1,0,0,0,0.000000," ","integrate(csc(d*x+c)**3*(a+a*csc(d*x+c))*(A+A*csc(d*x+c)),x)","A a \left(\int \csc^{3}{\left(c + d x \right)}\, dx + \int 2 \csc^{4}{\left(c + d x \right)}\, dx + \int \csc^{5}{\left(c + d x \right)}\, dx\right)"," ",0,"A*a*(Integral(csc(c + d*x)**3, x) + Integral(2*csc(c + d*x)**4, x) + Integral(csc(c + d*x)**5, x))","F",0
2,0,0,0,0.000000," ","integrate(csc(d*x+c)**2*(a+a*csc(d*x+c))*(A+A*csc(d*x+c)),x)","A a \left(\int \csc^{2}{\left(c + d x \right)}\, dx + \int 2 \csc^{3}{\left(c + d x \right)}\, dx + \int \csc^{4}{\left(c + d x \right)}\, dx\right)"," ",0,"A*a*(Integral(csc(c + d*x)**2, x) + Integral(2*csc(c + d*x)**3, x) + Integral(csc(c + d*x)**4, x))","F",0
3,0,0,0,0.000000," ","integrate(csc(d*x+c)*(a+a*csc(d*x+c))*(A+A*csc(d*x+c)),x)","A a \left(\int \csc{\left(c + d x \right)}\, dx + \int 2 \csc^{2}{\left(c + d x \right)}\, dx + \int \csc^{3}{\left(c + d x \right)}\, dx\right)"," ",0,"A*a*(Integral(csc(c + d*x), x) + Integral(2*csc(c + d*x)**2, x) + Integral(csc(c + d*x)**3, x))","F",0
4,0,0,0,0.000000," ","integrate((a+a*csc(d*x+c))*(A+A*csc(d*x+c))*sin(d*x+c),x)","A a \left(\int 2 \sin{\left(c + d x \right)} \csc{\left(c + d x \right)}\, dx + \int \sin{\left(c + d x \right)} \csc^{2}{\left(c + d x \right)}\, dx + \int \sin{\left(c + d x \right)}\, dx\right)"," ",0,"A*a*(Integral(2*sin(c + d*x)*csc(c + d*x), x) + Integral(sin(c + d*x)*csc(c + d*x)**2, x) + Integral(sin(c + d*x), x))","F",0
5,0,0,0,0.000000," ","integrate((a+a*csc(d*x+c))*(A+A*csc(d*x+c))*sin(d*x+c)**2,x)","A a \left(\int 2 \sin^{2}{\left(c + d x \right)} \csc{\left(c + d x \right)}\, dx + \int \sin^{2}{\left(c + d x \right)} \csc^{2}{\left(c + d x \right)}\, dx + \int \sin^{2}{\left(c + d x \right)}\, dx\right)"," ",0,"A*a*(Integral(2*sin(c + d*x)**2*csc(c + d*x), x) + Integral(sin(c + d*x)**2*csc(c + d*x)**2, x) + Integral(sin(c + d*x)**2, x))","F",0
6,0,0,0,0.000000," ","integrate((a+a*csc(d*x+c))*(A+A*csc(d*x+c))*sin(d*x+c)**3,x)","A a \left(\int 2 \sin^{3}{\left(c + d x \right)} \csc{\left(c + d x \right)}\, dx + \int \sin^{3}{\left(c + d x \right)} \csc^{2}{\left(c + d x \right)}\, dx + \int \sin^{3}{\left(c + d x \right)}\, dx\right)"," ",0,"A*a*(Integral(2*sin(c + d*x)**3*csc(c + d*x), x) + Integral(sin(c + d*x)**3*csc(c + d*x)**2, x) + Integral(sin(c + d*x)**3, x))","F",0
7,0,0,0,0.000000," ","integrate(csc(d*x+c)**3*(a-a*csc(d*x+c))*(A+A*csc(d*x+c)),x)","- A a \left(\int \left(- \csc^{3}{\left(c + d x \right)}\right)\, dx + \int \csc^{5}{\left(c + d x \right)}\, dx\right)"," ",0,"-A*a*(Integral(-csc(c + d*x)**3, x) + Integral(csc(c + d*x)**5, x))","F",0
8,1,54,0,2.406426," ","integrate(csc(d*x+c)**2*(a-a*csc(d*x+c))*(A+A*csc(d*x+c)),x)","\begin{cases} \frac{- A a \left(- \frac{\cot^{3}{\left(c + d x \right)}}{3} - \cot{\left(c + d x \right)}\right) - A a \cot{\left(c + d x \right)}}{d} & \text{for}\: d \neq 0 \\x \left(A \csc{\left(c \right)} + A\right) \left(- a \csc{\left(c \right)} + a\right) \csc^{2}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((-A*a*(-cot(c + d*x)**3/3 - cot(c + d*x)) - A*a*cot(c + d*x))/d, Ne(d, 0)), (x*(A*csc(c) + A)*(-a*csc(c) + a)*csc(c)**2, True))","A",0
9,0,0,0,0.000000," ","integrate(csc(d*x+c)*(a-a*csc(d*x+c))*(A+A*csc(d*x+c)),x)","- A a \left(\int \left(- \csc{\left(c + d x \right)}\right)\, dx + \int \csc^{3}{\left(c + d x \right)}\, dx\right)"," ",0,"-A*a*(Integral(-csc(c + d*x), x) + Integral(csc(c + d*x)**3, x))","F",0
10,0,0,0,0.000000," ","integrate((a-a*csc(d*x+c))*(A+A*csc(d*x+c))*sin(d*x+c),x)","- A a \left(\int \sin{\left(c + d x \right)} \csc^{2}{\left(c + d x \right)}\, dx + \int \left(- \sin{\left(c + d x \right)}\right)\, dx\right)"," ",0,"-A*a*(Integral(sin(c + d*x)*csc(c + d*x)**2, x) + Integral(-sin(c + d*x), x))","F",0
11,1,54,0,5.531187," ","integrate((a-a*csc(d*x+c))*(A+A*csc(d*x+c))*sin(d*x+c)**2,x)","- A a x + A a \left(\begin{cases} \frac{x \sin^{2}{\left(c + d x \right)}}{2} + \frac{x \cos^{2}{\left(c + d x \right)}}{2} - \frac{\sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2 d} & \text{for}\: d \neq 0 \\x \sin^{2}{\left(c \right)} & \text{otherwise} \end{cases}\right)"," ",0,"-A*a*x + A*a*Piecewise((x*sin(c + d*x)**2/2 + x*cos(c + d*x)**2/2 - sin(c + d*x)*cos(c + d*x)/(2*d), Ne(d, 0)), (x*sin(c)**2, True))","A",0
12,0,0,0,0.000000," ","integrate((a-a*csc(d*x+c))*(A+A*csc(d*x+c))*sin(d*x+c)**3,x)","- A a \left(\int \sin^{3}{\left(c + d x \right)} \csc^{2}{\left(c + d x \right)}\, dx + \int \left(- \sin^{3}{\left(c + d x \right)}\right)\, dx\right)"," ",0,"-A*a*(Integral(sin(c + d*x)**3*csc(c + d*x)**2, x) + Integral(-sin(c + d*x)**3, x))","F",0
13,0,0,0,0.000000," ","integrate(csc(d*x+c)**3*(a+a*csc(d*x+c))*(A-A*csc(d*x+c)),x)","- A a \left(\int \left(- \csc^{3}{\left(c + d x \right)}\right)\, dx + \int \csc^{5}{\left(c + d x \right)}\, dx\right)"," ",0,"-A*a*(Integral(-csc(c + d*x)**3, x) + Integral(csc(c + d*x)**5, x))","F",0
14,1,54,0,3.193882," ","integrate(csc(d*x+c)**2*(a+a*csc(d*x+c))*(A-A*csc(d*x+c)),x)","\begin{cases} \frac{- A a \left(- \frac{\cot^{3}{\left(c + d x \right)}}{3} - \cot{\left(c + d x \right)}\right) - A a \cot{\left(c + d x \right)}}{d} & \text{for}\: d \neq 0 \\x \left(- A \csc{\left(c \right)} + A\right) \left(a \csc{\left(c \right)} + a\right) \csc^{2}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((-A*a*(-cot(c + d*x)**3/3 - cot(c + d*x)) - A*a*cot(c + d*x))/d, Ne(d, 0)), (x*(-A*csc(c) + A)*(a*csc(c) + a)*csc(c)**2, True))","A",0
15,0,0,0,0.000000," ","integrate(csc(d*x+c)*(a+a*csc(d*x+c))*(A-A*csc(d*x+c)),x)","- A a \left(\int \left(- \csc{\left(c + d x \right)}\right)\, dx + \int \csc^{3}{\left(c + d x \right)}\, dx\right)"," ",0,"-A*a*(Integral(-csc(c + d*x), x) + Integral(csc(c + d*x)**3, x))","F",0
16,1,75,0,11.779780," ","integrate((a+a*csc(d*x+c))*(A-A*csc(d*x+c))/csc(d*x+c),x)","A a \left(\begin{cases} - \frac{\cot{\left(c + d x \right)}}{d \csc{\left(c + d x \right)}} & \text{for}\: d \neq 0 \\\frac{x}{\csc{\left(c \right)}} & \text{otherwise} \end{cases}\right) - A a \left(\begin{cases} \frac{x \cot{\left(c \right)} \csc{\left(c \right)}}{\cot{\left(c \right)} + \csc{\left(c \right)}} + \frac{x \csc^{2}{\left(c \right)}}{\cot{\left(c \right)} + \csc{\left(c \right)}} & \text{for}\: d = 0 \\- \frac{\log{\left(\cot{\left(c + d x \right)} + \csc{\left(c + d x \right)} \right)}}{d} & \text{otherwise} \end{cases}\right)"," ",0,"A*a*Piecewise((-cot(c + d*x)/(d*csc(c + d*x)), Ne(d, 0)), (x/csc(c), True)) - A*a*Piecewise((x*cot(c)*csc(c)/(cot(c) + csc(c)) + x*csc(c)**2/(cot(c) + csc(c)), Eq(d, 0)), (-log(cot(c + d*x) + csc(c + d*x))/d, True))","A",0
17,1,85,0,7.062911," ","integrate((a+a*csc(d*x+c))*(A-A*csc(d*x+c))/csc(d*x+c)**2,x)","\begin{cases} \frac{A a x \cot^{2}{\left(c + d x \right)}}{2 \csc^{2}{\left(c + d x \right)}} - A a x + \frac{A a x}{2 \csc^{2}{\left(c + d x \right)}} - \frac{A a \cot{\left(c + d x \right)}}{2 d \csc^{2}{\left(c + d x \right)}} & \text{for}\: d \neq 0 \\\frac{x \left(- A \csc{\left(c \right)} + A\right) \left(a \csc{\left(c \right)} + a\right)}{\csc^{2}{\left(c \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((A*a*x*cot(c + d*x)**2/(2*csc(c + d*x)**2) - A*a*x + A*a*x/(2*csc(c + d*x)**2) - A*a*cot(c + d*x)/(2*d*csc(c + d*x)**2), Ne(d, 0)), (x*(-A*csc(c) + A)*(a*csc(c) + a)/csc(c)**2, True))","A",0
18,1,83,0,10.965108," ","integrate((a+a*csc(d*x+c))*(A-A*csc(d*x+c))/csc(d*x+c)**3,x)","\begin{cases} - \frac{2 A a \cot^{3}{\left(c + d x \right)}}{3 d \csc^{3}{\left(c + d x \right)}} + \frac{A a \cot{\left(c + d x \right)}}{d \csc{\left(c + d x \right)}} - \frac{A a \cot{\left(c + d x \right)}}{d \csc^{3}{\left(c + d x \right)}} & \text{for}\: d \neq 0 \\\frac{x \left(- A \csc{\left(c \right)} + A\right) \left(a \csc{\left(c \right)} + a\right)}{\csc^{3}{\left(c \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2*A*a*cot(c + d*x)**3/(3*d*csc(c + d*x)**3) + A*a*cot(c + d*x)/(d*csc(c + d*x)) - A*a*cot(c + d*x)/(d*csc(c + d*x)**3), Ne(d, 0)), (x*(-A*csc(c) + A)*(a*csc(c) + a)/csc(c)**3, True))","A",0
19,0,0,0,0.000000," ","integrate(csc(d*x+c)**3*(a-a*csc(d*x+c))*(A-A*csc(d*x+c)),x)","A a \left(\int \csc^{3}{\left(c + d x \right)}\, dx + \int \left(- 2 \csc^{4}{\left(c + d x \right)}\right)\, dx + \int \csc^{5}{\left(c + d x \right)}\, dx\right)"," ",0,"A*a*(Integral(csc(c + d*x)**3, x) + Integral(-2*csc(c + d*x)**4, x) + Integral(csc(c + d*x)**5, x))","F",0
20,0,0,0,0.000000," ","integrate(csc(d*x+c)**2*(a-a*csc(d*x+c))*(A-A*csc(d*x+c)),x)","A a \left(\int \csc^{2}{\left(c + d x \right)}\, dx + \int \left(- 2 \csc^{3}{\left(c + d x \right)}\right)\, dx + \int \csc^{4}{\left(c + d x \right)}\, dx\right)"," ",0,"A*a*(Integral(csc(c + d*x)**2, x) + Integral(-2*csc(c + d*x)**3, x) + Integral(csc(c + d*x)**4, x))","F",0
21,0,0,0,0.000000," ","integrate(csc(d*x+c)*(a-a*csc(d*x+c))*(A-A*csc(d*x+c)),x)","A a \left(\int \csc{\left(c + d x \right)}\, dx + \int \left(- 2 \csc^{2}{\left(c + d x \right)}\right)\, dx + \int \csc^{3}{\left(c + d x \right)}\, dx\right)"," ",0,"A*a*(Integral(csc(c + d*x), x) + Integral(-2*csc(c + d*x)**2, x) + Integral(csc(c + d*x)**3, x))","F",0
22,1,82,0,12.972575," ","integrate((a-a*csc(d*x+c))*(A-A*csc(d*x+c))/csc(d*x+c),x)","- 2 A a x + A a \left(\begin{cases} - \frac{\cot{\left(c + d x \right)}}{d \csc{\left(c + d x \right)}} & \text{for}\: d \neq 0 \\\frac{x}{\csc{\left(c \right)}} & \text{otherwise} \end{cases}\right) + A a \left(\begin{cases} \frac{x \cot{\left(c \right)} \csc{\left(c \right)}}{\cot{\left(c \right)} + \csc{\left(c \right)}} + \frac{x \csc^{2}{\left(c \right)}}{\cot{\left(c \right)} + \csc{\left(c \right)}} & \text{for}\: d = 0 \\- \frac{\log{\left(\cot{\left(c + d x \right)} + \csc{\left(c + d x \right)} \right)}}{d} & \text{otherwise} \end{cases}\right)"," ",0,"-2*A*a*x + A*a*Piecewise((-cot(c + d*x)/(d*csc(c + d*x)), Ne(d, 0)), (x/csc(c), True)) + A*a*Piecewise((x*cot(c)*csc(c)/(cot(c) + csc(c)) + x*csc(c)**2/(cot(c) + csc(c)), Eq(d, 0)), (-log(cot(c + d*x) + csc(c + d*x))/d, True))","A",0
23,1,105,0,10.069479," ","integrate((a-a*csc(d*x+c))*(A-A*csc(d*x+c))/csc(d*x+c)**2,x)","\begin{cases} \frac{A a x \cot^{2}{\left(c + d x \right)}}{2 \csc^{2}{\left(c + d x \right)}} + A a x + \frac{A a x}{2 \csc^{2}{\left(c + d x \right)}} + \frac{2 A a \cot{\left(c + d x \right)}}{d \csc{\left(c + d x \right)}} - \frac{A a \cot{\left(c + d x \right)}}{2 d \csc^{2}{\left(c + d x \right)}} & \text{for}\: d \neq 0 \\\frac{x \left(- A \csc{\left(c \right)} + A\right) \left(- a \csc{\left(c \right)} + a\right)}{\csc^{2}{\left(c \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((A*a*x*cot(c + d*x)**2/(2*csc(c + d*x)**2) + A*a*x + A*a*x/(2*csc(c + d*x)**2) + 2*A*a*cot(c + d*x)/(d*csc(c + d*x)) - A*a*cot(c + d*x)/(2*d*csc(c + d*x)**2), Ne(d, 0)), (x*(-A*csc(c) + A)*(-a*csc(c) + a)/csc(c)**2, True))","A",0
24,1,139,0,13.239479," ","integrate((a-a*csc(d*x+c))*(A-A*csc(d*x+c))/csc(d*x+c)**3,x)","\begin{cases} - \frac{A a x \cot^{2}{\left(c + d x \right)}}{\csc^{2}{\left(c + d x \right)}} - \frac{A a x}{\csc^{2}{\left(c + d x \right)}} - \frac{2 A a \cot^{3}{\left(c + d x \right)}}{3 d \csc^{3}{\left(c + d x \right)}} - \frac{A a \cot{\left(c + d x \right)}}{d \csc{\left(c + d x \right)}} + \frac{A a \cot{\left(c + d x \right)}}{d \csc^{2}{\left(c + d x \right)}} - \frac{A a \cot{\left(c + d x \right)}}{d \csc^{3}{\left(c + d x \right)}} & \text{for}\: d \neq 0 \\\frac{x \left(- A \csc{\left(c \right)} + A\right) \left(- a \csc{\left(c \right)} + a\right)}{\csc^{3}{\left(c \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-A*a*x*cot(c + d*x)**2/csc(c + d*x)**2 - A*a*x/csc(c + d*x)**2 - 2*A*a*cot(c + d*x)**3/(3*d*csc(c + d*x)**3) - A*a*cot(c + d*x)/(d*csc(c + d*x)) + A*a*cot(c + d*x)/(d*csc(c + d*x)**2) - A*a*cot(c + d*x)/(d*csc(c + d*x)**3), Ne(d, 0)), (x*(-A*csc(c) + A)*(-a*csc(c) + a)/csc(c)**3, True))","A",0
