1,1,163,91,0.0786318,"\int \csc ^3(c+d x) (a+a \csc (c+d x)) (A+A \csc (c+d x)) \, dx","Integrate[Csc[c + d*x]^3*(a + a*Csc[c + d*x])*(A + A*Csc[c + d*x]),x]","-\frac{4 a A \cot (c+d x)}{3 d}-\frac{a A \csc ^4\left(\frac{1}{2} (c+d x)\right)}{64 d}-\frac{7 a A \csc ^2\left(\frac{1}{2} (c+d x)\right)}{32 d}+\frac{a A \sec ^4\left(\frac{1}{2} (c+d x)\right)}{64 d}+\frac{7 a A \sec ^2\left(\frac{1}{2} (c+d x)\right)}{32 d}+\frac{7 a A \log \left(\sin \left(\frac{1}{2} (c+d x)\right)\right)}{8 d}-\frac{7 a A \log \left(\cos \left(\frac{1}{2} (c+d x)\right)\right)}{8 d}-\frac{2 a A \cot (c+d x) \csc ^2(c+d x)}{3 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,"(-4*a*A*Cot[c + d*x])/(3*d) - (7*a*A*Csc[(c + d*x)/2]^2)/(32*d) - (a*A*Csc[(c + d*x)/2]^4)/(64*d) - (2*a*A*Cot[c + d*x]*Csc[c + d*x]^2)/(3*d) - (7*a*A*Log[Cos[(c + d*x)/2]])/(8*d) + (7*a*A*Log[Sin[(c + d*x)/2]])/(8*d) + (7*a*A*Sec[(c + d*x)/2]^2)/(32*d) + (a*A*Sec[(c + d*x)/2]^4)/(64*d)","A",1
2,1,116,72,0.0469115,"\int \csc ^2(c+d x) (a+a \csc (c+d x)) (A+A \csc (c+d x)) \, dx","Integrate[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 \csc ^2\left(\frac{1}{2} (c+d x)\right)}{4 d}+\frac{a A \sec ^2\left(\frac{1}{2} (c+d x)\right)}{4 d}+\frac{a A \log \left(\sin \left(\frac{1}{2} (c+d x)\right)\right)}{d}-\frac{a A \log \left(\cos \left(\frac{1}{2} (c+d x)\right)\right)}{d}-\frac{a A \cot (c+d x) \csc ^2(c+d x)}{3 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,"(-5*a*A*Cot[c + d*x])/(3*d) - (a*A*Csc[(c + d*x)/2]^2)/(4*d) - (a*A*Cot[c + d*x]*Csc[c + d*x]^2)/(3*d) - (a*A*Log[Cos[(c + d*x)/2]])/d + (a*A*Log[Sin[(c + d*x)/2]])/d + (a*A*Sec[(c + d*x)/2]^2)/(4*d)","A",1
3,1,137,51,0.0407244,"\int \csc (c+d x) (a+a \csc (c+d x)) (A+A \csc (c+d x)) \, dx","Integrate[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{a A \csc ^2\left(\frac{1}{2} (c+d x)\right)}{8 d}+\frac{a A \sec ^2\left(\frac{1}{2} (c+d x)\right)}{8 d}+\frac{a A \log \left(\sin \left(\frac{c}{2}+\frac{d x}{2}\right)\right)}{d}+\frac{a A \log \left(\sin \left(\frac{1}{2} (c+d x)\right)\right)}{2 d}-\frac{a A \log \left(\cos \left(\frac{c}{2}+\frac{d x}{2}\right)\right)}{d}-\frac{a A \log \left(\cos \left(\frac{1}{2} (c+d x)\right)\right)}{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,"(-2*a*A*Cot[c + d*x])/d - (a*A*Csc[(c + d*x)/2]^2)/(8*d) - (a*A*Log[Cos[c/2 + (d*x)/2]])/d - (a*A*Log[Cos[(c + d*x)/2]])/(2*d) + (a*A*Log[Sin[c/2 + (d*x)/2]])/d + (a*A*Log[Sin[(c + d*x)/2]])/(2*d) + (a*A*Sec[(c + d*x)/2]^2)/(8*d)","B",1
4,1,72,33,0.0240188,"\int (a+a \csc (c+d x)) (A+A \csc (c+d x)) \sin (c+d x) \, dx","Integrate[(a + a*Csc[c + d*x])*(A + A*Csc[c + d*x])*Sin[c + d*x],x]","\frac{a A \sin (c) \sin (d x)}{d}-\frac{a A \cos (c) \cos (d x)}{d}+\frac{a A \log \left(\sin \left(\frac{c}{2}+\frac{d x}{2}\right)\right)}{d}-\frac{a A \log \left(\cos \left(\frac{c}{2}+\frac{d x}{2}\right)\right)}{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*Cos[c]*Cos[d*x])/d - (a*A*Log[Cos[c/2 + (d*x)/2]])/d + (a*A*Log[Sin[c/2 + (d*x)/2]])/d + (a*A*Sin[c]*Sin[d*x])/d","B",1
5,1,33,42,0.06584,"\int (a+a \csc (c+d x)) (A+A \csc (c+d x)) \sin ^2(c+d x) \, dx","Integrate[(a + a*Csc[c + d*x])*(A + A*Csc[c + d*x])*Sin[c + d*x]^2,x]","-\frac{a A (-6 (c+d x)+\sin (2 (c+d x))+8 \cos (c+d x))}{4 d}","-\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,"-1/4*(a*A*(-6*(c + d*x) + 8*Cos[c + d*x] + Sin[2*(c + d*x)]))/d","A",1
6,1,43,54,0.0882372,"\int (a+a \csc (c+d x)) (A+A \csc (c+d x)) \sin ^3(c+d x) \, dx","Integrate[(a + a*Csc[c + d*x])*(A + A*Csc[c + d*x])*Sin[c + d*x]^3,x]","\frac{a A (-6 \sin (2 (c+d x))-21 \cos (c+d x)+\cos (3 (c+d x))+12 c+12 d x)}{12 d}","\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*(12*c + 12*d*x - 21*Cos[c + d*x] + Cos[3*(c + d*x)] - 6*Sin[2*(c + d*x)]))/(12*d)","A",1
7,1,117,61,0.0456075,"\int \csc ^3(c+d x) (a-a \csc (c+d x)) (A+A \csc (c+d x)) \, dx","Integrate[Csc[c + d*x]^3*(a - a*Csc[c + d*x])*(A + A*Csc[c + d*x]),x]","-a A \left(-\frac{\csc ^4\left(\frac{1}{2} (c+d x)\right)}{64 d}+\frac{\csc ^2\left(\frac{1}{2} (c+d x)\right)}{32 d}+\frac{\sec ^4\left(\frac{1}{2} (c+d x)\right)}{64 d}-\frac{\sec ^2\left(\frac{1}{2} (c+d x)\right)}{32 d}-\frac{\log \left(\sin \left(\frac{1}{2} (c+d x)\right)\right)}{8 d}+\frac{\log \left(\cos \left(\frac{1}{2} (c+d x)\right)\right)}{8 d}\right)","-\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*(Csc[(c + d*x)/2]^2/(32*d) - Csc[(c + d*x)/2]^4/(64*d) + Log[Cos[(c + d*x)/2]]/(8*d) - Log[Sin[(c + d*x)/2]]/(8*d) - Sec[(c + d*x)/2]^2/(32*d) + Sec[(c + d*x)/2]^4/(64*d)))","A",1
8,1,17,17,0.017045,"\int \csc ^2(c+d x) (a-a \csc (c+d x)) (A+A \csc (c+d x)) \, dx","Integrate[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",1
9,1,79,38,0.035323,"\int \csc (c+d x) (a-a \csc (c+d x)) (A+A \csc (c+d x)) \, dx","Integrate[Csc[c + d*x]*(a - a*Csc[c + d*x])*(A + A*Csc[c + d*x]),x]","-a A \left(-\frac{\csc ^2\left(\frac{1}{2} (c+d x)\right)}{8 d}+\frac{\sec ^2\left(\frac{1}{2} (c+d x)\right)}{8 d}-\frac{\log \left(\sin \left(\frac{1}{2} (c+d x)\right)\right)}{2 d}+\frac{\log \left(\cos \left(\frac{1}{2} (c+d x)\right)\right)}{2 d}\right)","\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*(-1/8*Csc[(c + d*x)/2]^2/d + Log[Cos[(c + d*x)/2]]/(2*d) - Log[Sin[(c + d*x)/2]]/(2*d) + Sec[(c + d*x)/2]^2/(8*d)))","B",1
10,1,46,27,0.0246282,"\int (a-a \csc (c+d x)) (A+A \csc (c+d x)) \sin (c+d x) \, dx","Integrate[(a - a*Csc[c + d*x])*(A + A*Csc[c + d*x])*Sin[c + d*x],x]","-a A \left(\frac{\cos (c+d x)}{d}+\frac{\log \left(\sin \left(\frac{1}{2} (c+d x)\right)\right)}{d}-\frac{\log \left(\cos \left(\frac{1}{2} (c+d x)\right)\right)}{d}\right)","\frac{a A \tanh ^{-1}(\cos (c+d x))}{d}-\frac{a A \cos (c+d x)}{d}",1,"-(a*A*(Cos[c + d*x]/d - Log[Cos[(c + d*x)/2]]/d + Log[Sin[(c + d*x)/2]]/d))","A",1
11,1,25,29,0.0234889,"\int (a-a \csc (c+d x)) (A+A \csc (c+d x)) \sin ^2(c+d x) \, dx","Integrate[(a - a*Csc[c + d*x])*(A + A*Csc[c + d*x])*Sin[c + d*x]^2,x]","-\frac{a A (2 (c+d x)+\sin (2 (c+d x)))}{4 d}","-\frac{a A \sin (c+d x) \cos (c+d x)}{2 d}-\frac{1}{2} a A x",1,"-1/4*(a*A*(2*(c + d*x) + Sin[2*(c + d*x)]))/d","A",1
12,1,17,17,0.0069475,"\int (a-a \csc (c+d x)) (A+A \csc (c+d x)) \sin ^3(c+d x) \, dx","Integrate[(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",1
13,1,117,61,0.0392655,"\int \csc ^3(c+d x) (a+a \csc (c+d x)) (A-A \csc (c+d x)) \, dx","Integrate[Csc[c + d*x]^3*(a + a*Csc[c + d*x])*(A - A*Csc[c + d*x]),x]","-a A \left(-\frac{\csc ^4\left(\frac{1}{2} (c+d x)\right)}{64 d}+\frac{\csc ^2\left(\frac{1}{2} (c+d x)\right)}{32 d}+\frac{\sec ^4\left(\frac{1}{2} (c+d x)\right)}{64 d}-\frac{\sec ^2\left(\frac{1}{2} (c+d x)\right)}{32 d}-\frac{\log \left(\sin \left(\frac{1}{2} (c+d x)\right)\right)}{8 d}+\frac{\log \left(\cos \left(\frac{1}{2} (c+d x)\right)\right)}{8 d}\right)","-\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*(Csc[(c + d*x)/2]^2/(32*d) - Csc[(c + d*x)/2]^4/(64*d) + Log[Cos[(c + d*x)/2]]/(8*d) - Log[Sin[(c + d*x)/2]]/(8*d) - Sec[(c + d*x)/2]^2/(32*d) + Sec[(c + d*x)/2]^4/(64*d)))","A",1
14,1,17,17,0.0129892,"\int \csc ^2(c+d x) (a+a \csc (c+d x)) (A-A \csc (c+d x)) \, dx","Integrate[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",1
15,1,79,38,0.0346702,"\int \csc (c+d x) (a+a \csc (c+d x)) (A-A \csc (c+d x)) \, dx","Integrate[Csc[c + d*x]*(a + a*Csc[c + d*x])*(A - A*Csc[c + d*x]),x]","-a A \left(-\frac{\csc ^2\left(\frac{1}{2} (c+d x)\right)}{8 d}+\frac{\sec ^2\left(\frac{1}{2} (c+d x)\right)}{8 d}-\frac{\log \left(\sin \left(\frac{1}{2} (c+d x)\right)\right)}{2 d}+\frac{\log \left(\cos \left(\frac{1}{2} (c+d x)\right)\right)}{2 d}\right)","\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*(-1/8*Csc[(c + d*x)/2]^2/d + Log[Cos[(c + d*x)/2]]/(2*d) - Log[Sin[(c + d*x)/2]]/(2*d) + Sec[(c + d*x)/2]^2/(8*d)))","B",1
16,1,46,27,0.0217981,"\int (a+a \csc (c+d x)) (A-A \csc (c+d x)) \sin (c+d x) \, dx","Integrate[(a + a*Csc[c + d*x])*(A - A*Csc[c + d*x])*Sin[c + d*x],x]","-a A \left(\frac{\cos (c+d x)}{d}+\frac{\log \left(\sin \left(\frac{1}{2} (c+d x)\right)\right)}{d}-\frac{\log \left(\cos \left(\frac{1}{2} (c+d x)\right)\right)}{d}\right)","\frac{a A \tanh ^{-1}(\cos (c+d x))}{d}-\frac{a A \cos (c+d x)}{d}",1,"-(a*A*(Cos[c + d*x]/d - Log[Cos[(c + d*x)/2]]/d + Log[Sin[(c + d*x)/2]]/d))","A",1
17,1,25,29,0.0139789,"\int (a+a \csc (c+d x)) (A-A \csc (c+d x)) \sin ^2(c+d x) \, dx","Integrate[(a + a*Csc[c + d*x])*(A - A*Csc[c + d*x])*Sin[c + d*x]^2,x]","-\frac{a A (2 (c+d x)+\sin (2 (c+d x)))}{4 d}","-\frac{a A \sin (c+d x) \cos (c+d x)}{2 d}-\frac{1}{2} a A x",1,"-1/4*(a*A*(2*(c + d*x) + Sin[2*(c + d*x)]))/d","A",1
18,1,17,17,0.0058261,"\int (a+a \csc (c+d x)) (A-A \csc (c+d x)) \sin ^3(c+d x) \, dx","Integrate[(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",1
19,1,163,91,0.0628147,"\int \csc ^3(c+d x) (a-a \csc (c+d x)) (A-A \csc (c+d x)) \, dx","Integrate[Csc[c + d*x]^3*(a - a*Csc[c + d*x])*(A - A*Csc[c + d*x]),x]","\frac{4 a A \cot (c+d x)}{3 d}-\frac{a A \csc ^4\left(\frac{1}{2} (c+d x)\right)}{64 d}-\frac{7 a A \csc ^2\left(\frac{1}{2} (c+d x)\right)}{32 d}+\frac{a A \sec ^4\left(\frac{1}{2} (c+d x)\right)}{64 d}+\frac{7 a A \sec ^2\left(\frac{1}{2} (c+d x)\right)}{32 d}+\frac{7 a A \log \left(\sin \left(\frac{1}{2} (c+d x)\right)\right)}{8 d}-\frac{7 a A \log \left(\cos \left(\frac{1}{2} (c+d x)\right)\right)}{8 d}+\frac{2 a A \cot (c+d x) \csc ^2(c+d x)}{3 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,"(4*a*A*Cot[c + d*x])/(3*d) - (7*a*A*Csc[(c + d*x)/2]^2)/(32*d) - (a*A*Csc[(c + d*x)/2]^4)/(64*d) + (2*a*A*Cot[c + d*x]*Csc[c + d*x]^2)/(3*d) - (7*a*A*Log[Cos[(c + d*x)/2]])/(8*d) + (7*a*A*Log[Sin[(c + d*x)/2]])/(8*d) + (7*a*A*Sec[(c + d*x)/2]^2)/(32*d) + (a*A*Sec[(c + d*x)/2]^4)/(64*d)","A",1
20,1,116,70,0.0451625,"\int \csc ^2(c+d x) (a-a \csc (c+d x)) (A-A \csc (c+d x)) \, dx","Integrate[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 \csc ^2\left(\frac{1}{2} (c+d x)\right)}{4 d}-\frac{a A \sec ^2\left(\frac{1}{2} (c+d x)\right)}{4 d}-\frac{a A \log \left(\sin \left(\frac{1}{2} (c+d x)\right)\right)}{d}+\frac{a A \log \left(\cos \left(\frac{1}{2} (c+d x)\right)\right)}{d}-\frac{a A \cot (c+d x) \csc ^2(c+d x)}{3 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,"(-5*a*A*Cot[c + d*x])/(3*d) + (a*A*Csc[(c + d*x)/2]^2)/(4*d) - (a*A*Cot[c + d*x]*Csc[c + d*x]^2)/(3*d) + (a*A*Log[Cos[(c + d*x)/2]])/d - (a*A*Log[Sin[(c + d*x)/2]])/d - (a*A*Sec[(c + d*x)/2]^2)/(4*d)","A",1
21,1,137,51,0.0381784,"\int \csc (c+d x) (a-a \csc (c+d x)) (A-A \csc (c+d x)) \, dx","Integrate[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{a A \csc ^2\left(\frac{1}{2} (c+d x)\right)}{8 d}+\frac{a A \sec ^2\left(\frac{1}{2} (c+d x)\right)}{8 d}+\frac{a A \log \left(\sin \left(\frac{c}{2}+\frac{d x}{2}\right)\right)}{d}+\frac{a A \log \left(\sin \left(\frac{1}{2} (c+d x)\right)\right)}{2 d}-\frac{a A \log \left(\cos \left(\frac{c}{2}+\frac{d x}{2}\right)\right)}{d}-\frac{a A \log \left(\cos \left(\frac{1}{2} (c+d x)\right)\right)}{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,"(2*a*A*Cot[c + d*x])/d - (a*A*Csc[(c + d*x)/2]^2)/(8*d) - (a*A*Log[Cos[c/2 + (d*x)/2]])/d - (a*A*Log[Cos[(c + d*x)/2]])/(2*d) + (a*A*Log[Sin[c/2 + (d*x)/2]])/d + (a*A*Log[Sin[(c + d*x)/2]])/(2*d) + (a*A*Sec[(c + d*x)/2]^2)/(8*d)","B",1
22,1,72,33,0.026197,"\int (a-a \csc (c+d x)) (A-A \csc (c+d x)) \sin (c+d x) \, dx","Integrate[(a - a*Csc[c + d*x])*(A - A*Csc[c + d*x])*Sin[c + d*x],x]","\frac{a A \sin (c) \sin (d x)}{d}-\frac{a A \cos (c) \cos (d x)}{d}+\frac{a A \log \left(\sin \left(\frac{c}{2}+\frac{d x}{2}\right)\right)}{d}-\frac{a A \log \left(\cos \left(\frac{c}{2}+\frac{d x}{2}\right)\right)}{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*Cos[c]*Cos[d*x])/d - (a*A*Log[Cos[c/2 + (d*x)/2]])/d + (a*A*Log[Sin[c/2 + (d*x)/2]])/d + (a*A*Sin[c]*Sin[d*x])/d","B",1
23,1,35,42,0.0558157,"\int (a-a \csc (c+d x)) (A-A \csc (c+d x)) \sin ^2(c+d x) \, dx","Integrate[(a - a*Csc[c + d*x])*(A - A*Csc[c + d*x])*Sin[c + d*x]^2,x]","\frac{a A (6 (c+d x)-\sin (2 (c+d x))+8 \cos (c+d x))}{4 d}","\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,"(a*A*(6*(c + d*x) + 8*Cos[c + d*x] - Sin[2*(c + d*x)]))/(4*d)","A",1
24,1,44,54,0.1186719,"\int (a-a \csc (c+d x)) (A-A \csc (c+d x)) \sin ^3(c+d x) \, dx","Integrate[(a - a*Csc[c + d*x])*(A - A*Csc[c + d*x])*Sin[c + d*x]^3,x]","\frac{a A (6 (\sin (2 (c+d x))-2 (c+d x))-21 \cos (c+d x)+\cos (3 (c+d x)))}{12 d}","\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*(-21*Cos[c + d*x] + Cos[3*(c + d*x)] + 6*(-2*(c + d*x) + Sin[2*(c + d*x)])))/(12*d)","A",1