# Maple integration test file: "4 Trig functions\4.6 Cosecant\4.6.3.1 (a+b csc)^m (d csc)^n (A+B csc).txt"

lst:=[

# Integrands of the form (a+b Csc[e+f x])^m (d Csc[e+f x])^n (A+B Csc[e+f x])

# Integrands of the form (a+a Csc[e+f x])^m (d Csc[e+f x])^n (A+B Csc[e+f x])

# Integrands of the form Csc[c+d x]^m (A+B Csc[c+d x]) (a+a Csc[c+d x])^n

# Integrands of the form Csc[c+d x]^m (A+B Csc[c+d x]) (a+a Csc[c+d x])^(n/2)

# Integrands of the form Csc[c+d x]^m (A+A Csc[c+d x]) (a+a Csc[c+d x])^n
[csc(c+d*x)^3*(a+a*csc(c+d*x))*(A+A*csc(c+d*x)),x,7,-7/8*a*A*arctanh(cos(c+d*x))/d-2*a*A*cot(c+d*x)/d-2/3*a*A*cot(c+d*x)^3/d-7/8*a*A*cot(c+d*x)*csc(c+d*x)/d-1/4*a*A*cot(c+d*x)*csc(c+d*x)^3/d],
[csc(c+d*x)^2*(a+a*csc(c+d*x))*(A+A*csc(c+d*x)),x,7,-a*A*arctanh(cos(c+d*x))/d-5/3*a*A*cot(c+d*x)/d-a*A*cot(c+d*x)*csc(c+d*x)/d-1/3*a*A*cot(c+d*x)*csc(c+d*x)^2/d],
[csc(c+d*x)*(a+a*csc(c+d*x))*(A+A*csc(c+d*x)),x,6,-3/2*a*A*arctanh(cos(c+d*x))/d-2*a*A*cot(c+d*x)/d-1/2*a*A*cot(c+d*x)*csc(c+d*x)/d],
[(a+a*csc(c+d*x))*(A+A*csc(c+d*x))*sin(c+d*x),x,5,2*a*A*x-a*A*arctanh(cos(c+d*x))/d-a*A*cos(c+d*x)/d],
[(a+a*csc(c+d*x))*(A+A*csc(c+d*x))*sin(c+d*x)^2,x,5,3/2*a*A*x-2*a*A*cos(c+d*x)/d-1/2*a*A*cos(c+d*x)*sin(c+d*x)/d],
[(a+a*csc(c+d*x))*(A+A*csc(c+d*x))*sin(c+d*x)^3,x,7,a*A*x-2*a*A*cos(c+d*x)/d+1/3*a*A*cos(c+d*x)^3/d-a*A*cos(c+d*x)*sin(c+d*x)/d],
[csc(c+d*x)^3*(a-a*csc(c+d*x))*(A+A*csc(c+d*x)),x,4,-1/8*a*A*arctanh(cos(c+d*x))/d-1/8*a*A*cot(c+d*x)*csc(c+d*x)/d+1/4*a*A*cot(c+d*x)*csc(c+d*x)^3/d],
[csc(c+d*x)^2*(a-a*csc(c+d*x))*(A+A*csc(c+d*x)),x,3,1/3*a*A*cot(c+d*x)^3/d],
[csc(c+d*x)*(a-a*csc(c+d*x))*(A+A*csc(c+d*x)),x,3,-1/2*a*A*arctanh(cos(c+d*x))/d+1/2*a*A*cot(c+d*x)*csc(c+d*x)/d],
[(a-a*csc(c+d*x))*(A+A*csc(c+d*x))*sin(c+d*x),x,4,a*A*arctanh(cos(c+d*x))/d-a*A*cos(c+d*x)/d],
[(a-a*csc(c+d*x))*(A+A*csc(c+d*x))*sin(c+d*x)^2,x,3,-1/2*a*A*x-1/2*a*A*cos(c+d*x)*sin(c+d*x)/d],
[(a-a*csc(c+d*x))*(A+A*csc(c+d*x))*sin(c+d*x)^3,x,3,1/3*a*A*cos(c+d*x)^3/d],

# Integrands of the form Csc[c+d x]^m (A-A Csc[c+d x]) (a+a Csc[c+d x])^n
[csc(c+d*x)^3*(a+a*csc(c+d*x))*(A-A*csc(c+d*x)),x,4,-1/8*a*A*arctanh(cos(c+d*x))/d-1/8*a*A*cot(c+d*x)*csc(c+d*x)/d+1/4*a*A*cot(c+d*x)*csc(c+d*x)^3/d],
[csc(c+d*x)^2*(a+a*csc(c+d*x))*(A-A*csc(c+d*x)),x,3,1/3*a*A*cot(c+d*x)^3/d],
[csc(c+d*x)*(a+a*csc(c+d*x))*(A-A*csc(c+d*x)),x,3,-1/2*a*A*arctanh(cos(c+d*x))/d+1/2*a*A*cot(c+d*x)*csc(c+d*x)/d],
[(a+a*csc(c+d*x))*(A-A*csc(c+d*x))/csc(c+d*x),x,4,a*A*arctanh(cos(c+d*x))/d-a*A*cos(c+d*x)/d],
[(a+a*csc(c+d*x))*(A-A*csc(c+d*x))/csc(c+d*x)^2,x,3,-1/2*a*A*x-1/2*a*A*cos(c+d*x)*sin(c+d*x)/d],
[(a+a*csc(c+d*x))*(A-A*csc(c+d*x))/csc(c+d*x)^3,x,3,1/3*a*A*cos(c+d*x)^3/d],
[csc(c+d*x)^3*(a-a*csc(c+d*x))*(A-A*csc(c+d*x)),x,7,-7/8*a*A*arctanh(cos(c+d*x))/d+2*a*A*cot(c+d*x)/d+2/3*a*A*cot(c+d*x)^3/d-7/8*a*A*cot(c+d*x)*csc(c+d*x)/d-1/4*a*A*cot(c+d*x)*csc(c+d*x)^3/d],
[csc(c+d*x)^2*(a-a*csc(c+d*x))*(A-A*csc(c+d*x)),x,7,a*A*arctanh(cos(c+d*x))/d-5/3*a*A*cot(c+d*x)/d+a*A*cot(c+d*x)*csc(c+d*x)/d-1/3*a*A*cot(c+d*x)*csc(c+d*x)^2/d],
[csc(c+d*x)*(a-a*csc(c+d*x))*(A-A*csc(c+d*x)),x,6,-3/2*a*A*arctanh(cos(c+d*x))/d+2*a*A*cot(c+d*x)/d-1/2*a*A*cot(c+d*x)*csc(c+d*x)/d],
[(a-a*csc(c+d*x))*(A-A*csc(c+d*x))/csc(c+d*x),x,5,-2*a*A*x-a*A*arctanh(cos(c+d*x))/d-a*A*cos(c+d*x)/d],
[(a-a*csc(c+d*x))*(A-A*csc(c+d*x))/csc(c+d*x)^2,x,5,3/2*a*A*x+2*a*A*cos(c+d*x)/d-1/2*a*A*cos(c+d*x)*sin(c+d*x)/d],
[(a-a*csc(c+d*x))*(A-A*csc(c+d*x))/csc(c+d*x)^3,x,7,-a*A*x-2*a*A*cos(c+d*x)/d+1/3*a*A*cos(c+d*x)^3/d+a*A*cos(c+d*x)*sin(c+d*x)/d]]:

# Integrands of the form (a+a Csc[e+f x])^m (d Sin[e+f x])^n (A+B Csc[e+f x])

# Integrands of the form (a+b Csc[e+f x])^m (d Csc[e+f x])^n (A+B Csc[e+f x])

# Integrands of the form Csc[c+d x]^m (A+B Csc[c+d x]) (a+b Csc[c+d x])^n

# Integrands of the form Csc[c+d x]^m (A+B Csc[c+d x]) (a+b Csc[c+d x])^(n/2)

# Integrands of the form (a+b Csc[e+f x])^m (d Sin[e+f x])^n (A+B Csc[e+f x])
