1,1,91,0,0.1023019,"\int \csc ^3(c+d x) (a+a \csc (c+d x)) (A+A \csc (c+d x)) \, dx","Int[Csc[c + d*x]^3*(a + a*Csc[c + d*x])*(A + A*Csc[c + d*x]),x]","-\frac{2 a A \cot ^3(c+d x)}{3 d}-\frac{2 a A \cot (c+d x)}{d}-\frac{7 a A \tanh ^{-1}(\cos (c+d x))}{8 d}-\frac{a A \cot (c+d x) \csc ^3(c+d x)}{4 d}-\frac{7 a A \cot (c+d x) \csc (c+d x)}{8 d}","-\frac{2 a A \cot ^3(c+d x)}{3 d}-\frac{2 a A \cot (c+d x)}{d}-\frac{7 a A \tanh ^{-1}(\cos (c+d x))}{8 d}-\frac{a A \cot (c+d x) \csc ^3(c+d x)}{4 d}-\frac{7 a A \cot (c+d x) \csc (c+d x)}{8 d}",1,"(-7*a*A*ArcTanh[Cos[c + d*x]])/(8*d) - (2*a*A*Cot[c + d*x])/d - (2*a*A*Cot[c + d*x]^3)/(3*d) - (7*a*A*Cot[c + d*x]*Csc[c + d*x])/(8*d) - (a*A*Cot[c + d*x]*Csc[c + d*x]^3)/(4*d)","A",7,6,29,0.2069,1,"{21, 3788, 3767, 4046, 3768, 3770}"
2,1,72,0,0.0962889,"\int \csc ^2(c+d x) (a+a \csc (c+d x)) (A+A \csc (c+d x)) \, dx","Int[Csc[c + d*x]^2*(a + a*Csc[c + d*x])*(A + A*Csc[c + d*x]),x]","-\frac{5 a A \cot (c+d x)}{3 d}-\frac{a A \tanh ^{-1}(\cos (c+d x))}{d}-\frac{a A \cot (c+d x) \csc ^2(c+d x)}{3 d}-\frac{a A \cot (c+d x) \csc (c+d x)}{d}","-\frac{5 a A \cot (c+d x)}{3 d}-\frac{a A \tanh ^{-1}(\cos (c+d x))}{d}-\frac{a A \cot (c+d x) \csc ^2(c+d x)}{3 d}-\frac{a A \cot (c+d x) \csc (c+d x)}{d}",1,"-((a*A*ArcTanh[Cos[c + d*x]])/d) - (5*a*A*Cot[c + d*x])/(3*d) - (a*A*Cot[c + d*x]*Csc[c + d*x])/d - (a*A*Cot[c + d*x]*Csc[c + d*x]^2)/(3*d)","A",7,7,29,0.2414,1,"{21, 3788, 3768, 3770, 4046, 3767, 8}"
3,1,51,0,0.0576248,"\int \csc (c+d x) (a+a \csc (c+d x)) (A+A \csc (c+d x)) \, dx","Int[Csc[c + d*x]*(a + a*Csc[c + d*x])*(A + A*Csc[c + d*x]),x]","-\frac{2 a A \cot (c+d x)}{d}-\frac{3 a A \tanh ^{-1}(\cos (c+d x))}{2 d}-\frac{a A \cot (c+d x) \csc (c+d x)}{2 d}","-\frac{2 a A \cot (c+d x)}{d}-\frac{3 a A \tanh ^{-1}(\cos (c+d x))}{2 d}-\frac{a A \cot (c+d x) \csc (c+d x)}{2 d}",1,"(-3*a*A*ArcTanh[Cos[c + d*x]])/(2*d) - (2*a*A*Cot[c + d*x])/d - (a*A*Cot[c + d*x]*Csc[c + d*x])/(2*d)","A",6,6,27,0.2222,1,"{21, 3788, 3767, 8, 4046, 3770}"
4,1,33,0,0.0594924,"\int (a+a \csc (c+d x)) (A+A \csc (c+d x)) \sin (c+d x) \, dx","Int[(a + a*Csc[c + d*x])*(A + A*Csc[c + d*x])*Sin[c + d*x],x]","-\frac{a A \cos (c+d x)}{d}-\frac{a A \tanh ^{-1}(\cos (c+d x))}{d}+2 a A x","-\frac{a A \cos (c+d x)}{d}-\frac{a A \tanh ^{-1}(\cos (c+d x))}{d}+2 a A x",1,"2*a*A*x - (a*A*ArcTanh[Cos[c + d*x]])/d - (a*A*Cos[c + d*x])/d","A",5,5,27,0.1852,1,"{21, 3788, 8, 4045, 3770}"
5,1,42,0,0.0733261,"\int (a+a \csc (c+d x)) (A+A \csc (c+d x)) \sin ^2(c+d x) \, dx","Int[(a + a*Csc[c + d*x])*(A + A*Csc[c + d*x])*Sin[c + d*x]^2,x]","-\frac{2 a A \cos (c+d x)}{d}-\frac{a A \sin (c+d x) \cos (c+d x)}{2 d}+\frac{3 a A x}{2}","-\frac{2 a A \cos (c+d x)}{d}-\frac{a A \sin (c+d x) \cos (c+d x)}{2 d}+\frac{3 a A x}{2}",1,"(3*a*A*x)/2 - (2*a*A*Cos[c + d*x])/d - (a*A*Cos[c + d*x]*Sin[c + d*x])/(2*d)","A",5,5,29,0.1724,1,"{21, 3788, 2638, 4045, 8}"
6,1,54,0,0.0940265,"\int (a+a \csc (c+d x)) (A+A \csc (c+d x)) \sin ^3(c+d x) \, dx","Int[(a + a*Csc[c + d*x])*(A + A*Csc[c + d*x])*Sin[c + d*x]^3,x]","\frac{a A \cos ^3(c+d x)}{3 d}-\frac{2 a A \cos (c+d x)}{d}-\frac{a A \sin (c+d x) \cos (c+d x)}{d}+a A x","\frac{a A \cos ^3(c+d x)}{3 d}-\frac{2 a A \cos (c+d x)}{d}-\frac{a A \sin (c+d x) \cos (c+d x)}{d}+a A x",1,"a*A*x - (2*a*A*Cos[c + d*x])/d + (a*A*Cos[c + d*x]^3)/(3*d) - (a*A*Cos[c + d*x]*Sin[c + d*x])/d","A",7,6,29,0.2069,1,"{21, 3788, 2635, 8, 4044, 3013}"
7,1,61,0,0.0924962,"\int \csc ^3(c+d x) (a-a \csc (c+d x)) (A+A \csc (c+d x)) \, dx","Int[Csc[c + d*x]^3*(a - a*Csc[c + d*x])*(A + A*Csc[c + d*x]),x]","-\frac{a A \tanh ^{-1}(\cos (c+d x))}{8 d}+\frac{a A \cot (c+d x) \csc ^3(c+d x)}{4 d}-\frac{a A \cot (c+d x) \csc (c+d x)}{8 d}","-\frac{a A \tanh ^{-1}(\cos (c+d x))}{8 d}+\frac{a A \cot (c+d x) \csc ^3(c+d x)}{4 d}-\frac{a A \cot (c+d x) \csc (c+d x)}{8 d}",1,"-(a*A*ArcTanh[Cos[c + d*x]])/(8*d) - (a*A*Cot[c + d*x]*Csc[c + d*x])/(8*d) + (a*A*Cot[c + d*x]*Csc[c + d*x]^3)/(4*d)","A",4,4,30,0.1333,1,"{3962, 2611, 3768, 3770}"
8,1,17,0,0.0724796,"\int \csc ^2(c+d x) (a-a \csc (c+d x)) (A+A \csc (c+d x)) \, dx","Int[Csc[c + d*x]^2*(a - a*Csc[c + d*x])*(A + A*Csc[c + d*x]),x]","\frac{a A \cot ^3(c+d x)}{3 d}","\frac{a A \cot ^3(c+d x)}{3 d}",1,"(a*A*Cot[c + d*x]^3)/(3*d)","A",3,3,30,0.1000,1,"{3962, 2607, 30}"
9,1,38,0,0.0509353,"\int \csc (c+d x) (a-a \csc (c+d x)) (A+A \csc (c+d x)) \, dx","Int[Csc[c + d*x]*(a - a*Csc[c + d*x])*(A + A*Csc[c + d*x]),x]","\frac{a A \cot (c+d x) \csc (c+d x)}{2 d}-\frac{a A \tanh ^{-1}(\cos (c+d x))}{2 d}","\frac{a A \cot (c+d x) \csc (c+d x)}{2 d}-\frac{a A \tanh ^{-1}(\cos (c+d x))}{2 d}",1,"-(a*A*ArcTanh[Cos[c + d*x]])/(2*d) + (a*A*Cot[c + d*x]*Csc[c + d*x])/(2*d)","A",3,3,28,0.1071,1,"{3958, 2611, 3770}"
10,1,27,0,0.0529919,"\int (a-a \csc (c+d x)) (A+A \csc (c+d x)) \sin (c+d x) \, dx","Int[(a - a*Csc[c + d*x])*(A + A*Csc[c + d*x])*Sin[c + d*x],x]","\frac{a A \tanh ^{-1}(\cos (c+d x))}{d}-\frac{a A \cos (c+d x)}{d}","\frac{a A \tanh ^{-1}(\cos (c+d x))}{d}-\frac{a A \cos (c+d x)}{d}",1,"(a*A*ArcTanh[Cos[c + d*x]])/d - (a*A*Cos[c + d*x])/d","A",4,4,28,0.1429,1,"{3962, 2592, 321, 206}"
11,1,29,0,0.0549121,"\int (a-a \csc (c+d x)) (A+A \csc (c+d x)) \sin ^2(c+d x) \, dx","Int[(a - a*Csc[c + d*x])*(A + A*Csc[c + d*x])*Sin[c + d*x]^2,x]","-\frac{a A \sin (c+d x) \cos (c+d x)}{2 d}-\frac{1}{2} a A x","-\frac{a A \sin (c+d x) \cos (c+d x)}{2 d}-\frac{1}{2} a A x",1,"-(a*A*x)/2 - (a*A*Cos[c + d*x]*Sin[c + d*x])/(2*d)","A",3,3,30,0.1000,1,"{3962, 2635, 8}"
12,1,17,0,0.0612404,"\int (a-a \csc (c+d x)) (A+A \csc (c+d x)) \sin ^3(c+d x) \, dx","Int[(a - a*Csc[c + d*x])*(A + A*Csc[c + d*x])*Sin[c + d*x]^3,x]","\frac{a A \cos ^3(c+d x)}{3 d}","\frac{a A \cos ^3(c+d x)}{3 d}",1,"(a*A*Cos[c + d*x]^3)/(3*d)","A",3,3,30,0.1000,1,"{3962, 2565, 30}"
13,1,61,0,0.0902824,"\int \csc ^3(c+d x) (a+a \csc (c+d x)) (A-A \csc (c+d x)) \, dx","Int[Csc[c + d*x]^3*(a + a*Csc[c + d*x])*(A - A*Csc[c + d*x]),x]","-\frac{a A \tanh ^{-1}(\cos (c+d x))}{8 d}+\frac{a A \cot (c+d x) \csc ^3(c+d x)}{4 d}-\frac{a A \cot (c+d x) \csc (c+d x)}{8 d}","-\frac{a A \tanh ^{-1}(\cos (c+d x))}{8 d}+\frac{a A \cot (c+d x) \csc ^3(c+d x)}{4 d}-\frac{a A \cot (c+d x) \csc (c+d x)}{8 d}",1,"-(a*A*ArcTanh[Cos[c + d*x]])/(8*d) - (a*A*Cot[c + d*x]*Csc[c + d*x])/(8*d) + (a*A*Cot[c + d*x]*Csc[c + d*x]^3)/(4*d)","A",4,4,30,0.1333,1,"{3962, 2611, 3768, 3770}"
14,1,17,0,0.0710912,"\int \csc ^2(c+d x) (a+a \csc (c+d x)) (A-A \csc (c+d x)) \, dx","Int[Csc[c + d*x]^2*(a + a*Csc[c + d*x])*(A - A*Csc[c + d*x]),x]","\frac{a A \cot ^3(c+d x)}{3 d}","\frac{a A \cot ^3(c+d x)}{3 d}",1,"(a*A*Cot[c + d*x]^3)/(3*d)","A",3,3,30,0.1000,1,"{3962, 2607, 30}"
15,1,38,0,0.0494713,"\int \csc (c+d x) (a+a \csc (c+d x)) (A-A \csc (c+d x)) \, dx","Int[Csc[c + d*x]*(a + a*Csc[c + d*x])*(A - A*Csc[c + d*x]),x]","\frac{a A \cot (c+d x) \csc (c+d x)}{2 d}-\frac{a A \tanh ^{-1}(\cos (c+d x))}{2 d}","\frac{a A \cot (c+d x) \csc (c+d x)}{2 d}-\frac{a A \tanh ^{-1}(\cos (c+d x))}{2 d}",1,"-(a*A*ArcTanh[Cos[c + d*x]])/(2*d) + (a*A*Cot[c + d*x]*Csc[c + d*x])/(2*d)","A",3,3,28,0.1071,1,"{3958, 2611, 3770}"
16,1,27,0,0.0522252,"\int (a+a \csc (c+d x)) (A-A \csc (c+d x)) \sin (c+d x) \, dx","Int[(a + a*Csc[c + d*x])*(A - A*Csc[c + d*x])*Sin[c + d*x],x]","\frac{a A \tanh ^{-1}(\cos (c+d x))}{d}-\frac{a A \cos (c+d x)}{d}","\frac{a A \tanh ^{-1}(\cos (c+d x))}{d}-\frac{a A \cos (c+d x)}{d}",1,"(a*A*ArcTanh[Cos[c + d*x]])/d - (a*A*Cos[c + d*x])/d","A",4,4,28,0.1429,1,"{3962, 2592, 321, 206}"
17,1,29,0,0.0551765,"\int (a+a \csc (c+d x)) (A-A \csc (c+d x)) \sin ^2(c+d x) \, dx","Int[(a + a*Csc[c + d*x])*(A - A*Csc[c + d*x])*Sin[c + d*x]^2,x]","-\frac{a A \sin (c+d x) \cos (c+d x)}{2 d}-\frac{1}{2} a A x","-\frac{a A \sin (c+d x) \cos (c+d x)}{2 d}-\frac{1}{2} a A x",1,"-(a*A*x)/2 - (a*A*Cos[c + d*x]*Sin[c + d*x])/(2*d)","A",3,3,30,0.1000,1,"{3962, 2635, 8}"
18,1,17,0,0.0606128,"\int (a+a \csc (c+d x)) (A-A \csc (c+d x)) \sin ^3(c+d x) \, dx","Int[(a + a*Csc[c + d*x])*(A - A*Csc[c + d*x])*Sin[c + d*x]^3,x]","\frac{a A \cos ^3(c+d x)}{3 d}","\frac{a A \cos ^3(c+d x)}{3 d}",1,"(a*A*Cos[c + d*x]^3)/(3*d)","A",3,3,30,0.1000,1,"{3962, 2565, 30}"
19,1,91,0,0.0959867,"\int \csc ^3(c+d x) (a-a \csc (c+d x)) (A-A \csc (c+d x)) \, dx","Int[Csc[c + d*x]^3*(a - a*Csc[c + d*x])*(A - A*Csc[c + d*x]),x]","\frac{2 a A \cot ^3(c+d x)}{3 d}+\frac{2 a A \cot (c+d x)}{d}-\frac{7 a A \tanh ^{-1}(\cos (c+d x))}{8 d}-\frac{a A \cot (c+d x) \csc ^3(c+d x)}{4 d}-\frac{7 a A \cot (c+d x) \csc (c+d x)}{8 d}","\frac{2 a A \cot ^3(c+d x)}{3 d}+\frac{2 a A \cot (c+d x)}{d}-\frac{7 a A \tanh ^{-1}(\cos (c+d x))}{8 d}-\frac{a A \cot (c+d x) \csc ^3(c+d x)}{4 d}-\frac{7 a A \cot (c+d x) \csc (c+d x)}{8 d}",1,"(-7*a*A*ArcTanh[Cos[c + d*x]])/(8*d) + (2*a*A*Cot[c + d*x])/d + (2*a*A*Cot[c + d*x]^3)/(3*d) - (7*a*A*Cot[c + d*x]*Csc[c + d*x])/(8*d) - (a*A*Cot[c + d*x]*Csc[c + d*x]^3)/(4*d)","A",7,6,31,0.1935,1,"{21, 3788, 3767, 4046, 3768, 3770}"
20,1,70,0,0.0898258,"\int \csc ^2(c+d x) (a-a \csc (c+d x)) (A-A \csc (c+d x)) \, dx","Int[Csc[c + d*x]^2*(a - a*Csc[c + d*x])*(A - A*Csc[c + d*x]),x]","-\frac{5 a A \cot (c+d x)}{3 d}+\frac{a A \tanh ^{-1}(\cos (c+d x))}{d}-\frac{a A \cot (c+d x) \csc ^2(c+d x)}{3 d}+\frac{a A \cot (c+d x) \csc (c+d x)}{d}","-\frac{5 a A \cot (c+d x)}{3 d}+\frac{a A \tanh ^{-1}(\cos (c+d x))}{d}-\frac{a A \cot (c+d x) \csc ^2(c+d x)}{3 d}+\frac{a A \cot (c+d x) \csc (c+d x)}{d}",1,"(a*A*ArcTanh[Cos[c + d*x]])/d - (5*a*A*Cot[c + d*x])/(3*d) + (a*A*Cot[c + d*x]*Csc[c + d*x])/d - (a*A*Cot[c + d*x]*Csc[c + d*x]^2)/(3*d)","A",7,7,31,0.2258,1,"{21, 3788, 3768, 3770, 4046, 3767, 8}"
21,1,51,0,0.0554934,"\int \csc (c+d x) (a-a \csc (c+d x)) (A-A \csc (c+d x)) \, dx","Int[Csc[c + d*x]*(a - a*Csc[c + d*x])*(A - A*Csc[c + d*x]),x]","\frac{2 a A \cot (c+d x)}{d}-\frac{3 a A \tanh ^{-1}(\cos (c+d x))}{2 d}-\frac{a A \cot (c+d x) \csc (c+d x)}{2 d}","\frac{2 a A \cot (c+d x)}{d}-\frac{3 a A \tanh ^{-1}(\cos (c+d x))}{2 d}-\frac{a A \cot (c+d x) \csc (c+d x)}{2 d}",1,"(-3*a*A*ArcTanh[Cos[c + d*x]])/(2*d) + (2*a*A*Cot[c + d*x])/d - (a*A*Cot[c + d*x]*Csc[c + d*x])/(2*d)","A",6,6,29,0.2069,1,"{21, 3788, 3767, 8, 4046, 3770}"
22,1,33,0,0.0575666,"\int (a-a \csc (c+d x)) (A-A \csc (c+d x)) \sin (c+d x) \, dx","Int[(a - a*Csc[c + d*x])*(A - A*Csc[c + d*x])*Sin[c + d*x],x]","-\frac{a A \cos (c+d x)}{d}-\frac{a A \tanh ^{-1}(\cos (c+d x))}{d}-2 a A x","-\frac{a A \cos (c+d x)}{d}-\frac{a A \tanh ^{-1}(\cos (c+d x))}{d}-2 a A x",1,"-2*a*A*x - (a*A*ArcTanh[Cos[c + d*x]])/d - (a*A*Cos[c + d*x])/d","A",5,5,29,0.1724,1,"{21, 3788, 8, 4045, 3770}"
23,1,42,0,0.0687744,"\int (a-a \csc (c+d x)) (A-A \csc (c+d x)) \sin ^2(c+d x) \, dx","Int[(a - a*Csc[c + d*x])*(A - A*Csc[c + d*x])*Sin[c + d*x]^2,x]","\frac{2 a A \cos (c+d x)}{d}-\frac{a A \sin (c+d x) \cos (c+d x)}{2 d}+\frac{3 a A x}{2}","\frac{2 a A \cos (c+d x)}{d}-\frac{a A \sin (c+d x) \cos (c+d x)}{2 d}+\frac{3 a A x}{2}",1,"(3*a*A*x)/2 + (2*a*A*Cos[c + d*x])/d - (a*A*Cos[c + d*x]*Sin[c + d*x])/(2*d)","A",5,5,31,0.1613,1,"{21, 3788, 2638, 4045, 8}"
24,1,54,0,0.0902227,"\int (a-a \csc (c+d x)) (A-A \csc (c+d x)) \sin ^3(c+d x) \, dx","Int[(a - a*Csc[c + d*x])*(A - A*Csc[c + d*x])*Sin[c + d*x]^3,x]","\frac{a A \cos ^3(c+d x)}{3 d}-\frac{2 a A \cos (c+d x)}{d}+\frac{a A \sin (c+d x) \cos (c+d x)}{d}-a A x","\frac{a A \cos ^3(c+d x)}{3 d}-\frac{2 a A \cos (c+d x)}{d}+\frac{a A \sin (c+d x) \cos (c+d x)}{d}-a A x",1,"-(a*A*x) - (2*a*A*Cos[c + d*x])/d + (a*A*Cos[c + d*x]^3)/(3*d) + (a*A*Cos[c + d*x]*Sin[c + d*x])/d","A",7,6,31,0.1935,1,"{21, 3788, 2635, 8, 4044, 3013}"