1,1,99,83,1.234000," ","int(csc(d*x+c)^3*(a+a*csc(d*x+c))*(A+A*csc(d*x+c)),x)","-\frac{a A \cot \left(d x +c \right) \left(\csc^{3}\left(d x +c \right)\right)}{4 d}-\frac{7 a A \cot \left(d x +c \right) \csc \left(d x +c \right)}{8 d}+\frac{7 a A \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{8 d}-\frac{4 a A \cot \left(d x +c \right)}{3 d}-\frac{2 a A \cot \left(d x +c \right) \left(\csc^{2}\left(d x +c \right)\right)}{3 d}"," ",0,"-1/4*a*A*cot(d*x+c)*csc(d*x+c)^3/d-7/8*a*A*cot(d*x+c)*csc(d*x+c)/d+7/8/d*a*A*ln(csc(d*x+c)-cot(d*x+c))-4/3*a*A*cot(d*x+c)/d-2/3*a*A*cot(d*x+c)*csc(d*x+c)^2/d","A"
2,1,77,68,1.224000," ","int(csc(d*x+c)^2*(a+a*csc(d*x+c))*(A+A*csc(d*x+c)),x)","-\frac{5 a A \cot \left(d x +c \right)}{3 d}-\frac{a A \cot \left(d x +c \right) \left(\csc^{2}\left(d x +c \right)\right)}{3 d}-\frac{a A \cot \left(d x +c \right) \csc \left(d x +c \right)}{d}+\frac{a A \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{d}"," ",0,"-5/3*a*A*cot(d*x+c)/d-1/3*a*A*cot(d*x+c)*csc(d*x+c)^2/d-a*A*cot(d*x+c)*csc(d*x+c)/d+1/d*a*A*ln(csc(d*x+c)-cot(d*x+c))","A"
3,1,57,47,1.220000," ","int(csc(d*x+c)*(a+a*csc(d*x+c))*(A+A*csc(d*x+c)),x)","-\frac{a A \cot \left(d x +c \right) \csc \left(d x +c \right)}{2 d}+\frac{3 a A \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{2 d}-\frac{2 a A \cot \left(d x +c \right)}{d}"," ",0,"-1/2*a*A*cot(d*x+c)*csc(d*x+c)/d+3/2/d*a*A*ln(csc(d*x+c)-cot(d*x+c))-2*a*A*cot(d*x+c)/d","A"
4,1,50,33,1.256000," ","int((a+a*csc(d*x+c))*(A+A*csc(d*x+c))*sin(d*x+c),x)","2 a A x -\frac{a A \cos \left(d x +c \right)}{d}+\frac{a A \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{d}+\frac{2 A a c}{d}"," ",0,"2*a*A*x-a*A*cos(d*x+c)/d+1/d*a*A*ln(csc(d*x+c)-cot(d*x+c))+2/d*A*a*c","A"
5,1,49,38,0.908000," ","int((a+a*csc(d*x+c))*(A+A*csc(d*x+c))*sin(d*x+c)^2,x)","\frac{a A \left(-\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{2}+\frac{d x}{2}+\frac{c}{2}\right)-2 A \cos \left(d x +c \right) a +a A \left(d x +c \right)}{d}"," ",0,"1/d*(a*A*(-1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c)-2*A*cos(d*x+c)*a+a*A*(d*x+c))","A"
6,1,62,52,1.270000," ","int((a+a*csc(d*x+c))*(A+A*csc(d*x+c))*sin(d*x+c)^3,x)","\frac{-\frac{a A \left(2+\sin^{2}\left(d x +c \right)\right) \cos \left(d x +c \right)}{3}+2 a A \left(-\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{2}+\frac{d x}{2}+\frac{c}{2}\right)-A \cos \left(d x +c \right) a}{d}"," ",0,"1/d*(-1/3*a*A*(2+sin(d*x+c)^2)*cos(d*x+c)+2*a*A*(-1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c)-A*cos(d*x+c)*a)","A"
7,1,65,55,1.042000," ","int(csc(d*x+c)^3*(a-a*csc(d*x+c))*(A+A*csc(d*x+c)),x)","\frac{a A \cot \left(d x +c \right) \left(\csc^{3}\left(d x +c \right)\right)}{4 d}-\frac{a A \cot \left(d x +c \right) \csc \left(d x +c \right)}{8 d}+\frac{a A \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{8 d}"," ",0,"1/4*a*A*cot(d*x+c)*csc(d*x+c)^3/d-1/8*a*A*cot(d*x+c)*csc(d*x+c)/d+1/8/d*a*A*ln(csc(d*x+c)-cot(d*x+c))","A"
8,1,38,15,1.000000," ","int(csc(d*x+c)^2*(a-a*csc(d*x+c))*(A+A*csc(d*x+c)),x)","\frac{-a A \left(-\frac{2}{3}-\frac{\left(\csc^{2}\left(d x +c \right)\right)}{3}\right) \cot \left(d x +c \right)-a A \cot \left(d x +c \right)}{d}"," ",0,"1/d*(-a*A*(-2/3-1/3*csc(d*x+c)^2)*cot(d*x+c)-a*A*cot(d*x+c))","B"
9,1,44,34,0.786000," ","int(csc(d*x+c)*(a-a*csc(d*x+c))*(A+A*csc(d*x+c)),x)","\frac{a A \cot \left(d x +c \right) \csc \left(d x +c \right)}{2 d}+\frac{a A \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{2 d}"," ",0,"1/2*a*A*cot(d*x+c)*csc(d*x+c)/d+1/2/d*a*A*ln(csc(d*x+c)-cot(d*x+c))","A"
10,1,38,27,0.595000," ","int((a-a*csc(d*x+c))*(A+A*csc(d*x+c))*sin(d*x+c),x)","-\frac{a A \cos \left(d x +c \right)}{d}-\frac{a A \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{d}"," ",0,"-a*A*cos(d*x+c)/d-1/d*a*A*ln(csc(d*x+c)-cot(d*x+c))","A"
11,1,40,25,0.502000," ","int((a-a*csc(d*x+c))*(A+A*csc(d*x+c))*sin(d*x+c)^2,x)","\frac{a A \left(-\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{2}+\frac{d x}{2}+\frac{c}{2}\right)-a A \left(d x +c \right)}{d}"," ",0,"1/d*(a*A*(-1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c)-a*A*(d*x+c))","A"
12,1,35,15,0.768000," ","int((a-a*csc(d*x+c))*(A+A*csc(d*x+c))*sin(d*x+c)^3,x)","\frac{-\frac{a A \left(2+\sin^{2}\left(d x +c \right)\right) \cos \left(d x +c \right)}{3}+A \cos \left(d x +c \right) a}{d}"," ",0,"1/d*(-1/3*a*A*(2+sin(d*x+c)^2)*cos(d*x+c)+A*cos(d*x+c)*a)","B"
13,1,65,55,1.024000," ","int(csc(d*x+c)^3*(a+a*csc(d*x+c))*(A-A*csc(d*x+c)),x)","\frac{a A \cot \left(d x +c \right) \left(\csc^{3}\left(d x +c \right)\right)}{4 d}-\frac{a A \cot \left(d x +c \right) \csc \left(d x +c \right)}{8 d}+\frac{a A \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{8 d}"," ",0,"1/4*a*A*cot(d*x+c)*csc(d*x+c)^3/d-1/8*a*A*cot(d*x+c)*csc(d*x+c)/d+1/8/d*a*A*ln(csc(d*x+c)-cot(d*x+c))","A"
14,1,38,15,1.038000," ","int(csc(d*x+c)^2*(a+a*csc(d*x+c))*(A-A*csc(d*x+c)),x)","\frac{-a A \left(-\frac{2}{3}-\frac{\left(\csc^{2}\left(d x +c \right)\right)}{3}\right) \cot \left(d x +c \right)-a A \cot \left(d x +c \right)}{d}"," ",0,"1/d*(-a*A*(-2/3-1/3*csc(d*x+c)^2)*cot(d*x+c)-a*A*cot(d*x+c))","B"
15,1,44,34,0.811000," ","int(csc(d*x+c)*(a+a*csc(d*x+c))*(A-A*csc(d*x+c)),x)","\frac{a A \cot \left(d x +c \right) \csc \left(d x +c \right)}{2 d}+\frac{a A \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{2 d}"," ",0,"1/2*a*A*cot(d*x+c)*csc(d*x+c)/d+1/2/d*a*A*ln(csc(d*x+c)-cot(d*x+c))","A"
16,1,38,27,0.148000," ","int((a+a*csc(d*x+c))*(A-A*csc(d*x+c))/csc(d*x+c),x)","-\frac{a A \cos \left(d x +c \right)}{d}-\frac{a A \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{d}"," ",0,"-a*A*cos(d*x+c)/d-1/d*a*A*ln(csc(d*x+c)-cot(d*x+c))","A"
17,1,40,25,0.204000," ","int((a+a*csc(d*x+c))*(A-A*csc(d*x+c))/csc(d*x+c)^2,x)","\frac{a A \left(-\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{2}+\frac{d x}{2}+\frac{c}{2}\right)-a A \left(d x +c \right)}{d}"," ",0,"1/d*(a*A*(-1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c)-a*A*(d*x+c))","A"
18,1,35,15,0.883000," ","int((a+a*csc(d*x+c))*(A-A*csc(d*x+c))/csc(d*x+c)^3,x)","\frac{-\frac{a A \left(2+\sin^{2}\left(d x +c \right)\right) \cos \left(d x +c \right)}{3}+A \cos \left(d x +c \right) a}{d}"," ",0,"1/d*(-1/3*a*A*(2+sin(d*x+c)^2)*cos(d*x+c)+A*cos(d*x+c)*a)","B"
19,1,99,83,1.425000," ","int(csc(d*x+c)^3*(a-a*csc(d*x+c))*(A-A*csc(d*x+c)),x)","-\frac{a A \cot \left(d x +c \right) \left(\csc^{3}\left(d x +c \right)\right)}{4 d}-\frac{7 a A \cot \left(d x +c \right) \csc \left(d x +c \right)}{8 d}+\frac{7 a A \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{8 d}+\frac{4 a A \cot \left(d x +c \right)}{3 d}+\frac{2 a A \cot \left(d x +c \right) \left(\csc^{2}\left(d x +c \right)\right)}{3 d}"," ",0,"-1/4*a*A*cot(d*x+c)*csc(d*x+c)^3/d-7/8*a*A*cot(d*x+c)*csc(d*x+c)/d+7/8/d*a*A*ln(csc(d*x+c)-cot(d*x+c))+4/3*a*A*cot(d*x+c)/d+2/3*a*A*cot(d*x+c)*csc(d*x+c)^2/d","A"
20,1,77,66,1.320000," ","int(csc(d*x+c)^2*(a-a*csc(d*x+c))*(A-A*csc(d*x+c)),x)","-\frac{5 a A \cot \left(d x +c \right)}{3 d}-\frac{a A \cot \left(d x +c \right) \left(\csc^{2}\left(d x +c \right)\right)}{3 d}+\frac{a A \cot \left(d x +c \right) \csc \left(d x +c \right)}{d}-\frac{a A \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{d}"," ",0,"-5/3*a*A*cot(d*x+c)/d-1/3*a*A*cot(d*x+c)*csc(d*x+c)^2/d+a*A*cot(d*x+c)*csc(d*x+c)/d-1/d*a*A*ln(csc(d*x+c)-cot(d*x+c))","A"
21,1,57,47,1.173000," ","int(csc(d*x+c)*(a-a*csc(d*x+c))*(A-A*csc(d*x+c)),x)","-\frac{a A \cot \left(d x +c \right) \csc \left(d x +c \right)}{2 d}+\frac{3 a A \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{2 d}+\frac{2 a A \cot \left(d x +c \right)}{d}"," ",0,"-1/2*a*A*cot(d*x+c)*csc(d*x+c)/d+3/2/d*a*A*ln(csc(d*x+c)-cot(d*x+c))+2*a*A*cot(d*x+c)/d","A"
22,1,50,33,0.434000," ","int((a-a*csc(d*x+c))*(A-A*csc(d*x+c))/csc(d*x+c),x)","-2 a A x -\frac{a A \cos \left(d x +c \right)}{d}+\frac{a A \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{d}-\frac{2 A a c}{d}"," ",0,"-2*a*A*x-a*A*cos(d*x+c)/d+1/d*a*A*ln(csc(d*x+c)-cot(d*x+c))-2/d*A*a*c","A"
23,1,49,38,0.435000," ","int((a-a*csc(d*x+c))*(A-A*csc(d*x+c))/csc(d*x+c)^2,x)","\frac{a A \left(d x +c \right)+2 A \cos \left(d x +c \right) a +a A \left(-\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{2}+\frac{d x}{2}+\frac{c}{2}\right)}{d}"," ",0,"1/d*(a*A*(d*x+c)+2*A*cos(d*x+c)*a+a*A*(-1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c))","A"
24,1,62,52,0.905000," ","int((a-a*csc(d*x+c))*(A-A*csc(d*x+c))/csc(d*x+c)^3,x)","\frac{-A \cos \left(d x +c \right) a -2 a A \left(-\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{2}+\frac{d x}{2}+\frac{c}{2}\right)-\frac{a A \left(2+\sin^{2}\left(d x +c \right)\right) \cos \left(d x +c \right)}{3}}{d}"," ",0,"1/d*(-A*cos(d*x+c)*a-2*a*A*(-1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c)-1/3*a*A*(2+sin(d*x+c)^2)*cos(d*x+c))","A"