}",1,"(-14*EllipticE[a - Pi/4 + b*x, 2])/(15*b) - (14*Cos[2*a + 2*b*x])/(45*b*Sin[2*a + 2*b*x]^(5/2)) - Csc[a + b*x]^2/(9*b*Sin[2*a + 2*b*x]^(5/2)) - (14*Cos[2*a + 2*b*x])/(15*b*Sqrt[Sin[2*a + 2*b*x]])","A",4,3,22,0.1364,1,"{4300, 2636, 2639}"
114,1,106,0,0.059475,"\int \frac{\csc ^2(a+b x)}{\sin ^{\frac{9}{2}}(2 a+2 b x)} \, dx","Int[Csc[a + b*x]^2/Sin[2*a + 2*b*x]^(9/2),x]","\frac{30 F\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{77 b}-\frac{30 \cos (2 a+2 b x)}{77 b \sin ^{\frac{3}{2}}(2 a+2 b x)}-\frac{18 \cos (2 a+2 b x)}{77 b \sin ^{\frac{7}{2}}(2 a+2 b x)}-\frac{\csc ^2(a+b x)}{11 b \sin ^{\frac{7}{2}}(2 a+2 b x)}","\frac{30 F\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{77 b}-\frac{30 \cos (2 a+2 b x)}{77 b \sin ^{\frac{3}{2}}(2 a+2 b x)}-\frac{18 \cos (2 a+2 b x)}{77 b \sin ^{\frac{7}{2}}(2 a+2 b x)}-\frac{\csc ^2(a+b x)}{11 b \sin ^{\frac{7}{2}}(2 a+2 b x)}",1,"(30*EllipticF[a - Pi/4 + b*x, 2])/(77*b) - (18*Cos[2*a + 2*b*x])/(77*b*Sin[2*a + 2*b*x]^(7/2)) - Csc[a + b*x]^2/(11*b*Sin[2*a + 2*b*x]^(7/2)) - (30*Cos[2*a + 2*b*x])/(77*b*Sin[2*a + 2*b*x]^(3/2))","A",4,3,22,0.1364,1,"{4300, 2636, 2641}"
115,1,190,0,0.1861875,"\int \csc ^3(a+b x) \sin ^{\frac{9}{2}}(2 a+2 b x) \, dx","Int[Csc[a + b*x]^3*Sin[2*a + 2*b*x]^(9/2),x]","\frac{4 \sin (a+b x) \sin ^{\frac{7}{2}}(2 a+2 b x)}{5 b}+\frac{7 \sin (a+b x) \sin ^{\frac{3}{2}}(2 a+2 b x)}{6 b}-\frac{14 \sin ^{\frac{5}{2}}(2 a+2 b x) \cos (a+b x)}{15 b}-\frac{7 \sin ^{-1}(\cos (a+b x)-\sin (a+b x))}{8 b}-\frac{7 \sqrt{\sin (2 a+2 b x)} \cos (a+b x)}{4 b}+\frac{\sin ^{\frac{11}{2}}(2 a+2 b x) \csc ^3(a+b x)}{5 b}+\frac{7 \log \left(\sin (a+b x)+\sqrt{\sin (2 a+2 b x)}+\cos (a+b x)\right)}{8 b}","\frac{4 \sin (a+b x) \sin ^{\frac{7}{2}}(2 a+2 b x)}{5 b}+\frac{7 \sin (a+b x) \sin ^{\frac{3}{2}}(2 a+2 b x)}{6 b}-\frac{14 \sin ^{\frac{5}{2}}(2 a+2 b x) \cos (a+b x)}{15 b}-\frac{7 \sin ^{-1}(\cos (a+b x)-\sin (a+b x))}{8 b}-\frac{7 \sqrt{\sin (2 a+2 b x)} \cos (a+b x)}{4 b}+\frac{\sin ^{\frac{11}{2}}(2 a+2 b x) \csc ^3(a+b x)}{5 b}+\frac{7 \log \left(\sin (a+b x)+\sqrt{\sin (2 a+2 b x)}+\cos (a+b x)\right)}{8 b}",1,"(-7*ArcSin[Cos[a + b*x] - Sin[a + b*x]])/(8*b) + (7*Log[Cos[a + b*x] + Sin[a + b*x] + Sqrt[Sin[2*a + 2*b*x]]])/(8*b) - (7*Cos[a + b*x]*Sqrt[Sin[2*a + 2*b*x]])/(4*b) + (7*Sin[a + b*x]*Sin[2*a + 2*b*x]^(3/2))/(6*b) - (14*Cos[a + b*x]*Sin[2*a + 2*b*x]^(5/2))/(15*b) + (4*Sin[a + b*x]*Sin[2*a + 2*b*x]^(7/2))/(5*b) + (Csc[a + b*x]^3*Sin[2*a + 2*b*x]^(11/2))/(5*b)","A",7,5,22,0.2273,1,"{4300, 4308, 4301, 4302, 4305}"
116,1,164,0,0.1560324,"\int \csc ^3(a+b x) \sin ^{\frac{7}{2}}(2 a+2 b x) \, dx","Int[Csc[a + b*x]^3*Sin[2*a + 2*b*x]^(7/2),x]","\frac{4 \sin (a+b x) \sin ^{\frac{5}{2}}(2 a+2 b x)}{3 b}+\frac{5 \sin (a+b x) \sqrt{\sin (2 a+2 b x)}}{2 b}-\frac{5 \sin ^{\frac{3}{2}}(2 a+2 b x) \cos (a+b x)}{3 b}-\frac{5 \sin ^{-1}(\cos (a+b x)-\sin (a+b x))}{4 b}+\frac{\sin ^{\frac{9}{2}}(2 a+2 b x) \csc ^3(a+b x)}{3 b}-\frac{5 \log \left(\sin (a+b x)+\sqrt{\sin (2 a+2 b x)}+\cos (a+b x)\right)}{4 b}","\frac{4 \sin (a+b x) \sin ^{\frac{5}{2}}(2 a+2 b x)}{3 b}+\frac{5 \sin (a+b x) \sqrt{\sin (2 a+2 b x)}}{2 b}-\frac{5 \sin ^{\frac{3}{2}}(2 a+2 b x) \cos (a+b x)}{3 b}-\frac{5 \sin ^{-1}(\cos (a+b x)-\sin (a+b x))}{4 b}+\frac{\sin ^{\frac{9}{2}}(2 a+2 b x) \csc ^3(a+b x)}{3 b}-\frac{5 \log \left(\sin (a+b x)+\sqrt{\sin (2 a+2 b x)}+\cos (a+b x)\right)}{4 b}",1,"(-5*ArcSin[Cos[a + b*x] - Sin[a + b*x]])/(4*b) - (5*Log[Cos[a + b*x] + Sin[a + b*x] + Sqrt[Sin[2*a + 2*b*x]]])/(4*b) + (5*Sin[a + b*x]*Sqrt[Sin[2*a + 2*b*x]])/(2*b) - (5*Cos[a + b*x]*Sin[2*a + 2*b*x]^(3/2))/(3*b) + (4*Sin[a + b*x]*Sin[2*a + 2*b*x]^(5/2))/(3*b) + (Csc[a + b*x]^3*Sin[2*a + 2*b*x]^(9/2))/(3*b)","A",6,5,22,0.2273,1,"{4300, 4308, 4301, 4302, 4306}"
117,1,127,0,0.1309109,"\int \csc ^3(a+b x) \sin ^{\frac{5}{2}}(2 a+2 b x) \, dx","Int[Csc[a + b*x]^3*Sin[2*a + 2*b*x]^(5/2),x]","\frac{4 \sin (a+b x) \sin ^{\frac{3}{2}}(2 a+2 b x)}{b}-\frac{3 \sin ^{-1}(\cos (a+b x)-\sin (a+b x))}{b}-\frac{6 \sqrt{\sin (2 a+2 b x)} \cos (a+b x)}{b}+\frac{\sin ^{\frac{7}{2}}(2 a+2 b x) \csc ^3(a+b x)}{b}+\frac{3 \log \left(\sin (a+b x)+\sqrt{\sin (2 a+2 b x)}+\cos (a+b x)\right)}{b}","\frac{4 \sin (a+b x) \sin ^{\frac{3}{2}}(2 a+2 b x)}{b}-\frac{3 \sin ^{-1}(\cos (a+b x)-\sin (a+b x))}{b}-\frac{6 \sqrt{\sin (2 a+2 b x)} \cos (a+b x)}{b}+\frac{\sin ^{\frac{7}{2}}(2 a+2 b x) \csc ^3(a+b x)}{b}+\frac{3 \log \left(\sin (a+b x)+\sqrt{\sin (2 a+2 b x)}+\cos (a+b x)\right)}{b}",1,"(-3*ArcSin[Cos[a + b*x] - Sin[a + b*x]])/b + (3*Log[Cos[a + b*x] + Sin[a + b*x] + Sqrt[Sin[2*a + 2*b*x]]])/b - (6*Cos[a + b*x]*Sqrt[Sin[2*a + 2*b*x]])/b + (4*Sin[a + b*x]*Sin[2*a + 2*b*x]^(3/2))/b + (Csc[a + b*x]^3*Sin[2*a + 2*b*x]^(7/2))/b","A",5,5,22,0.2273,1,"{4300, 4308, 4301, 4302, 4305}"
118,1,104,0,0.1020617,"\int \csc ^3(a+b x) \sin ^{\frac{3}{2}}(2 a+2 b x) \, dx","Int[Csc[a + b*x]^3*Sin[2*a + 2*b*x]^(3/2),x]","-\frac{4 \sin (a+b x) \sqrt{\sin (2 a+2 b x)}}{b}+\frac{2 \sin ^{-1}(\cos (a+b x)-\sin (a+b x))}{b}-\frac{\sin ^{\frac{5}{2}}(2 a+2 b x) \csc ^3(a+b x)}{b}+\frac{2 \log \left(\sin (a+b x)+\sqrt{\sin (2 a+2 b x)}+\cos (a+b x)\right)}{b}","-\frac{4 \sin (a+b x) \sqrt{\sin (2 a+2 b x)}}{b}+\frac{2 \sin ^{-1}(\cos (a+b x)-\sin (a+b x))}{b}-\frac{\sin ^{\frac{5}{2}}(2 a+2 b x) \csc ^3(a+b x)}{b}+\frac{2 \log \left(\sin (a+b x)+\sqrt{\sin (2 a+2 b x)}+\cos (a+b x)\right)}{b}",1,"(2*ArcSin[Cos[a + b*x] - Sin[a + b*x]])/b + (2*Log[Cos[a + b*x] + Sin[a + b*x] + Sqrt[Sin[2*a + 2*b*x]]])/b - (4*Sin[a + b*x]*Sqrt[Sin[2*a + 2*b*x]])/b - (Csc[a + b*x]^3*Sin[2*a + 2*b*x]^(5/2))/b","A",4,4,22,0.1818,1,"{4300, 4308, 4301, 4306}"
119,1,28,0,0.0281631,"\int \csc ^3(a+b x) \sqrt{\sin (2 a+2 b x)} \, dx","Int[Csc[a + b*x]^3*Sqrt[Sin[2*a + 2*b*x]],x]","-\frac{\sin ^{\frac{3}{2}}(2 a+2 b x) \csc ^3(a+b x)}{3 b}","-\frac{\sin ^{\frac{3}{2}}(2 a+2 b x) \csc ^3(a+b x)}{3 b}",1,"-(Csc[a + b*x]^3*Sin[2*a + 2*b*x]^(3/2))/(3*b)","A",1,1,22,0.04545,1,"{4292}"
120,1,55,0,0.0533406,"\int \frac{\csc ^3(a+b x)}{\sqrt{\sin (2 a+2 b x)}} \, dx","Int[Csc[a + b*x]^3/Sqrt[Sin[2*a + 2*b*x]],x]","-\frac{\sqrt{\sin (2 a+2 b x)} \csc ^3(a+b x)}{5 b}-\frac{4 \sqrt{\sin (2 a+2 b x)} \csc (a+b x)}{5 b}","-\frac{\sqrt{\sin (2 a+2 b x)} \csc ^3(a+b x)}{5 b}-\frac{4 \sqrt{\sin (2 a+2 b x)} \csc (a+b x)}{5 b}",1,"(-4*Csc[a + b*x]*Sqrt[Sin[2*a + 2*b*x]])/(5*b) - (Csc[a + b*x]^3*Sqrt[Sin[2*a + 2*b*x]])/(5*b)","A",2,2,22,0.09091,1,"{4300, 4292}"
121,1,81,0,0.0918782,"\int \frac{\csc ^3(a+b x)}{\sin ^{\frac{3}{2}}(2 a+2 b x)} \, dx","Int[Csc[a + b*x]^3/Sin[2*a + 2*b*x]^(3/2),x]","\frac{32 \sin (a+b x)}{21 b \sqrt{\sin (2 a+2 b x)}}-\frac{16 \cos (a+b x)}{21 b \sin ^{\frac{3}{2}}(2 a+2 b x)}-\frac{\csc ^3(a+b x)}{7 b \sqrt{\sin (2 a+2 b x)}}","\frac{32 \sin (a+b x)}{21 b \sqrt{\sin (2 a+2 b x)}}-\frac{16 \cos (a+b x)}{21 b \sin ^{\frac{3}{2}}(2 a+2 b x)}-\frac{\csc ^3(a+b x)}{7 b \sqrt{\sin (2 a+2 b x)}}",1,"(-16*Cos[a + b*x])/(21*b*Sin[2*a + 2*b*x]^(3/2)) - Csc[a + b*x]^3/(7*b*Sqrt[Sin[2*a + 2*b*x]]) + (32*Sin[a + b*x])/(21*b*Sqrt[Sin[2*a + 2*b*x]])","A",4,4,22,0.1818,1,"{4300, 4308, 4303, 4292}"
122,1,107,0,0.1155071,"\int \frac{\csc ^3(a+b x)}{\sin ^{\frac{5}{2}}(2 a+2 b x)} \, dx","Int[Csc[a + b*x]^3/Sin[2*a + 2*b*x]^(5/2),x]","\frac{32 \sin (a+b x)}{45 b \sin ^{\frac{3}{2}}(2 a+2 b x)}-\frac{8 \cos (a+b x)}{15 b \sin ^{\frac{5}{2}}(2 a+2 b x)}-\frac{64 \cos (a+b x)}{45 b \sqrt{\sin (2 a+2 b x)}}-\frac{\csc ^3(a+b x)}{9 b \sin ^{\frac{3}{2}}(2 a+2 b x)}","\frac{32 \sin (a+b x)}{45 b \sin ^{\frac{3}{2}}(2 a+2 b x)}-\frac{8 \cos (a+b x)}{15 b \sin ^{\frac{5}{2}}(2 a+2 b x)}-\frac{64 \cos (a+b x)}{45 b \sqrt{\sin (2 a+2 b x)}}-\frac{\csc ^3(a+b x)}{9 b \sin ^{\frac{3}{2}}(2 a+2 b x)}",1,"(-8*Cos[a + b*x])/(15*b*Sin[2*a + 2*b*x]^(5/2)) - Csc[a + b*x]^3/(9*b*Sin[2*a + 2*b*x]^(3/2)) + (32*Sin[a + b*x])/(45*b*Sin[2*a + 2*b*x]^(3/2)) - (64*Cos[a + b*x])/(45*b*Sqrt[Sin[2*a + 2*b*x]])","A",5,5,22,0.2273,1,"{4300, 4308, 4303, 4304, 4291}"
123,1,84,0,0.0744873,"\int \sin ^3(a+b x) \sin ^m(2 a+2 b x) \, dx","Int[Sin[a + b*x]^3*Sin[2*a + 2*b*x]^m,x]","\frac{\sin ^3(a+b x) \tan (a+b x) \sin ^m(2 a+2 b x) \cos ^2(a+b x)^{\frac{1-m}{2}} \, _2F_1\left(\frac{1-m}{2},\frac{m+4}{2};\frac{m+6}{2};\sin ^2(a+b x)\right)}{b (m+4)}","\frac{\sin ^3(a+b x) \tan (a+b x) \sin ^m(2 a+2 b x) \cos ^2(a+b x)^{\frac{1-m}{2}} \, _2F_1\left(\frac{1-m}{2},\frac{m+4}{2};\frac{m+6}{2};\sin ^2(a+b x)\right)}{b (m+4)}",1,"((Cos[a + b*x]^2)^((1 - m)/2)*Hypergeometric2F1[(1 - m)/2, (4 + m)/2, (6 + m)/2, Sin[a + b*x]^2]*Sin[a + b*x]^3*Sin[2*a + 2*b*x]^m*Tan[a + b*x])/(b*(4 + m))","A",2,2,20,0.1000,1,"{4310, 2577}"
124,1,84,0,0.0765246,"\int \sin ^2(a+b x) \sin ^m(2 a+2 b x) \, dx","Int[Sin[a + b*x]^2*Sin[2*a + 2*b*x]^m,x]","\frac{\sin ^2(a+b x) \tan (a+b x) \sin ^m(2 a+2 b x) \cos ^2(a+b x)^{\frac{1-m}{2}} \, _2F_1\left(\frac{1-m}{2},\frac{m+3}{2};\frac{m+5}{2};\sin ^2(a+b x)\right)}{b (m+3)}","\frac{\sin ^2(a+b x) \tan (a+b x) \sin ^m(2 a+2 b x) \cos ^2(a+b x)^{\frac{1-m}{2}} \, _2F_1\left(\frac{1-m}{2},\frac{m+3}{2};\frac{m+5}{2};\sin ^2(a+b x)\right)}{b (m+3)}",1,"((Cos[a + b*x]^2)^((1 - m)/2)*Hypergeometric2F1[(1 - m)/2, (3 + m)/2, (5 + m)/2, Sin[a + b*x]^2]*Sin[a + b*x]^2*Sin[2*a + 2*b*x]^m*Tan[a + b*x])/(b*(3 + m))","A",2,2,20,0.1000,1,"{4310, 2577}"
125,1,82,0,0.0639865,"\int \sin (a+b x) \sin ^m(2 a+2 b x) \, dx","Int[Sin[a + b*x]*Sin[2*a + 2*b*x]^m,x]","\frac{\sin (a+b x) \tan (a+b x) \sin ^m(2 a+2 b x) \cos ^2(a+b x)^{\frac{1-m}{2}} \, _2F_1\left(\frac{1-m}{2},\frac{m+2}{2};\frac{m+4}{2};\sin ^2(a+b x)\right)}{b (m+2)}","\frac{\sin (a+b x) \tan (a+b x) \sin ^m(2 a+2 b x) \cos ^2(a+b x)^{\frac{1-m}{2}} \, _2F_1\left(\frac{1-m}{2},\frac{m+2}{2};\frac{m+4}{2};\sin ^2(a+b x)\right)}{b (m+2)}",1,"((Cos[a + b*x]^2)^((1 - m)/2)*Hypergeometric2F1[(1 - m)/2, (2 + m)/2, (4 + m)/2, Sin[a + b*x]^2]*Sin[a + b*x]*Sin[2*a + 2*b*x]^m*Tan[a + b*x])/(b*(2 + m))","A",2,2,18,0.1111,1,"{4310, 2577}"
126,1,72,0,0.0702846,"\int \csc (a+b x) \sin ^m(2 a+2 b x) \, dx","Int[Csc[a + b*x]*Sin[2*a + 2*b*x]^m,x]","\frac{\sec (a+b x) \sin ^m(2 a+2 b x) \cos ^2(a+b x)^{\frac{1-m}{2}} \, _2F_1\left(\frac{1-m}{2},\frac{m}{2};\frac{m+2}{2};\sin ^2(a+b x)\right)}{b m}","\frac{\sec (a+b x) \sin ^m(2 a+2 b x) \cos ^2(a+b x)^{\frac{1-m}{2}} \, _2F_1\left(\frac{1-m}{2},\frac{m}{2};\frac{m+2}{2};\sin ^2(a+b x)\right)}{b m}",1,"((Cos[a + b*x]^2)^((1 - m)/2)*Hypergeometric2F1[(1 - m)/2, m/2, (2 + m)/2, Sin[a + b*x]^2]*Sec[a + b*x]*Sin[2*a + 2*b*x]^m)/(b*m)","A",2,2,18,0.1111,1,"{4310, 2577}"
127,1,85,0,0.0819772,"\int \csc ^2(a+b x) \sin ^m(2 a+2 b x) \, dx","Int[Csc[a + b*x]^2*Sin[2*a + 2*b*x]^m,x]","-\frac{\csc (a+b x) \sec (a+b x) \sin ^m(2 a+2 b x) \cos ^2(a+b x)^{\frac{1-m}{2}} \, _2F_1\left(\frac{1-m}{2},\frac{m-1}{2};\frac{m+1}{2};\sin ^2(a+b x)\right)}{b (1-m)}","-\frac{\csc (a+b x) \sec (a+b x) \sin ^m(2 a+2 b x) \cos ^2(a+b x)^{\frac{1-m}{2}} \, _2F_1\left(\frac{1-m}{2},\frac{m-1}{2};\frac{m+1}{2};\sin ^2(a+b x)\right)}{b (1-m)}",1,"-(((Cos[a + b*x]^2)^((1 - m)/2)*Csc[a + b*x]*Hypergeometric2F1[(1 - m)/2, (-1 + m)/2, (1 + m)/2, Sin[a + b*x]^2]*Sec[a + b*x]*Sin[2*a + 2*b*x]^m)/(b*(1 - m)))","A",2,2,20,0.1000,1,"{4310, 2577}"
128,1,85,0,0.0807039,"\int \csc ^3(a+b x) \sin ^m(2 a+2 b x) \, dx","Int[Csc[a + b*x]^3*Sin[2*a + 2*b*x]^m,x]","-\frac{\csc ^2(a+b x) \sec (a+b x) \sin ^m(2 a+2 b x) \cos ^2(a+b x)^{\frac{1-m}{2}} \, _2F_1\left(\frac{1-m}{2},\frac{m-2}{2};\frac{m}{2};\sin ^2(a+b x)\right)}{b (2-m)}","-\frac{\csc ^2(a+b x) \sec (a+b x) \sin ^m(2 a+2 b x) \cos ^2(a+b x)^{\frac{1-m}{2}} \, _2F_1\left(\frac{1-m}{2},\frac{m-2}{2};\frac{m}{2};\sin ^2(a+b x)\right)}{b (2-m)}",1,"-(((Cos[a + b*x]^2)^((1 - m)/2)*Csc[a + b*x]^2*Hypergeometric2F1[(1 - m)/2, (-2 + m)/2, m/2, Sin[a + b*x]^2]*Sec[a + b*x]*Sin[2*a + 2*b*x]^m)/(b*(2 - m)))","A",2,2,20,0.1000,1,"{4310, 2577}"
129,1,61,0,0.0598614,"\int \cos (a+b x) \sin ^7(2 a+2 b x) \, dx","Int[Cos[a + b*x]*Sin[2*a + 2*b*x]^7,x]","\frac{128 \cos ^{15}(a+b x)}{15 b}-\frac{384 \cos ^{13}(a+b x)}{13 b}+\frac{384 \cos ^{11}(a+b x)}{11 b}-\frac{128 \cos ^9(a+b x)}{9 b}","\frac{128 \cos ^{15}(a+b x)}{15 b}-\frac{384 \cos ^{13}(a+b x)}{13 b}+\frac{384 \cos ^{11}(a+b x)}{11 b}-\frac{128 \cos ^9(a+b x)}{9 b}",1,"(-128*Cos[a + b*x]^9)/(9*b) + (384*Cos[a + b*x]^11)/(11*b) - (384*Cos[a + b*x]^13)/(13*b) + (128*Cos[a + b*x]^15)/(15*b)","A",4,3,18,0.1667,1,"{4287, 2565, 270}"
130,1,61,0,0.0608379,"\int \cos (a+b x) \sin ^6(2 a+2 b x) \, dx","Int[Cos[a + b*x]*Sin[2*a + 2*b*x]^6,x]","-\frac{64 \sin ^{13}(a+b x)}{13 b}+\frac{192 \sin ^{11}(a+b x)}{11 b}-\frac{64 \sin ^9(a+b x)}{3 b}+\frac{64 \sin ^7(a+b x)}{7 b}","-\frac{64 \sin ^{13}(a+b x)}{13 b}+\frac{192 \sin ^{11}(a+b x)}{11 b}-\frac{64 \sin ^9(a+b x)}{3 b}+\frac{64 \sin ^7(a+b x)}{7 b}",1,"(64*Sin[a + b*x]^7)/(7*b) - (64*Sin[a + b*x]^9)/(3*b) + (192*Sin[a + b*x]^11)/(11*b) - (64*Sin[a + b*x]^13)/(13*b)","A",4,3,18,0.1667,1,"{4287, 2564, 270}"
131,1,46,0,0.0554593,"\int \cos (a+b x) \sin ^5(2 a+2 b x) \, dx","Int[Cos[a + b*x]*Sin[2*a + 2*b*x]^5,x]","-\frac{32 \cos ^{11}(a+b x)}{11 b}+\frac{64 \cos ^9(a+b x)}{9 b}-\frac{32 \cos ^7(a+b x)}{7 b}","-\frac{32 \cos ^{11}(a+b x)}{11 b}+\frac{64 \cos ^9(a+b x)}{9 b}-\frac{32 \cos ^7(a+b x)}{7 b}",1,"(-32*Cos[a + b*x]^7)/(7*b) + (64*Cos[a + b*x]^9)/(9*b) - (32*Cos[a + b*x]^11)/(11*b)","A",4,3,18,0.1667,1,"{4287, 2565, 270}"
132,1,46,0,0.0537951,"\int \cos (a+b x) \sin ^4(2 a+2 b x) \, dx","Int[Cos[a + b*x]*Sin[2*a + 2*b*x]^4,x]","\frac{16 \sin ^9(a+b x)}{9 b}-\frac{32 \sin ^7(a+b x)}{7 b}+\frac{16 \sin ^5(a+b x)}{5 b}","\frac{16 \sin ^9(a+b x)}{9 b}-\frac{32 \sin ^7(a+b x)}{7 b}+\frac{16 \sin ^5(a+b x)}{5 b}",1,"(16*Sin[a + b*x]^5)/(5*b) - (32*Sin[a + b*x]^7)/(7*b) + (16*Sin[a + b*x]^9)/(9*b)","A",4,3,18,0.1667,1,"{4287, 2564, 270}"
133,1,31,0,0.0500029,"\int \cos (a+b x) \sin ^3(2 a+2 b x) \, dx","Int[Cos[a + b*x]*Sin[2*a + 2*b*x]^3,x]","\frac{8 \cos ^7(a+b x)}{7 b}-\frac{8 \cos ^5(a+b x)}{5 b}","\frac{8 \cos ^7(a+b x)}{7 b}-\frac{8 \cos ^5(a+b x)}{5 b}",1,"(-8*Cos[a + b*x]^5)/(5*b) + (8*Cos[a + b*x]^7)/(7*b)","A",4,3,18,0.1667,1,"{4287, 2565, 14}"
134,1,31,0,0.0483909,"\int \cos (a+b x) \sin ^2(2 a+2 b x) \, dx","Int[Cos[a + b*x]*Sin[2*a + 2*b*x]^2,x]","\frac{4 \sin ^3(a+b x)}{3 b}-\frac{4 \sin ^5(a+b x)}{5 b}","\frac{4 \sin ^3(a+b x)}{3 b}-\frac{4 \sin ^5(a+b x)}{5 b}",1,"(4*Sin[a + b*x]^3)/(3*b) - (4*Sin[a + b*x]^5)/(5*b)","A",4,3,18,0.1667,1,"{4287, 2564, 14}"
135,1,30,0,0.01103,"\int \cos (a+b x) \sin (2 a+2 b x) \, dx","Int[Cos[a + b*x]*Sin[2*a + 2*b*x],x]","-\frac{\cos (a+b x)}{2 b}-\frac{\cos (3 a+3 b x)}{6 b}","-\frac{\cos (a+b x)}{2 b}-\frac{\cos (3 a+3 b x)}{6 b}",1,"-Cos[a + b*x]/(2*b) - Cos[3*a + 3*b*x]/(6*b)","A",1,1,16,0.06250,1,"{4284}"
136,1,14,0,0.0163863,"\int \cos (a+b x) \csc (2 a+2 b x) \, dx","Int[Cos[a + b*x]*Csc[2*a + 2*b*x],x]","-\frac{\tanh ^{-1}(\cos (a+b x))}{2 b}","-\frac{\tanh ^{-1}(\cos (a+b x))}{2 b}",1,"-ArcTanh[Cos[a + b*x]]/(2*b)","A",2,2,16,0.1250,1,"{4287, 3770}"
137,1,28,0,0.0377685,"\int \cos (a+b x) \csc ^2(2 a+2 b x) \, dx","Int[Cos[a + b*x]*Csc[2*a + 2*b*x]^2,x]","\frac{\tanh ^{-1}(\sin (a+b x))}{4 b}-\frac{\csc (a+b x)}{4 b}","\frac{\tanh ^{-1}(\sin (a+b x))}{4 b}-\frac{\csc (a+b x)}{4 b}",1,"ArcTanh[Sin[a + b*x]]/(4*b) - Csc[a + b*x]/(4*b)","A",4,4,18,0.2222,1,"{4287, 2621, 321, 207}"
138,1,49,0,0.0549493,"\int \cos (a+b x) \csc ^3(2 a+2 b x) \, dx","Int[Cos[a + b*x]*Csc[2*a + 2*b*x]^3,x]","\frac{3 \sec (a+b x)}{16 b}-\frac{3 \tanh ^{-1}(\cos (a+b x))}{16 b}-\frac{\csc ^2(a+b x) \sec (a+b x)}{16 b}","\frac{3 \sec (a+b x)}{16 b}-\frac{3 \tanh ^{-1}(\cos (a+b x))}{16 b}-\frac{\csc ^2(a+b x) \sec (a+b x)}{16 b}",1,"(-3*ArcTanh[Cos[a + b*x]])/(16*b) + (3*Sec[a + b*x])/(16*b) - (Csc[a + b*x]^2*Sec[a + b*x])/(16*b)","A",5,5,18,0.2778,1,"{4287, 2622, 288, 321, 207}"
139,1,66,0,0.0586615,"\int \cos (a+b x) \csc ^4(2 a+2 b x) \, dx","Int[Cos[a + b*x]*Csc[2*a + 2*b*x]^4,x]","-\frac{5 \csc ^3(a+b x)}{96 b}-\frac{5 \csc (a+b x)}{32 b}+\frac{5 \tanh ^{-1}(\sin (a+b x))}{32 b}+\frac{\csc ^3(a+b x) \sec ^2(a+b x)}{32 b}","-\frac{5 \csc ^3(a+b x)}{96 b}-\frac{5 \csc (a+b x)}{32 b}+\frac{5 \tanh ^{-1}(\sin (a+b x))}{32 b}+\frac{\csc ^3(a+b x) \sec ^2(a+b x)}{32 b}",1,"(5*ArcTanh[Sin[a + b*x]])/(32*b) - (5*Csc[a + b*x])/(32*b) - (5*Csc[a + b*x]^3)/(96*b) + (Csc[a + b*x]^3*Sec[a + b*x]^2)/(32*b)","A",6,5,18,0.2778,1,"{4287, 2621, 288, 302, 207}"
140,1,89,0,0.0672624,"\int \cos (a+b x) \csc ^5(2 a+2 b x) \, dx","Int[Cos[a + b*x]*Csc[2*a + 2*b*x]^5,x]","\frac{35 \sec ^3(a+b x)}{768 b}+\frac{35 \sec (a+b x)}{256 b}-\frac{35 \tanh ^{-1}(\cos (a+b x))}{256 b}-\frac{\csc ^4(a+b x) \sec ^3(a+b x)}{128 b}-\frac{7 \csc ^2(a+b x) \sec ^3(a+b x)}{256 b}","\frac{35 \sec ^3(a+b x)}{768 b}+\frac{35 \sec (a+b x)}{256 b}-\frac{35 \tanh ^{-1}(\cos (a+b x))}{256 b}-\frac{\csc ^4(a+b x) \sec ^3(a+b x)}{128 b}-\frac{7 \csc ^2(a+b x) \sec ^3(a+b x)}{256 b}",1,"(-35*ArcTanh[Cos[a + b*x]])/(256*b) + (35*Sec[a + b*x])/(256*b) + (35*Sec[a + b*x]^3)/(768*b) - (7*Csc[a + b*x]^2*Sec[a + b*x]^3)/(256*b) - (Csc[a + b*x]^4*Sec[a + b*x]^3)/(128*b)","A",7,5,18,0.2778,1,"{4287, 2622, 288, 302, 207}"
141,1,44,0,0.066743,"\int \cos ^2(a+b x) \sin ^5(2 a+2 b x) \, dx","Int[Cos[a + b*x]^2*Sin[2*a + 2*b*x]^5,x]","-\frac{8 \cos ^{12}(a+b x)}{3 b}+\frac{32 \cos ^{10}(a+b x)}{5 b}-\frac{4 \cos ^8(a+b x)}{b}","-\frac{8 \cos ^{12}(a+b x)}{3 b}+\frac{32 \cos ^{10}(a+b x)}{5 b}-\frac{4 \cos ^8(a+b x)}{b}",1,"(-4*Cos[a + b*x]^8)/b + (32*Cos[a + b*x]^10)/(5*b) - (8*Cos[a + b*x]^12)/(3*b)","A",5,4,20,0.2000,1,"{4287, 2565, 266, 43}"
142,1,76,0,0.0644401,"\int \cos ^2(a+b x) \sin ^4(2 a+2 b x) \, dx","Int[Cos[a + b*x]^2*Sin[2*a + 2*b*x]^4,x]","\frac{\sin ^5(2 a+2 b x)}{20 b}-\frac{\sin ^3(2 a+2 b x) \cos (2 a+2 b x)}{16 b}-\frac{3 \sin (2 a+2 b x) \cos (2 a+2 b x)}{32 b}+\frac{3 x}{16}","\frac{\sin ^5(2 a+2 b x)}{20 b}-\frac{\sin ^3(2 a+2 b x) \cos (2 a+2 b x)}{16 b}-\frac{3 \sin (2 a+2 b x) \cos (2 a+2 b x)}{32 b}+\frac{3 x}{16}",1,"(3*x)/16 - (3*Cos[2*a + 2*b*x]*Sin[2*a + 2*b*x])/(32*b) - (Cos[2*a + 2*b*x]*Sin[2*a + 2*b*x]^3)/(16*b) + Sin[2*a + 2*b*x]^5/(20*b)","A",6,5,20,0.2500,1,"{4285, 2635, 8, 2564, 30}"
143,1,28,0,0.0565491,"\int \cos ^2(a+b x) \sin ^3(2 a+2 b x) \, dx","Int[Cos[a + b*x]^2*Sin[2*a + 2*b*x]^3,x]","\frac{\cos ^8(a+b x)}{b}-\frac{4 \cos ^6(a+b x)}{3 b}","\frac{\cos ^8(a+b x)}{b}-\frac{4 \cos ^6(a+b x)}{3 b}",1,"(-4*Cos[a + b*x]^6)/(3*b) + Cos[a + b*x]^8/b","A",4,3,20,0.1500,1,"{4287, 2565, 14}"
144,1,49,0,0.0536167,"\int \cos ^2(a+b x) \sin ^2(2 a+2 b x) \, dx","Int[Cos[a + b*x]^2*Sin[2*a + 2*b*x]^2,x]","\frac{\sin ^3(2 a+2 b x)}{12 b}-\frac{\sin (2 a+2 b x) \cos (2 a+2 b x)}{8 b}+\frac{x}{4}","\frac{\sin ^3(2 a+2 b x)}{12 b}-\frac{\sin (2 a+2 b x) \cos (2 a+2 b x)}{8 b}+\frac{x}{4}",1,"x/4 - (Cos[2*a + 2*b*x]*Sin[2*a + 2*b*x])/(8*b) + Sin[2*a + 2*b*x]^3/(12*b)","A",5,5,20,0.2500,1,"{4285, 2635, 8, 2564, 30}"
145,1,15,0,0.0328988,"\int \cos ^2(a+b x) \sin (2 a+2 b x) \, dx","Int[Cos[a + b*x]^2*Sin[2*a + 2*b*x],x]","-\frac{\cos ^4(a+b x)}{2 b}","-\frac{\cos ^4(a+b x)}{2 b}",1,"-Cos[a + b*x]^4/(2*b)","A",3,3,18,0.1667,1,"{4287, 2565, 30}"
146,1,14,0,0.02515,"\int \cos ^2(a+b x) \csc (2 a+2 b x) \, dx","Int[Cos[a + b*x]^2*Csc[2*a + 2*b*x],x]","\frac{\log (\sin (a+b x))}{2 b}","\frac{\log (\sin (a+b x))}{2 b}",1,"Log[Sin[a + b*x]]/(2*b)","A",2,2,18,0.1111,1,"{4287, 3475}"
147,1,13,0,0.0329684,"\int \cos ^2(a+b x) \csc ^2(2 a+2 b x) \, dx","Int[Cos[a + b*x]^2*Csc[2*a + 2*b*x]^2,x]","-\frac{\cot (a+b x)}{4 b}","-\frac{\cot (a+b x)}{4 b}",1,"-Cot[a + b*x]/(4*b)","A",3,3,20,0.1500,1,"{4287, 3767, 8}"
148,1,30,0,0.0467969,"\int \cos ^2(a+b x) \csc ^3(2 a+2 b x) \, dx","Int[Cos[a + b*x]^2*Csc[2*a + 2*b*x]^3,x]","\frac{\log (\tan (a+b x))}{8 b}-\frac{\cot ^2(a+b x)}{16 b}","\frac{\log (\tan (a+b x))}{8 b}-\frac{\cot ^2(a+b x)}{16 b}",1,"-Cot[a + b*x]^2/(16*b) + Log[Tan[a + b*x]]/(8*b)","A",4,3,20,0.1500,1,"{4287, 2620, 14}"
149,1,42,0,0.0595376,"\int \cos ^2(a+b x) \csc ^4(2 a+2 b x) \, dx","Int[Cos[a + b*x]^2*Csc[2*a + 2*b*x]^4,x]","\frac{\tan (a+b x)}{16 b}-\frac{\cot ^3(a+b x)}{48 b}-\frac{\cot (a+b x)}{8 b}","\frac{\tan (a+b x)}{16 b}-\frac{\cot ^3(a+b x)}{48 b}-\frac{\cot (a+b x)}{8 b}",1,"-Cot[a + b*x]/(8*b) - Cot[a + b*x]^3/(48*b) + Tan[a + b*x]/(16*b)","A",4,3,20,0.1500,1,"{4287, 2620, 270}"
150,1,60,0,0.067544,"\int \cos ^2(a+b x) \csc ^5(2 a+2 b x) \, dx","Int[Cos[a + b*x]^2*Csc[2*a + 2*b*x]^5,x]","\frac{\tan ^2(a+b x)}{64 b}-\frac{\cot ^4(a+b x)}{128 b}-\frac{3 \cot ^2(a+b x)}{64 b}+\frac{3 \log (\tan (a+b x))}{32 b}","\frac{\tan ^2(a+b x)}{64 b}-\frac{\cot ^4(a+b x)}{128 b}-\frac{3 \cot ^2(a+b x)}{64 b}+\frac{3 \log (\tan (a+b x))}{32 b}",1,"(-3*Cot[a + b*x]^2)/(64*b) - Cot[a + b*x]^4/(128*b) + (3*Log[Tan[a + b*x]])/(32*b) + Tan[a + b*x]^2/(64*b)","A",5,4,20,0.2000,1,"{4287, 2620, 266, 43}"
151,1,46,0,0.0612923,"\int \cos ^3(a+b x) \sin ^5(2 a+2 b x) \, dx","Int[Cos[a + b*x]^3*Sin[2*a + 2*b*x]^5,x]","-\frac{32 \cos ^{13}(a+b x)}{13 b}+\frac{64 \cos ^{11}(a+b x)}{11 b}-\frac{32 \cos ^9(a+b x)}{9 b}","-\frac{32 \cos ^{13}(a+b x)}{13 b}+\frac{64 \cos ^{11}(a+b x)}{11 b}-\frac{32 \cos ^9(a+b x)}{9 b}",1,"(-32*Cos[a + b*x]^9)/(9*b) + (64*Cos[a + b*x]^11)/(11*b) - (32*Cos[a + b*x]^13)/(13*b)","A",4,3,20,0.1500,1,"{4287, 2565, 270}"
152,1,61,0,0.064816,"\int \cos ^3(a+b x) \sin ^4(2 a+2 b x) \, dx","Int[Cos[a + b*x]^3*Sin[2*a + 2*b*x]^4,x]","-\frac{16 \sin ^{11}(a+b x)}{11 b}+\frac{16 \sin ^9(a+b x)}{3 b}-\frac{48 \sin ^7(a+b x)}{7 b}+\frac{16 \sin ^5(a+b x)}{5 b}","-\frac{16 \sin ^{11}(a+b x)}{11 b}+\frac{16 \sin ^9(a+b x)}{3 b}-\frac{48 \sin ^7(a+b x)}{7 b}+\frac{16 \sin ^5(a+b x)}{5 b}",1,"(16*Sin[a + b*x]^5)/(5*b) - (48*Sin[a + b*x]^7)/(7*b) + (16*Sin[a + b*x]^9)/(3*b) - (16*Sin[a + b*x]^11)/(11*b)","A",4,3,20,0.1500,1,"{4287, 2564, 270}"
153,1,31,0,0.0560466,"\int \cos ^3(a+b x) \sin ^3(2 a+2 b x) \, dx","Int[Cos[a + b*x]^3*Sin[2*a + 2*b*x]^3,x]","\frac{8 \cos ^9(a+b x)}{9 b}-\frac{8 \cos ^7(a+b x)}{7 b}","\frac{8 \cos ^9(a+b x)}{9 b}-\frac{8 \cos ^7(a+b x)}{7 b}",1,"(-8*Cos[a + b*x]^7)/(7*b) + (8*Cos[a + b*x]^9)/(9*b)","A",4,3,20,0.1500,1,"{4287, 2565, 14}"
154,1,46,0,0.0603713,"\int \cos ^3(a+b x) \sin ^2(2 a+2 b x) \, dx","Int[Cos[a + b*x]^3*Sin[2*a + 2*b*x]^2,x]","\frac{4 \sin ^7(a+b x)}{7 b}-\frac{8 \sin ^5(a+b x)}{5 b}+\frac{4 \sin ^3(a+b x)}{3 b}","\frac{4 \sin ^7(a+b x)}{7 b}-\frac{8 \sin ^5(a+b x)}{5 b}+\frac{4 \sin ^3(a+b x)}{3 b}",1,"(4*Sin[a + b*x]^3)/(3*b) - (8*Sin[a + b*x]^5)/(5*b) + (4*Sin[a + b*x]^7)/(7*b)","A",4,3,20,0.1500,1,"{4287, 2564, 270}"
155,1,15,0,0.0329056,"\int \cos ^3(a+b x) \sin (2 a+2 b x) \, dx","Int[Cos[a + b*x]^3*Sin[2*a + 2*b*x],x]","-\frac{2 \cos ^5(a+b x)}{5 b}","-\frac{2 \cos ^5(a+b x)}{5 b}",1,"(-2*Cos[a + b*x]^5)/(5*b)","A",3,3,18,0.1667,1,"{4287, 2565, 30}"
156,1,28,0,0.0352463,"\int \cos ^3(a+b x) \csc (2 a+2 b x) \, dx","Int[Cos[a + b*x]^3*Csc[2*a + 2*b*x],x]","\frac{\cos (a+b x)}{2 b}-\frac{\tanh ^{-1}(\cos (a+b x))}{2 b}","\frac{\cos (a+b x)}{2 b}-\frac{\tanh ^{-1}(\cos (a+b x))}{2 b}",1,"-ArcTanh[Cos[a + b*x]]/(2*b) + Cos[a + b*x]/(2*b)","A",4,4,18,0.2222,1,"{4287, 2592, 321, 206}"
157,1,13,0,0.0345041,"\int \cos ^3(a+b x) \csc ^2(2 a+2 b x) \, dx","Int[Cos[a + b*x]^3*Csc[2*a + 2*b*x]^2,x]","-\frac{\csc (a+b x)}{4 b}","-\frac{\csc (a+b x)}{4 b}",1,"-Csc[a + b*x]/(4*b)","A",3,3,20,0.1500,1,"{4287, 2606, 8}"
158,1,34,0,0.040758,"\int \cos ^3(a+b x) \csc ^3(2 a+2 b x) \, dx","Int[Cos[a + b*x]^3*Csc[2*a + 2*b*x]^3,x]","-\frac{\tanh ^{-1}(\cos (a+b x))}{16 b}-\frac{\cot (a+b x) \csc (a+b x)}{16 b}","-\frac{\tanh ^{-1}(\cos (a+b x))}{16 b}-\frac{\cot (a+b x) \csc (a+b x)}{16 b}",1,"-ArcTanh[Cos[a + b*x]]/(16*b) - (Cot[a + b*x]*Csc[a + b*x])/(16*b)","A",3,3,20,0.1500,1,"{4287, 3768, 3770}"
159,1,43,0,0.0513725,"\int \cos ^3(a+b x) \csc ^4(2 a+2 b x) \, dx","Int[Cos[a + b*x]^3*Csc[2*a + 2*b*x]^4,x]","-\frac{\csc ^3(a+b x)}{48 b}-\frac{\csc (a+b x)}{16 b}+\frac{\tanh ^{-1}(\sin (a+b x))}{16 b}","-\frac{\csc ^3(a+b x)}{48 b}-\frac{\csc (a+b x)}{16 b}+\frac{\tanh ^{-1}(\sin (a+b x))}{16 b}",1,"ArcTanh[Sin[a + b*x]]/(16*b) - Csc[a + b*x]/(16*b) - Csc[a + b*x]^3/(48*b)","A",5,4,20,0.2000,1,"{4287, 2621, 302, 207}"
160,1,70,0,0.069867,"\int \cos ^3(a+b x) \csc ^5(2 a+2 b x) \, dx","Int[Cos[a + b*x]^3*Csc[2*a + 2*b*x]^5,x]","\frac{15 \sec (a+b x)}{256 b}-\frac{15 \tanh ^{-1}(\cos (a+b x))}{256 b}-\frac{\csc ^4(a+b x) \sec (a+b x)}{128 b}-\frac{5 \csc ^2(a+b x) \sec (a+b x)}{256 b}","\frac{15 \sec (a+b x)}{256 b}-\frac{15 \tanh ^{-1}(\cos (a+b x))}{256 b}-\frac{\csc ^4(a+b x) \sec (a+b x)}{128 b}-\frac{5 \csc ^2(a+b x) \sec (a+b x)}{256 b}",1,"(-15*ArcTanh[Cos[a + b*x]])/(256*b) + (15*Sec[a + b*x])/(256*b) - (5*Csc[a + b*x]^2*Sec[a + b*x])/(256*b) - (Csc[a + b*x]^4*Sec[a + b*x])/(128*b)","A",6,5,20,0.2500,1,"{4287, 2622, 288, 321, 207}"
161,1,136,0,0.0913343,"\int \cos (a+b x) \sin ^{\frac{5}{2}}(2 a+2 b x) \, dx","Int[Cos[a + b*x]*Sin[2*a + 2*b*x]^(5/2),x]","\frac{\sin (a+b x) \sin ^{\frac{5}{2}}(2 a+2 b x)}{6 b}+\frac{5 \sin (a+b x) \sqrt{\sin (2 a+2 b x)}}{16 b}-\frac{5 \sin ^{\frac{3}{2}}(2 a+2 b x) \cos (a+b x)}{24 b}-\frac{5 \sin ^{-1}(\cos (a+b x)-\sin (a+b x))}{32 b}-\frac{5 \log \left(\sin (a+b x)+\sqrt{\sin (2 a+2 b x)}+\cos (a+b x)\right)}{32 b}","\frac{\sin (a+b x) \sin ^{\frac{5}{2}}(2 a+2 b x)}{6 b}+\frac{5 \sin (a+b x) \sqrt{\sin (2 a+2 b x)}}{16 b}-\frac{5 \sin ^{\frac{3}{2}}(2 a+2 b x) \cos (a+b x)}{24 b}-\frac{5 \sin ^{-1}(\cos (a+b x)-\sin (a+b x))}{32 b}-\frac{5 \log \left(\sin (a+b x)+\sqrt{\sin (2 a+2 b x)}+\cos (a+b x)\right)}{32 b}",1,"(-5*ArcSin[Cos[a + b*x] - Sin[a + b*x]])/(32*b) - (5*Log[Cos[a + b*x] + Sin[a + b*x] + Sqrt[Sin[2*a + 2*b*x]]])/(32*b) + (5*Sin[a + b*x]*Sqrt[Sin[2*a + 2*b*x]])/(16*b) - (5*Cos[a + b*x]*Sin[2*a + 2*b*x]^(3/2))/(24*b) + (Sin[a + b*x]*Sin[2*a + 2*b*x]^(5/2))/(6*b)","A",4,3,20,0.1500,1,"{4301, 4302, 4306}"
162,1,110,0,0.0666506,"\int \cos (a+b x) \sin ^{\frac{3}{2}}(2 a+2 b x) \, dx","Int[Cos[a + b*x]*Sin[2*a + 2*b*x]^(3/2),x]","\frac{\sin (a+b x) \sin ^{\frac{3}{2}}(2 a+2 b x)}{4 b}-\frac{3 \sin ^{-1}(\cos (a+b x)-\sin (a+b x))}{16 b}-\frac{3 \sqrt{\sin (2 a+2 b x)} \cos (a+b x)}{8 b}+\frac{3 \log \left(\sin (a+b x)+\sqrt{\sin (2 a+2 b x)}+\cos (a+b x)\right)}{16 b}","\frac{\sin (a+b x) \sin ^{\frac{3}{2}}(2 a+2 b x)}{4 b}-\frac{3 \sin ^{-1}(\cos (a+b x)-\sin (a+b x))}{16 b}-\frac{3 \sqrt{\sin (2 a+2 b x)} \cos (a+b x)}{8 b}+\frac{3 \log \left(\sin (a+b x)+\sqrt{\sin (2 a+2 b x)}+\cos (a+b x)\right)}{16 b}",1,"(-3*ArcSin[Cos[a + b*x] - Sin[a + b*x]])/(16*b) + (3*Log[Cos[a + b*x] + Sin[a + b*x] + Sqrt[Sin[2*a + 2*b*x]]])/(16*b) - (3*Cos[a + b*x]*Sqrt[Sin[2*a + 2*b*x]])/(8*b) + (Sin[a + b*x]*Sin[2*a + 2*b*x]^(3/2))/(4*b)","A",3,3,20,0.1500,1,"{4301, 4302, 4305}"
163,1,84,0,0.0432653,"\int \cos (a+b x) \sqrt{\sin (2 a+2 b x)} \, dx","Int[Cos[a + b*x]*Sqrt[Sin[2*a + 2*b*x]],x]","\frac{\sin (a+b x) \sqrt{\sin (2 a+2 b x)}}{2 b}-\frac{\sin ^{-1}(\cos (a+b x)-\sin (a+b x))}{4 b}-\frac{\log \left(\sin (a+b x)+\sqrt{\sin (2 a+2 b x)}+\cos (a+b x)\right)}{4 b}","\frac{\sin (a+b x) \sqrt{\sin (2 a+2 b x)}}{2 b}-\frac{\sin ^{-1}(\cos (a+b x)-\sin (a+b x))}{4 b}-\frac{\log \left(\sin (a+b x)+\sqrt{\sin (2 a+2 b x)}+\cos (a+b x)\right)}{4 b}",1,"-ArcSin[Cos[a + b*x] - Sin[a + b*x]]/(4*b) - Log[Cos[a + b*x] + Sin[a + b*x] + Sqrt[Sin[2*a + 2*b*x]]]/(4*b) + (Sin[a + b*x]*Sqrt[Sin[2*a + 2*b*x]])/(2*b)","A",2,2,20,0.1000,1,"{4301, 4306}"
164,1,58,0,0.0212411,"\int \frac{\cos (a+b x)}{\sqrt{\sin (2 a+2 b x)}} \, dx","Int[Cos[a + b*x]/Sqrt[Sin[2*a + 2*b*x]],x]","\frac{\log \left(\sin (a+b x)+\sqrt{\sin (2 a+2 b x)}+\cos (a+b x)\right)}{2 b}-\frac{\sin ^{-1}(\cos (a+b x)-\sin (a+b x))}{2 b}","\frac{\log \left(\sin (a+b x)+\sqrt{\sin (2 a+2 b x)}+\cos (a+b x)\right)}{2 b}-\frac{\sin ^{-1}(\cos (a+b x)-\sin (a+b x))}{2 b}",1,"-ArcSin[Cos[a + b*x] - Sin[a + b*x]]/(2*b) + Log[Cos[a + b*x] + Sin[a + b*x] + Sqrt[Sin[2*a + 2*b*x]]]/(2*b)","A",1,1,20,0.05000,1,"{4305}"
165,1,24,0,0.0178053,"\int \frac{\cos (a+b x)}{\sin ^{\frac{3}{2}}(2 a+2 b x)} \, dx","Int[Cos[a + b*x]/Sin[2*a + 2*b*x]^(3/2),x]","-\frac{\cos (a+b x)}{b \sqrt{\sin (2 a+2 b x)}}","-\frac{\cos (a+b x)}{b \sqrt{\sin (2 a+2 b x)}}",1,"-(Cos[a + b*x]/(b*Sqrt[Sin[2*a + 2*b*x]]))","A",1,1,20,0.05000,1,"{4291}"
166,1,53,0,0.0376203,"\int \frac{\cos (a+b x)}{\sin ^{\frac{5}{2}}(2 a+2 b x)} \, dx","Int[Cos[a + b*x]/Sin[2*a + 2*b*x]^(5/2),x]","\frac{2 \sin (a+b x)}{3 b \sqrt{\sin (2 a+2 b x)}}-\frac{\cos (a+b x)}{3 b \sin ^{\frac{3}{2}}(2 a+2 b x)}","\frac{2 \sin (a+b x)}{3 b \sqrt{\sin (2 a+2 b x)}}-\frac{\cos (a+b x)}{3 b \sin ^{\frac{3}{2}}(2 a+2 b x)}",1,"-Cos[a + b*x]/(3*b*Sin[2*a + 2*b*x]^(3/2)) + (2*Sin[a + b*x])/(3*b*Sqrt[Sin[2*a + 2*b*x]])","A",2,2,20,0.1000,1,"{4303, 4292}"
167,1,79,0,0.0589234,"\int \frac{\cos (a+b x)}{\sin ^{\frac{7}{2}}(2 a+2 b x)} \, dx","Int[Cos[a + b*x]/Sin[2*a + 2*b*x]^(7/2),x]","\frac{4 \sin (a+b x)}{15 b \sin ^{\frac{3}{2}}(2 a+2 b x)}-\frac{\cos (a+b x)}{5 b \sin ^{\frac{5}{2}}(2 a+2 b x)}-\frac{8 \cos (a+b x)}{15 b \sqrt{\sin (2 a+2 b x)}}","\frac{4 \sin (a+b x)}{15 b \sin ^{\frac{3}{2}}(2 a+2 b x)}-\frac{\cos (a+b x)}{5 b \sin ^{\frac{5}{2}}(2 a+2 b x)}-\frac{8 \cos (a+b x)}{15 b \sqrt{\sin (2 a+2 b x)}}",1,"-Cos[a + b*x]/(5*b*Sin[2*a + 2*b*x]^(5/2)) + (4*Sin[a + b*x])/(15*b*Sin[2*a + 2*b*x]^(3/2)) - (8*Cos[a + b*x])/(15*b*Sqrt[Sin[2*a + 2*b*x]])","A",3,3,20,0.1500,1,"{4303, 4304, 4291}"
168,1,105,0,0.0799988,"\int \frac{\cos (a+b x)}{\sin ^{\frac{9}{2}}(2 a+2 b x)} \, dx","Int[Cos[a + b*x]/Sin[2*a + 2*b*x]^(9/2),x]","\frac{6 \sin (a+b x)}{35 b \sin ^{\frac{5}{2}}(2 a+2 b x)}+\frac{16 \sin (a+b x)}{35 b \sqrt{\sin (2 a+2 b x)}}-\frac{8 \cos (a+b x)}{35 b \sin ^{\frac{3}{2}}(2 a+2 b x)}-\frac{\cos (a+b x)}{7 b \sin ^{\frac{7}{2}}(2 a+2 b x)}","\frac{6 \sin (a+b x)}{35 b \sin ^{\frac{5}{2}}(2 a+2 b x)}+\frac{16 \sin (a+b x)}{35 b \sqrt{\sin (2 a+2 b x)}}-\frac{8 \cos (a+b x)}{35 b \sin ^{\frac{3}{2}}(2 a+2 b x)}-\frac{\cos (a+b x)}{7 b \sin ^{\frac{7}{2}}(2 a+2 b x)}",1,"-Cos[a + b*x]/(7*b*Sin[2*a + 2*b*x]^(7/2)) + (6*Sin[a + b*x])/(35*b*Sin[2*a + 2*b*x]^(5/2)) - (8*Cos[a + b*x])/(35*b*Sin[2*a + 2*b*x]^(3/2)) + (16*Sin[a + b*x])/(35*b*Sqrt[Sin[2*a + 2*b*x]])","A",4,3,20,0.1500,1,"{4303, 4304, 4292}"
169,1,98,0,0.0573313,"\int \cos ^2(a+b x) \sin ^{\frac{7}{2}}(2 a+2 b x) \, dx","Int[Cos[a + b*x]^2*Sin[2*a + 2*b*x]^(7/2),x]","\frac{\sin ^{\frac{9}{2}}(2 a+2 b x)}{18 b}+\frac{5 F\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{42 b}-\frac{\sin ^{\frac{5}{2}}(2 a+2 b x) \cos (2 a+2 b x)}{14 b}-\frac{5 \sqrt{\sin (2 a+2 b x)} \cos (2 a+2 b x)}{42 b}","\frac{\sin ^{\frac{9}{2}}(2 a+2 b x)}{18 b}+\frac{5 F\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{42 b}-\frac{\sin ^{\frac{5}{2}}(2 a+2 b x) \cos (2 a+2 b x)}{14 b}-\frac{5 \sqrt{\sin (2 a+2 b x)} \cos (2 a+2 b x)}{42 b}",1,"(5*EllipticF[a - Pi/4 + b*x, 2])/(42*b) - (5*Cos[2*a + 2*b*x]*Sqrt[Sin[2*a + 2*b*x]])/(42*b) - (Cos[2*a + 2*b*x]*Sin[2*a + 2*b*x]^(5/2))/(14*b) + Sin[2*a + 2*b*x]^(9/2)/(18*b)","A",4,3,22,0.1364,1,"{4297, 2635, 2641}"
170,1,69,0,0.0453035,"\int \cos ^2(a+b x) \sin ^{\frac{5}{2}}(2 a+2 b x) \, dx","Int[Cos[a + b*x]^2*Sin[2*a + 2*b*x]^(5/2),x]","\frac{\sin ^{\frac{7}{2}}(2 a+2 b x)}{14 b}+\frac{3 E\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{10 b}-\frac{\sin ^{\frac{3}{2}}(2 a+2 b x) \cos (2 a+2 b x)}{10 b}","\frac{\sin ^{\frac{7}{2}}(2 a+2 b x)}{14 b}+\frac{3 E\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{10 b}-\frac{\sin ^{\frac{3}{2}}(2 a+2 b x) \cos (2 a+2 b x)}{10 b}",1,"(3*EllipticE[a - Pi/4 + b*x, 2])/(10*b) - (Cos[2*a + 2*b*x]*Sin[2*a + 2*b*x]^(3/2))/(10*b) + Sin[2*a + 2*b*x]^(7/2)/(14*b)","A",3,3,22,0.1364,1,"{4297, 2635, 2639}"
171,1,69,0,0.045327,"\int \cos ^2(a+b x) \sin ^{\frac{3}{2}}(2 a+2 b x) \, dx","Int[Cos[a + b*x]^2*Sin[2*a + 2*b*x]^(3/2),x]","\frac{\sin ^{\frac{5}{2}}(2 a+2 b x)}{10 b}+\frac{F\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{6 b}-\frac{\sqrt{\sin (2 a+2 b x)} \cos (2 a+2 b x)}{6 b}","\frac{\sin ^{\frac{5}{2}}(2 a+2 b x)}{10 b}+\frac{F\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{6 b}-\frac{\sqrt{\sin (2 a+2 b x)} \cos (2 a+2 b x)}{6 b}",1,"EllipticF[a - Pi/4 + b*x, 2]/(6*b) - (Cos[2*a + 2*b*x]*Sqrt[Sin[2*a + 2*b*x]])/(6*b) + Sin[2*a + 2*b*x]^(5/2)/(10*b)","A",3,3,22,0.1364,1,"{4297, 2635, 2641}"
172,1,40,0,0.0345386,"\int \cos ^2(a+b x) \sqrt{\sin (2 a+2 b x)} \, dx","Int[Cos[a + b*x]^2*Sqrt[Sin[2*a + 2*b*x]],x]","\frac{\sin ^{\frac{3}{2}}(2 a+2 b x)}{6 b}+\frac{E\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{2 b}","\frac{\sin ^{\frac{3}{2}}(2 a+2 b x)}{6 b}+\frac{E\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{2 b}",1,"EllipticE[a - Pi/4 + b*x, 2]/(2*b) + Sin[2*a + 2*b*x]^(3/2)/(6*b)","A",2,2,22,0.09091,1,"{4297, 2639}"
173,1,40,0,0.0350123,"\int \frac{\cos ^2(a+b x)}{\sqrt{\sin (2 a+2 b x)}} \, dx","Int[Cos[a + b*x]^2/Sqrt[Sin[2*a + 2*b*x]],x]","\frac{\sqrt{\sin (2 a+2 b x)}}{2 b}+\frac{F\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{2 b}","\frac{\sqrt{\sin (2 a+2 b x)}}{2 b}+\frac{F\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{2 b}",1,"EllipticF[a - Pi/4 + b*x, 2]/(2*b) + Sqrt[Sin[2*a + 2*b*x]]/(2*b)","A",2,2,22,0.09091,1,"{4297, 2641}"
174,1,46,0,0.035921,"\int \frac{\cos ^2(a+b x)}{\sin ^{\frac{3}{2}}(2 a+2 b x)} \, dx","Int[Cos[a + b*x]^2/Sin[2*a + 2*b*x]^(3/2),x]","-\frac{E\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{2 b}-\frac{\cos ^2(a+b x)}{b \sqrt{\sin (2 a+2 b x)}}","-\frac{E\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{2 b}-\frac{\cos ^2(a+b x)}{b \sqrt{\sin (2 a+2 b x)}}",1,"-EllipticE[a - Pi/4 + b*x, 2]/(2*b) - Cos[a + b*x]^2/(b*Sqrt[Sin[2*a + 2*b*x]])","A",2,2,22,0.09091,1,"{4295, 2639}"
175,1,48,0,0.0357419,"\int \frac{\cos ^2(a+b x)}{\sin ^{\frac{5}{2}}(2 a+2 b x)} \, dx","Int[Cos[a + b*x]^2/Sin[2*a + 2*b*x]^(5/2),x]","\frac{F\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{6 b}-\frac{\cos ^2(a+b x)}{3 b \sin ^{\frac{3}{2}}(2 a+2 b x)}","\frac{F\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{6 b}-\frac{\cos ^2(a+b x)}{3 b \sin ^{\frac{3}{2}}(2 a+2 b x)}",1,"EllipticF[a - Pi/4 + b*x, 2]/(6*b) - Cos[a + b*x]^2/(3*b*Sin[2*a + 2*b*x]^(3/2))","A",2,2,22,0.09091,1,"{4295, 2641}"
176,1,77,0,0.0463152,"\int \frac{\cos ^2(a+b x)}{\sin ^{\frac{7}{2}}(2 a+2 b x)} \, dx","Int[Cos[a + b*x]^2/Sin[2*a + 2*b*x]^(7/2),x]","-\frac{3 E\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{10 b}-\frac{\cos ^2(a+b x)}{5 b \sin ^{\frac{5}{2}}(2 a+2 b x)}-\frac{3 \cos (2 a+2 b x)}{10 b \sqrt{\sin (2 a+2 b x)}}","-\frac{3 E\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{10 b}-\frac{\cos ^2(a+b x)}{5 b \sin ^{\frac{5}{2}}(2 a+2 b x)}-\frac{3 \cos (2 a+2 b x)}{10 b \sqrt{\sin (2 a+2 b x)}}",1,"(-3*EllipticE[a - Pi/4 + b*x, 2])/(10*b) - Cos[a + b*x]^2/(5*b*Sin[2*a + 2*b*x]^(5/2)) - (3*Cos[2*a + 2*b*x])/(10*b*Sqrt[Sin[2*a + 2*b*x]])","A",3,3,22,0.1364,1,"{4295, 2636, 2639}"
177,1,136,0,0.0987861,"\int \cos ^3(a+b x) \sin ^{\frac{3}{2}}(2 a+2 b x) \, dx","Int[Cos[a + b*x]^3*Sin[2*a + 2*b*x]^(3/2),x]","\frac{7 \sin (a+b x) \sin ^{\frac{3}{2}}(2 a+2 b x)}{48 b}+\frac{\sin ^{\frac{5}{2}}(2 a+2 b x) \cos (a+b x)}{12 b}-\frac{7 \sin ^{-1}(\cos (a+b x)-\sin (a+b x))}{64 b}-\frac{7 \sqrt{\sin (2 a+2 b x)} \cos (a+b x)}{32 b}+\frac{7 \log \left(\sin (a+b x)+\sqrt{\sin (2 a+2 b x)}+\cos (a+b x)\right)}{64 b}","\frac{7 \sin (a+b x) \sin ^{\frac{3}{2}}(2 a+2 b x)}{48 b}+\frac{\sin ^{\frac{5}{2}}(2 a+2 b x) \cos (a+b x)}{12 b}-\frac{7 \sin ^{-1}(\cos (a+b x)-\sin (a+b x))}{64 b}-\frac{7 \sqrt{\sin (2 a+2 b x)} \cos (a+b x)}{32 b}+\frac{7 \log \left(\sin (a+b x)+\sqrt{\sin (2 a+2 b x)}+\cos (a+b x)\right)}{64 b}",1,"(-7*ArcSin[Cos[a + b*x] - Sin[a + b*x]])/(64*b) + (7*Log[Cos[a + b*x] + Sin[a + b*x] + Sqrt[Sin[2*a + 2*b*x]]])/(64*b) - (7*Cos[a + b*x]*Sqrt[Sin[2*a + 2*b*x]])/(32*b) + (7*Sin[a + b*x]*Sin[2*a + 2*b*x]^(3/2))/(48*b) + (Cos[a + b*x]*Sin[2*a + 2*b*x]^(5/2))/(12*b)","A",4,4,22,0.1818,1,"{4297, 4301, 4302, 4305}"
178,1,110,0,0.075635,"\int \cos ^3(a+b x) \sqrt{\sin (2 a+2 b x)} \, dx","Int[Cos[a + b*x]^3*Sqrt[Sin[2*a + 2*b*x]],x]","\frac{5 \sin (a+b x) \sqrt{\sin (2 a+2 b x)}}{16 b}+\frac{\sin ^{\frac{3}{2}}(2 a+2 b x) \cos (a+b x)}{8 b}-\frac{5 \sin ^{-1}(\cos (a+b x)-\sin (a+b x))}{32 b}-\frac{5 \log \left(\sin (a+b x)+\sqrt{\sin (2 a+2 b x)}+\cos (a+b x)\right)}{32 b}","\frac{5 \sin (a+b x) \sqrt{\sin (2 a+2 b x)}}{16 b}+\frac{\sin ^{\frac{3}{2}}(2 a+2 b x) \cos (a+b x)}{8 b}-\frac{5 \sin ^{-1}(\cos (a+b x)-\sin (a+b x))}{32 b}-\frac{5 \log \left(\sin (a+b x)+\sqrt{\sin (2 a+2 b x)}+\cos (a+b x)\right)}{32 b}",1,"(-5*ArcSin[Cos[a + b*x] - Sin[a + b*x]])/(32*b) - (5*Log[Cos[a + b*x] + Sin[a + b*x] + Sqrt[Sin[2*a + 2*b*x]]])/(32*b) + (5*Sin[a + b*x]*Sqrt[Sin[2*a + 2*b*x]])/(16*b) + (Cos[a + b*x]*Sin[2*a + 2*b*x]^(3/2))/(8*b)","A",3,3,22,0.1364,1,"{4297, 4301, 4306}"
179,1,84,0,0.0524824,"\int \frac{\cos ^3(a+b x)}{\sqrt{\sin (2 a+2 b x)}} \, dx","Int[Cos[a + b*x]^3/Sqrt[Sin[2*a + 2*b*x]],x]","-\frac{3 \sin ^{-1}(\cos (a+b x)-\sin (a+b x))}{8 b}+\frac{\sqrt{\sin (2 a+2 b x)} \cos (a+b x)}{4 b}+\frac{3 \log \left(\sin (a+b x)+\sqrt{\sin (2 a+2 b x)}+\cos (a+b x)\right)}{8 b}","-\frac{3 \sin ^{-1}(\cos (a+b x)-\sin (a+b x))}{8 b}+\frac{\sqrt{\sin (2 a+2 b x)} \cos (a+b x)}{4 b}+\frac{3 \log \left(\sin (a+b x)+\sqrt{\sin (2 a+2 b x)}+\cos (a+b x)\right)}{8 b}",1,"(-3*ArcSin[Cos[a + b*x] - Sin[a + b*x]])/(8*b) + (3*Log[Cos[a + b*x] + Sin[a + b*x] + Sqrt[Sin[2*a + 2*b*x]]])/(8*b) + (Cos[a + b*x]*Sqrt[Sin[2*a + 2*b*x]])/(4*b)","A",2,2,22,0.09091,1,"{4297, 4305}"
180,1,82,0,0.0760366,"\int \frac{\cos ^3(a+b x)}{\sin ^{\frac{3}{2}}(2 a+2 b x)} \, dx","Int[Cos[a + b*x]^3/Sin[2*a + 2*b*x]^(3/2),x]","\frac{\sin ^{-1}(\cos (a+b x)-\sin (a+b x))}{4 b}-\frac{\cos (a+b x)}{b \sqrt{\sin (2 a+2 b x)}}+\frac{\log \left(\sin (a+b x)+\sqrt{\sin (2 a+2 b x)}+\cos (a+b x)\right)}{4 b}","\frac{\sin ^{-1}(\cos (a+b x)-\sin (a+b x))}{4 b}-\frac{\cos (a+b x)}{b \sqrt{\sin (2 a+2 b x)}}+\frac{\log \left(\sin (a+b x)+\sqrt{\sin (2 a+2 b x)}+\cos (a+b x)\right)}{4 b}",1,"ArcSin[Cos[a + b*x] - Sin[a + b*x]]/(4*b) + Log[Cos[a + b*x] + Sin[a + b*x] + Sqrt[Sin[2*a + 2*b*x]]]/(4*b) - Cos[a + b*x]/(b*Sqrt[Sin[2*a + 2*b*x]])","A",3,3,22,0.1364,1,"{4293, 4307, 4306}"
181,1,28,0,0.027477,"\int \frac{\cos ^3(a+b x)}{\sin ^{\frac{5}{2}}(2 a+2 b x)} \, dx","Int[Cos[a + b*x]^3/Sin[2*a + 2*b*x]^(5/2),x]","-\frac{\cos ^3(a+b x)}{3 b \sin ^{\frac{3}{2}}(2 a+2 b x)}","-\frac{\cos ^3(a+b x)}{3 b \sin ^{\frac{3}{2}}(2 a+2 b x)}",1,"-Cos[a + b*x]^3/(3*b*Sin[2*a + 2*b*x]^(3/2))","A",1,1,22,0.04545,1,"{4291}"
182,1,55,0,0.0471591,"\int \frac{\cos ^3(a+b x)}{\sin ^{\frac{7}{2}}(2 a+2 b x)} \, dx","Int[Cos[a + b*x]^3/Sin[2*a + 2*b*x]^(7/2),x]","-\frac{\cos ^3(a+b x)}{5 b \sin ^{\frac{5}{2}}(2 a+2 b x)}-\frac{\cos (a+b x)}{5 b \sqrt{\sin (2 a+2 b x)}}","-\frac{\cos ^3(a+b x)}{5 b \sin ^{\frac{5}{2}}(2 a+2 b x)}-\frac{\cos (a+b x)}{5 b \sqrt{\sin (2 a+2 b x)}}",1,"-Cos[a + b*x]^3/(5*b*Sin[2*a + 2*b*x]^(5/2)) - Cos[a + b*x]/(5*b*Sqrt[Sin[2*a + 2*b*x]])","A",2,2,22,0.09091,1,"{4295, 4291}"
183,1,81,0,0.0678956,"\int \frac{\cos ^3(a+b x)}{\sin ^{\frac{9}{2}}(2 a+2 b x)} \, dx","Int[Cos[a + b*x]^3/Sin[2*a + 2*b*x]^(9/2),x]","\frac{4 \sin (a+b x)}{21 b \sqrt{\sin (2 a+2 b x)}}-\frac{\cos ^3(a+b x)}{7 b \sin ^{\frac{7}{2}}(2 a+2 b x)}-\frac{2 \cos (a+b x)}{21 b \sin ^{\frac{3}{2}}(2 a+2 b x)}","\frac{4 \sin (a+b x)}{21 b \sqrt{\sin (2 a+2 b x)}}-\frac{\cos ^3(a+b x)}{7 b \sin ^{\frac{7}{2}}(2 a+2 b x)}-\frac{2 \cos (a+b x)}{21 b \sin ^{\frac{3}{2}}(2 a+2 b x)}",1,"-Cos[a + b*x]^3/(7*b*Sin[2*a + 2*b*x]^(7/2)) - (2*Cos[a + b*x])/(21*b*Sin[2*a + 2*b*x]^(3/2)) + (4*Sin[a + b*x])/(21*b*Sqrt[Sin[2*a + 2*b*x]])","A",3,3,22,0.1364,1,"{4295, 4303, 4292}"
184,1,107,0,0.0904905,"\int \frac{\cos ^3(a+b x)}{\sin ^{\frac{11}{2}}(2 a+2 b x)} \, dx","Int[Cos[a + b*x]^3/Sin[2*a + 2*b*x]^(11/2),x]","\frac{4 \sin (a+b x)}{45 b \sin ^{\frac{3}{2}}(2 a+2 b x)}-\frac{\cos ^3(a+b x)}{9 b \sin ^{\frac{9}{2}}(2 a+2 b x)}-\frac{\cos (a+b x)}{15 b \sin ^{\frac{5}{2}}(2 a+2 b x)}-\frac{8 \cos (a+b x)}{45 b \sqrt{\sin (2 a+2 b x)}}","\frac{4 \sin (a+b x)}{45 b \sin ^{\frac{3}{2}}(2 a+2 b x)}-\frac{\cos ^3(a+b x)}{9 b \sin ^{\frac{9}{2}}(2 a+2 b x)}-\frac{\cos (a+b x)}{15 b \sin ^{\frac{5}{2}}(2 a+2 b x)}-\frac{8 \cos (a+b x)}{45 b \sqrt{\sin (2 a+2 b x)}}",1,"-Cos[a + b*x]^3/(9*b*Sin[2*a + 2*b*x]^(9/2)) - Cos[a + b*x]/(15*b*Sin[2*a + 2*b*x]^(5/2)) + (4*Sin[a + b*x])/(45*b*Sin[2*a + 2*b*x]^(3/2)) - (8*Cos[a + b*x])/(45*b*Sqrt[Sin[2*a + 2*b*x]])","A",4,4,22,0.1818,1,"{4295, 4303, 4304, 4291}"
185,1,31,0,0.0129827,"\int \frac{\cos (x)}{\sqrt{\sin (2 x)}} \, dx","Int[Cos[x]/Sqrt[Sin[2*x]],x]","\frac{1}{2} \log \left(\sin (x)+\sqrt{\sin (2 x)}+\cos (x)\right)-\frac{1}{2} \sin ^{-1}(\cos (x)-\sin (x))","\frac{1}{2} \log \left(\sin (x)+\sqrt{\sin (2 x)}+\cos (x)\right)-\frac{1}{2} \sin ^{-1}(\cos (x)-\sin (x))",1,"-ArcSin[Cos[x] - Sin[x]]/2 + Log[Cos[x] + Sin[x] + Sqrt[Sin[2*x]]]/2","A",1,1,11,0.09091,1,"{4305}"
186,1,25,0,0.0303279,"\int \csc (x) \sqrt{\sin (2 x)} \, dx","Int[Csc[x]*Sqrt[Sin[2*x]],x]","\log \left(\sin (x)+\sqrt{\sin (2 x)}+\cos (x)\right)-\sin ^{-1}(\cos (x)-\sin (x))","\log \left(\sin (x)+\sqrt{\sin (2 x)}+\cos (x)\right)-\sin ^{-1}(\cos (x)-\sin (x))",1,"-ArcSin[Cos[x] - Sin[x]] + Log[Cos[x] + Sin[x] + Sqrt[Sin[2*x]]]","A",2,2,11,0.1818,1,"{4308, 4305}"
187,1,85,0,0.0712569,"\int \cos ^3(a+b x) \sin ^m(2 a+2 b x) \, dx","Int[Cos[a + b*x]^3*Sin[2*a + 2*b*x]^m,x]","-\frac{\cos ^3(a+b x) \cot (a+b x) \sin ^2(a+b x)^{\frac{1-m}{2}} \sin ^m(2 a+2 b x) \, _2F_1\left(\frac{1-m}{2},\frac{m+4}{2};\frac{m+6}{2};\cos ^2(a+b x)\right)}{b (m+4)}","-\frac{\cos ^3(a+b x) \cot (a+b x) \sin ^2(a+b x)^{\frac{1-m}{2}} \sin ^m(2 a+2 b x) \, _2F_1\left(\frac{1-m}{2},\frac{m+4}{2};\frac{m+6}{2};\cos ^2(a+b x)\right)}{b (m+4)}",1,"-((Cos[a + b*x]^3*Cot[a + b*x]*Hypergeometric2F1[(1 - m)/2, (4 + m)/2, (6 + m)/2, Cos[a + b*x]^2]*(Sin[a + b*x]^2)^((1 - m)/2)*Sin[2*a + 2*b*x]^m)/(b*(4 + m)))","A",2,2,20,0.1000,1,"{4309, 2576}"
188,1,85,0,0.0707474,"\int \cos ^2(a+b x) \sin ^m(2 a+2 b x) \, dx","Int[Cos[a + b*x]^2*Sin[2*a + 2*b*x]^m,x]","-\frac{\cos ^2(a+b x) \cot (a+b x) \sin ^2(a+b x)^{\frac{1-m}{2}} \sin ^m(2 a+2 b x) \, _2F_1\left(\frac{1-m}{2},\frac{m+3}{2};\frac{m+5}{2};\cos ^2(a+b x)\right)}{b (m+3)}","-\frac{\cos ^2(a+b x) \cot (a+b x) \sin ^2(a+b x)^{\frac{1-m}{2}} \sin ^m(2 a+2 b x) \, _2F_1\left(\frac{1-m}{2},\frac{m+3}{2};\frac{m+5}{2};\cos ^2(a+b x)\right)}{b (m+3)}",1,"-((Cos[a + b*x]^2*Cot[a + b*x]*Hypergeometric2F1[(1 - m)/2, (3 + m)/2, (5 + m)/2, Cos[a + b*x]^2]*(Sin[a + b*x]^2)^((1 - m)/2)*Sin[2*a + 2*b*x]^m)/(b*(3 + m)))","A",2,2,20,0.1000,1,"{4309, 2576}"
189,1,83,0,0.0608929,"\int \cos (a+b x) \sin ^m(2 a+2 b x) \, dx","Int[Cos[a + b*x]*Sin[2*a + 2*b*x]^m,x]","-\frac{\cos (a+b x) \cot (a+b x) \sin ^2(a+b x)^{\frac{1-m}{2}} \sin ^m(2 a+2 b x) \, _2F_1\left(\frac{1-m}{2},\frac{m+2}{2};\frac{m+4}{2};\cos ^2(a+b x)\right)}{b (m+2)}","-\frac{\cos (a+b x) \cot (a+b x) \sin ^2(a+b x)^{\frac{1-m}{2}} \sin ^m(2 a+2 b x) \, _2F_1\left(\frac{1-m}{2},\frac{m+2}{2};\frac{m+4}{2};\cos ^2(a+b x)\right)}{b (m+2)}",1,"-((Cos[a + b*x]*Cot[a + b*x]*Hypergeometric2F1[(1 - m)/2, (2 + m)/2, (4 + m)/2, Cos[a + b*x]^2]*(Sin[a + b*x]^2)^((1 - m)/2)*Sin[2*a + 2*b*x]^m)/(b*(2 + m)))","A",2,2,18,0.1111,1,"{4309, 2576}"
190,1,46,0,0.0966612,"\int \cos ^2(a+b x) \sin ^3(a+b x) \sin ^2(2 a+2 b x) \, dx","Int[Cos[a + b*x]^2*Sin[a + b*x]^3*Sin[2*a + 2*b*x]^2,x]","-\frac{4 \cos ^9(a+b x)}{9 b}+\frac{8 \cos ^7(a+b x)}{7 b}-\frac{4 \cos ^5(a+b x)}{5 b}","-\frac{4 \cos ^9(a+b x)}{9 b}+\frac{8 \cos ^7(a+b x)}{7 b}-\frac{4 \cos ^5(a+b x)}{5 b}",1,"(-4*Cos[a + b*x]^5)/(5*b) + (8*Cos[a + b*x]^7)/(7*b) - (4*Cos[a + b*x]^9)/(9*b)","A",4,3,28,0.1071,1,"{4312, 2565, 270}"
191,1,293,0,0.8483798,"\int \sin (a+b x) \sin ^n(c+d x) \, dx","Int[Sin[a + b*x]*Sin[c + d*x]^n,x]","-\frac{2^{-n-1} \left(i e^{-i (c+d x)}-i e^{i (c+d x)}\right)^n \left(1-e^{2 i c+2 i d x}\right)^{-n} \, _2F_1\left(-n,\frac{b-d n}{2 d};\frac{1}{2} \left(\frac{b}{d}-n+2\right);e^{2 i (c+d x)}\right) \exp (i (a-c n)+i x (b-d n)+i n (c+d x))}{b-d n}-\frac{2^{-n-1} \left(i e^{-i (c+d x)}-i e^{i (c+d x)}\right)^n \left(1-e^{2 i c+2 i d x}\right)^{-n} \, _2F_1\left(-n,-\frac{b+d n}{2 d};1-\frac{b+d n}{2 d};e^{2 i (c+d x)}\right) \exp (-i (a+c n)-i x (b+d n)+i n (c+d x))}{b+d n}","-\frac{2^{-n-1} \left(i e^{-i (c+d x)}-i e^{i (c+d x)}\right)^n \left(1-e^{2 i c+2 i d x}\right)^{-n} \, _2F_1\left(-n,\frac{b-d n}{2 d};\frac{1}{2} \left(\frac{b}{d}-n+2\right);e^{2 i (c+d x)}\right) \exp (i (a-c n)+i x (b-d n)+i n (c+d x))}{b-d n}-\frac{2^{-n-1} \left(i e^{-i (c+d x)}-i e^{i (c+d x)}\right)^n \left(1-e^{2 i c+2 i d x}\right)^{-n} \, _2F_1\left(-n,-\frac{b+d n}{2 d};1-\frac{b+d n}{2 d};e^{2 i (c+d x)}\right) \exp (-i (a+c n)-i x (b+d n)+i n (c+d x))}{b+d n}",1,"-((2^(-1 - n)*E^(I*(a - c*n) + I*(b - d*n)*x + I*n*(c + d*x))*(I/E^(I*(c + d*x)) - I*E^(I*(c + d*x)))^n*Hypergeometric2F1[-n, (b - d*n)/(2*d), (2 + b/d - n)/2, E^((2*I)*(c + d*x))])/((1 - E^((2*I)*c + (2*I)*d*x))^n*(b - d*n))) - (2^(-1 - n)*E^((-I)*(a + c*n) - I*(b + d*n)*x + I*n*(c + d*x))*(I/E^(I*(c + d*x)) - I*E^(I*(c + d*x)))^n*Hypergeometric2F1[-n, -(b + d*n)/(2*d), 1 - (b + d*n)/(2*d), E^((2*I)*(c + d*x))])/((1 - E^((2*I)*c + (2*I)*d*x))^n*(b + d*n))","A",10,5,15,0.3333,1,"{4553, 2285, 2253, 2252, 2251}"
192,1,91,0,0.0764363,"\int \sin (a+b x) \sin ^3(c+d x) \, dx","Int[Sin[a + b*x]*Sin[c + d*x]^3,x]","-\frac{\sin (a+x (b-3 d)-3 c)}{8 (b-3 d)}+\frac{3 \sin (a+x (b-d)-c)}{8 (b-d)}-\frac{3 \sin (a+x (b+d)+c)}{8 (b+d)}+\frac{\sin (a+x (b+3 d)+3 c)}{8 (b+3 d)}","-\frac{\sin (a+x (b-3 d)-3 c)}{8 (b-3 d)}+\frac{3 \sin (a+x (b-d)-c)}{8 (b-d)}-\frac{3 \sin (a+x (b+d)+c)}{8 (b+d)}+\frac{\sin (a+x (b+3 d)+3 c)}{8 (b+3 d)}",1,"-Sin[a - 3*c + (b - 3*d)*x]/(8*(b - 3*d)) + (3*Sin[a - c + (b - d)*x])/(8*(b - d)) - (3*Sin[a + c + (b + d)*x])/(8*(b + d)) + Sin[a + 3*c + (b + 3*d)*x]/(8*(b + 3*d))","A",6,2,15,0.1333,1,"{4569, 2637}"
193,1,62,0,0.0533329,"\int \sin (a+b x) \sin ^2(c+d x) \, dx","Int[Sin[a + b*x]*Sin[c + d*x]^2,x]","\frac{\cos (a+x (b-2 d)-2 c)}{4 (b-2 d)}+\frac{\cos (a+x (b+2 d)+2 c)}{4 (b+2 d)}-\frac{\cos (a+b x)}{2 b}","\frac{\cos (a+x (b-2 d)-2 c)}{4 (b-2 d)}+\frac{\cos (a+x (b+2 d)+2 c)}{4 (b+2 d)}-\frac{\cos (a+b x)}{2 b}",1,"-Cos[a + b*x]/(2*b) + Cos[a - 2*c + (b - 2*d)*x]/(4*(b - 2*d)) + Cos[a + 2*c + (b + 2*d)*x]/(4*(b + 2*d))","A",5,2,15,0.1333,1,"{4569, 2638}"
194,1,43,0,0.0352663,"\int \sin (a+b x) \sin (c+d x) \, dx","Int[Sin[a + b*x]*Sin[c + d*x],x]","\frac{\sin (a+x (b-d)-c)}{2 (b-d)}-\frac{\sin (a+x (b+d)+c)}{2 (b+d)}","\frac{\sin (a+x (b-d)-c)}{2 (b-d)}-\frac{\sin (a+x (b+d)+c)}{2 (b+d)}",1,"Sin[a - c + (b - d)*x]/(2*(b - d)) - Sin[a + c + (b + d)*x]/(2*(b + d))","A",4,2,13,0.1538,1,"{4569, 2637}"
195,1,26,0,0.0274765,"\int \csc (c+b x) \sin (a+b x) \, dx","Int[Csc[c + b*x]*Sin[a + b*x],x]","\frac{\sin (a-c) \log (\sin (b x+c))}{b}+x \cos (a-c)","\frac{\sin (a-c) \log (\sin (b x+c))}{b}+x \cos (a-c)",1,"x*Cos[a - c] + (Log[Sin[c + b*x]]*Sin[a - c])/b","A",3,3,13,0.2308,1,"{4582, 3475, 8}"
196,1,36,0,0.0327012,"\int \csc ^2(c+b x) \sin (a+b x) \, dx","Int[Csc[c + b*x]^2*Sin[a + b*x],x]","-\frac{\cos (a-c) \tanh ^{-1}(\cos (b x+c))}{b}-\frac{\sin (a-c) \csc (b x+c)}{b}","-\frac{\cos (a-c) \tanh ^{-1}(\cos (b x+c))}{b}-\frac{\sin (a-c) \csc (b x+c)}{b}",1,"-((ArcTanh[Cos[c + b*x]]*Cos[a - c])/b) - (Csc[c + b*x]*Sin[a - c])/b","A",4,4,15,0.2667,1,"{4582, 2606, 8, 3770}"
197,1,39,0,0.0437446,"\int \csc ^3(c+b x) \sin (a+b x) \, dx","Int[Csc[c + b*x]^3*Sin[a + b*x],x]","-\frac{\cos (a-c) \cot (b x+c)}{b}-\frac{\sin (a-c) \csc ^2(b x+c)}{2 b}","-\frac{\cos (a-c) \cot (b x+c)}{b}-\frac{\sin (a-c) \csc ^2(b x+c)}{2 b}",1,"-((Cos[a - c]*Cot[c + b*x])/b) - (Csc[c + b*x]^2*Sin[a - c])/(2*b)","A",5,5,15,0.3333,1,"{4582, 2606, 30, 3767, 8}"
198,1,67,0,0.0464963,"\int \csc ^4(c+b x) \sin (a+b x) \, dx","Int[Csc[c + b*x]^4*Sin[a + b*x],x]","-\frac{\cos (a-c) \tanh ^{-1}(\cos (b x+c))}{2 b}-\frac{\sin (a-c) \csc ^3(b x+c)}{3 b}-\frac{\cos (a-c) \cot (b x+c) \csc (b x+c)}{2 b}","-\frac{\cos (a-c) \tanh ^{-1}(\cos (b x+c))}{2 b}-\frac{\sin (a-c) \csc ^3(b x+c)}{3 b}-\frac{\cos (a-c) \cot (b x+c) \csc (b x+c)}{2 b}",1,"-(ArcTanh[Cos[c + b*x]]*Cos[a - c])/(2*b) - (Cos[a - c]*Cot[c + b*x]*Csc[c + b*x])/(2*b) - (Csc[c + b*x]^3*Sin[a - c])/(3*b)","A",5,5,15,0.3333,1,"{4582, 2606, 30, 3768, 3770}"
199,1,60,0,0.0466843,"\int \csc ^5(c+b x) \sin (a+b x) \, dx","Int[Csc[c + b*x]^5*Sin[a + b*x],x]","-\frac{\cos (a-c) \cot ^3(b x+c)}{3 b}-\frac{\cos (a-c) \cot (b x+c)}{b}-\frac{\sin (a-c) \csc ^4(b x+c)}{4 b}","-\frac{\cos (a-c) \cot ^3(b x+c)}{3 b}-\frac{\cos (a-c) \cot (b x+c)}{b}-\frac{\sin (a-c) \csc ^4(b x+c)}{4 b}",1,"-((Cos[a - c]*Cot[c + b*x])/b) - (Cos[a - c]*Cot[c + b*x]^3)/(3*b) - (Csc[c + b*x]^4*Sin[a - c])/(4*b)","A",5,4,15,0.2667,1,"{4582, 2606, 30, 3767}"
200,1,94,0,0.0582293,"\int \csc ^6(c+b x) \sin (a+b x) \, dx","Int[Csc[c + b*x]^6*Sin[a + b*x],x]","-\frac{3 \cos (a-c) \tanh ^{-1}(\cos (b x+c))}{8 b}-\frac{\sin (a-c) \csc ^5(b x+c)}{5 b}-\frac{\cos (a-c) \cot (b x+c) \csc ^3(b x+c)}{4 b}-\frac{3 \cos (a-c) \cot (b x+c) \csc (b x+c)}{8 b}","-\frac{3 \cos (a-c) \tanh ^{-1}(\cos (b x+c))}{8 b}-\frac{\sin (a-c) \csc ^5(b x+c)}{5 b}-\frac{\cos (a-c) \cot (b x+c) \csc ^3(b x+c)}{4 b}-\frac{3 \cos (a-c) \cot (b x+c) \csc (b x+c)}{8 b}",1,"(-3*ArcTanh[Cos[c + b*x]]*Cos[a - c])/(8*b) - (3*Cos[a - c]*Cot[c + b*x]*Csc[c + b*x])/(8*b) - (Cos[a - c]*Cot[c + b*x]*Csc[c + b*x]^3)/(4*b) - (Csc[c + b*x]^5*Sin[a - c])/(5*b)","A",6,5,15,0.3333,1,"{4582, 2606, 30, 3768, 3770}"
201,1,410,0,0.9729735,"\int \sin ^2(a+b x) \sin ^n(c+d x) \, dx","Int[Sin[a + b*x]^2*Sin[c + d*x]^n,x]","-\frac{i 2^{-n-2} \left(i e^{-i (c+d x)}-i e^{i (c+d x)}\right)^n \left(1-e^{2 i c+2 i d x}\right)^{-n} \, _2F_1\left(\frac{1}{2} \left(-\frac{2 b}{d}-n\right),-n;\frac{1}{2} \left(-\frac{2 b}{d}-n+2\right);e^{2 i (c+d x)}\right) \exp (-i (2 a+c n)-i x (2 b+d n)+i n (c+d x))}{2 b+d n}+\frac{i 2^{-n-2} \left(i e^{-i (c+d x)}-i e^{i (c+d x)}\right)^n \left(1-e^{2 i c+2 i d x}\right)^{-n} \, _2F_1\left(\frac{1}{2} \left(\frac{2 b}{d}-n\right),-n;\frac{1}{2} \left(\frac{2 b}{d}-n+2\right);e^{2 i (c+d x)}\right) \exp (i (2 a-c n)+i x (2 b-d n)+i n (c+d x))}{2 b-d n}+\frac{i 2^{-n-1} \left(i e^{-i (c+d x)}-i e^{i (c+d x)}\right)^n \left(1-e^{2 i (c+d x)}\right)^{-n} \, _2F_1\left(-n,-\frac{n}{2};1-\frac{n}{2};e^{2 i (c+d x)}\right)}{d n}","-\frac{i 2^{-n-2} \left(i e^{-i (c+d x)}-i e^{i (c+d x)}\right)^n \left(1-e^{2 i c+2 i d x}\right)^{-n} \, _2F_1\left(\frac{1}{2} \left(-\frac{2 b}{d}-n\right),-n;\frac{1}{2} \left(-\frac{2 b}{d}-n+2\right);e^{2 i (c+d x)}\right) \exp (-i (2 a+c n)-i x (2 b+d n)+i n (c+d x))}{2 b+d n}+\frac{i 2^{-n-2} \left(i e^{-i (c+d x)}-i e^{i (c+d x)}\right)^n \left(1-e^{2 i c+2 i d x}\right)^{-n} \, _2F_1\left(\frac{1}{2} \left(\frac{2 b}{d}-n\right),-n;\frac{1}{2} \left(\frac{2 b}{d}-n+2\right);e^{2 i (c+d x)}\right) \exp (i (2 a-c n)+i x (2 b-d n)+i n (c+d x))}{2 b-d n}+\frac{i 2^{-n-1} \left(i e^{-i (c+d x)}-i e^{i (c+d x)}\right)^n \left(1-e^{2 i (c+d x)}\right)^{-n} \, _2F_1\left(-n,-\frac{n}{2};1-\frac{n}{2};e^{2 i (c+d x)}\right)}{d n}",1,"((-I)*2^(-2 - n)*E^((-I)*(2*a + c*n) - I*(2*b + d*n)*x + I*n*(c + d*x))*(I/E^(I*(c + d*x)) - I*E^(I*(c + d*x)))^n*Hypergeometric2F1[((-2*b)/d - n)/2, -n, (2 - (2*b)/d - n)/2, E^((2*I)*(c + d*x))])/((1 - E^((2*I)*c + (2*I)*d*x))^n*(2*b + d*n)) + (I*2^(-2 - n)*E^(I*(2*a - c*n) + I*(2*b - d*n)*x + I*n*(c + d*x))*(I/E^(I*(c + d*x)) - I*E^(I*(c + d*x)))^n*Hypergeometric2F1[((2*b)/d - n)/2, -n, (2 + (2*b)/d - n)/2, E^((2*I)*(c + d*x))])/((1 - E^((2*I)*c + (2*I)*d*x))^n*(2*b - d*n)) + (I*2^(-1 - n)*(I/E^(I*(c + d*x)) - I*E^(I*(c + d*x)))^n*Hypergeometric2F1[-n, -n/2, 1 - n/2, E^((2*I)*(c + d*x))])/(d*(1 - E^((2*I)*(c + d*x)))^n*n)","A",15,10,17,0.5882,1,"{4553, 2282, 1980, 2032, 365, 364, 2285, 2253, 2252, 2251}"
202,1,68,0,0.0536243,"\int \sin ^2(a+b x) \sin (c+d x) \, dx","Int[Sin[a + b*x]^2*Sin[c + d*x],x]","-\frac{\cos (2 a+x (2 b-d)-c)}{4 (2 b-d)}+\frac{\cos (2 a+x (2 b+d)+c)}{4 (2 b+d)}-\frac{\cos (c+d x)}{2 d}","-\frac{\cos (2 a+x (2 b-d)-c)}{4 (2 b-d)}+\frac{\cos (2 a+x (2 b+d)+c)}{4 (2 b+d)}-\frac{\cos (c+d x)}{2 d}",1,"-Cos[2*a - c + (2*b - d)*x]/(4*(2*b - d)) - Cos[c + d*x]/(2*d) + Cos[2*a + c + (2*b + d)*x]/(4*(2*b + d))","A",5,2,15,0.1333,1,"{4569, 2638}"
203,1,88,0,0.0650691,"\int \sin ^2(a+b x) \sin ^2(c+d x) \, dx","Int[Sin[a + b*x]^2*Sin[c + d*x]^2,x]","\frac{\sin (2 (a-c)+2 x (b-d))}{16 (b-d)}+\frac{\sin (2 (a+c)+2 x (b+d))}{16 (b+d)}-\frac{\sin (2 a+2 b x)}{8 b}-\frac{\sin (2 c+2 d x)}{8 d}+\frac{x}{4}","\frac{\sin (2 (a-c)+2 x (b-d))}{16 (b-d)}+\frac{\sin (2 (a+c)+2 x (b+d))}{16 (b+d)}-\frac{\sin (2 a+2 b x)}{8 b}-\frac{\sin (2 c+2 d x)}{8 d}+\frac{x}{4}",1,"x/4 - Sin[2*a + 2*b*x]/(8*b) + Sin[2*(a - c) + 2*(b - d)*x]/(16*(b - d)) - Sin[2*c + 2*d*x]/(8*d) + Sin[2*(a + c) + 2*(b + d)*x]/(16*(b + d))","A",6,2,17,0.1176,1,"{4569, 2637}"
204,1,144,0,0.0972936,"\int \sin ^2(a+b x) \sin ^3(c+d x) \, dx","Int[Sin[a + b*x]^2*Sin[c + d*x]^3,x]","\frac{\cos (2 a+x (2 b-3 d)-3 c)}{16 (2 b-3 d)}-\frac{3 \cos (2 a+x (2 b-d)-c)}{16 (2 b-d)}+\frac{3 \cos (2 a+x (2 b+d)+c)}{16 (2 b+d)}-\frac{\cos (2 a+x (2 b+3 d)+3 c)}{16 (2 b+3 d)}-\frac{3 \cos (c+d x)}{8 d}+\frac{\cos (3 c+3 d x)}{24 d}","\frac{\cos (2 a+x (2 b-3 d)-3 c)}{16 (2 b-3 d)}-\frac{3 \cos (2 a+x (2 b-d)-c)}{16 (2 b-d)}+\frac{3 \cos (2 a+x (2 b+d)+c)}{16 (2 b+d)}-\frac{\cos (2 a+x (2 b+3 d)+3 c)}{16 (2 b+3 d)}-\frac{3 \cos (c+d x)}{8 d}+\frac{\cos (3 c+3 d x)}{24 d}",1,"Cos[2*a - 3*c + (2*b - 3*d)*x]/(16*(2*b - 3*d)) - (3*Cos[2*a - c + (2*b - d)*x])/(16*(2*b - d)) - (3*Cos[c + d*x])/(8*d) + Cos[3*c + 3*d*x]/(24*d) + (3*Cos[2*a + c + (2*b + d)*x])/(16*(2*b + d)) - Cos[2*a + 3*c + (2*b + 3*d)*x]/(16*(2*b + 3*d))","A",8,2,17,0.1176,1,"{4569, 2638}"
205,1,600,0,1.7215882,"\int \sin ^3(a+b x) \sin ^n(c+d x) \, dx","Int[Sin[a + b*x]^3*Sin[c + d*x]^n,x]","\frac{2^{-n-3} \left(i e^{-i (c+d x)}-i e^{i (c+d x)}\right)^n \left(1-e^{2 i c+2 i d x}\right)^{-n} \, _2F_1\left(\frac{1}{2} \left(\frac{3 b}{d}-n\right),-n;\frac{1}{2} \left(\frac{3 b}{d}-n+2\right);e^{2 i (c+d x)}\right) \exp (i (3 a-c n)+i x (3 b-d n)+i n (c+d x))}{3 b-d n}-\frac{3\ 2^{-n-3} \left(i e^{-i (c+d x)}-i e^{i (c+d x)}\right)^n \left(1-e^{2 i c+2 i d x}\right)^{-n} \, _2F_1\left(-n,\frac{b-d n}{2 d};\frac{1}{2} \left(\frac{b}{d}-n+2\right);e^{2 i (c+d x)}\right) \exp (i (a-c n)+i x (b-d n)+i n (c+d x))}{b-d n}-\frac{3\ 2^{-n-3} \left(i e^{-i (c+d x)}-i e^{i (c+d x)}\right)^n \left(1-e^{2 i c+2 i d x}\right)^{-n} \, _2F_1\left(-n,-\frac{b+d n}{2 d};1-\frac{b+d n}{2 d};e^{2 i (c+d x)}\right) \exp (-i (a+c n)-i x (b+d n)+i n (c+d x))}{b+d n}+\frac{2^{-n-3} \left(i e^{-i (c+d x)}-i e^{i (c+d x)}\right)^n \left(1-e^{2 i c+2 i d x}\right)^{-n} \, _2F_1\left(-n,-\frac{3 b+d n}{2 d};\frac{1}{2} \left(-\frac{3 b}{d}-n+2\right);e^{2 i (c+d x)}\right) \exp (-i (3 a+c n)-i x (3 b+d n)+i n (c+d x))}{3 b+d n}","\frac{2^{-n-3} \left(i e^{-i (c+d x)}-i e^{i (c+d x)}\right)^n \left(1-e^{2 i c+2 i d x}\right)^{-n} \, _2F_1\left(\frac{1}{2} \left(\frac{3 b}{d}-n\right),-n;\frac{1}{2} \left(\frac{3 b}{d}-n+2\right);e^{2 i (c+d x)}\right) \exp (i (3 a-c n)+i x (3 b-d n)+i n (c+d x))}{3 b-d n}-\frac{3\ 2^{-n-3} \left(i e^{-i (c+d x)}-i e^{i (c+d x)}\right)^n \left(1-e^{2 i c+2 i d x}\right)^{-n} \, _2F_1\left(-n,\frac{b-d n}{2 d};\frac{1}{2} \left(\frac{b}{d}-n+2\right);e^{2 i (c+d x)}\right) \exp (i (a-c n)+i x (b-d n)+i n (c+d x))}{b-d n}-\frac{3\ 2^{-n-3} \left(i e^{-i (c+d x)}-i e^{i (c+d x)}\right)^n \left(1-e^{2 i c+2 i d x}\right)^{-n} \, _2F_1\left(-n,-\frac{b+d n}{2 d};1-\frac{b+d n}{2 d};e^{2 i (c+d x)}\right) \exp (-i (a+c n)-i x (b+d n)+i n (c+d x))}{b+d n}+\frac{2^{-n-3} \left(i e^{-i (c+d x)}-i e^{i (c+d x)}\right)^n \left(1-e^{2 i c+2 i d x}\right)^{-n} \, _2F_1\left(-n,-\frac{3 b+d n}{2 d};\frac{1}{2} \left(-\frac{3 b}{d}-n+2\right);e^{2 i (c+d x)}\right) \exp (-i (3 a+c n)-i x (3 b+d n)+i n (c+d x))}{3 b+d n}",1,"(2^(-3 - n)*E^(I*(3*a - c*n) + I*(3*b - d*n)*x + I*n*(c + d*x))*(I/E^(I*(c + d*x)) - I*E^(I*(c + d*x)))^n*Hypergeometric2F1[((3*b)/d - n)/2, -n, (2 + (3*b)/d - n)/2, E^((2*I)*(c + d*x))])/((1 - E^((2*I)*c + (2*I)*d*x))^n*(3*b - d*n)) - (3*2^(-3 - n)*E^(I*(a - c*n) + I*(b - d*n)*x + I*n*(c + d*x))*(I/E^(I*(c + d*x)) - I*E^(I*(c + d*x)))^n*Hypergeometric2F1[-n, (b - d*n)/(2*d), (2 + b/d - n)/2, E^((2*I)*(c + d*x))])/((1 - E^((2*I)*c + (2*I)*d*x))^n*(b - d*n)) - (3*2^(-3 - n)*E^((-I)*(a + c*n) - I*(b + d*n)*x + I*n*(c + d*x))*(I/E^(I*(c + d*x)) - I*E^(I*(c + d*x)))^n*Hypergeometric2F1[-n, -(b + d*n)/(2*d), 1 - (b + d*n)/(2*d), E^((2*I)*(c + d*x))])/((1 - E^((2*I)*c + (2*I)*d*x))^n*(b + d*n)) + (2^(-3 - n)*E^((-I)*(3*a + c*n) - I*(3*b + d*n)*x + I*n*(c + d*x))*(I/E^(I*(c + d*x)) - I*E^(I*(c + d*x)))^n*Hypergeometric2F1[-n, -(3*b + d*n)/(2*d), (2 - (3*b)/d - n)/2, E^((2*I)*(c + d*x))])/((1 - E^((2*I)*c + (2*I)*d*x))^n*(3*b + d*n))","A",18,5,17,0.2941,1,"{4553, 2285, 2253, 2252, 2251}"
206,1,97,0,0.074767,"\int \sin ^3(a+b x) \sin (c+d x) \, dx","Int[Sin[a + b*x]^3*Sin[c + d*x],x]","\frac{3 \sin (a+x (b-d)-c)}{8 (b-d)}-\frac{\sin (3 a+x (3 b-d)-c)}{8 (3 b-d)}-\frac{3 \sin (a+x (b+d)+c)}{8 (b+d)}+\frac{\sin (3 a+x (3 b+d)+c)}{8 (3 b+d)}","\frac{3 \sin (a+x (b-d)-c)}{8 (b-d)}-\frac{\sin (3 a+x (3 b-d)-c)}{8 (3 b-d)}-\frac{3 \sin (a+x (b+d)+c)}{8 (b+d)}+\frac{\sin (3 a+x (3 b+d)+c)}{8 (3 b+d)}",1,"(3*Sin[a - c + (b - d)*x])/(8*(b - d)) - Sin[3*a - c + (3*b - d)*x]/(8*(3*b - d)) - (3*Sin[a + c + (b + d)*x])/(8*(b + d)) + Sin[3*a + c + (3*b + d)*x]/(8*(3*b + d))","A",6,2,15,0.1333,1,"{4569, 2637}"
207,1,138,0,0.0984789,"\int \sin ^3(a+b x) \sin ^2(c+d x) \, dx","Int[Sin[a + b*x]^3*Sin[c + d*x]^2,x]","\frac{3 \cos (a+x (b-2 d)-2 c)}{16 (b-2 d)}-\frac{\cos (3 a+x (3 b-2 d)-2 c)}{16 (3 b-2 d)}+\frac{3 \cos (a+x (b+2 d)+2 c)}{16 (b+2 d)}-\frac{\cos (3 a+x (3 b+2 d)+2 c)}{16 (3 b+2 d)}-\frac{3 \cos (a+b x)}{8 b}+\frac{\cos (3 a+3 b x)}{24 b}","\frac{3 \cos (a+x (b-2 d)-2 c)}{16 (b-2 d)}-\frac{\cos (3 a+x (3 b-2 d)-2 c)}{16 (3 b-2 d)}+\frac{3 \cos (a+x (b+2 d)+2 c)}{16 (b+2 d)}-\frac{\cos (3 a+x (3 b+2 d)+2 c)}{16 (3 b+2 d)}-\frac{3 \cos (a+b x)}{8 b}+\frac{\cos (3 a+3 b x)}{24 b}",1,"(-3*Cos[a + b*x])/(8*b) + Cos[3*a + 3*b*x]/(24*b) + (3*Cos[a - 2*c + (b - 2*d)*x])/(16*(b - 2*d)) - Cos[3*a - 2*c + (3*b - 2*d)*x]/(16*(3*b - 2*d)) + (3*Cos[a + 2*c + (b + 2*d)*x])/(16*(b + 2*d)) - Cos[3*a + 2*c + (3*b + 2*d)*x]/(16*(3*b + 2*d))","A",8,2,17,0.1176,1,"{4569, 2638}"
208,1,195,0,0.1318912,"\int \sin ^3(a+b x) \sin ^3(c+d x) \, dx","Int[Sin[a + b*x]^3*Sin[c + d*x]^3,x]","-\frac{3 \sin (a+x (b-3 d)-3 c)}{32 (b-3 d)}+\frac{9 \sin (a+x (b-d)-c)}{32 (b-d)}+\frac{\sin (3 (a-c)+3 x (b-d))}{96 (b-d)}-\frac{3 \sin (3 a+x (3 b-d)-c)}{32 (3 b-d)}-\frac{9 \sin (a+x (b+d)+c)}{32 (b+d)}-\frac{\sin (3 (a+c)+3 x (b+d))}{96 (b+d)}+\frac{3 \sin (3 a+x (3 b+d)+c)}{32 (3 b+d)}+\frac{3 \sin (a+x (b+3 d)+3 c)}{32 (b+3 d)}","-\frac{3 \sin (a+x (b-3 d)-3 c)}{32 (b-3 d)}+\frac{9 \sin (a+x (b-d)-c)}{32 (b-d)}+\frac{\sin (3 (a-c)+3 x (b-d))}{96 (b-d)}-\frac{3 \sin (3 a+x (3 b-d)-c)}{32 (3 b-d)}-\frac{9 \sin (a+x (b+d)+c)}{32 (b+d)}-\frac{\sin (3 (a+c)+3 x (b+d))}{96 (b+d)}+\frac{3 \sin (3 a+x (3 b+d)+c)}{32 (3 b+d)}+\frac{3 \sin (a+x (b+3 d)+3 c)}{32 (b+3 d)}",1,"(-3*Sin[a - 3*c + (b - 3*d)*x])/(32*(b - 3*d)) + (9*Sin[a - c + (b - d)*x])/(32*(b - d)) + Sin[3*(a - c) + 3*(b - d)*x]/(96*(b - d)) - (3*Sin[3*a - c + (3*b - d)*x])/(32*(3*b - d)) - (9*Sin[a + c + (b + d)*x])/(32*(b + d)) - Sin[3*(a + c) + 3*(b + d)*x]/(96*(b + d)) + (3*Sin[3*a + c + (3*b + d)*x])/(32*(3*b + d)) + (3*Sin[a + 3*c + (b + 3*d)*x])/(32*(b + 3*d))","A",10,2,17,0.1176,1,"{4569, 2637}"
209,1,277,0,0.5886792,"\int \cos ^n(c+d x) \sin (a+b x) \, dx","Int[Cos[c + d*x]^n*Sin[a + b*x],x]","-\frac{2^{-n-1} \left(e^{-i (c+d x)}+e^{i (c+d x)}\right)^n \left(1+e^{2 i c+2 i d x}\right)^{-n} \, _2F_1\left(-n,\frac{b-d n}{2 d};\frac{1}{2} \left(\frac{b}{d}-n+2\right);-e^{2 i (c+d x)}\right) \exp (i (a-c n)+i x (b-d n)+i n (c+d x))}{b-d n}-\frac{2^{-n-1} \left(e^{-i (c+d x)}+e^{i (c+d x)}\right)^n \left(1+e^{2 i c+2 i d x}\right)^{-n} \, _2F_1\left(-n,-\frac{b+d n}{2 d};1-\frac{b+d n}{2 d};-e^{2 i (c+d x)}\right) \exp (-i (a+c n)-i x (b+d n)+i n (c+d x))}{b+d n}","-\frac{2^{-n-1} \left(e^{-i (c+d x)}+e^{i (c+d x)}\right)^n \left(1+e^{2 i c+2 i d x}\right)^{-n} \, _2F_1\left(-n,\frac{b-d n}{2 d};\frac{1}{2} \left(\frac{b}{d}-n+2\right);-e^{2 i (c+d x)}\right) \exp (i (a-c n)+i x (b-d n)+i n (c+d x))}{b-d n}-\frac{2^{-n-1} \left(e^{-i (c+d x)}+e^{i (c+d x)}\right)^n \left(1+e^{2 i c+2 i d x}\right)^{-n} \, _2F_1\left(-n,-\frac{b+d n}{2 d};1-\frac{b+d n}{2 d};-e^{2 i (c+d x)}\right) \exp (-i (a+c n)-i x (b+d n)+i n (c+d x))}{b+d n}",1,"-((2^(-1 - n)*E^(I*(a - c*n) + I*(b - d*n)*x + I*n*(c + d*x))*(E^((-I)*(c + d*x)) + E^(I*(c + d*x)))^n*Hypergeometric2F1[-n, (b - d*n)/(2*d), (2 + b/d - n)/2, -E^((2*I)*(c + d*x))])/((1 + E^((2*I)*c + (2*I)*d*x))^n*(b - d*n))) - (2^(-1 - n)*E^((-I)*(a + c*n) - I*(b + d*n)*x + I*n*(c + d*x))*(E^((-I)*(c + d*x)) + E^(I*(c + d*x)))^n*Hypergeometric2F1[-n, -(b + d*n)/(2*d), 1 - (b + d*n)/(2*d), -E^((2*I)*(c + d*x))])/((1 + E^((2*I)*c + (2*I)*d*x))^n*(b + d*n))","A",8,4,15,0.2667,1,"{4555, 2285, 2253, 2251}"
210,1,91,0,0.0662915,"\int \cos ^3(c+d x) \sin (a+b x) \, dx","Int[Cos[c + d*x]^3*Sin[a + b*x],x]","-\frac{\cos (a+x (b-3 d)-3 c)}{8 (b-3 d)}-\frac{3 \cos (a+x (b-d)-c)}{8 (b-d)}-\frac{3 \cos (a+x (b+d)+c)}{8 (b+d)}-\frac{\cos (a+x (b+3 d)+3 c)}{8 (b+3 d)}","-\frac{\cos (a+x (b-3 d)-3 c)}{8 (b-3 d)}-\frac{3 \cos (a+x (b-d)-c)}{8 (b-d)}-\frac{3 \cos (a+x (b+d)+c)}{8 (b+d)}-\frac{\cos (a+x (b+3 d)+3 c)}{8 (b+3 d)}",1,"-Cos[a - 3*c + (b - 3*d)*x]/(8*(b - 3*d)) - (3*Cos[a - c + (b - d)*x])/(8*(b - d)) - (3*Cos[a + c + (b + d)*x])/(8*(b + d)) - Cos[a + 3*c + (b + 3*d)*x]/(8*(b + 3*d))","A",6,2,15,0.1333,1,"{4574, 2638}"
211,1,62,0,0.0469182,"\int \cos ^2(c+d x) \sin (a+b x) \, dx","Int[Cos[c + d*x]^2*Sin[a + b*x],x]","-\frac{\cos (a+x (b-2 d)-2 c)}{4 (b-2 d)}-\frac{\cos (a+x (b+2 d)+2 c)}{4 (b+2 d)}-\frac{\cos (a+b x)}{2 b}","-\frac{\cos (a+x (b-2 d)-2 c)}{4 (b-2 d)}-\frac{\cos (a+x (b+2 d)+2 c)}{4 (b+2 d)}-\frac{\cos (a+b x)}{2 b}",1,"-Cos[a + b*x]/(2*b) - Cos[a - 2*c + (b - 2*d)*x]/(4*(b - 2*d)) - Cos[a + 2*c + (b + 2*d)*x]/(4*(b + 2*d))","A",5,2,15,0.1333,1,"{4574, 2638}"
212,1,43,0,0.0357136,"\int \cos (c+d x) \sin (a+b x) \, dx","Int[Cos[c + d*x]*Sin[a + b*x],x]","-\frac{\cos (a+x (b-d)-c)}{2 (b-d)}-\frac{\cos (a+x (b+d)+c)}{2 (b+d)}","-\frac{\cos (a+x (b-d)-c)}{2 (b-d)}-\frac{\cos (a+x (b+d)+c)}{2 (b+d)}",1,"-Cos[a - c + (b - d)*x]/(2*(b - d)) - Cos[a + c + (b + d)*x]/(2*(b + d))","A",4,2,13,0.1538,1,"{4574, 2638}"
213,1,27,0,0.0175518,"\int \sec (c+b x) \sin (a+b x) \, dx","Int[Sec[c + b*x]*Sin[a + b*x],x]","x \sin (a-c)-\frac{\cos (a-c) \log (\cos (b x+c))}{b}","x \sin (a-c)-\frac{\cos (a-c) \log (\cos (b x+c))}{b}",1,"-((Cos[a - c]*Log[Cos[c + b*x]])/b) + x*Sin[a - c]","A",3,3,13,0.2308,1,"{4580, 3475, 8}"
214,1,34,0,0.0268219,"\int \sec ^2(c+b x) \sin (a+b x) \, dx","Int[Sec[c + b*x]^2*Sin[a + b*x],x]","\frac{\sin (a-c) \tanh ^{-1}(\sin (b x+c))}{b}+\frac{\cos (a-c) \sec (b x+c)}{b}","\frac{\sin (a-c) \tanh ^{-1}(\sin (b x+c))}{b}+\frac{\cos (a-c) \sec (b x+c)}{b}",1,"(Cos[a - c]*Sec[c + b*x])/b + (ArcTanh[Sin[c + b*x]]*Sin[a - c])/b","A",4,4,15,0.2667,1,"{4580, 2606, 8, 3770}"
215,1,38,0,0.0367189,"\int \sec ^3(c+b x) \sin (a+b x) \, dx","Int[Sec[c + b*x]^3*Sin[a + b*x],x]","\frac{\sin (a-c) \tan (b x+c)}{b}+\frac{\cos (a-c) \sec ^2(b x+c)}{2 b}","\frac{\sin (a-c) \tan (b x+c)}{b}+\frac{\cos (a-c) \sec ^2(b x+c)}{2 b}",1,"(Cos[a - c]*Sec[c + b*x]^2)/(2*b) + (Sin[a - c]*Tan[c + b*x])/b","A",5,5,15,0.3333,1,"{4580, 2606, 30, 3767, 8}"
216,1,67,0,0.0417556,"\int \sec ^4(c+b x) \sin (a+b x) \, dx","Int[Sec[c + b*x]^4*Sin[a + b*x],x]","\frac{\sin (a-c) \tanh ^{-1}(\sin (b x+c))}{2 b}+\frac{\cos (a-c) \sec ^3(b x+c)}{3 b}+\frac{\sin (a-c) \tan (b x+c) \sec (b x+c)}{2 b}","\frac{\sin (a-c) \tanh ^{-1}(\sin (b x+c))}{2 b}+\frac{\cos (a-c) \sec ^3(b x+c)}{3 b}+\frac{\sin (a-c) \tan (b x+c) \sec (b x+c)}{2 b}",1,"(Cos[a - c]*Sec[c + b*x]^3)/(3*b) + (ArcTanh[Sin[c + b*x]]*Sin[a - c])/(2*b) + (Sec[c + b*x]*Sin[a - c]*Tan[c + b*x])/(2*b)","A",5,5,15,0.3333,1,"{4580, 2606, 30, 3768, 3770}"
217,1,59,0,0.0513425,"\int \sec ^5(c+b x) \sin (a+b x) \, dx","Int[Sec[c + b*x]^5*Sin[a + b*x],x]","\frac{\sin (a-c) \tan ^3(b x+c)}{3 b}+\frac{\sin (a-c) \tan (b x+c)}{b}+\frac{\cos (a-c) \sec ^4(b x+c)}{4 b}","\frac{\sin (a-c) \tan ^3(b x+c)}{3 b}+\frac{\sin (a-c) \tan (b x+c)}{b}+\frac{\cos (a-c) \sec ^4(b x+c)}{4 b}",1,"(Cos[a - c]*Sec[c + b*x]^4)/(4*b) + (Sin[a - c]*Tan[c + b*x])/b + (Sin[a - c]*Tan[c + b*x]^3)/(3*b)","A",5,4,15,0.2667,1,"{4580, 2606, 30, 3767}"
218,1,94,0,0.0703124,"\int \sec ^6(c+b x) \sin (a+b x) \, dx","Int[Sec[c + b*x]^6*Sin[a + b*x],x]","\frac{3 \sin (a-c) \tanh ^{-1}(\sin (b x+c))}{8 b}+\frac{\cos (a-c) \sec ^5(b x+c)}{5 b}+\frac{\sin (a-c) \tan (b x+c) \sec ^3(b x+c)}{4 b}+\frac{3 \sin (a-c) \tan (b x+c) \sec (b x+c)}{8 b}","\frac{3 \sin (a-c) \tanh ^{-1}(\sin (b x+c))}{8 b}+\frac{\cos (a-c) \sec ^5(b x+c)}{5 b}+\frac{\sin (a-c) \tan (b x+c) \sec ^3(b x+c)}{4 b}+\frac{3 \sin (a-c) \tan (b x+c) \sec (b x+c)}{8 b}",1,"(Cos[a - c]*Sec[c + b*x]^5)/(5*b) + (3*ArcTanh[Sin[c + b*x]]*Sin[a - c])/(8*b) + (3*Sec[c + b*x]*Sin[a - c]*Tan[c + b*x])/(8*b) + (Sec[c + b*x]^3*Sin[a - c]*Tan[c + b*x])/(4*b)","A",6,5,15,0.3333,1,"{4580, 2606, 30, 3768, 3770}"
219,1,386,0,0.7001746,"\int \cos ^n(c+d x) \sin ^2(a+b x) \, dx","Int[Cos[c + d*x]^n*Sin[a + b*x]^2,x]","-\frac{i 2^{-n-2} \left(e^{-i (c+d x)}+e^{i (c+d x)}\right)^n \left(1+e^{2 i c+2 i d x}\right)^{-n} \, _2F_1\left(\frac{1}{2} \left(-\frac{2 b}{d}-n\right),-n;\frac{1}{2} \left(-\frac{2 b}{d}-n+2\right);-e^{2 i (c+d x)}\right) \exp (-i (2 a+c n)-i x (2 b+d n)+i n (c+d x))}{2 b+d n}+\frac{i 2^{-n-2} \left(e^{-i (c+d x)}+e^{i (c+d x)}\right)^n \left(1+e^{2 i c+2 i d x}\right)^{-n} \, _2F_1\left(\frac{1}{2} \left(\frac{2 b}{d}-n\right),-n;\frac{1}{2} \left(\frac{2 b}{d}-n+2\right);-e^{2 i (c+d x)}\right) \exp (i (2 a-c n)+i x (2 b-d n)+i n (c+d x))}{2 b-d n}+\frac{i 2^{-n-1} \left(e^{-i (c+d x)}+e^{i (c+d x)}\right)^n \left(1+e^{2 i (c+d x)}\right)^{-n} \, _2F_1\left(-n,-\frac{n}{2};1-\frac{n}{2};-e^{2 i (c+d x)}\right)}{d n}","-\frac{i 2^{-n-2} \left(e^{-i (c+d x)}+e^{i (c+d x)}\right)^n \left(1+e^{2 i c+2 i d x}\right)^{-n} \, _2F_1\left(\frac{1}{2} \left(-\frac{2 b}{d}-n\right),-n;\frac{1}{2} \left(-\frac{2 b}{d}-n+2\right);-e^{2 i (c+d x)}\right) \exp (-i (2 a+c n)-i x (2 b+d n)+i n (c+d x))}{2 b+d n}+\frac{i 2^{-n-2} \left(e^{-i (c+d x)}+e^{i (c+d x)}\right)^n \left(1+e^{2 i c+2 i d x}\right)^{-n} \, _2F_1\left(\frac{1}{2} \left(\frac{2 b}{d}-n\right),-n;\frac{1}{2} \left(\frac{2 b}{d}-n+2\right);-e^{2 i (c+d x)}\right) \exp (i (2 a-c n)+i x (2 b-d n)+i n (c+d x))}{2 b-d n}+\frac{i 2^{-n-1} \left(e^{-i (c+d x)}+e^{i (c+d x)}\right)^n \left(1+e^{2 i (c+d x)}\right)^{-n} \, _2F_1\left(-n,-\frac{n}{2};1-\frac{n}{2};-e^{2 i (c+d x)}\right)}{d n}",1,"((-I)*2^(-2 - n)*E^((-I)*(2*a + c*n) - I*(2*b + d*n)*x + I*n*(c + d*x))*(E^((-I)*(c + d*x)) + E^(I*(c + d*x)))^n*Hypergeometric2F1[((-2*b)/d - n)/2, -n, (2 - (2*b)/d - n)/2, -E^((2*I)*(c + d*x))])/((1 + E^((2*I)*c + (2*I)*d*x))^n*(2*b + d*n)) + (I*2^(-2 - n)*E^(I*(2*a - c*n) + I*(2*b - d*n)*x + I*n*(c + d*x))*(E^((-I)*(c + d*x)) + E^(I*(c + d*x)))^n*Hypergeometric2F1[((2*b)/d - n)/2, -n, (2 + (2*b)/d - n)/2, -E^((2*I)*(c + d*x))])/((1 + E^((2*I)*c + (2*I)*d*x))^n*(2*b - d*n)) + (I*2^(-1 - n)*(E^((-I)*(c + d*x)) + E^(I*(c + d*x)))^n*Hypergeometric2F1[-n, -n/2, 1 - n/2, -E^((2*I)*(c + d*x))])/(d*(1 + E^((2*I)*(c + d*x)))^n*n)","A",11,7,17,0.4118,1,"{4555, 2282, 2032, 364, 2285, 2253, 2251}"
220,1,68,0,0.0510584,"\int \cos (c+d x) \sin ^2(a+b x) \, dx","Int[Cos[c + d*x]*Sin[a + b*x]^2,x]","-\frac{\sin (2 a+x (2 b-d)-c)}{4 (2 b-d)}-\frac{\sin (2 a+x (2 b+d)+c)}{4 (2 b+d)}+\frac{\sin (c+d x)}{2 d}","-\frac{\sin (2 a+x (2 b-d)-c)}{4 (2 b-d)}-\frac{\sin (2 a+x (2 b+d)+c)}{4 (2 b+d)}+\frac{\sin (c+d x)}{2 d}",1,"-Sin[2*a - c + (2*b - d)*x]/(4*(2*b - d)) + Sin[c + d*x]/(2*d) - Sin[2*a + c + (2*b + d)*x]/(4*(2*b + d))","A",5,2,15,0.1333,1,"{4574, 2637}"
221,1,88,0,0.067894,"\int \cos ^2(c+d x) \sin ^2(a+b x) \, dx","Int[Cos[c + d*x]^2*Sin[a + b*x]^2,x]","-\frac{\sin (2 (a-c)+2 x (b-d))}{16 (b-d)}-\frac{\sin (2 (a+c)+2 x (b+d))}{16 (b+d)}-\frac{\sin (2 a+2 b x)}{8 b}+\frac{\sin (2 c+2 d x)}{8 d}+\frac{x}{4}","-\frac{\sin (2 (a-c)+2 x (b-d))}{16 (b-d)}-\frac{\sin (2 (a+c)+2 x (b+d))}{16 (b+d)}-\frac{\sin (2 a+2 b x)}{8 b}+\frac{\sin (2 c+2 d x)}{8 d}+\frac{x}{4}",1,"x/4 - Sin[2*a + 2*b*x]/(8*b) - Sin[2*(a - c) + 2*(b - d)*x]/(16*(b - d)) + Sin[2*c + 2*d*x]/(8*d) - Sin[2*(a + c) + 2*(b + d)*x]/(16*(b + d))","A",6,2,17,0.1176,1,"{4574, 2637}"
222,1,144,0,0.0957972,"\int \cos ^3(c+d x) \sin ^2(a+b x) \, dx","Int[Cos[c + d*x]^3*Sin[a + b*x]^2,x]","-\frac{\sin (2 a+x (2 b-3 d)-3 c)}{16 (2 b-3 d)}-\frac{3 \sin (2 a+x (2 b-d)-c)}{16 (2 b-d)}-\frac{3 \sin (2 a+x (2 b+d)+c)}{16 (2 b+d)}-\frac{\sin (2 a+x (2 b+3 d)+3 c)}{16 (2 b+3 d)}+\frac{3 \sin (c+d x)}{8 d}+\frac{\sin (3 c+3 d x)}{24 d}","-\frac{\sin (2 a+x (2 b-3 d)-3 c)}{16 (2 b-3 d)}-\frac{3 \sin (2 a+x (2 b-d)-c)}{16 (2 b-d)}-\frac{3 \sin (2 a+x (2 b+d)+c)}{16 (2 b+d)}-\frac{\sin (2 a+x (2 b+3 d)+3 c)}{16 (2 b+3 d)}+\frac{3 \sin (c+d x)}{8 d}+\frac{\sin (3 c+3 d x)}{24 d}",1,"-Sin[2*a - 3*c + (2*b - 3*d)*x]/(16*(2*b - 3*d)) - (3*Sin[2*a - c + (2*b - d)*x])/(16*(2*b - d)) + (3*Sin[c + d*x])/(8*d) + Sin[3*c + 3*d*x]/(24*d) - (3*Sin[2*a + c + (2*b + d)*x])/(16*(2*b + d)) - Sin[2*a + 3*c + (2*b + 3*d)*x]/(16*(2*b + 3*d))","A",8,2,17,0.1176,1,"{4574, 2637}"
223,1,568,0,1.1803597,"\int \cos ^n(c+d x) \sin ^3(a+b x) \, dx","Int[Cos[c + d*x]^n*Sin[a + b*x]^3,x]","\frac{2^{-n-3} \left(e^{-i (c+d x)}+e^{i (c+d x)}\right)^n \left(1+e^{2 i c+2 i d x}\right)^{-n} \, _2F_1\left(\frac{1}{2} \left(\frac{3 b}{d}-n\right),-n;\frac{1}{2} \left(\frac{3 b}{d}-n+2\right);-e^{2 i (c+d x)}\right) \exp (i (3 a-c n)+i x (3 b-d n)+i n (c+d x))}{3 b-d n}-\frac{3\ 2^{-n-3} \left(e^{-i (c+d x)}+e^{i (c+d x)}\right)^n \left(1+e^{2 i c+2 i d x}\right)^{-n} \, _2F_1\left(-n,\frac{b-d n}{2 d};\frac{1}{2} \left(\frac{b}{d}-n+2\right);-e^{2 i (c+d x)}\right) \exp (i (a-c n)+i x (b-d n)+i n (c+d x))}{b-d n}-\frac{3\ 2^{-n-3} \left(e^{-i (c+d x)}+e^{i (c+d x)}\right)^n \left(1+e^{2 i c+2 i d x}\right)^{-n} \, _2F_1\left(-n,-\frac{b+d n}{2 d};1-\frac{b+d n}{2 d};-e^{2 i (c+d x)}\right) \exp (-i (a+c n)-i x (b+d n)+i n (c+d x))}{b+d n}+\frac{2^{-n-3} \left(e^{-i (c+d x)}+e^{i (c+d x)}\right)^n \left(1+e^{2 i c+2 i d x}\right)^{-n} \, _2F_1\left(-n,-\frac{3 b+d n}{2 d};\frac{1}{2} \left(-\frac{3 b}{d}-n+2\right);-e^{2 i (c+d x)}\right) \exp (-i (3 a+c n)-i x (3 b+d n)+i n (c+d x))}{3 b+d n}","\frac{2^{-n-3} \left(e^{-i (c+d x)}+e^{i (c+d x)}\right)^n \left(1+e^{2 i c+2 i d x}\right)^{-n} \, _2F_1\left(\frac{1}{2} \left(\frac{3 b}{d}-n\right),-n;\frac{1}{2} \left(\frac{3 b}{d}-n+2\right);-e^{2 i (c+d x)}\right) \exp (i (3 a-c n)+i x (3 b-d n)+i n (c+d x))}{3 b-d n}-\frac{3\ 2^{-n-3} \left(e^{-i (c+d x)}+e^{i (c+d x)}\right)^n \left(1+e^{2 i c+2 i d x}\right)^{-n} \, _2F_1\left(-n,\frac{b-d n}{2 d};\frac{1}{2} \left(\frac{b}{d}-n+2\right);-e^{2 i (c+d x)}\right) \exp (i (a-c n)+i x (b-d n)+i n (c+d x))}{b-d n}-\frac{3\ 2^{-n-3} \left(e^{-i (c+d x)}+e^{i (c+d x)}\right)^n \left(1+e^{2 i c+2 i d x}\right)^{-n} \, _2F_1\left(-n,-\frac{b+d n}{2 d};1-\frac{b+d n}{2 d};-e^{2 i (c+d x)}\right) \exp (-i (a+c n)-i x (b+d n)+i n (c+d x))}{b+d n}+\frac{2^{-n-3} \left(e^{-i (c+d x)}+e^{i (c+d x)}\right)^n \left(1+e^{2 i c+2 i d x}\right)^{-n} \, _2F_1\left(-n,-\frac{3 b+d n}{2 d};\frac{1}{2} \left(-\frac{3 b}{d}-n+2\right);-e^{2 i (c+d x)}\right) \exp (-i (3 a+c n)-i x (3 b+d n)+i n (c+d x))}{3 b+d n}",1,"(2^(-3 - n)*E^(I*(3*a - c*n) + I*(3*b - d*n)*x + I*n*(c + d*x))*(E^((-I)*(c + d*x)) + E^(I*(c + d*x)))^n*Hypergeometric2F1[((3*b)/d - n)/2, -n, (2 + (3*b)/d - n)/2, -E^((2*I)*(c + d*x))])/((1 + E^((2*I)*c + (2*I)*d*x))^n*(3*b - d*n)) - (3*2^(-3 - n)*E^(I*(a - c*n) + I*(b - d*n)*x + I*n*(c + d*x))*(E^((-I)*(c + d*x)) + E^(I*(c + d*x)))^n*Hypergeometric2F1[-n, (b - d*n)/(2*d), (2 + b/d - n)/2, -E^((2*I)*(c + d*x))])/((1 + E^((2*I)*c + (2*I)*d*x))^n*(b - d*n)) - (3*2^(-3 - n)*E^((-I)*(a + c*n) - I*(b + d*n)*x + I*n*(c + d*x))*(E^((-I)*(c + d*x)) + E^(I*(c + d*x)))^n*Hypergeometric2F1[-n, -(b + d*n)/(2*d), 1 - (b + d*n)/(2*d), -E^((2*I)*(c + d*x))])/((1 + E^((2*I)*c + (2*I)*d*x))^n*(b + d*n)) + (2^(-3 - n)*E^((-I)*(3*a + c*n) - I*(3*b + d*n)*x + I*n*(c + d*x))*(E^((-I)*(c + d*x)) + E^(I*(c + d*x)))^n*Hypergeometric2F1[-n, -(3*b + d*n)/(2*d), (2 - (3*b)/d - n)/2, -E^((2*I)*(c + d*x))])/((1 + E^((2*I)*c + (2*I)*d*x))^n*(3*b + d*n))","A",14,4,17,0.2353,1,"{4555, 2285, 2253, 2251}"
224,1,97,0,0.0682744,"\int \cos (c+d x) \sin ^3(a+b x) \, dx","Int[Cos[c + d*x]*Sin[a + b*x]^3,x]","-\frac{3 \cos (a+x (b-d)-c)}{8 (b-d)}+\frac{\cos (3 a+x (3 b-d)-c)}{8 (3 b-d)}-\frac{3 \cos (a+x (b+d)+c)}{8 (b+d)}+\frac{\cos (3 a+x (3 b+d)+c)}{8 (3 b+d)}","-\frac{3 \cos (a+x (b-d)-c)}{8 (b-d)}+\frac{\cos (3 a+x (3 b-d)-c)}{8 (3 b-d)}-\frac{3 \cos (a+x (b+d)+c)}{8 (b+d)}+\frac{\cos (3 a+x (3 b+d)+c)}{8 (3 b+d)}",1,"(-3*Cos[a - c + (b - d)*x])/(8*(b - d)) + Cos[3*a - c + (3*b - d)*x]/(8*(3*b - d)) - (3*Cos[a + c + (b + d)*x])/(8*(b + d)) + Cos[3*a + c + (3*b + d)*x]/(8*(3*b + d))","A",6,2,15,0.1333,1,"{4574, 2638}"
225,1,138,0,0.095632,"\int \cos ^2(c+d x) \sin ^3(a+b x) \, dx","Int[Cos[c + d*x]^2*Sin[a + b*x]^3,x]","-\frac{3 \cos (a+x (b-2 d)-2 c)}{16 (b-2 d)}+\frac{\cos (3 a+x (3 b-2 d)-2 c)}{16 (3 b-2 d)}-\frac{3 \cos (a+x (b+2 d)+2 c)}{16 (b+2 d)}+\frac{\cos (3 a+x (3 b+2 d)+2 c)}{16 (3 b+2 d)}-\frac{3 \cos (a+b x)}{8 b}+\frac{\cos (3 a+3 b x)}{24 b}","-\frac{3 \cos (a+x (b-2 d)-2 c)}{16 (b-2 d)}+\frac{\cos (3 a+x (3 b-2 d)-2 c)}{16 (3 b-2 d)}-\frac{3 \cos (a+x (b+2 d)+2 c)}{16 (b+2 d)}+\frac{\cos (3 a+x (3 b+2 d)+2 c)}{16 (3 b+2 d)}-\frac{3 \cos (a+b x)}{8 b}+\frac{\cos (3 a+3 b x)}{24 b}",1,"(-3*Cos[a + b*x])/(8*b) + Cos[3*a + 3*b*x]/(24*b) - (3*Cos[a - 2*c + (b - 2*d)*x])/(16*(b - 2*d)) + Cos[3*a - 2*c + (3*b - 2*d)*x]/(16*(3*b - 2*d)) - (3*Cos[a + 2*c + (b + 2*d)*x])/(16*(b + 2*d)) + Cos[3*a + 2*c + (3*b + 2*d)*x]/(16*(3*b + 2*d))","A",8,2,17,0.1176,1,"{4574, 2638}"
226,1,195,0,0.1242175,"\int \cos ^3(c+d x) \sin ^3(a+b x) \, dx","Int[Cos[c + d*x]^3*Sin[a + b*x]^3,x]","-\frac{3 \cos (a+x (b-3 d)-3 c)}{32 (b-3 d)}-\frac{9 \cos (a+x (b-d)-c)}{32 (b-d)}+\frac{\cos (3 (a-c)+3 x (b-d))}{96 (b-d)}+\frac{3 \cos (3 a+x (3 b-d)-c)}{32 (3 b-d)}-\frac{9 \cos (a+x (b+d)+c)}{32 (b+d)}+\frac{\cos (3 (a+c)+3 x (b+d))}{96 (b+d)}+\frac{3 \cos (3 a+x (3 b+d)+c)}{32 (3 b+d)}-\frac{3 \cos (a+x (b+3 d)+3 c)}{32 (b+3 d)}","-\frac{3 \cos (a+x (b-3 d)-3 c)}{32 (b-3 d)}-\frac{9 \cos (a+x (b-d)-c)}{32 (b-d)}+\frac{\cos (3 (a-c)+3 x (b-d))}{96 (b-d)}+\frac{3 \cos (3 a+x (3 b-d)-c)}{32 (3 b-d)}-\frac{9 \cos (a+x (b+d)+c)}{32 (b+d)}+\frac{\cos (3 (a+c)+3 x (b+d))}{96 (b+d)}+\frac{3 \cos (3 a+x (3 b+d)+c)}{32 (3 b+d)}-\frac{3 \cos (a+x (b+3 d)+3 c)}{32 (b+3 d)}",1,"(-3*Cos[a - 3*c + (b - 3*d)*x])/(32*(b - 3*d)) - (9*Cos[a - c + (b - d)*x])/(32*(b - d)) + Cos[3*(a - c) + 3*(b - d)*x]/(96*(b - d)) + (3*Cos[3*a - c + (3*b - d)*x])/(32*(3*b - d)) - (9*Cos[a + c + (b + d)*x])/(32*(b + d)) + Cos[3*(a + c) + 3*(b + d)*x]/(96*(b + d)) + (3*Cos[3*a + c + (3*b + d)*x])/(32*(3*b + d)) - (3*Cos[a + 3*c + (b + 3*d)*x])/(32*(b + 3*d))","A",10,2,17,0.1176,1,"{4574, 2638}"
227,1,27,0,0.0168558,"\int \cos (a+b x) \csc (c+b x) \, dx","Int[Cos[a + b*x]*Csc[c + b*x],x]","\frac{\cos (a-c) \log (\sin (b x+c))}{b}-x \sin (a-c)","\frac{\cos (a-c) \log (\sin (b x+c))}{b}-x \sin (a-c)",1,"(Cos[a - c]*Log[Sin[c + b*x]])/b - x*Sin[a - c]","A",3,3,13,0.2308,1,"{4581, 3475, 8}"
228,1,35,0,0.028113,"\int \cos (a+b x) \csc ^2(c+b x) \, dx","Int[Cos[a + b*x]*Csc[c + b*x]^2,x]","\frac{\sin (a-c) \tanh ^{-1}(\cos (b x+c))}{b}-\frac{\cos (a-c) \csc (b x+c)}{b}","\frac{\sin (a-c) \tanh ^{-1}(\cos (b x+c))}{b}-\frac{\cos (a-c) \csc (b x+c)}{b}",1,"-((Cos[a - c]*Csc[c + b*x])/b) + (ArcTanh[Cos[c + b*x]]*Sin[a - c])/b","A",4,4,15,0.2667,1,"{4581, 2606, 8, 3770}"
229,1,38,0,0.0425368,"\int \cos (a+b x) \csc ^3(c+b x) \, dx","Int[Cos[a + b*x]*Csc[c + b*x]^3,x]","\frac{\sin (a-c) \cot (b x+c)}{b}-\frac{\cos (a-c) \csc ^2(b x+c)}{2 b}","\frac{\sin (a-c) \cot (b x+c)}{b}-\frac{\cos (a-c) \csc ^2(b x+c)}{2 b}",1,"-(Cos[a - c]*Csc[c + b*x]^2)/(2*b) + (Cot[c + b*x]*Sin[a - c])/b","A",5,5,15,0.3333,1,"{4581, 2606, 30, 3767, 8}"
230,1,72,0,0.0707118,"\int \sin (a+b x) \tan ^3(c+b x) \, dx","Int[Sin[a + b*x]*Tan[c + b*x]^3,x]","\frac{\sin (a-c) \sec (b x+c)}{b}-\frac{3 \cos (a-c) \tanh ^{-1}(\sin (b x+c))}{2 b}+\frac{\cos (a-c) \tan (b x+c) \sec (b x+c)}{2 b}+\frac{\sin (a+b x)}{b}","\frac{\sin (a-c) \sec (b x+c)}{b}-\frac{3 \cos (a-c) \tanh ^{-1}(\sin (b x+c))}{2 b}+\frac{\cos (a-c) \tan (b x+c) \sec (b x+c)}{2 b}+\frac{\sin (a+b x)}{b}",1,"(-3*ArcTanh[Sin[c + b*x]]*Cos[a - c])/(2*b) + (Sec[c + b*x]*Sin[a - c])/b + Sin[a + b*x]/b + (Cos[a - c]*Sec[c + b*x]*Tan[c + b*x])/(2*b)","A",9,7,15,0.4667,1,"{4576, 4579, 2637, 3770, 2606, 8, 2611}"
231,1,44,0,0.035963,"\int \sin (a+b x) \tan ^2(c+b x) \, dx","Int[Sin[a + b*x]*Tan[c + b*x]^2,x]","\frac{\sin (a-c) \tanh ^{-1}(\sin (b x+c))}{b}+\frac{\cos (a-c) \sec (b x+c)}{b}+\frac{\cos (a+b x)}{b}","\frac{\sin (a-c) \tanh ^{-1}(\sin (b x+c))}{b}+\frac{\cos (a-c) \sec (b x+c)}{b}+\frac{\cos (a+b x)}{b}",1,"Cos[a + b*x]/b + (Cos[a - c]*Sec[c + b*x])/b + (ArcTanh[Sin[c + b*x]]*Sin[a - c])/b","A",6,6,15,0.4000,1,"{4576, 4579, 2638, 3770, 2606, 8}"
232,1,29,0,0.015958,"\int \sin (a+b x) \tan (c+b x) \, dx","Int[Sin[a + b*x]*Tan[c + b*x],x]","\frac{\cos (a-c) \tanh ^{-1}(\sin (b x+c))}{b}-\frac{\sin (a+b x)}{b}","\frac{\cos (a-c) \tanh ^{-1}(\sin (b x+c))}{b}-\frac{\sin (a+b x)}{b}",1,"(ArcTanh[Sin[c + b*x]]*Cos[a - c])/b - Sin[a + b*x]/b","A",3,3,13,0.2308,1,"{4576, 2637, 3770}"
233,1,29,0,0.0155587,"\int \cot (c+b x) \sin (a+b x) \, dx","Int[Cot[c + b*x]*Sin[a + b*x],x]","\frac{\sin (a+b x)}{b}-\frac{\sin (a-c) \tanh ^{-1}(\cos (b x+c))}{b}","\frac{\sin (a+b x)}{b}-\frac{\sin (a-c) \tanh ^{-1}(\cos (b x+c))}{b}",1,"-((ArcTanh[Cos[c + b*x]]*Sin[a - c])/b) + Sin[a + b*x]/b","A",3,3,13,0.2308,1,"{4578, 2637, 3770}"
234,1,46,0,0.0404453,"\int \cot ^2(c+b x) \sin (a+b x) \, dx","Int[Cot[c + b*x]^2*Sin[a + b*x],x]","-\frac{\cos (a-c) \tanh ^{-1}(\cos (b x+c))}{b}-\frac{\sin (a-c) \csc (b x+c)}{b}+\frac{\cos (a+b x)}{b}","-\frac{\cos (a-c) \tanh ^{-1}(\cos (b x+c))}{b}-\frac{\sin (a-c) \csc (b x+c)}{b}+\frac{\cos (a+b x)}{b}",1,"-((ArcTanh[Cos[c + b*x]]*Cos[a - c])/b) + Cos[a + b*x]/b - (Csc[c + b*x]*Sin[a - c])/b","A",6,6,15,0.4000,1,"{4578, 4577, 2638, 3770, 2606, 8}"
235,1,74,0,0.0717082,"\int \cot ^3(c+b x) \sin (a+b x) \, dx","Int[Cot[c + b*x]^3*Sin[a + b*x],x]","-\frac{\cos (a-c) \csc (b x+c)}{b}+\frac{3 \sin (a-c) \tanh ^{-1}(\cos (b x+c))}{2 b}-\frac{\sin (a-c) \cot (b x+c) \csc (b x+c)}{2 b}-\frac{\sin (a+b x)}{b}","-\frac{\cos (a-c) \csc (b x+c)}{b}+\frac{3 \sin (a-c) \tanh ^{-1}(\cos (b x+c))}{2 b}-\frac{\sin (a-c) \cot (b x+c) \csc (b x+c)}{2 b}-\frac{\sin (a+b x)}{b}",1,"-((Cos[a - c]*Csc[c + b*x])/b) + (3*ArcTanh[Cos[c + b*x]]*Sin[a - c])/(2*b) - (Cot[c + b*x]*Csc[c + b*x]*Sin[a - c])/(2*b) - Sin[a + b*x]/b","A",9,7,15,0.4667,1,"{4578, 4577, 2637, 3770, 2606, 8, 2611}"
236,1,143,0,0.1120925,"\int \sin (a+b x) \tan (c+d x) \, dx","Int[Sin[a + b*x]*Tan[c + d*x],x]","-\frac{i e^{-i (a+b x)} \, _2F_1\left(1,-\frac{b}{2 d};1-\frac{b}{2 d};-e^{2 i (c+d x)}\right)}{b}-\frac{i e^{i (a+b x)} \, _2F_1\left(1,\frac{b}{2 d};\frac{b}{2 d}+1;-e^{2 i (c+d x)}\right)}{b}+\frac{i e^{-i (a+b x)}}{2 b}+\frac{i e^{i (a+b x)}}{2 b}","-\frac{i e^{-i (a+b x)} \, _2F_1\left(1,-\frac{b}{2 d};1-\frac{b}{2 d};-e^{2 i (c+d x)}\right)}{b}-\frac{i e^{i (a+b x)} \, _2F_1\left(1,\frac{b}{2 d};\frac{b}{2 d}+1;-e^{2 i (c+d x)}\right)}{b}+\frac{i e^{-i (a+b x)}}{2 b}+\frac{i e^{i (a+b x)}}{2 b}",1,"(I/2)/(b*E^(I*(a + b*x))) + ((I/2)*E^(I*(a + b*x)))/b - (I*Hypergeometric2F1[1, -b/(2*d), 1 - b/(2*d), -E^((2*I)*(c + d*x))])/(b*E^(I*(a + b*x))) - (I*E^(I*(a + b*x))*Hypergeometric2F1[1, b/(2*d), 1 + b/(2*d), -E^((2*I)*(c + d*x))])/b","A",6,3,13,0.2308,1,"{4557, 2194, 2251}"
237,1,139,0,0.1107636,"\int \cot (c+d x) \sin (a+b x) \, dx","Int[Cot[c + d*x]*Sin[a + b*x],x]","\frac{i e^{-i (a+b x)} \, _2F_1\left(1,-\frac{b}{2 d};1-\frac{b}{2 d};e^{2 i (c+d x)}\right)}{b}+\frac{i e^{i (a+b x)} \, _2F_1\left(1,\frac{b}{2 d};\frac{b}{2 d}+1;e^{2 i (c+d x)}\right)}{b}-\frac{i e^{-i (a+b x)}}{2 b}-\frac{i e^{i (a+b x)}}{2 b}","\frac{i e^{-i (a+b x)} \, _2F_1\left(1,-\frac{b}{2 d};1-\frac{b}{2 d};e^{2 i (c+d x)}\right)}{b}+\frac{i e^{i (a+b x)} \, _2F_1\left(1,\frac{b}{2 d};\frac{b}{2 d}+1;e^{2 i (c+d x)}\right)}{b}-\frac{i e^{-i (a+b x)}}{2 b}-\frac{i e^{i (a+b x)}}{2 b}",1,"(-I/2)/(b*E^(I*(a + b*x))) - ((I/2)*E^(I*(a + b*x)))/b + (I*Hypergeometric2F1[1, -b/(2*d), 1 - b/(2*d), E^((2*I)*(c + d*x))])/(b*E^(I*(a + b*x))) + (I*E^(I*(a + b*x))*Hypergeometric2F1[1, b/(2*d), 1 + b/(2*d), E^((2*I)*(c + d*x))])/b","A",6,3,13,0.2308,1,"{4559, 2194, 2251}"
238,1,91,0,0.0654962,"\int \cos (a+b x) \cos ^3(c+d x) \, dx","Int[Cos[a + b*x]*Cos[c + d*x]^3,x]","\frac{\sin (a+x (b-3 d)-3 c)}{8 (b-3 d)}+\frac{3 \sin (a+x (b-d)-c)}{8 (b-d)}+\frac{3 \sin (a+x (b+d)+c)}{8 (b+d)}+\frac{\sin (a+x (b+3 d)+3 c)}{8 (b+3 d)}","\frac{\sin (a+x (b-3 d)-3 c)}{8 (b-3 d)}+\frac{3 \sin (a+x (b-d)-c)}{8 (b-d)}+\frac{3 \sin (a+x (b+d)+c)}{8 (b+d)}+\frac{\sin (a+x (b+3 d)+3 c)}{8 (b+3 d)}",1,"Sin[a - 3*c + (b - 3*d)*x]/(8*(b - 3*d)) + (3*Sin[a - c + (b - d)*x])/(8*(b - d)) + (3*Sin[a + c + (b + d)*x])/(8*(b + d)) + Sin[a + 3*c + (b + 3*d)*x]/(8*(b + 3*d))","A",6,2,15,0.1333,1,"{4570, 2637}"
239,1,62,0,0.0454893,"\int \cos (a+b x) \cos ^2(c+d x) \, dx","Int[Cos[a + b*x]*Cos[c + d*x]^2,x]","\frac{\sin (a+x (b-2 d)-2 c)}{4 (b-2 d)}+\frac{\sin (a+x (b+2 d)+2 c)}{4 (b+2 d)}+\frac{\sin (a+b x)}{2 b}","\frac{\sin (a+x (b-2 d)-2 c)}{4 (b-2 d)}+\frac{\sin (a+x (b+2 d)+2 c)}{4 (b+2 d)}+\frac{\sin (a+b x)}{2 b}",1,"Sin[a + b*x]/(2*b) + Sin[a - 2*c + (b - 2*d)*x]/(4*(b - 2*d)) + Sin[a + 2*c + (b + 2*d)*x]/(4*(b + 2*d))","A",5,2,15,0.1333,1,"{4570, 2637}"
240,1,43,0,0.0334101,"\int \cos (a+b x) \cos (c+d x) \, dx","Int[Cos[a + b*x]*Cos[c + d*x],x]","\frac{\sin (a+x (b-d)-c)}{2 (b-d)}+\frac{\sin (a+x (b+d)+c)}{2 (b+d)}","\frac{\sin (a+x (b-d)-c)}{2 (b-d)}+\frac{\sin (a+x (b+d)+c)}{2 (b+d)}",1,"Sin[a - c + (b - d)*x]/(2*(b - d)) + Sin[a + c + (b + d)*x]/(2*(b + d))","A",4,2,13,0.1538,1,"{4570, 2637}"
241,1,26,0,0.0132681,"\int \cos (a+b x) \sec (c+b x) \, dx","Int[Cos[a + b*x]*Sec[c + b*x],x]","\frac{\sin (a-c) \log (\cos (b x+c))}{b}+x \cos (a-c)","\frac{\sin (a-c) \log (\cos (b x+c))}{b}+x \cos (a-c)",1,"x*Cos[a - c] + (Log[Cos[c + b*x]]*Sin[a - c])/b","A",3,3,13,0.2308,1,"{4583, 3475, 8}"
242,1,35,0,0.0287126,"\int \cos (a+b x) \sec ^2(c+b x) \, dx","Int[Cos[a + b*x]*Sec[c + b*x]^2,x]","\frac{\cos (a-c) \tanh ^{-1}(\sin (b x+c))}{b}-\frac{\sin (a-c) \sec (b x+c)}{b}","\frac{\cos (a-c) \tanh ^{-1}(\sin (b x+c))}{b}-\frac{\sin (a-c) \sec (b x+c)}{b}",1,"(ArcTanh[Sin[c + b*x]]*Cos[a - c])/b - (Sec[c + b*x]*Sin[a - c])/b","A",4,4,15,0.2667,1,"{4583, 2606, 8, 3770}"
243,1,38,0,0.0390639,"\int \cos (a+b x) \sec ^3(c+b x) \, dx","Int[Cos[a + b*x]*Sec[c + b*x]^3,x]","\frac{\cos (a-c) \tan (b x+c)}{b}-\frac{\sin (a-c) \sec ^2(b x+c)}{2 b}","\frac{\cos (a-c) \tan (b x+c)}{b}-\frac{\sin (a-c) \sec ^2(b x+c)}{2 b}",1,"-(Sec[c + b*x]^2*Sin[a - c])/(2*b) + (Cos[a - c]*Tan[c + b*x])/b","A",5,5,15,0.3333,1,"{4583, 2606, 30, 3767, 8}"
244,1,144,0,0.0887541,"\int \cos ^2(a+b x) \cos ^3(c+d x) \, dx","Int[Cos[a + b*x]^2*Cos[c + d*x]^3,x]","\frac{\sin (2 a+x (2 b-3 d)-3 c)}{16 (2 b-3 d)}+\frac{3 \sin (2 a+x (2 b-d)-c)}{16 (2 b-d)}+\frac{3 \sin (2 a+x (2 b+d)+c)}{16 (2 b+d)}+\frac{\sin (2 a+x (2 b+3 d)+3 c)}{16 (2 b+3 d)}+\frac{3 \sin (c+d x)}{8 d}+\frac{\sin (3 c+3 d x)}{24 d}","\frac{\sin (2 a+x (2 b-3 d)-3 c)}{16 (2 b-3 d)}+\frac{3 \sin (2 a+x (2 b-d)-c)}{16 (2 b-d)}+\frac{3 \sin (2 a+x (2 b+d)+c)}{16 (2 b+d)}+\frac{\sin (2 a+x (2 b+3 d)+3 c)}{16 (2 b+3 d)}+\frac{3 \sin (c+d x)}{8 d}+\frac{\sin (3 c+3 d x)}{24 d}",1,"Sin[2*a - 3*c + (2*b - 3*d)*x]/(16*(2*b - 3*d)) + (3*Sin[2*a - c + (2*b - d)*x])/(16*(2*b - d)) + (3*Sin[c + d*x])/(8*d) + Sin[3*c + 3*d*x]/(24*d) + (3*Sin[2*a + c + (2*b + d)*x])/(16*(2*b + d)) + Sin[2*a + 3*c + (2*b + 3*d)*x]/(16*(2*b + 3*d))","A",8,2,17,0.1176,1,"{4570, 2637}"
245,1,88,0,0.0686459,"\int \cos ^2(a+b x) \cos ^2(c+d x) \, dx","Int[Cos[a + b*x]^2*Cos[c + d*x]^2,x]","\frac{\sin (2 (a-c)+2 x (b-d))}{16 (b-d)}+\frac{\sin (2 (a+c)+2 x (b+d))}{16 (b+d)}+\frac{\sin (2 a+2 b x)}{8 b}+\frac{\sin (2 c+2 d x)}{8 d}+\frac{x}{4}","\frac{\sin (2 (a-c)+2 x (b-d))}{16 (b-d)}+\frac{\sin (2 (a+c)+2 x (b+d))}{16 (b+d)}+\frac{\sin (2 a+2 b x)}{8 b}+\frac{\sin (2 c+2 d x)}{8 d}+\frac{x}{4}",1,"x/4 + Sin[2*a + 2*b*x]/(8*b) + Sin[2*(a - c) + 2*(b - d)*x]/(16*(b - d)) + Sin[2*c + 2*d*x]/(8*d) + Sin[2*(a + c) + 2*(b + d)*x]/(16*(b + d))","A",6,2,17,0.1176,1,"{4570, 2637}"
246,1,195,0,0.1346262,"\int \cos ^3(a+b x) \cos ^3(c+d x) \, dx","Int[Cos[a + b*x]^3*Cos[c + d*x]^3,x]","\frac{3 \sin (a+x (b-3 d)-3 c)}{32 (b-3 d)}+\frac{9 \sin (a+x (b-d)-c)}{32 (b-d)}+\frac{\sin (3 (a-c)+3 x (b-d))}{96 (b-d)}+\frac{3 \sin (3 a+x (3 b-d)-c)}{32 (3 b-d)}+\frac{9 \sin (a+x (b+d)+c)}{32 (b+d)}+\frac{\sin (3 (a+c)+3 x (b+d))}{96 (b+d)}+\frac{3 \sin (3 a+x (3 b+d)+c)}{32 (3 b+d)}+\frac{3 \sin (a+x (b+3 d)+3 c)}{32 (b+3 d)}","\frac{3 \sin (a+x (b-3 d)-3 c)}{32 (b-3 d)}+\frac{9 \sin (a+x (b-d)-c)}{32 (b-d)}+\frac{\sin (3 (a-c)+3 x (b-d))}{96 (b-d)}+\frac{3 \sin (3 a+x (3 b-d)-c)}{32 (3 b-d)}+\frac{9 \sin (a+x (b+d)+c)}{32 (b+d)}+\frac{\sin (3 (a+c)+3 x (b+d))}{96 (b+d)}+\frac{3 \sin (3 a+x (3 b+d)+c)}{32 (3 b+d)}+\frac{3 \sin (a+x (b+3 d)+3 c)}{32 (b+3 d)}",1,"(3*Sin[a - 3*c + (b - 3*d)*x])/(32*(b - 3*d)) + (9*Sin[a - c + (b - d)*x])/(32*(b - d)) + Sin[3*(a - c) + 3*(b - d)*x]/(96*(b - d)) + (3*Sin[3*a - c + (3*b - d)*x])/(32*(3*b - d)) + (9*Sin[a + c + (b + d)*x])/(32*(b + d)) + Sin[3*(a + c) + 3*(b + d)*x]/(96*(b + d)) + (3*Sin[3*a + c + (3*b + d)*x])/(32*(3*b + d)) + (3*Sin[a + 3*c + (b + 3*d)*x])/(32*(b + 3*d))","A",10,2,17,0.1176,1,"{4570, 2637}"
247,1,72,0,0.0779723,"\int \cos (a+b x) \tan ^3(c+b x) \, dx","Int[Cos[a + b*x]*Tan[c + b*x]^3,x]","\frac{3 \sin (a-c) \tanh ^{-1}(\sin (b x+c))}{2 b}+\frac{\cos (a-c) \sec (b x+c)}{b}-\frac{\sin (a-c) \tan (b x+c) \sec (b x+c)}{2 b}+\frac{\cos (a+b x)}{b}","\frac{3 \sin (a-c) \tanh ^{-1}(\sin (b x+c))}{2 b}+\frac{\cos (a-c) \sec (b x+c)}{b}-\frac{\sin (a-c) \tan (b x+c) \sec (b x+c)}{2 b}+\frac{\cos (a+b x)}{b}",1,"Cos[a + b*x]/b + (Cos[a - c]*Sec[c + b*x])/b + (3*ArcTanh[Sin[c + b*x]]*Sin[a - c])/(2*b) - (Sec[c + b*x]*Sin[a - c]*Tan[c + b*x])/(2*b)","A",9,7,15,0.4667,1,"{4579, 4576, 2638, 3770, 2606, 8, 2611}"
248,1,46,0,0.0391638,"\int \cos (a+b x) \tan ^2(c+b x) \, dx","Int[Cos[a + b*x]*Tan[c + b*x]^2,x]","-\frac{\sin (a-c) \sec (b x+c)}{b}+\frac{\cos (a-c) \tanh ^{-1}(\sin (b x+c))}{b}-\frac{\sin (a+b x)}{b}","-\frac{\sin (a-c) \sec (b x+c)}{b}+\frac{\cos (a-c) \tanh ^{-1}(\sin (b x+c))}{b}-\frac{\sin (a+b x)}{b}",1,"(ArcTanh[Sin[c + b*x]]*Cos[a - c])/b - (Sec[c + b*x]*Sin[a - c])/b - Sin[a + b*x]/b","A",6,6,15,0.4000,1,"{4579, 4576, 2637, 3770, 2606, 8}"
249,1,30,0,0.0176683,"\int \cos (a+b x) \tan (c+b x) \, dx","Int[Cos[a + b*x]*Tan[c + b*x],x]","-\frac{\sin (a-c) \tanh ^{-1}(\sin (b x+c))}{b}-\frac{\cos (a+b x)}{b}","-\frac{\sin (a-c) \tanh ^{-1}(\sin (b x+c))}{b}-\frac{\cos (a+b x)}{b}",1,"-(Cos[a + b*x]/b) - (ArcTanh[Sin[c + b*x]]*Sin[a - c])/b","A",3,3,13,0.2308,1,"{4579, 2638, 3770}"
250,1,29,0,0.0209471,"\int \cos (a+b x) \cot (c+b x) \, dx","Int[Cos[a + b*x]*Cot[c + b*x],x]","\frac{\cos (a+b x)}{b}-\frac{\cos (a-c) \tanh ^{-1}(\cos (b x+c))}{b}","\frac{\cos (a+b x)}{b}-\frac{\cos (a-c) \tanh ^{-1}(\cos (b x+c))}{b}",1,"-((ArcTanh[Cos[c + b*x]]*Cos[a - c])/b) + Cos[a + b*x]/b","A",3,3,13,0.2308,1,"{4577, 2638, 3770}"
251,1,46,0,0.0413559,"\int \cos (a+b x) \cot ^2(c+b x) \, dx","Int[Cos[a + b*x]*Cot[c + b*x]^2,x]","-\frac{\cos (a-c) \csc (b x+c)}{b}+\frac{\sin (a-c) \tanh ^{-1}(\cos (b x+c))}{b}-\frac{\sin (a+b x)}{b}","-\frac{\cos (a-c) \csc (b x+c)}{b}+\frac{\sin (a-c) \tanh ^{-1}(\cos (b x+c))}{b}-\frac{\sin (a+b x)}{b}",1,"-((Cos[a - c]*Csc[c + b*x])/b) + (ArcTanh[Cos[c + b*x]]*Sin[a - c])/b - Sin[a + b*x]/b","A",6,6,15,0.4000,1,"{4577, 4578, 2637, 3770, 2606, 8}"
252,1,73,0,0.07673,"\int \cos (a+b x) \cot ^3(c+b x) \, dx","Int[Cos[a + b*x]*Cot[c + b*x]^3,x]","\frac{3 \cos (a-c) \tanh ^{-1}(\cos (b x+c))}{2 b}+\frac{\sin (a-c) \csc (b x+c)}{b}-\frac{\cos (a-c) \cot (b x+c) \csc (b x+c)}{2 b}-\frac{\cos (a+b x)}{b}","\frac{3 \cos (a-c) \tanh ^{-1}(\cos (b x+c))}{2 b}+\frac{\sin (a-c) \csc (b x+c)}{b}-\frac{\cos (a-c) \cot (b x+c) \csc (b x+c)}{2 b}-\frac{\cos (a+b x)}{b}",1,"(3*ArcTanh[Cos[c + b*x]]*Cos[a - c])/(2*b) - Cos[a + b*x]/b - (Cos[a - c]*Cot[c + b*x]*Csc[c + b*x])/(2*b) + (Csc[c + b*x]*Sin[a - c])/b","A",9,7,15,0.4667,1,"{4577, 4578, 2638, 3770, 2606, 8, 2611}"
253,1,134,0,0.1192833,"\int \cos (a+b x) \tan (c+d x) \, dx","Int[Cos[a + b*x]*Tan[c + d*x],x]","-\frac{e^{-i (a+b x)} \, _2F_1\left(1,-\frac{b}{2 d};1-\frac{b}{2 d};-e^{2 i (c+d x)}\right)}{b}+\frac{e^{i (a+b x)} \, _2F_1\left(1,\frac{b}{2 d};\frac{b}{2 d}+1;-e^{2 i (c+d x)}\right)}{b}+\frac{e^{-i (a+b x)}}{2 b}-\frac{e^{i (a+b x)}}{2 b}","-\frac{e^{-i (a+b x)} \, _2F_1\left(1,-\frac{b}{2 d};1-\frac{b}{2 d};-e^{2 i (c+d x)}\right)}{b}+\frac{e^{i (a+b x)} \, _2F_1\left(1,\frac{b}{2 d};\frac{b}{2 d}+1;-e^{2 i (c+d x)}\right)}{b}+\frac{e^{-i (a+b x)}}{2 b}-\frac{e^{i (a+b x)}}{2 b}",1,"1/(2*b*E^(I*(a + b*x))) - E^(I*(a + b*x))/(2*b) - Hypergeometric2F1[1, -b/(2*d), 1 - b/(2*d), -E^((2*I)*(c + d*x))]/(b*E^(I*(a + b*x))) + (E^(I*(a + b*x))*Hypergeometric2F1[1, b/(2*d), 1 + b/(2*d), -E^((2*I)*(c + d*x))])/b","A",6,3,13,0.2308,1,"{4560, 2194, 2251}"
254,1,130,0,0.1201407,"\int \cos (a+b x) \cot (c+d x) \, dx","Int[Cos[a + b*x]*Cot[c + d*x],x]","\frac{e^{-i (a+b x)} \, _2F_1\left(1,-\frac{b}{2 d};1-\frac{b}{2 d};e^{2 i (c+d x)}\right)}{b}-\frac{e^{i (a+b x)} \, _2F_1\left(1,\frac{b}{2 d};\frac{b}{2 d}+1;e^{2 i (c+d x)}\right)}{b}-\frac{e^{-i (a+b x)}}{2 b}+\frac{e^{i (a+b x)}}{2 b}","\frac{e^{-i (a+b x)} \, _2F_1\left(1,-\frac{b}{2 d};1-\frac{b}{2 d};e^{2 i (c+d x)}\right)}{b}-\frac{e^{i (a+b x)} \, _2F_1\left(1,\frac{b}{2 d};\frac{b}{2 d}+1;e^{2 i (c+d x)}\right)}{b}-\frac{e^{-i (a+b x)}}{2 b}+\frac{e^{i (a+b x)}}{2 b}",1,"-1/(2*b*E^(I*(a + b*x))) + E^(I*(a + b*x))/(2*b) + Hypergeometric2F1[1, -b/(2*d), 1 - b/(2*d), E^((2*I)*(c + d*x))]/(b*E^(I*(a + b*x))) - (E^(I*(a + b*x))*Hypergeometric2F1[1, b/(2*d), 1 + b/(2*d), E^((2*I)*(c + d*x))])/b","A",6,3,13,0.2308,1,"{4558, 2194, 2251}"