1,1,161,0,0.435490," ","integrate(csc(d*x+c)^3*(a+a*csc(d*x+c))*(A+A*csc(d*x+c)),x, algorithm=""fricas"")","\frac{42 \, A a \cos\left(d x + c\right)^{3} - 54 \, A a \cos\left(d x + c\right) - 21 \, {\left(A a \cos\left(d x + c\right)^{4} - 2 \, A a \cos\left(d x + c\right)^{2} + A a\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 21 \, {\left(A a \cos\left(d x + c\right)^{4} - 2 \, A a \cos\left(d x + c\right)^{2} + A a\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 32 \, {\left(2 \, A a \cos\left(d x + c\right)^{3} - 3 \, A a \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{48 \, {\left(d \cos\left(d x + c\right)^{4} - 2 \, d \cos\left(d x + c\right)^{2} + d\right)}}"," ",0,"1/48*(42*A*a*cos(d*x + c)^3 - 54*A*a*cos(d*x + c) - 21*(A*a*cos(d*x + c)^4 - 2*A*a*cos(d*x + c)^2 + A*a)*log(1/2*cos(d*x + c) + 1/2) + 21*(A*a*cos(d*x + c)^4 - 2*A*a*cos(d*x + c)^2 + A*a)*log(-1/2*cos(d*x + c) + 1/2) + 32*(2*A*a*cos(d*x + c)^3 - 3*A*a*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^4 - 2*d*cos(d*x + c)^2 + d)","A",0
2,1,135,0,0.441476," ","integrate(csc(d*x+c)^2*(a+a*csc(d*x+c))*(A+A*csc(d*x+c)),x, algorithm=""fricas"")","-\frac{10 \, A a \cos\left(d x + c\right)^{3} - 6 \, A a \cos\left(d x + c\right) \sin\left(d x + c\right) - 12 \, A a \cos\left(d x + c\right) + 3 \, {\left(A a \cos\left(d x + c\right)^{2} - A a\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 3 \, {\left(A a \cos\left(d x + c\right)^{2} - A a\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right)}{6 \, {\left(d \cos\left(d x + c\right)^{2} - d\right)} \sin\left(d x + c\right)}"," ",0,"-1/6*(10*A*a*cos(d*x + c)^3 - 6*A*a*cos(d*x + c)*sin(d*x + c) - 12*A*a*cos(d*x + c) + 3*(A*a*cos(d*x + c)^2 - A*a)*log(1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - 3*(A*a*cos(d*x + c)^2 - A*a)*log(-1/2*cos(d*x + c) + 1/2)*sin(d*x + c))/((d*cos(d*x + c)^2 - d)*sin(d*x + c))","A",0
3,1,103,0,0.431239," ","integrate(csc(d*x+c)*(a+a*csc(d*x+c))*(A+A*csc(d*x+c)),x, algorithm=""fricas"")","\frac{8 \, A a \cos\left(d x + c\right) \sin\left(d x + c\right) + 2 \, A a \cos\left(d x + c\right) - 3 \, {\left(A a \cos\left(d x + c\right)^{2} - A a\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 3 \, {\left(A a \cos\left(d x + c\right)^{2} - A a\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right)}{4 \, {\left(d \cos\left(d x + c\right)^{2} - d\right)}}"," ",0,"1/4*(8*A*a*cos(d*x + c)*sin(d*x + c) + 2*A*a*cos(d*x + c) - 3*(A*a*cos(d*x + c)^2 - A*a)*log(1/2*cos(d*x + c) + 1/2) + 3*(A*a*cos(d*x + c)^2 - A*a)*log(-1/2*cos(d*x + c) + 1/2))/(d*cos(d*x + c)^2 - d)","B",0
4,1,51,0,0.458617," ","integrate((a+a*csc(d*x+c))*(A+A*csc(d*x+c))*sin(d*x+c),x, algorithm=""fricas"")","\frac{4 \, A a d x - 2 \, A a \cos\left(d x + c\right) - A a \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + A a \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right)}{2 \, d}"," ",0,"1/2*(4*A*a*d*x - 2*A*a*cos(d*x + c) - A*a*log(1/2*cos(d*x + c) + 1/2) + A*a*log(-1/2*cos(d*x + c) + 1/2))/d","A",0
5,1,38,0,0.494281," ","integrate((a+a*csc(d*x+c))*(A+A*csc(d*x+c))*sin(d*x+c)^2,x, algorithm=""fricas"")","\frac{3 \, A a d x - A a \cos\left(d x + c\right) \sin\left(d x + c\right) - 4 \, A a \cos\left(d x + c\right)}{2 \, d}"," ",0,"1/2*(3*A*a*d*x - A*a*cos(d*x + c)*sin(d*x + c) - 4*A*a*cos(d*x + c))/d","A",0
6,1,49,0,0.486521," ","integrate((a+a*csc(d*x+c))*(A+A*csc(d*x+c))*sin(d*x+c)^3,x, algorithm=""fricas"")","\frac{A a \cos\left(d x + c\right)^{3} + 3 \, A a d x - 3 \, A a \cos\left(d x + c\right) \sin\left(d x + c\right) - 6 \, A a \cos\left(d x + c\right)}{3 \, d}"," ",0,"1/3*(A*a*cos(d*x + c)^3 + 3*A*a*d*x - 3*A*a*cos(d*x + c)*sin(d*x + c) - 6*A*a*cos(d*x + c))/d","A",0
7,1,129,0,0.640569," ","integrate(csc(d*x+c)^3*(a-a*csc(d*x+c))*(A+A*csc(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, A a \cos\left(d x + c\right)^{3} + 2 \, A a \cos\left(d x + c\right) - {\left(A a \cos\left(d x + c\right)^{4} - 2 \, A a \cos\left(d x + c\right)^{2} + A a\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + {\left(A a \cos\left(d x + c\right)^{4} - 2 \, A a \cos\left(d x + c\right)^{2} + A a\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right)}{16 \, {\left(d \cos\left(d x + c\right)^{4} - 2 \, d \cos\left(d x + c\right)^{2} + d\right)}}"," ",0,"1/16*(2*A*a*cos(d*x + c)^3 + 2*A*a*cos(d*x + c) - (A*a*cos(d*x + c)^4 - 2*A*a*cos(d*x + c)^2 + A*a)*log(1/2*cos(d*x + c) + 1/2) + (A*a*cos(d*x + c)^4 - 2*A*a*cos(d*x + c)^2 + A*a)*log(-1/2*cos(d*x + c) + 1/2))/(d*cos(d*x + c)^4 - 2*d*cos(d*x + c)^2 + d)","B",0
8,1,36,0,0.472812," ","integrate(csc(d*x+c)^2*(a-a*csc(d*x+c))*(A+A*csc(d*x+c)),x, algorithm=""fricas"")","-\frac{A a \cos\left(d x + c\right)^{3}}{3 \, {\left(d \cos\left(d x + c\right)^{2} - d\right)} \sin\left(d x + c\right)}"," ",0,"-1/3*A*a*cos(d*x + c)^3/((d*cos(d*x + c)^2 - d)*sin(d*x + c))","B",0
9,1,86,0,0.637064," ","integrate(csc(d*x+c)*(a-a*csc(d*x+c))*(A+A*csc(d*x+c)),x, algorithm=""fricas"")","-\frac{2 \, A a \cos\left(d x + c\right) + {\left(A a \cos\left(d x + c\right)^{2} - A a\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - {\left(A a \cos\left(d x + c\right)^{2} - A a\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right)}{4 \, {\left(d \cos\left(d x + c\right)^{2} - d\right)}}"," ",0,"-1/4*(2*A*a*cos(d*x + c) + (A*a*cos(d*x + c)^2 - A*a)*log(1/2*cos(d*x + c) + 1/2) - (A*a*cos(d*x + c)^2 - A*a)*log(-1/2*cos(d*x + c) + 1/2))/(d*cos(d*x + c)^2 - d)","B",0
10,1,45,0,0.519839," ","integrate((a-a*csc(d*x+c))*(A+A*csc(d*x+c))*sin(d*x+c),x, algorithm=""fricas"")","-\frac{2 \, A a \cos\left(d x + c\right) - A a \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + A a \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right)}{2 \, d}"," ",0,"-1/2*(2*A*a*cos(d*x + c) - A*a*log(1/2*cos(d*x + c) + 1/2) + A*a*log(-1/2*cos(d*x + c) + 1/2))/d","A",0
11,1,26,0,0.485584," ","integrate((a-a*csc(d*x+c))*(A+A*csc(d*x+c))*sin(d*x+c)^2,x, algorithm=""fricas"")","-\frac{A a d x + A a \cos\left(d x + c\right) \sin\left(d x + c\right)}{2 \, d}"," ",0,"-1/2*(A*a*d*x + A*a*cos(d*x + c)*sin(d*x + c))/d","A",0
12,1,15,0,0.454346," ","integrate((a-a*csc(d*x+c))*(A+A*csc(d*x+c))*sin(d*x+c)^3,x, algorithm=""fricas"")","\frac{A a \cos\left(d x + c\right)^{3}}{3 \, d}"," ",0,"1/3*A*a*cos(d*x + c)^3/d","A",0
13,1,129,0,0.489258," ","integrate(csc(d*x+c)^3*(a+a*csc(d*x+c))*(A-A*csc(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, A a \cos\left(d x + c\right)^{3} + 2 \, A a \cos\left(d x + c\right) - {\left(A a \cos\left(d x + c\right)^{4} - 2 \, A a \cos\left(d x + c\right)^{2} + A a\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + {\left(A a \cos\left(d x + c\right)^{4} - 2 \, A a \cos\left(d x + c\right)^{2} + A a\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right)}{16 \, {\left(d \cos\left(d x + c\right)^{4} - 2 \, d \cos\left(d x + c\right)^{2} + d\right)}}"," ",0,"1/16*(2*A*a*cos(d*x + c)^3 + 2*A*a*cos(d*x + c) - (A*a*cos(d*x + c)^4 - 2*A*a*cos(d*x + c)^2 + A*a)*log(1/2*cos(d*x + c) + 1/2) + (A*a*cos(d*x + c)^4 - 2*A*a*cos(d*x + c)^2 + A*a)*log(-1/2*cos(d*x + c) + 1/2))/(d*cos(d*x + c)^4 - 2*d*cos(d*x + c)^2 + d)","B",0
14,1,36,0,0.488909," ","integrate(csc(d*x+c)^2*(a+a*csc(d*x+c))*(A-A*csc(d*x+c)),x, algorithm=""fricas"")","-\frac{A a \cos\left(d x + c\right)^{3}}{3 \, {\left(d \cos\left(d x + c\right)^{2} - d\right)} \sin\left(d x + c\right)}"," ",0,"-1/3*A*a*cos(d*x + c)^3/((d*cos(d*x + c)^2 - d)*sin(d*x + c))","B",0
15,1,86,0,0.628317," ","integrate(csc(d*x+c)*(a+a*csc(d*x+c))*(A-A*csc(d*x+c)),x, algorithm=""fricas"")","-\frac{2 \, A a \cos\left(d x + c\right) + {\left(A a \cos\left(d x + c\right)^{2} - A a\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - {\left(A a \cos\left(d x + c\right)^{2} - A a\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right)}{4 \, {\left(d \cos\left(d x + c\right)^{2} - d\right)}}"," ",0,"-1/4*(2*A*a*cos(d*x + c) + (A*a*cos(d*x + c)^2 - A*a)*log(1/2*cos(d*x + c) + 1/2) - (A*a*cos(d*x + c)^2 - A*a)*log(-1/2*cos(d*x + c) + 1/2))/(d*cos(d*x + c)^2 - d)","B",0
16,1,45,0,0.583567," ","integrate((a+a*csc(d*x+c))*(A-A*csc(d*x+c))/csc(d*x+c),x, algorithm=""fricas"")","-\frac{2 \, A a \cos\left(d x + c\right) - A a \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + A a \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right)}{2 \, d}"," ",0,"-1/2*(2*A*a*cos(d*x + c) - A*a*log(1/2*cos(d*x + c) + 1/2) + A*a*log(-1/2*cos(d*x + c) + 1/2))/d","A",0
17,1,26,0,0.454550," ","integrate((a+a*csc(d*x+c))*(A-A*csc(d*x+c))/csc(d*x+c)^2,x, algorithm=""fricas"")","-\frac{A a d x + A a \cos\left(d x + c\right) \sin\left(d x + c\right)}{2 \, d}"," ",0,"-1/2*(A*a*d*x + A*a*cos(d*x + c)*sin(d*x + c))/d","A",0
18,1,15,0,0.512899," ","integrate((a+a*csc(d*x+c))*(A-A*csc(d*x+c))/csc(d*x+c)^3,x, algorithm=""fricas"")","\frac{A a \cos\left(d x + c\right)^{3}}{3 \, d}"," ",0,"1/3*A*a*cos(d*x + c)^3/d","A",0
19,1,161,0,0.428154," ","integrate(csc(d*x+c)^3*(a-a*csc(d*x+c))*(A-A*csc(d*x+c)),x, algorithm=""fricas"")","\frac{42 \, A a \cos\left(d x + c\right)^{3} - 54 \, A a \cos\left(d x + c\right) - 21 \, {\left(A a \cos\left(d x + c\right)^{4} - 2 \, A a \cos\left(d x + c\right)^{2} + A a\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 21 \, {\left(A a \cos\left(d x + c\right)^{4} - 2 \, A a \cos\left(d x + c\right)^{2} + A a\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 32 \, {\left(2 \, A a \cos\left(d x + c\right)^{3} - 3 \, A a \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{48 \, {\left(d \cos\left(d x + c\right)^{4} - 2 \, d \cos\left(d x + c\right)^{2} + d\right)}}"," ",0,"1/48*(42*A*a*cos(d*x + c)^3 - 54*A*a*cos(d*x + c) - 21*(A*a*cos(d*x + c)^4 - 2*A*a*cos(d*x + c)^2 + A*a)*log(1/2*cos(d*x + c) + 1/2) + 21*(A*a*cos(d*x + c)^4 - 2*A*a*cos(d*x + c)^2 + A*a)*log(-1/2*cos(d*x + c) + 1/2) - 32*(2*A*a*cos(d*x + c)^3 - 3*A*a*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^4 - 2*d*cos(d*x + c)^2 + d)","A",0
20,1,135,0,0.549580," ","integrate(csc(d*x+c)^2*(a-a*csc(d*x+c))*(A-A*csc(d*x+c)),x, algorithm=""fricas"")","-\frac{10 \, A a \cos\left(d x + c\right)^{3} + 6 \, A a \cos\left(d x + c\right) \sin\left(d x + c\right) - 12 \, A a \cos\left(d x + c\right) - 3 \, {\left(A a \cos\left(d x + c\right)^{2} - A a\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) + 3 \, {\left(A a \cos\left(d x + c\right)^{2} - A a\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right)}{6 \, {\left(d \cos\left(d x + c\right)^{2} - d\right)} \sin\left(d x + c\right)}"," ",0,"-1/6*(10*A*a*cos(d*x + c)^3 + 6*A*a*cos(d*x + c)*sin(d*x + c) - 12*A*a*cos(d*x + c) - 3*(A*a*cos(d*x + c)^2 - A*a)*log(1/2*cos(d*x + c) + 1/2)*sin(d*x + c) + 3*(A*a*cos(d*x + c)^2 - A*a)*log(-1/2*cos(d*x + c) + 1/2)*sin(d*x + c))/((d*cos(d*x + c)^2 - d)*sin(d*x + c))","B",0
21,1,103,0,0.527167," ","integrate(csc(d*x+c)*(a-a*csc(d*x+c))*(A-A*csc(d*x+c)),x, algorithm=""fricas"")","-\frac{8 \, A a \cos\left(d x + c\right) \sin\left(d x + c\right) - 2 \, A a \cos\left(d x + c\right) + 3 \, {\left(A a \cos\left(d x + c\right)^{2} - A a\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 3 \, {\left(A a \cos\left(d x + c\right)^{2} - A a\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right)}{4 \, {\left(d \cos\left(d x + c\right)^{2} - d\right)}}"," ",0,"-1/4*(8*A*a*cos(d*x + c)*sin(d*x + c) - 2*A*a*cos(d*x + c) + 3*(A*a*cos(d*x + c)^2 - A*a)*log(1/2*cos(d*x + c) + 1/2) - 3*(A*a*cos(d*x + c)^2 - A*a)*log(-1/2*cos(d*x + c) + 1/2))/(d*cos(d*x + c)^2 - d)","B",0
22,1,51,0,0.572132," ","integrate((a-a*csc(d*x+c))*(A-A*csc(d*x+c))/csc(d*x+c),x, algorithm=""fricas"")","-\frac{4 \, A a d x + 2 \, A a \cos\left(d x + c\right) + A a \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - A a \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right)}{2 \, d}"," ",0,"-1/2*(4*A*a*d*x + 2*A*a*cos(d*x + c) + A*a*log(1/2*cos(d*x + c) + 1/2) - A*a*log(-1/2*cos(d*x + c) + 1/2))/d","A",0
23,1,38,0,0.601176," ","integrate((a-a*csc(d*x+c))*(A-A*csc(d*x+c))/csc(d*x+c)^2,x, algorithm=""fricas"")","\frac{3 \, A a d x - A a \cos\left(d x + c\right) \sin\left(d x + c\right) + 4 \, A a \cos\left(d x + c\right)}{2 \, d}"," ",0,"1/2*(3*A*a*d*x - A*a*cos(d*x + c)*sin(d*x + c) + 4*A*a*cos(d*x + c))/d","A",0
24,1,49,0,0.489075," ","integrate((a-a*csc(d*x+c))*(A-A*csc(d*x+c))/csc(d*x+c)^3,x, algorithm=""fricas"")","\frac{A a \cos\left(d x + c\right)^{3} - 3 \, A a d x + 3 \, A a \cos\left(d x + c\right) \sin\left(d x + c\right) - 6 \, A a \cos\left(d x + c\right)}{3 \, d}"," ",0,"1/3*(A*a*cos(d*x + c)^3 - 3*A*a*d*x + 3*A*a*cos(d*x + c)*sin(d*x + c) - 6*A*a*cos(d*x + c))/d","A",0
